text:
Inventors list
Assignees list
Classification tree browser
Top 100 Inventors
Top 100 Assignees
Subclass of:
359 - Optical: systems and elements
Patent class list (only not empty are listed)
Deeper subclasses:
|Class / Patent application number
|Number of patent applications / Date published
|Harmonic generator
|Parametric oscillator
|Dielectric optical waveguide type
|Raman type
|TUNABLE LIGHT SOURCE APPARATUS, AND ADJUSTMENT METHOD AND CONTROL PROGRAM OF THE SAME - The present invention aims to provide a tuning light source apparatus including a multiple-optical resonator, where the resonance frequencies of the respective optical resonators in a multiple-optical resonator are exactly coincided with the set frequency, and the frequency of the output laser beam is locked within a range of about 1 GHz from the set frequency. Current is flowed to TO phase shifters based on lights detected by light receiving elements, and the resonance wavelengths of resonators are adjusted in an aim of obtaining a state in which an intensity of an oscillation light becomes a maximum and at the same time an intensity of a light from a through port becomes a minimum.
|Laser light source device, illumination device, image display device, and monitor - A laser light source device includes: a light source; an external resonator constituting a resonator structure with the light source; a wavelength conversion element disposed between the light source and the external resonator, and converting the wavelength of the light emitted from the light source; and a first spacing member maintaining a state in which at least the wavelength conversion element is separated from the external resonator by a predetermined distance.
|OPTICAL WAVELENGTH CONVERSION ELEMENT, WAVELENGTH CONVERSION LASER DEVICE, AND IMAGE DISPLAY DEVICE - An optical wavelength conversion element includes: a wavelength conversion waveguide that has a periodic polarization reversal structure having alternately and cyclically formed domains of which polarization directions are inverted, that guides light as a fundamental wave corresponding to the periodic polarization reversal structure, and performs a wavelength conversion of the guided fundamental wave; a first clad that is made of a dielectric having a refractive index lower than that of the wavelength conversion waveguide and is provided in contact with the domains; a second clad that is made of a dielectric having a refractive index lower than that of the wavelength conversion waveguide and is provided in contact with the domains such that the second clad is opposed to the first clad film; a first conducting unit that electrically connects the domains in parallel via the first clad; and a second conducting unit that electrically connects the domains in parallel via the second clad.
|WAVELENGTH-CONVERTED LIGHT GENERATING APPARATUS AND GENERATING METHOD - A wavelength-converted light generating apparatus
|WAVELENGTH CONVERSION DEVICE PACKAGE - A nonlinear optical device is provided. More specifically, a wavelength conversion device package with less optical loss stabilizes optical alignment under an external environmental change, for example, in a temperature variation by providing a temperature regulating block and a temperature sensor to an optical oscillator and a wavelength modulator and fixing a flexible optical transmitter to the optical oscillator and the wavelength modulator.
|NANO-ANTENNA ENHANCED IR UP-CONVERSION MATERIALS - Robust composite materials containing nanoscale antennae for molecules are used in the up-conversion process. Antennae can be used to locally enhance the electric fields near an upconverting phosphor or material to enhance both absorption of energy, such as with a television or radio receiver, and emission of energy, such as by the transmitter at the radio station.
|SPECTRAL WIDTH NARROWING METHOD, OPTICAL ELEMENT AND LIGHT SOURCE DEVICE - The present invention provides a method for narrowing a spectral width that can also be adapted to an ultrashort optical pulse emitted from a wavelength tunable light source, and that can provide an output optical pulse with a narrow spectral width and a low noise component, and an optical element and a light source device that use the method for narrowing a spectral width. The method includes using an optical waveguide member (
|Optical antenna with phase control - An optical antenna assembly including multiple optical antenna elements, each of the optical antenna elements are arranged in a regular pattern and carried by a supporting body. The regular pattern of the plurality of optical antenna elements is nonuniform. Certain ones of the optical antenna elements are configured to respond to the one or more waves of light.
|HIGH-POWER WHITE LEDS - A light emitting apparatus has a radiation source for emitting short wavelength radiation. A down conversion material receives and down converts at least some of the short wavelength radiation emitted by the radiation source and back transfers a portion of the received and down converted radiation. An optic device adjacent the down conversion material at least partially surrounds the radiation source. The optic device is configured to extract at least some of the back transferred radiation. A sealant substantially seals a space between the radiation source and the optic device.
|QUASI NON-CRITICAL PHASE MATCHED AND CONTRA-PHASE MATCHED STRUCTURES - Adhesive-free bond non-linear optical (NLO) components, devices and systems including one or more engineered quasi non-critical phase matched or contra-phase matched NLO crystal doublets. Such systems and devices advantageously increase the efficiency of NLO frequency conversion and improve beam quality. Devices are applicable to any uniaxial and biaxial NLO crystals in a wide range of wavelengths, e.g., from far ultraviolet to visible to far infrared. Devices employing engineered AFB NLO components according to certain embodiments include any conventional frequency converting architectures. Systems and methods are also provided to unambiguously determine and correct walk-off for any arbitrary uniaxial and biaxial crystal orientation.
|MEDIUM FOR PHOTON ENERGY UP-CONVERSION - The present invention relates to a medium for photon energy up-conversion, a photon-energy up-conversion device comprising said medium and to uses of said medium. The present invention also relates to a method of photon energy up-conversion using said medium or said device.
|UP -CONVERSION OF ELECTROMAGNETIC RADIATION WITHIN A WAVELENGTH RANGE - Prior art techniques for converting the wavelength of electromagnetic radiation by non-linear interactions such as sum frequency generation SFG produces blurred images when applied to polychromatic images. The invention provides an improved arrangement (
|METHOD AND APPARATUS FOR GENERATION AND DETECTION OF ROGUE WAVES - Methods and systems are provided for generation and detection of rogue waves, including hydrodynamic rogue waves and optical rogue waves. A method for generating an optical rogue wave comprises the steps of generating an input pulse into a nonlinear optical medium, and perturbing the input pulse by directing a narrow-band seed radiation into the input pulse. The seed radiation has a frequency and timing to generate broadband radiation within the nonlinear optical medium.
|PARAMETRIC GENERATOR - A method of optimizing parametric gain in a nonlinear optical crystal that in response to application of a pump beam generates through a parametric generation process signal and idler beams, wherein the signal beam is non-collinear with the pump beam and the signal beam is subject to absorption due to the nonlinear material, the method involving shaping the pump beam to have an elliptical cross section, wherein the method further involves determining the width w of the pump beam depending on the absorption co-efficient of the optical crystal.
|ENGINEERED NONLINEAR OPTICAL CRYSTAL COMPOSITES FOR FREQUENCY CONVERSION - Walk-off corrected (WOC) non-linear optical (NLO) components, devices and systems including one or more engineered WOC NLO crystal doublets. Such systems and devices advantageously increase the efficiency of an OPO operation. Devices are applicable to any uniaxial and biaxial NLO crystals in a wide range of wavelengths, e.g., from far ultraviolet to visible to far infrared. Devices employing engineered WOC NLO components according to embodiments of the present invention include any conventional frequency converting architectures. Systems and methods are also provided to unambiguously determine and correct walk-off for any arbitrary uniaxial and biaxial crystal orientation. The correct crystal orientation is also experimentally confirmed. This allows the use of WOC crystal doublet assemblies for a wide range of wavelengths and NLO crystals that until now have not been used because of low efficiency due to walk-off and inability of readily correcting walk-off.
|IR FIBER BROADBAND MID-IR LIGHT SOURCE - A method of generating a supercontinuum in chalcogenide fiber with a pump light comprising a short pulse fiber laser or diode laser operating with a wavelength of
|DEEP BLUE EXTENDED SUPER CONTINUUM LIGHT SOURCE - A new deep blue extended super continuum light source is provided wherein said super continuum at least extends to a low wavelength border λ
|WAVELENGTH CONVERSION ELEMENT - In a wavelength conversion element in which a periodic poled crystal that converts an input laser light into a laser light of a predetermined wavelength is provided on a thick-film resistance substrate including a heating unit, a heat spreader having a predetermined thermal conductivity, which equalizes a temperature distribution of the periodic poled crystal, is provided between the thick-film resistance substrate and the periodic poled crystal, and the thick-film resistance substrate and the heat spreader, and the heat spreader and the periodic poled crystal are adhered by an adhesive member having a predetermined thermal conductivity.
|WHITE LIGHT SOURCE WITH CRYSTAL FIBER AND METHOD FOR COLOR TEMPERATURE TUNING THEREOF - The present invention relates to a white light source, and particularly to a white light source with crystal fiber and a method for color temperature tuning thereof. The white light source of the present invention comprises a pumping source for providing a first-color light, and a gradient index lens for coupling the first-color light into a crystal fiber. The crystal fiber absorbs a portion of the first-color light and generates a second-color light and a third-color light, and a white light with high color rendering index can be obtained. The crystal fiber is made of a first rare earth element oxide and a second rare earth element oxide co-doped yttrium aluminum garnet. The color temperature of the white light can be tuned by adjusting the position of the focus of the pumping light on the end section of the crystal fiber.
|ELECTRIC FIELD POLING OF FERROELECTRIC MATERIALS - A method of inducing a periodic variation of nonlinearity value in a sample of ferroelectric material comprises arranging a pair of electrodes on opposite faces of the sample, one electrode defining a desired pattern of nonlinearity variation, applying a pre-bias voltage across the sample for a predetermined time using the electrodes, the pre-bias voltage being less than the coercive field of the ferroelectric material; and after the predetermined time, applying a current-controlled poling voltage across the sample using the electrodes, to produce domain inversion in the sample according to the desired pattern of nonlinearity variation. The pre-bias voltage may be 75% of the coercive field or more, and applied for a pre-determined time between 1 and 100 seconds.
|WAVELENGTH CONVERTING APPARATUS - A wavelength converting apparatus that improves output performance of laser light subjected to wavelength conversion while improving the efficiency of laser light wavelength conversion. Wavelength converting apparatus (
|WAVELENGTH CONVERSION DEVICE AND LASER DEVICE - The present invention relates to a wavelength conversion device and others. The wavelength conversion device is provided with an input port, a beam homogenizer, a wavefront aberration compensating element, and a nonlinear conversion element of a nonlinear optical crystal. The beam homogenizer forms a flat-top light intensity distribution of an output laser beam at a position different from a beam waist position thereof. Thereafter, the wavefront aberration compensating element outputs the laser beam coming from the beam homogenizer, as a phase-aligned collimated beam to the wavelength conversion element.
|Wavelength Converter Manufacturing Method and Wavelength Converter - Affords a wavelength converter manufacturing method and a wavelength converter whereby the transmissivity can be improved. A method of manufacturing a wavelength converter (
|WAVELENGTH CONVERSION LASER DEVICE AND IMAGE DISPLAY DEVICE USING THE SAME - A wavelength conversion laser device includes a laser light source which emits a laser beam, two reflective surfaces which reflect therefrom a laser beam, a wavelength converter provided between the two reflective surfaces, which converts a laser beam into a wavelength-converted laser beam, and condensing optics which condense the laser beams to be injected between the two reflective surfaces, wherein at least one of the two reflective surfaces has a curvature for reflecting a laser beam to be re-injected into the wavelength converter between the two reflective surfaces repeatedly while forming multi paths of laser beams injected into the wavelength converter at different incident angles, and the condensing optics are arranged to disperse beam waists of the laser beams in the wavelength converter, which reciprocate between the two reflective surfaces.
|WAVELENGTH CONVERSION LIGHT SOURCE APPARATUS AND WAVELENGTH CONVERSION METHOD - A wavelength conversion light source apparatus includes a fundamental wave light source configured to emit a fundamental wave, a nonlinear crystal configured to convert a wavelength of the fundamental wave by being irradiated with the fundamental wave and making the fundamental wave pass therethrough, and a movement unit configured to place the nonlinear crystal thereon and continuously move the nonlinear crystal within a plane, where a phase matching condition is not violated, so that a passage path of the fundamental wave passing through the nonlinear crystal is changed.
|WAVELENGTH CONVERSION DEVICES AND A METHOD OF PRODUCING THE SAME - A wavelength conversion device
|LIGHT SOURCE DEVICE AND PROJECTOR - A light source device includes: a first light source unit and a second light source unit emitting light; and a wavelength conversion element converting wavelengths of lights emitted from the first light source unit and from the second light source unit. Chief ray of light emitted from the first light source unit and transmitted through the wavelength conversion element is not parallel with chief ray of light emitted from the second light source unit and transmitted through the wavelength conversion element.
|CRYSTAL FOR OPTICAL CONVERSION - An efficient broadband crystal for wavelength conversion, the crystal being a quasi-phase matched non-linear crystal, having an aperiodic poled structure, each period being tuned, and wherein said tuning varies adiabatically along a length of said crystal from a first end wherein said tuning is a strong negative mismatch to a second end wherein said tuning is a strong positive mismatch or vice versa. The crystal is able to provide efficient wavelength conversion over a range of frequencies.
|WAVELENGTH CONVERSION DEVICE AND WAVELENGTH CONVERSION METHOD - A wavelength conversion device is disclosed. The wavelength conversion device includes at least a fundamental wave light source and an external resonator, where a reflectance R
|Optical Comb Frequency Source - This invention relates to methods and apparatus for generating an optical frequency comb. In embodiments a passive mode locked optical waveguide comb uses electrical or optical tuning for the mode spacing frequency (df) and the carrier envelope offset frequency (f
|FOUR-WAVE MIXING SOURCE OF SQUEEZED LIGHT FOR IMAGE PROCESSING AND INTERFEROMETRY - A four-wave mixing squeezed light source includes: a mixing medium having chi(3) non-linear characteristics including two atomic ground states coupled to each other by transitions through optically-excited states; a pump beam having a polarization and a frequency, said frequency being near the ground-to-excited atomic transition but far enough from the atomic transition such that the pump beam is substantially unabsorbed; and a probe beam having a polarization that is orthogonal with respect to the pump beam polarization, the probe beam having a frequency of the pump beam frequency plus or minus a frequency splitting of the two atomic ground states. The mixing medium, the pump beam and the probe beam interact to produce a phase conjugate beam having a polarization that is orthogonal to the pump beam polarization, such that the beams are non-degenerate with the pump beam, and the probe beam is amplified.
|OPTICAL OUTPUT CONTROLLER AND ITS CONTROL METHOD - An optical output controller includes a wavelength conversion device operable to change the wavelength of pumped laser light; a heating/cooling unit operable to control the temperature of the wavelength conversion device; a temperature detector which detects the temperature of the wavelength conversion device; a temperature controller operable to control the heating/cooling unit such that the detected temperature corresponds to a target temperature; an optical output detector operable to detect the optical output from the wavelength conversion device; an optical-output maximization controller operable to determine a temperature at which the optical output is maximized according to the optical output detected by the optical output detector and from the detected temperature detected by the temperature detector and, further, outputs the temperature difference between the determined temperature and the detected temperature; and an adder which adds the temperature difference outputted from the optical-output maximization controller to the target temperature; wherein the temperature difference is added to the target temperature to correct the target temperature for maximizing the optical output.
|DEVICE FOR CONTROLLING OPTICAL FREQUENCY, METHOD OF MANUFACTURING SUCH A DEVICE - The present invention relates to a device for controlling optical frequency (F
|ADVANCED SHIFTING ALGORITHM FOR PROLONGING THE LIFE OF AN OPTICALLY NONLINEAR CRYSTAL - In a shifting algorithm for an optically nonlinear crystal arranged to frequency-convert beam of radiation, the location of one or more defects in the crystal is recorded as an exclusion zone. The location of the beam is stepped incrementally over a surface around a closed or open loop path in increments less than a beam dimension. The path is arranged such that the beam does not enter the exclusion zone.
|Device for generating or receiving terahertz radiation - A device for generating or receiving electromagnetic radiation in a frequency range from 10 GHz to 100 THz is provided. The device includes a housing and a wave guide fiber leading into the housing. The wave guide fiber is adapted for guiding pulsed laser light with a first central wavelength. Within the housing, a terahertz converter is provided for generating or receiving the electromagnetic radiation in the terahertz range. The device also includes a frequency converter for converting the light exiting from the wave guide fiber to a second central wavelength being arranged between the end of the wave guide fiber and the terahertz converter in such a way that the terahertz converter is impinged by the frequency converted light.
|OPTICAL WAVELENGTH CONVERSION DEVICE, AND COHERENT LIGHT SOURCE USING SAME - The invention relates to an optical wavelength conversion device adapted to receive at least one first pump beam (λ
|APPARATUS AND METHOD FOR GENERATING AN RF SIGNAL - An apparatus for generating an RF signal is provided includes a driver configured to generate a timing control for two optical signals. The apparatus further includes at least one optical pulse source configured to generate the two optical signals based on the timing control. In addition, the apparatus includes a photodetector configured to receive the two optical signals as input and further configured to generate an RF signal based on the two optical signals. A method for generating an RF signal is also provided.
|Optical antenna array for harmonic generation, mixing and signal amplification - An optical antenna collects, modifies and emits energy at light wavelengths. Linear conductors sized to correspond to the light wavelengths are used. Nonlinear junctions of small dimension are used to rectify an alternating waveform induced upon the conductors by the lightwave electromagnetic energy. The optical antenna and junctions are effective to produce harmonic energy at light wavelengths. The linear conductors may be comprised of carbon nanotubes that are attached to a substrate material, which may then be connected to an electrical port.
|ALL-OPTICAL, CONTINUOUSLY TUNABLE, PULSE DELAY GENERATOR USING WAVELENGTH CONVERSION AND DISPERSION - A technique for generating variable pulse delays uses one or more nonlinear-optical processes such as cross-phase modulation, cross-gain modulation, self-phase modulation, four-wave mixing or parametric mixing, combined with group-velocity dispersion. The delay is controllable by changing the wavelength and/or power of a control laser. The delay is generated by introducing a controllable wavelength shift to a pulse of light, propagating the pulse through a material or an optical component that generates a wavelength dependent time delay, and wavelength shifting again to return the pulse to its original wavelength.
|METHOD FOR PREPARING A POLED STRUCTURE BY USING DOUBLE-SIDED ELECTRODES - A method for preparing a poled structure by using double-sided electrodes to perform a poling process first provides a ferroelectric substrate with a first polarization direction having a top surface and a bottom surface. Fabrication processes are then performed to form an electrode structure including a first electrode and a second electrode on the top surface and a third electrode in a portion of the bottom surface between the first electrode and the second electrode. Subsequently, a poling process is performed on the electrode structure to form a plurality of inverted domains having a second polarization direction in the ferroelectric substrate, and the second polarization direction is substantially opposite to the first polarization direction.
|Laser ray wavelength modification apparatus - A laser ray wavelength modification apparatus that includes a semiconductor laser element, a fundamental wave light reflecting element, a wavelength modification element, a selective reflection member and a dichroic mirror. The selective reflection member permits fundamental wave light among light rays emitted from the wavelength modification element to pass through to the fundamental wave light reflecting element while reflecting the wavelength modification light. The dichroic mirror is arranged between the semiconductor laser element and the wavelength modification element. The dichroic mirror transmits the fundamental wave light and removes by reflection out the wavelength modification light.
|COMPOSITION FOR PHOTON-ENERGY UP-CONVERSION - The present invention relates to a composition for photon energy up-conversion, a system comprising said composition and to uses of said composition and said system.
|SOURCE OF LIGHT WITH CONVERSION ELEMENT AND FIBER OPTICS, PROCEDURE FOR THE PRODUCTION OF THE SOURCE OF LIGHT AND THEIR USE - Proposed is a light source having a conversion element (
|BURST OSCILLATION METHOD IN LASER SYSTEM AND APPARATUS FOR SAME - Disclosed is a burst mode oscillation method for burst mode oscillation by controlling the peak output of light pulses in a laser system. The burst mode oscillation apparatus includes a seed beam generator which receives electrical input signals having different pulse widths, modulates pulse widths and amplitudes of outputs in output light according to the received electrical input signals, and outputs the modulated pulse light, an amplifier which amplifies the modulated pulse light and outputs amplified pulse light, and a non-linear wavelength converter which can control wavelength-converted output light according to the amplitudes of the peak output changed through the pulse widths of the amplified pulse light.
|LASER MODULE - A laser module including a light emitter, a polarizing and filtering unit, a nonlinear optical crystal, and a first filter is provided. The light emitter emits a first beam. The polarizing and filtering unit is disposed on a transmission path of the first beam. A part of the first beam passes through the polarizing and filtering unit to become as a second beam with a specific polarization direction. The nonlinear optical crystal is disposed on a transmission path of the second beam from the polarizing and filtering unit. The nonlinear optical crystal converts a part of the second beam into a third beam. The first filter is disposed on a transmission path of the other part of the second beam and the third beam from the nonlinear optical crystal. The other part of the second beam is reflected by the first filter. The third beam passes through the first filter.
|LIGHT SOURCE DEVICE AND PROJECTOR - A light source device includes a light source having a plurality of light emitting sections, a plurality of wavelength conversion elements each having a periodic polarization inversion structure, and for converting wavelengths of light beams emitted from the plurality of light emitting sections into predetermined wavelengths, a temperature control medium for controlling temperature of the plurality of wavelength conversion elements, a holding member having a housing space for housing the temperature control medium, and for holding the plurality of wavelength conversion elements, and a temperature control section for controlling the temperature of the plurality of wavelength conversion elements with the temperature control medium, and the temperature control section controls the temperature of the wavelength conversion elements so that the wavelength of the light beam emitted from at least one of the plurality of wavelength conversion elements is different from the wavelength of the light beam emitted from another of the plurality of wavelength conversion elements.
|Device for modifying the wavelength range of a spectrum of light - The present invention relates to a device for modifying, e.g. narrowing the wavelength range of a spectrum of light.
|WAVELENGTH CONVERSION ELEMENT - A wavelength conversion element
|MOPA Seed Source With Wavelength Control For Resonant Frequency Conversion - A method and system for converting one frequency into another include a MOPA configuration radiating a light at a first frequency which is coupled into a frequency conversion unit. Further included are a control unit operative to monitor the other frequency and a pump unit operative to vary its output power provided that the monitored frequency does not substantially match a reference value stored in the control unit. The output power of the pump unit varies while the master oscillator scans its cavity in search for the desired resonant frequency.
|WAVELENGTH CONVERSION LASER LIGHT SOURCE AND IMAGE DISPLAY DEVICE - A wavelength conversion laser light source includes a fundamental wave laser light source (
|DEVICE FOR REDUCING TIME DISTORTION GENERATED IN LIGHT PULSES BY A NONLINEAR OPTICAL FREQUENCY CONVERTER SYSTEM - A device for reducing time distortion generated in light pulses by an optical frequency converter including at least one nonlinear optical component (
|TERAHERTZ WAVE GENERATION DEVICE - A terahertz wave generating apparatus
|Methods for Controlling Wavelength-Converted Light Sources to Reduce Speckle - A method for operating a wavelength-converted light source includes directing a pump beam having a fundamental wavelength from the laser source into an input facet of the wavelength conversion device such that a wavelength-converted output beam is emitted from an output facet of the wavelength conversion device in the field of view of an optical detector. A physical property of the wavelength conversion device is varied within individual ones of a succession of consecutive speckle reduction intervals having durations less than the integration time of the optical detector. The physical property of the wavelength conversion device is varied by an amount that is sufficient to change in a phase-matched (PM) wavelength of the wavelength conversion device. The fundamental wavelength of the pump beam is thereafter adjusted based on the change in the PM wavelength to maintain an efficiency of the wavelength conversion in the wavelength conversion device.
|ELECTROMAGNETIC RADIATION FREQUENCY OPTIMIZING DEVICE AND METHOD WITH AMBIENT HEAT CONVERSION DEVICE - A device comprising a conversion channel including: a first end configured to accept ambient electromagnetic radiation, the ambient electromagnetic radiation having an initial frequency, a second end configured to allow the ambient electromagnetic radiation to exit, and at least two opposing walls connecting the first end and the second end, wherein the at least two opposing walls include one or more crystals, the at least two opposing walls being separated by at least one-half of a wave length; wherein when the ambient electromagnetic radiation interacts with the one or more crystals of the at least two opposing side walls, the initial frequency of the ambient electromagnetic radiation being repeatedly increased to an optimal frequency is provided. Furthermore, an associated method is also provided
|HIGH-POWER ELECTROMAGNETIC SUM FREQUENCY GENERATOR SYSTEM - A High-power sum frequency generator system including a first electromagnetic source for generating a first fundamental field and a second fundamental field emitted along a propagation path, and a first nonlinear component and a second nonlinear component arranged in series along the propagation path. The first nonlinear component generates a first sum frequency field from the first fundamental field and the second fundamental field, the first sum frequency field having a first polarization. The second nonlinear component generates a second sum frequency field from the first and second fundamental fields, the second sum frequency field having a second polarization. The system has an output that includes the first sum frequency field and the second sum frequency field, and a direction of the first polarization forms a mutual angle with a direction of the second polarization such that the two polarizations are non-parallel.
|STABILIZED LIGHT SOURCE - A light source including a light emitting unit, a nonlinear medium, and a resonant grating. The light emitting unit is arranged to emit a first light into the nonlinear medium. The nonlinear medium is arranged to generate a second light such that an optical frequency of the second light is higher than an optical frequency of the first light. The resonant grating is arranged to stabilize an optical frequency of the first light by providing optical feedback to the light emitting unit.
|WAVELENGTH CONVERSION DEVICE - A wavelength conversion device
|WAVELENGTH CONVERSION LASER LIGHT SOURCE AND IMAGE DISPLAY APPARATUS - A wavelength conversion laser light source
|WAVELENGTH CONVERSION ELEMENT AND METHOD FOR MANUFACTURING WAVELENGTH CONVERSION ELEMENT - A wavelength conversion element having an improved property-maintaining life and a method for manufacturing the wavelength conversion element are provided. A wavelength conversion element
|LASER LIGHT SOURCE, AND IMAGE DISPLAY APPARATUS AND PROCESSING APPARATUS USING THE SAME - A laser light source (
|WAVELENGTH CONVERSION ELEMENT, LASER LIGHT SOURCE, TWO-DIMENSIONAL IMAGE DISPLAY AND LASER PROCESSING SYSTEM - A wavelength conversion element is provided with a substrate including a nonlinear optical single crystal having a periodically poled structure, the visible light transmittance of the substrate is 85% or higher when ultraviolet light is irradiated to the substrate, and laser light having an average output of 1 W or more is outputted by shortening the wavelength of laser light having a wavelength of 640 nm to 2000 nm. By improving visible light transmission characteristics when the ultraviolet light is irradiated in this way, the breakdown of crystal can be prevented and the stabilization of output characteristics at high output can be realized. As a result, the absorption of green light induced by ultraviolet light can also be suppressed, and the saturation of output and the breakdown of crystal can be avoided.
|METHOD AND SYSTEM FOR GENERATING FLAT OR ARBITRARY SHAPED OPTICAL FREQUENCY COMBS - A method and system for generating an optical frequency comb that employs a dual parallel modulator that inputs an optical signal at a center frequency of a desired optical frequency comb and an RF signal at a frequency corresponding to a desired spacing of the teeth of the optical frequency comb. The amplitudes of the teeth of the optical frequency comb are controlled by controlling the amplitudes of the two RF inputs to the DPM and the phase shift between the two RF inputs. In some embodiments, the three bias voltages for the three interferometers in the DPM are also controlled. In some embodiments, all three interferometers are all biased at the same point (e.g, quadrature). Preferably, but not necessarily, the three interferometers of the DPM are formed on a single substrate.
|STABLE MOUNTING OF NON-LINEAR OPTICAL CRYSTAL - A nonlinear optical crystal can be mounted to a mounting block configured to receive the crystal. The crystal can be mounted to the mounting block with a face of the crystal abutting a surface of the mounting block. An adhesive secures the crystal to the mounting block by adhering to the bottom and/or sidewall of the channel and to at least corresponding a portion of the bottom and/or side face of the crystal proximate an edge of the crystal.
|PLASMONIC ELEMENTS - A surface plasmon element comprising an array of metal nanoparticles (
|NONLINEAR OPTICAL DEVICE USING NONCENTROSYMMETRIC CUBIC MATERIALS FOR FREQUENCY CONVERSION - This invention is directed to a new class of nonlinear optical device (NLO). For this purpose, in one aspect of this invention, a nonlinear optical device including a first nonlinear optical grating is presented. According to one version of the invention, the first nonlinear optical grating comprises a plurality of adjacent nonlinear optical units arranged in series. Each NLO unit has a single crystal segment and a polycrystalline segment. The single crystal segment is composed of a nonlinear optical crystal material and has its length adapted to provide the nonlinear optical effect. The polycrystalline segments are adapted in length to compensate the phase mismatch among the waves that occur in the single crystal segment.
|WAVELENGTH CONVERTER SYSTEM, CRYSTAL STORAGE APPARATUS, AND CRYSTAL REPLACEMENT METHOD OF WAVELENGTH CONVERTER - A wavelength converter system capable of replacing a nonlinear crystal in a wavelength converter in a short time with ease is provided. The wavelength converter system includes the wavelength converter for converting a wavelength by passing light through the nonlinear crystal and a crystal storage apparatus for storing a nonlinear crystal for replacement used by the wavelength converter, wherein the wavelength converter has a first crystal holder for fixing the nonlinear crystal and a first heater for heating the nonlinear crystal and the crystal storage apparatus has a container, a second crystal holder that is in the container to fix the nonlinear crystal for replacement and interchangeable with the first crystal holder, and a second heater for heating the nonlinear crystal for replacement.
|HIGH-POWER WHITE LEDS AND MANUFACTURING METHOD THEREOF - A light emitting apparatus has a radiation source for emitting short wavelength radiation. A down conversion material receives and down converts at least some of the short wavelength radiation emitted by the radiation source and back transfers a portion of the received and down converted radiation. An optic device adjacent the down conversion material at least partially surrounds the radiation source. The optic device is configured to extract at least some of the back transferred radiation. A sealant substantially seals a space between the radiation source and the optic device.
|HIGH-POWER WHITE LEDS AND MANUFACTURING METHOD THEREOF - A light emitting apparatus has a radiation source for emitting short wavelength radiation. A down conversion material receives and down converts at least some of the short wavelength radiation emitted by the radiation source and back transfers a portion of the received and down converted radiation. An optic device adjacent the down conversion material at least partially surrounds the radiation source. The optic device is configured to extract at least some of the back transferred radiation. A sealant substantially seals a space between the radiation source and the optic device.
|BLUE EXTENDED SUPER CONTINUUM LIGHT SOURCE - A new blue extended super continuum light source is claimed. When pulses of partly coherent monochromatic "pump" radiation of essentially constant amplitude is propagating through a microstructure fibre medium within a region of anomalous dispersion of the medium, then, provided the medium has a finite nonlinear coefficient of the index of refraction, the pump pulse is subject to a modulation instability. This instability results in the generation and exponential growth of sidebands, the two closest to the "pump" frequency being the dominant ones. The modulation frequency is proportional to the square root of the power in the carrier wave. In the time domain this leads to that the interaction between the medium and the radiation results in contraction of the width of the amplitude peaks, which results in formation of a train of narrow pulses with Tera Hertz repetition rate.
|Wavelength converting devices - A wavelength converting substrate
|TERAHERTZ CONTINUOUS WAVE GENERATOR - A terahertz continuous wave generator includes: an optical intensity modulator configured to modulate an optical signal into DSB optical signals; a local oscillator configured to generate a modulation signal for modulating the optical signal inputted to the optical intensity modulator into DSB optical signals; a notch filter configured to filter an optical signal with a specific frequency; an optical fiber amplifier configured to amplify an output signal of the optical intensity modulator; an optical circulator configured to transmit the optical signal inputted to the optical fiber amplifier to the notch filter and transmit the optical signal reflected from the notch filter to an input of the optical intensity modulator; an optical coupler configured to apply the optical signal to the optical intensity modulator; and an OE converter configured to photomix the DSB signals outputted through the notch filter.
|OPTICAL FIBER DELIVERY SYSTEM FOR DELIVERING OPTICAL SHORT PULSES AND OPTICAL FIBER DELIVERY METHOD - The optical fiber delivery system for delivering optical short pulses includes: a chirped pulse source (
|CHIRPED-PULSE QUADRATIC NONLINEARITY-BASED HIGH-ENERGY PULSE COMPRESSOR - A pulse compression technique for compressing femtosecond-duration high-energy pulses first linearly chirps and thus broadens an input pulse before compressing it by nonlinear soliton compression. The technique simultaneously decreases the final compressed pulse duration and improves of the compressed pulse quality. In the preferred embodiment, a linear dispersive delay (
|OPTICAL APPARATUS, AND WAVELENGTH CONVERSION LASER LIGHT SOURCE, IMAGE DISPLAY APPARATUS, AND LASER LIGHT SOURCE DEVICE ADOPTING SUCH OPTICAL APPARATUS - A wavelength conversion laser light source includes: a non-linear optical crystal of an oxygen octahedral structure, having added thereto a metal ion in other components than a main component; a light source for projecting light into the non-linear optical crystal in an operation mode; and a refractive index recovery mechanism for carrying out a recovery operation for recovering a refractive index of said non-linear optical crystal as shifted overtime due to light projected into the non-linear optical crystal in the operation mode with an applied external energy into the non-linear optical crystal in a non-operation mode in which light is not injected to the non-linear optical crystal.
|TUNABLE OPTICAL FREQUENCY COMB GENERATOR - An optical device comprising a tunable optical frequency comb generator. The comb generator includes an interferometer, and an optical feed-back loop waveguide and an electronic controller.
|INTEGRATED DEVICE AND MANUFACTURING METHOD - An integrated device includes an optical element and an electrical element that are implemented on a substrate. The optical element and the electrical element are bonded by surface-activated bonding technology to a bonding portion that is formed on the substrate and made of metal material.
|PULSED FIBER-MOPA WITH WIDELY-VARIABLE PULSE-DURATION - Master oscillator power amplifier (MOPA) apparatus includes two seed-pulse sources coupled to a single fiber amplifier including one or more stages of amplification. One of the seed-pulse sources is a single-mode source generating pulses having a duration selectively variable between about 0.1 ns and 10 ns. The other seed-pulse source is a multi-mode source generating pulses having a duration selectively variable between about 1 ns and 10 μs. Selectively operating one or the other of the seed-pulse sources provides that the apparatus can deliver pulses selectively variable in a range between about 0.1 ns and 10 μs.
|PHOTON PAIR GENERATING APPARATUS AND PHOTON PAIR GENERATING METHOD - In a photon pair generating apparatus for generating a pair of correlated photons by hyper-parametric scattering, a light-shaping section irradiates an optical resonator with two beams of light of equal wavelength from different directions, and the optical resonator is configured to emit two correlated photons of different wavelengths in one direction as a pair of correlated photons. This makes it possible to provide a photon pair generating apparatus capable of achieving generation of a pair of correlated photons by a simpler configuration.
|TERAHERTZ WAVE GENERATING METHOD AND APPARATUS - A first laser beam 1
|System for Continuously Generating Polychromatic Light By Means of Doped Microstructured Optical Fibre - A system for generating polychromatic light, which includes: an optical pumping device suitable for continuously or quasi-continuously emitting a monochromatic or quasi-monochromatic radiation according to a pumping wavelength; a device for guiding light arranged such as to emit polychromatic radiation continuously or quasi continuously, at the output thereof, and a device for coupling between the pumping and coupling device. In the system, the guiding device, includes a microstructured optical fiber in which the core is at least partially doped with a material having a high intrinsic non-linear response, and the geometry of the optical fiber and the doping rate of the core thereof are predetermined such as to adapt the zero dispersion length of the optical fiber to the pumping wavelength.
|MOBILE CHARGE INDUCED PERIODIC POLING AND DEVICE - Devices and methods are disclosed for realizing a high quality bulk domain grating structure utilizing mobile charges that are generated by means of photo-excitation in a substrate. An effect of light exposure (UV, visible, or a combination of wavelengths) is to generate photo-induced charges. The application of a voltage across the substrate combined with the application of light exposure causes a photo-induced current to flow through the substrate. The photo-induced charges (behaving like virtual electrode inside the material) and the photo-induced current result in both reduction of the coercive field required for domain inversion in the material and improve realization of the domain inversion pattern, which previously has not been possible at room temperature.
|Method and Devices for Generating Stable and Tunable Light Pulses - Methods and devices for generating stable, tunable and intense output light pulses are provided. A primary beam of light pulses is used to form a filament in an interaction zone. A secondary bean of light pulses is superposed with the filament and interacts therewith to generate the output light pulses. The parameters of the primary and secondary beams in the interaction zone can be controlled to obtain targeted optical characteristics of the output pulses. Multiple secondary beaus may also be used.
|Enhanced continuum generation in nonlinear bulk optic materials - In accordance with the present invention, a bulk optic material (for example, silica) is processed to form a spatially microstructured element, such as a photonic bandgap (PBG) structure. An ultra-short laser pulse source is used as an input signal that is applied to the bulk optic PBG structure to generate an enhanced continuum output. The PBG structure may comprise any type of one-, two- or three-dimensional grating structure, where the selected structure will dictate the type(s) of enhancement(s) that are present in the generated continuum—generally in the form of a broadened continuum and/or the inclusion of one or peaks in the continuum. The use of a relatively small-dimensioned bulk material allows for the continuum to be generated without the need for any type of optical confinement (waveguide). In one embodiment, the bulk PBG structure may be is subjected to one or more additional processes (such as UV exposure, electromagnetic field application, etc.) to modify the nonlinearity of the bulk optic material, in one case resulting in the reduction of the inherent chromatic dispersion and enhancement of the generated continuum.
|WAVELENGTH CONVERSION DEVICES - It is provided a wavelength conversion device
|Method For Preparing A Periodically Poled Structure - A method for preparing a periodically poled structure according to this aspect of the present invention comprises the steps of providing a ferroelectric substrate and performing a poling process by applying a poling current to at least one portion of the ferroelectric substrate according to a current waveform. The current waveform include a major phase and a tailed phase accompanying the major phase; the major phase has at least one peak current (Ip) and terminates when the current drops substantially equal to Ip/e, and the charge delivered to the portion of the ferroelectric substrate during the major phase is larger than that delivered during the tailed phase. The nucleation phase is configured to generate nucleation sites in the portion of the ferroelectric substrate and the spreading phase is configured to increase the size of the nucleation sites.
|PROXIMITY COUPLED ATHERMAL OPTICAL PACKAGE COMPRISING LASER SOURCE AND COMPOUND FACET WAVELENGTH CONVERSION DEVICE - Particular embodiments of the present disclosure bring an SHG crystal, or other type of wavelength conversion device, into close proximity with a laser source to eliminate the need for coupling optics, reduce the number of package components, and reduce package volume. According to one embodiment of the present disclosure, an optical package is provided comprising a laser source and a wavelength conversion device. The laser source is positioned such that the output face of the laser source is proximity-coupled to a waveguide portion of the input face of the wavelength conversion device. The input face of the wavelength conversion device comprises an α-cut facet and β-cut facet. The α-cut facet of the input face is oriented at a horizontal angle α, relative to the waveguide of the wavelength conversion device to permit proximity coupling of the output face of the laser source and the input face of the wavelength conversion device. The β-cut facet of the input face is oriented at a horizontal angle β, relative to the waveguide of the wavelength conversion device to cooperate with the horizontal tilt angle of the device to reduce back reflections from the input face of the wavelength conversion device into the laser source. Additional embodiments are disclosed.
|NONLINEAR OPTICAL CdSiP2 CRYSTAL FOR USE IN SURGICAL LASER
|OPTICAL COMB GENERATOR - Provided is an optical comb generator including a light source, a first waveguide region, a modulation region, and a second waveguide region. The light source is configured to output single-mode light. The first waveguide region divides an output of the light source into first light and second light. The modulation region includes a first modulator and a second modulator modulating the first light and the second light respectively. The second waveguide region combines outputs of the first modulator and the second modulator to output an optical comb. Here, the first modulator and the second modulator respectively include a first quantum well and a second quantum well having an asymmetric structure with respect to each other. The light source, the first waveguide region, the modulation region, and the second waveguide region are integrated into one substrate.
|Modular ring resonator - An optical resonator with an optical mode has a resonator block with and opening. At least one optical component is mounted on a holder that is positioned in the opening to locate the component in the mode of the resonator. The holder is contrained by the resonator block so that the orientation of the component in the plane of the resonator is substantially fixed by the opening. The component is simply aligned in the resonator by rotating the holder in the opening. The resonator block may also have a mirror reference surfaces that automatically aligns a mirror that is pressed against the surface. The resonator has a high degree of optomechanical assembly and facilitates initial component alignment and the interchange of optical components and mirrors.
|METHOD AND SYSTEM FOR REGENERATING AND RESHAPING OF OPTICAL SIGNALS - A method and an apparatus for processing an optical signal are disclosed wherein an input optical signal having an amplitude profile is combined by means of Bragg scattering with a first pulsed pump signal having a first waveshape and a second pulsed pump signal having a second waveshape. The combined optical signal is input in a nonlinear optical material for frequency converting the input optical signal thereby obtaining an idler signal wherein the first pulsed pump signal co-propagates with the input optical signal and the second pulsed pump signal co-propagates with the idler signal. The idler signal produced has a peak amplitude proportional to the peak amplitude of the input optical signal and a shape corresponding to the second pump waveshape.
|METAMATERIALS WITH ENHANCED NONLINEARITY - Embodiments provide metamaterials having an enhanced nonlinear response to light. The metamaterials are artificially manufactured materials having a nonlinear response to light greater than that typically found in naturally occurring materials. A two-dimensional periodic metal-dielectric array can be mathematically mapped as an effective uniform dielectric slab with enhanced optical nonlinearity. The enhanced nonlinearity is controlled by the geometry of the array. Further, the configuration of the array can be applied to form three-dimensional structures having an enhanced nonlinear response to light.
|Flexible and Stable Supercontinuum Source - Optical pulse source comprising optical pump laser for generating optical pump pulses at repetition rate Rf; a nonlinear optical element comprising an optical fiber for generating supercontinuum pulses; a gating device provided operable to selectively control the launch of pump pulses into the optical fiber at a reduced, lower repetition rate Rr=Rf/N in order to generate supercontinuum pulses at different user selectable repetition rates lower than the pump pulse repetition rate; first and second optical amplifiers; wavelength tunable optical bandpass filter; wherein the optical fiber can generate supercontinuum pulses having a supercontinuum spanning from below 450 nm to greater than 2000 nm; and wherein said optical pulse source comprises an all-fiber source wherein said optical pump laser comprises a fiber oscillator, said gating device comprises a fiber coupled optical modulator, and the optical pump pulses are launched into the optical fiber without the use of free space optics.
Patent applications in class OPTICAL FREQUENCY CONVERTER
Patent applications in all subclasses OPTICAL FREQUENCY CONVERTER


text:
High School Sports
Xavier Gators good to go despite graduation of champ runner
Note: This article includes schools in the writer's area of coverage, which is as follows: from Fountain Hills west through Scottsdale, all of Phoenix (except for Ahwatukee), the southwest, northwest and northern sections of the metro area. Other locales include northern, northeast and northwest Arizona. Most of this information was obtained from e-mail questionnaires returned by the coaches.
Star Sarah Fakler has graduated, now scampering through the greener pastures at the University of Virginia, but the team she leaves behind at Phoenix Xavier Prep has a good chance to earn its seventh straight big-school cross-country championship.
Coach Dave Van Sickle's Gators are led by a pair of seniors, Samantha Mattice and Shelby Brown. Junior Lauren Kinzle also should be a factor, along with Jane Miller and Sierra Brown.
Other Gators to watch are Julianne Vice, Savannah Gaffney, Shannon Molvin and incoming freshman Sarah Carter.
Glendale Mountain Ridge finished ninth a year ago, and coach Rich Stein thinks that this year's group might have more depth.
The team's top runners are seniors Christiana Benites and Cari Steen and freshman Tatum Stafford.
Neil Young is switching from coaching boys to the girls this season at Glendale Cactus, and hopes for a top-five finish. Many of his athletes participated in the Arizona Road Racers Summer Series.
The Cobras will be led by juniors Kenzi Fitzgerald and Libby Rath, sophomore Drianna Mustin and freshman Alexis Wilkes.
Phoenix Greenway always seems to be competitive, and this year's version should be no different.
Leading the way are senior Summer Ankrum and sophomore Hailey Femrite.
Scottsdale Saguaro is moving up from Division III to Division II, and coach John Prather has a good group.
The team is led by junior Jelani Huma, also a starting guard on the school's state championship basketball team. Other key runners are senior Megan Boyd and sophomore Hailey Prestwood.
The teams from Glendale High and Phoenix Sierra Linda are attempting to make some strides.
Glendale is led by Natalia Gonzales, and Sierra Linda's top runner is Zyanne Baxter.
Other area teams in the D-I top 10 and their top returnees: No. 6 Scottsdale Chaparral (Ali Kallner), No. 7 Phoenix Pinnacle (Andrea Arriaga), Phoenix Sandra Day O'Connor (Kyra Lopez).
Flagstaff High appears to be in a good position to repeat in Division II.
The Eagles have three top 10 finishers returning, including champion Tatiana Gillick. The others are Alix Manci and Rae Johnson.
Other teams that could challenge and their top returnees: Cave Creek Cactus Shadows (Sloane Myers-Lenz), Phoenix Arcadia (Megan Reniewicki) and Glendale Ironwood (Shea Bonine).
In Division III, defending champion Page High lost its top three finishers (all in the top 10) to graduation. Senior Tomeka Church will have to lead this year's group.
Second-place Cottonwood Mingus is led by returning senior Justine Taylor. No. 3 Chinle has Tamarie Tracey back. Junior Danielle Smiley is back to lead No. 10 Fort Defiance Window Rock.
Among D-III individuals, Fountain Hills sophomore Sierra Jarriel is back, as is Courtney Lewis of River Valley.
In Division IV, Keams Canyon Hopi is the favorite to pick up another title trophy with three seniors who finished in the top 10 – Kaitlyn Billy, Christen Ben and Claryn Josytewa.
Other key teams and their top returnees: Flagstaff Northland Prep (Regan Gee), Ganado (individual champion Nikesha Eagleman), Scottsdale Prep (Charlotte Moore), Whiteriver Alchesay (Carmilyn Pinal), Phoenix Northwest Christian (Megan Davis) and Sanders Valley (Kristen Quigley).
Most Popular
Upcoming Games Streaming Live
Preps Interviews
- Romanus Amukamara, father of New York Giant and ASU Basketball sistersRomanus Amukamara discusses athletic success of his son Prince Amukamara of the New York Giants, and
- NFSHSA chief product officer Monisha Longacre National Federation of State High School Associations chief product officer Monisha Longacre talks A
- Hamilton Baseball Coach Mike WoodsHamilton Baseball Coach Mike Woods discusses the success of his program, the challenges of coaching
- University of Oregon Basketball Player and Corona Del Sol Alum Casey Benson InterviewCasey Benson discusses freshman season at University of Oregon, playing in the NCAA tournament, and
Arizona Sports Preps 365
- March 28, 2015 - Hour: 1Arizona Sports Preps 365 gets you caught up on everything going on in Arizona's High School sports scene.
- March 28, 2015 - Hour: 2Arizona Sports Preps 365 gets you caught up on everything Arizona High School sports.
- March 21, 2015 - Hour: 1Arizona Sports Preps 365 gets you caught up on everything going on AZ's High School Sports Scene.
- March 21, 2015 - Hour: 2Arizona Sports Preps 365 gets you caught up on everything going on AZ's High School Sports Scene.
- March 7, 2015 - Hour: 1Arizona Sports Preps gets you caught up on everything on the Arizona High School sports scene.

subset: commoncrawl


text:
Scholarship offered for ag students
The Minnesota Soybean Research and Promotion Council is offering high school and college scholarships to students who plan to continue education in college or vocational school programs focused on agriculture.
Get the full story
Subscribe or Log In
Are you a newspaper subscriber but you don't have a Digital Access account yet? Activate your account.
You will need your subscription account number and phone number. Not sure if you have an account? Call 218-855-5897 and we can help you.


text:
Sign in now to view, license and download this image or contact us to see this image without a watermark. Want to embed this image on a non-commercial website or blog? Learn more.
Similar imagesView all
Boston Skyline At Dusk Stock PhotoBoston - Massachusetts,Urban Skyline,Outdoors,Architecture,City,City Life,Cloud - Sky,Connection,Dusk,Famous Place,Horizontal,Massachusetts,No People,Photography,Sea,Skyscraper,Transportation,Travel Destinations,USA,WaterPhotographer Adam JonesCollection: The Image Bank Adam Jones


text:
BACnet System Controller - Facility Management Product Release
Delta Controls
website | Company information
The Delta 16x16 Controller is a Native BACnet Controller that communicates either on an RS-485 LAN using the MS/TP BACnet protocol, or optionally over Twisted-Pair Ethernet.
It also supports other Application-based Controllers. The controller is designed for a wide range of applications with mid-sized I/O requirements, and strategies are written in Delta�s GCL programming language. Both firmware and controller databases are loadable over the network.
Content Category: Building Automation
- 3 Common Mistakes in Wireless System Design
- When Installing Wireless, Consider Signal Coverage, Interference, Security
- During Design, Think Ahead in Planning Wireless Needs
- Analytics, Fault Detection Improve Building Automation Capabilities
- BAS Can Help Facility Managers Take Advantage of Smart Grid
- BAS Has an Important Role with Demand Response
posted: 9/20/2007
Search BACnet System Controller on FacilityZone.com


text:
Upload Photo
Top 10 outdoor entertainment events on LI this summer
Outdoor concerts and festivals, from Great Neck to Orient, will keep us plenty busy this summer. A new batch of entertainers is making its debut at the crowd favorite Nikon at Jones Beach Theater, and Glen Cove is launching its own new summer tradition: a seaside festival. Here are our 10 favorite special outdoor events going on around Long Island this summer.
Kate Middleton's royal baby bump Songs we hate to love Recent notable deaths New York City parties Barclays Center concerts Women of pro wrestling March Madness: Famous alumni from each school Concerts coming to Jones Beach this summer 10 must-read books out in April Upcoming LI, NYC concerts 'Idol' season 14 finals 10 big sales this weekend


text:
with(Physics) :t:=Intc(Dirac(k1+k2+k3)*phi(k1)*phi(k2)*phi(k3),k1,k2,k3) ;
# how to forceFundiff(t,phi(-k));# to find3*Intc(Dirac(k2+k3-k)*phi(k2)*phi(k3),k2,k3) ;
The physics package is pretty awesome, but one thing that would be a big help is some functionality for entering and resolving vectors in angle/magnitude format (50 angle 45 degrees, or what have you.) Is there a way to do this?
Hi guys,
After my calculations, I got the Lagrange function having three gereralized co-ordinates namely u,v and w. Hence, according to theory it should give three equations of motion.
I have trouble finding equations of motion from following Lagrange function(L = T -U), Can anyone guide me with this?
Moreover, kinetic energy and strain energy equations are in the form of double integral!!
Hello. I am engaged in independent study of tensor calculus (in the annex to the theory of elasticity) and package Maple. Currently engaged in the action of a solution of the normal point force on elastic half-space (Boussinesq problem, for example, see http://solidmechanics.org/Text/Chapter5_4/Chapter5_4.php#Sect5_4_4). The point is this: you need to create a vector displacement field U, differentiate and create a strain tensor, and then using Hooke's law to obtain the stress tensor. Actually only started to understand and immediately raised the question. Creating vector displacement field using the VectorField package VectorCalculus or any team or package DifferentialGeometry Physic? How then create a tensor with components equal to the partial derivatives of the displacement vector? My attempts Boussinesq_problem.mw. Thanks for your help.
1. can not define equation when not known E
This post aims at summarizing the developments of the last 12 months of the Physics package, which were focused on: Vector Analysis, symbolic Tensor manipulations, Quantum Mechanics, and General Relativity including a new Tetrads subpackage. Besides that, there is a new command, Assume with valuable new features, and a new computing modality: automaticsimplification, as well as an enlargement of the database of solutions to Einstein's equations with more than 100 new metrics. As is always the case, there is still a lot more to do, of course. But It has been an year of tremendous developments, worth recapping.
I would also like to acknowledge and specially thank Pascal Szriftgiser, Directeur de recherche CNRS from the "Laboratoire de Physique des Lasers Atomes et Molécules" (Lille, France), and Denitsa Staicova from the Bulgarian Academy of Science, "Institute for Nuclear Research and Nuclear Energy", for their constant, constructive and valuable feedback along the year, respectively in the areas of Quantum Mechanics and General Relativity. Thanks also to all of you who reported bugs and emailed suggestions as email@example.com; this kind of feedback is a pillar of the development of this Physics project. As usual, the latest version of the package including the developments mentioned below can be downloaded from the Maple Physics: Research and Development web site. Some examples illustrating the use of the new capabilities in the context of more general problems are found in the 2014 MaplePrimes post Computer Algebra for Theoretical Physics. (At the end of this post there are two links: a pdf file with all the sections open, and this worksheet itself for whoever wants to play around).
Simplification is perhaps the most common operation performed in a computer algebra system. In Physics, this typically entails simplifying tensorial expressions, or expressions involving noncommutative operators that satisfy certain commutator/anticommutator rules, or sums and integrals involving quantum operators and Dirac delta functions in the summands and integrands. Relevant enhancements were introduced for all these cases, including enhancements in the simplification of:
Products of LeviCivita tensors in curved spacetimes when LeviCivita represents the Galilean pseudo-tensor (related to Setup(levicivita = Galilean) ), instead of its generalization to curved spaces (related to Setup(levicivita = nongalilean) ).
Tensorial expressions in general that have spacetime, space, and/or tetrad contracted indices, possibly at the same time.
New option tryhard, that resolves zero recognition in an important number of nontrivial situations.
Expressions involving the Dirac function.
Vectorial expressions involving cylindrical or spherical coordinates and related unit vectors.
Expressions simplified with respect to side relations (equations) in the presence of quantum vectorial equations.
Expressions involving products of quantum operators entering parameterized algebra rules.
Expressions involving vectorial quantum operators simplified with respect to other vectorial equations.
Add support for the simplification and integration of spherical harmonics ( SphericalY ) relevant in quantum mechanics.
A number of relevant changes happened in the tensor routines of the Physics package, towards making the routines pack more functionality, the simplification more powerful, and the handling of symmetries, substitutions, and other operations more flexible and natural.
Physics now works with four kinds of Minkowski spaces (different signatures) to accommodate the typical situations seen in textbooks; to these, correspond the signatures +---, ---+, -+++ and +++-.
Allow setting the metric by specifying the signature directly, as in g_[`-`] or g_[`+---`], or or .
The signature keyword of the Physics Setup is now in use, to set the metric and to indicate the form of the orthonormal tetrad, in turn used to derive the form of a null tetrad.
Automatic detection of the position of t as the time variable when you set the coordinates automatically sets the signature of the default Minkowski spacetime metric accordingly to ---+ or +---.
New keywords with special meaning when indexing the Physics (also the user defined) tensors: · `~`; for example g_[`~`] returns the all-contravariant matrix form of the metric. · definition; for example Ricci[definition] returns the definition of the Ricci tensor; works also with user-defined tensors. · scalars; for example Weyl[scalars] and Ricci[scalars] return the five Weyl and seven Ricci scalars used to perform a Petrof classification and in the Newman-Penrose formalism. · scalarsdefinition, and invariantsdefinition; for example Weyl[scalarsdefinition] or Riemann[invariantsdefinition] return the corresponding definitions for the scalars and invariants. · nullvectors; for example, when the new Tetrads subpackage is loaded, e_[nullvectors] returns a sequence of null vectors with their products normalized according to the Newman-Penrose formalism. · matrix; this keyword was introduced in previous releases, and now it can appear after a space index (not spacetime), in which case a matrix with only the space components is returned.
Tensorial expressions can now have spacetime indices (related to a global system of references) and tetrad indices (related to a local system of references) at the same time, or they be rewritten in one (spacetime) or the other (tetrad) frames.
The matrix keyword can be used with spacetime, space, or tetrad indices, resulting in the corresponding matrix
Implement automatic determination of symmetry under permutation of tensor indices when the tensor is defined as a matrix.
New conversions from the Weyl to the Ricci tensors, and from Weyl to the Christoffel symbols.
New option evaluatetrace = true or false within convert/Ricci, to avoid automatically evaluating the Ricci trace when performing conversions that involve this trace.
New option 'evaluate' to convert/g_, convert/Christoffel and convert/Ricci. With this option set to false, it is possible to see the algebraic form of the result (that is, of the tensors involved) before evaluating it.
The Maple 18 Library:-SubstituteTensor command, got enhanced and transformed into one of the main Physics commands, that substitutes tensorial equation(s) Eqs into an expression, taking care of the free and repeated indices, such that: 1) equations in Eqs are interpreted as mappings having the free indices as parameters, 2) repeated indices in Eqs do not clash with repeated indices in the expression and 3) spacetime, space, and tetrad indices are handled independently, so they can all be present in Eqs and in the expression at the same time. This new command can also substitute algebraic sub-expressions of type product or sum within the expression, generalizing and unifying the functionality of the subs and algsubs commands for algebraic tensor expressions.
Tetrads in General Relativity
The formalism of tetrads in general relativity got implemented within Physics as a new package, Physics:-Tetrads , with 13 commands, mainly the null vectors of the Newman-Penrose formalism, the tetrad tensors , respectively: the tetrad, the tetrad metric, the Ricci rotation coefficients, and the lambda tensor, plus five algebraic manipulation commands: IsTetrad , NullTetrad , OrthonormalTetrad , SimplifyTetrad , and TransformTetrad to construct orthonormal and null tetrads of different forms and using different methods.
More Metrics in the Database of Solutions to Einstein's Equations
A database of solutions to Einstein's equations was added to the Maple library in Maple 15 with a selection of metrics from "Stephani, H.; Kramer, D.; MacCallum, M.; Hoenselaers, C.; and Herlt, E., Exact Solutions to Einstein's Field Equations" and "Hawking, Stephen; and Ellis, G. F. R., The Large Scale Structure of Space-Time". More metrics from these two books were added for Maple 16, Maple 17, and Maple 18. These metrics can be searched using g_ (the Physics command representing the spacetime metric that also sets the metric to your choice in one go) or using the command DifferentialGeometry:-Library:-MetricSearch .
New, one hundred and four more metrics were added to the database from various Chapters of the aforementioned book entitled "Exact Solutions to Einstein's Field Equations". Among new metrics for other chapters, with this addition, the solutions found in the literature and collected in Chapters 13 and 14 of this book are all present as well in database of solutions to Einstein's equations.
It is now possible to manipulate algebraically the properties of these metrics, for example, computing tetrads and null vectors for them - using the 13 commands of new Physics:-Tetrads package.
Commutators, AntiCommutators, and Dirac notation in quantum mechanics
When computing with products of noncommutative operators, the results depend on the algebra of commutators and anticommutators that you previously set. Besides that, in Physics, various mathematical objects themselves satisfy specific commutation rules. You can query about these rules using the Library commands Commute and AntiCommute . Previously existing functionality and enhancements in this area were refined. These include:
Computing Commutators and Anticommutators between equations, or of an expression with an equation.
whenever A is a quantum operator and F is a commutative mapping (see Cohen-Tannoudji, Quantum Mechanics, page 171).
Differentiating with respect to a noncommutative variable whenever all the variables present in the derivand commute with the differentiation variable.
Automatic computation of , that is the automatic computation of a function of an operator applied to its eigenkets (see Cohen-Tannoudji, Quantum Mechanics, page 171).
Parameterized commutators; for example: when setting the rule , take as a parameter, so now returns , not
Automatic derivation of a commutator rule: Commutator(A, F(B)) = F '(B) when Commutator(A, C) = Commutator(B, C) = 0 and C = Commutator(A, B), as shown in (see Cohen-Tannoudji, Quantum Mechanics, page 171).
, including cases like for instance , or .
New mechanism to have more than one algebra rule related to the same function (for example, a function of two arguments that come in different order).
The dot product of the inverse of an operator, Inverse(A) · Ket, now returns the same as 1/A · Ket.
is Hermitian if is Hermitian and F is assumed to be real, via Assume, assuming, or .
Implement that is Hermitian if is Hermitian and F is a mathematical real function, that is, one that maps real objects into real objects; in this change only exp, the trigonometric functions and their inert forms are included.
Add a few previously missing Unitary and Hermitian operator cases:
a) if \035U and V are unitary, the U V is also unitary.
b) if A is Hermitian then is unitary.
c) if U is unitary and A is Hermitian, then is also Hermitian.
Make the type definition for ExtendedQuantumOperator more precise to include as such any arbitrary function of an ExtendedQuantumOperator.
New Assume command and new enhanced Mode: automaticsimplification
One new enhanced mode was added to the Physics setup, automaticsimplification, and a new Physics:-Assume command make expressions be automatically expressed in simpler forms and allow for very flexible ways of implementing assumptions, making the Physics environment concretely more expressive.
In almost any mathematical formulation in Physics, there are objects that are real, positive, or just angles that have a restricted range; for example: Planck's constant, time, the mass and position of particles, and so on. When placing assumptions using the assume command, however, expressions entered before placing the assumptions and those entered with the assumptions cannot be reused in case the the assumptions are removed. Also, when using assume variables get redefined so that geometrical coordinates (spacetime, Cartesian, cylindrical, and spherical) loss their identity. These issues got addressed with a new Assume command, that does not redefine the variables, implementing the concept of an "extended assuming ", allowing for reusing expressions entered before placing assumptions and also after removing them. Assume also includes the functionality of the additionally command.
Automatic simplification
This new Physics mode of computation means that, after you enter , the output corresponding to every single input (not just related to Physics) gets automatically simplified in size before being returned to the screen. This is fantastically convenient for interactive work in most situations.
Vectors Package
A number of changes were performed in the Vectors subpackage to make the computations more natural and versatile:
Enhancement in the algebraic manipulations of inert vectorial differential operators.
Improvements in the manipulation of of scalar products of vector or scalar functions (to the left) with vectorial differential operators (to the right), that result in vectorial or scalar differential operators.
Several improvements in the use of trigonometric simplifications when changing the basis or the coordinates in vectorial expressions.
Add new functionality mapping Vectors:-Component over equations, automatically changing basis if the two sides are not projected over the same base.
Implement the expansion of the square of a vectorial expression as the scalar (dot) product of the expression with itself, including the case of a vectorial quantum operator expression.
Allow multiplying equations also when the product operator is in scalar and vector products (Vectors:-`.` and Vectors:-`&x`).
ChangeBasis : allow changing coordinates between sets of orthogonal coordinates also when the expression is not vectorial.
New command: ChangeCoordinates , to rewrite an algebraic expression, using Cartesian, cylindrical, and spherical coordinates, an expression that involves these coordinates, either a scalar expression, or vectorial one but then not changing the orthonormal basis.
The Physics Library
Twenty-six new commands, useful for programming and interactive computation, have been added to the Physics:-Library package. These are:
Additionally, several improvements in the previously existing Physics:-Library commands have been implemented:
Add the types spacetimeindex, spaceindex, spinorindex, gaugeindex, and tetradindex to the exports of the Library:-PhysicsType package.
Library:-ToCovariant and Library:-ToContravariant when the spacetime is curved and some 'tensors' involved are not actually a tensor in a curved space.
Add new options changefreeindices and flipcharacterofindices to the Library:-ToCovariant and Library:-ToContravariant commands, to actually lower and raise the free indices as necessary, instead of the default behavior of returning an expression that is mathematically equivalent to the given one.
Extend the Library commands GetCommutativeSymbol , GetAntiCommutativeSymbol , and GetNonCommutativeSymbol to return vectorial symbols when Vectors is loaded and a vectorial symbol is requested.
Add functionality to the Library command GetSymbolsWithSameType so that when the input is a list of objects, it returns a list with new symbols of the corresponding types, automatically taking into account the vectorial (Y/N) kind of the symbols.
Add several fields to the Physics:-Setup() applet in order to allow for manipulating all the Physics settings from within the applet.
New Physics:-Setup options: automaticsimplification and normusesconjugate.
When any of Physics or Physics:-Vectors are loaded, dtheta, dphi, etc. are now displayed as , , etc.
Implement, within the `*` operator, both the global and the Physics one , the product of equations as the product of left-hand sides equal the product of right-hand sides, eliminating the frequently tedious typing "". You can now just enter "".
Automatically distribute dot products over lists, as in .
Allow (A = B) - C also when A, B, and C are Matrices.
Add and to convert Physics:-Vectors, Matrices of equations, etc. into sets or lists of equations.
Annihilation and Creation operators are now displayed as in textbooks using and .
It is now possible to use equation labels to copy and paste expressions involving Annihilation and Creation operators.
Implement the ability in Fundiff to compute functional derivatives by passing only a function name as second argument. This works okay when the derivand contains this function with only one dependency (perhaps with many variables), say X, permitting varying a function quite like that done using paper and pencil.
The determination of symmetries and antisymmetries of tensorial expressions got enhanced.
The metric as well as the tetrad and tetrad metric can now be (re)defined using the standard Physics:-Define command for defining tensors. Also, the definition can now be given directly in terms of a tensorial expression.
Add keyword option attemptzerorecognition in TensorArray , so that each component of the array is tested for 0.
Allow to sum over a list of objects, or over `in` structures like '' when redefining sum, and also in Physics:-Library:-Add .
Harmonize the use of simplify/siderels with Physics, so that anticommutative and noncommutative objects, whether they are vectorial or not, are respected as such and not transformed into commutative objects when the simplification is performed.
Changes in design:
The output of KillingVectors has now the format of a vector solution by default, that is, a 4-D vector on the left-hand side and a list with its components on the right-hand side and as such can be repassed to the Define command for posterior use as a tensor. To recover the old format of a set of equation solutions for each vector component, a new optional argument, output = componentsolutions, got implemented.
Vectors:-Norm now returns the Euclidean real norm by default, that is: , and only return using conjugate, as in , when the option conjugate is passed, or the setting normusesconjugate is set using Physics:-Setup .
The output of FeynmanDiagrams now discards, by default, all terms that include tadpoles. Also, an option, includetadpoles, to have these terms included as in previous releases, got implemented.
When Physics is loaded, does not return , in view that, in Maple, returns 1.
The dot product of quantum operators and now returns as a (noncommutative) product when neither nor involve Bras or Kets .
If is a quantum operator and Vectors is loaded, then is also a quantum operator; likewise, if is a noncommutative prefix and Vectors is loaded then is also a noncommutative object.
When Vectors is loaded, the Hermitian and Unitary properties of operators set using the Setup command are now propagated to "the name under the arrow" and vice versa, so that if is a Hermitian Operator, or Unitary, then is too.
The SpaceTimeVector can now have dependency other than a coordinate system.
It is now possible to enter even when the index is repeated twice, considering that in is actually a dummy, so that a collision with in can be programmatically avoided.
Diminish the use of KroneckerDelta as a tensor, using the metric g_ instead in the output of Physics commands, reserving KroneckerDelta to be used as the standard corresponding symbol in quantum mechanics, so not as a tensor.
See Also
Physics , Computer Algebra for Theoretical Physics, The Physics project
Edgardo S. Cheb-TerrabPhysics, Differential Equations and Mathematical Functions, Maplesoft
At the internet site of The Heun Project, a strong declaration is made that only Maple incorporates Heun functions, which arise in the solution of differential equations that are extremely important in physics, such as the solution of Schroedinger's equation for the hydrogen atom. Indeed solutions appear in Heun functions, which are highly obscure and complicated to use because of their five or six arguments, but when one tries to convert them to another function, nothing seems to work. For instance, if one inquires of FunctionAdvisor(display, HeunG), the resulting list contains
"The location of the "branch cuts" for HeunG are [sic, is] unknown ..." followed by several other "unknown" and an "unable". Such a solution of a differential equation is hollow.
Incidentally, Maple's treatment of integral equations is very weak -- only linear equations with simple solutions, although procedures by David Stoutemyer from 40 years ago are available to enhance this capability.
When can we expect these aspects of Maple to work properly, for applications in physics?
how to demonstrate the first quantization and second quantization of maxwell equation with physics package
how to calculate the curvature of discrete data?
if discrete data have curvature, does it mean that it has quantum gravity?
but it may be some random data, it seems contradicts the fact
how to quantization of this curvature in maple?
Hi all,
I'm trying to initialize a 4-vector and promote it as a tensor in Maple 16 using the Physics package. My attempt so far has been unsuccessful :)
This 4-vector needs to be a function of the coordinates X. What I'm trying to do is to allocate terms by terms my tensor as indicated in my attempt below. Everything looks fine (the query is telling me F2 is a tensor) but when I'm trying to compute contravariant quantities, I can't obtain an answer for a given coordinate (here F2[~n](X) is not equal du v_1(X))... Finally, the last line, computing the sum over all the indexes is not giving me an answer...
restart; with(Physics):Setup(mathematicalnotation=true):Setup(coordinatesystems = cartesian):Define();g_[]:
Surely, something is wrong in my way of defining a spacetime tensor. What would be the solution to obtain a decent contravariant F2?
Another more or less related question would be to know how to compute a taylor expansion of a function itself i.e. 1/(1+f(X))~ 1-f(X) since f<<1? Would there be a built-in fonction to do such a thing?
Many thanks!
I`m new with the Physics package. I have a Hamiltonian in a lattice written in terms of creation and annihilation operators. The Question is, How can I label a Creation and an Annihiliation operator for each site in the Lattice. WIth this, I can compute mean values and other stuffs associated with the Hamiltonian.
Many thanks in advance
HiTwo new things recently added to the latest version of Physics available on Maplesoft's R&D Physics webpage are worth mentioning outside the framework of Physics.
This new Assume implements the concept of an "extended assuming". It permits re-using expressions involving the variables being assumed, expressions that were entered before the assumptions were placed, as well as reusing all the expressions computed while the variables had assumptions, even after removing the variable's assumptions. None of this is possible when placing assumptions using the standard assume. The new routine also permits placing assumptions on global variables that have special meaning, that cannot be redefined, e.g. the cartesian, cylindrical or spherical coordinates sets, or the coordinates of a coordinate spacetime system within the Physics package, etc.
This is Physics from today:
Automatic simplification is here. At this point automaticsimplification is OFF by default.
Hence, for instance, if you input the following expression, the computer just echoes your input:
There is however some structure behind (1.3) and, in most situations, it is convenient to have these structures apparent, in part because they frequently provide hints on how to proceed ahead, but also because a more compact expression is, roughly speaking, simpler to understand. To see this automaticsimplification in action, turn it ON:
Recall this same expression (you could input it with the equation label (1.3) as well)
What happened: this output, as everything else after you set and with no exceptions, is now further processed with simplify/size before being returned. And enjoy computing with frankly shorter expressions all around! And no need anymore for "simplify(%, size)" every three or four input lines. Another example, typical in computer algebra where expressions become uncomfortably large and difficult to read: convert the following input to 2D math input mode first, in order to compare what is being entered with the automatically simplified output on the screen
You can turn automaticsimplification OFF the same way
New facility; welcome to the world of "extended assuming" :)
Consider a generic variable, x. Nothing is known about it
nothing known about this object
Each variable has associated a number that depends on the session, and the computer (internally) uses this number to refer to the variable.
When using the assume command to place assumptions on a variable, this number, associated to it, changes, for example:
Indeed, the variable x got redefined and renamed, it is not anymore the variable x referenced in (1.8).
Originally x, renamed x~:
is assumed to be: RealRange(Open(0),Open(1/2*Pi))
The semantics may seem confusing but that is what happened, you enter x and the computer thinks x~, not x anymore.This means two things:
1) all the equations/expressions, entered before placing the assumptions on x using assume, involve a variable x that is different than the one that exists after placing the assumptions, and so these previous expressions cannot be reused. They involve a different variable.
2) Also, because, after placing the assumptions using assume, x refers to a different object, programs that depend on the x that existed before placing the assumptions will not recognize the new x redefined by assume .
For example, if x was part of a coordinate system and the spacetime metric depends on it, the new variable xredefined within assume, being a different symbol, will not be recognized as part of the dependency of This posed constant obstacles to working with curved spacetimes that depend on parameters or on coordinates that have a restricted range. These problems are resolved entirely with this new Library:-Assume, because it does not redefine the variables. It only places assumptions on them, and in this sense it works like assuming , not assume . As another example, all the Physics:-Vectors commands look for the cartesian, cylindrical or spherical coordinates sets in order to determine how to proceed, but these variables disappear if you use assume to place assumptions on them. For that reason, only assuming was fully compatible with Physics, not assume.
To undo assumptions placed using the assume command one reassigns the variable x to itself:
Check the numerical address: it is again equal to (1.8)
·All these issues get resolved with the new Library:-Assume, that uses all the implementation of the existing assume command but with a different approach: the variables being assumed do not get redefined, and hence: a) you can reuse expressions/equations entered before placing the assumptions, you can also undo the assumptions and reuse results obtained with assumptions. This is the concept of an extended assuming. Also, commands that depend on these assumed variables will all continue to work normally, before, during or after placing the assumption, because the variables do not get redefined.
So this simplification attempt accomplishes nothing
Let's assume now that
The new command echoes the internal format representing the assumption placed.
a) The address is still the same as (1.8)
So the variable did not get redefined. The system however knows about the assumption - all the machinery of the assume command is being used
Originally x, renamed x:
Note that the renaming is to the variable itself - i.e. no renaming.
Hence, expressions entered before placing assumptions can be reused. For example, for (1.12), we now have
To clear the assumptions on x, you can use either of Library:-Assume(x=x) or Library:-Assume(clear = {x, ...}) in the case of many variables being cleared in one go, or in the case of a single variable being cleared:
The implementation includes the additionally functionality, for that purpose add the keyword additionally anywhere in the calling sequence. For example:
is assumed to be: RealRange(Open(0),infinity)
In summary, the new Library:-Assume command implements the concept of an extended assuming, that can be turned ON and OFF at will at any moment without changing the variables involved.
Download AutomaticSimplificationAndAssume.mw
Edgardo S. Cheb-Terrab Physics, Differential Equations and Mathematical Functions, Maplesoft
Hello everybody,
I will start a course in mastering QM in a MOOC format (Massive Open Online Course). Up to now, I always do the calculation by hand and sometimes with the LinearAlgebra package. But now I need to do the calculation more rapidly. So I decided to learn how to use this package for this course.
The help system give a too generalized way to do it. Even by looking the example, I didn't find praticle example to it. So is there a generous person who could take a little bit of hi time to show me how to do it by using an exemple that yo will find attach to this post.
Thank you in advance for your trouble.
Besgt regards.
Mario Lemelin
Maple 18.2 Win 7 and Ubuntu 14.04 - 64 bitsMapleSim 7 Win 7 and Ubuntu 14.04 - 64 bits
messagerie : email@example.com
téléphone : (819) 376-0987
Partial rectification for the Physics:-Simplify and Physics:-Library:-SortProducts procedures dealing with Fermi annihilation/creation operators
This post will be useful for physicists dealing with Fermi annihilation/creation operators. Physics Package provides plenty of powerful tools for quantum operators handling, however some of them often fail to render correct result. In particular incorrect behaviour with respect to Fermi annihilation/creation operators is observed for routines Simplify and SortProducts. In this post I present my procedures and which partially solve these issues.
Problems with Physics Package routines
Short explanation of custom routines and
Weak points
Final notes
Download FermiCreationAnnihilation.mw
You must be logged into your Facebook account in order to share via Facebook.
Click the button below to share this on Google+. A new window will open.
You must be logged in to your Twitter account in order to share. Click the button below to login (a new window will open.)
Please log-in to your MaplePrimes account.
Wrong Email/Password. Please try again.
Please log-in to your MaplePrimes account.
Wrong Email/Password. Please try again.
Questions | Posts | Tags
| Users | Unanswered |
Maplesoft Blog | Badges | Recent
About | MaplePrimes Help |
© Maplesoft, a division of Waterloo Maple Inc. maplesoft.com | Terms of
Use | Privacy | Trademarks


text:
Holdays.net Home
1965 Press Photo Dwight D. Eisenhower And George V. Allen
This is an 8 x 10 photograph of Dwight D. Eisenhower And George V. Allen. Dated Feb 9, 1961.
The images below depict the actual vintage photograph offered for sale in this listing and will give you the best idea of the condition of the photo.
Be Sure ToCheck Our Other IDs!
Three simple reasons: 1) We are passionate about photographs, 2) we have assembled the largest collection of original press photos available on , and 3) we are fiercely committed to total customer satisfaction. Every team member here at Historic Images Inc is committed to taking care of our customers. Our leadership team is constantly seeking out unique archives and photo collections to ensure you have access to unique items across a wide area of subjects and from different parts of the country. Once we take possession of the photos, we take great care of them throughout their life cycle of prepping, scanning, captioning, and storing. When you purchase from us, we sandwich your photo between two pieces of cross-corrugated cardboard, enclose it in plastic, and send it your way. We only sell original press photos on , so offer now before its gone!
We prefer PayPal. Contact us for additional options. You may contact us through messaging or:
Historic Images Inc. 6073 Mt. Moriah Ext. Suite 12 Memphis, TN 38115
Local pickup is available at the above address between 10 a.m. And 4 p.m. for customers in the Memphis, TN area.
Tennessee residents will be charged 9.25% sales tax on each order.
We ship orders Monday through Friday. We do not ship on weekends or holidays. Our standard processing time is one business day from time of payment.
USPS First Class $2.99 USPS Priority $5.99 ExpeditedFedEx Overnight $19.99
We charge $2.99 flat shipping via First Class US Postal Service for all US orders purchased through this ID.
Shipping is charged per order, and may not be combined with our other seller IDs (per 's policy). We encourage customers interested in multiple items to use 's shopping cart so that multiple items will be in the same order and subject to one shipping charge. Our systems automatically open unpaid item cases at 21 days, so please close your tab within 3 weeks of your first purchase.
Please ensure your shipping address is accurate in and PayPal.
USPS First Class $9.99 USPS Priority $24.99 FedEx International Priority $19.99
We charge $9.99 flat shipping via US Postal Service First Class for all international orders, any size. USPS Priority is available for $24.99. FedEx International Priority is available for $19.99
Customs charges, import taxes, duties, etc. are the sole responsibility of the buyer. You may contact your local Customs office to help you determine what these fees may be.
Shipping is charged per order, and may not be combined with our other seller IDs (per 's policy). We encourage customers interested in multiple items to use 's shopping cart so that multiple items will be in the same order and subject to one shipping charge. Our systems automatically open unpaid item cases at 21 days, so please close your tab within 3 weeks of your first purchase.
Copyright 2009 - Present, Historic Images, Inc.
This item has been shown 21 times.
1939 Press Photo Nash On Sandy Bill Vs Soisne & Free Child At Jamaica Track Ny
1949 Press Photo Red Schoendienst Of Cardinals Steals 2nd Vs Cubs Roy Smally
1949 Press Photo Glen Lasswell On Grey Shadow 2nd Vs B Shoemaker On Intended
1955 Press Photo Harry Agganis Of Red Sox & Boys At Bowling Tournament
1962 Press Photo Nicole Hassler Practices Skating Moves At Richmond England
1932 Press Photo Milford Orlitz Us Speed Skater At Lake Placid Ny
1939 Press Photo Tommy Hitchcock, John Hay Jock Whitney & Fans At Polo In Ny
1957 Press Photo Ray Robinson, Boxing Commissioner Julius Helfand
1951 Press Photo Philadelphia Phillies Tom Casagrande At Clearwater Fla Training
Vintage Nasacar Photo Finish - 1981 Talladega 500 Finish Line Duel