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A semiconductor laser having an external cavity including a single-mode optical fiber. A Bragg grating is written onto the fiber which defines the end of the optical cavity, selects the lasing wavelength, and discriminates against the lasing of higher-order transverse modes in the multi-mode gain region. In one embodiment, the semiconductor laser includes an optically active vertical-cavity semiconductor stack similar to a vertical-cavity surface emitting laser. The stack is optically pumped either from the front or the back over a relatively large area such a multi-mode beam is output. Optics couple the multi-mode beam to the single-mode input of the fiber. A partially transmissive mirror of reflectivity between 25 and 40% may be placed on the output surface of the semiconductor stack to form a coupled-cavity laser. A plurality of laser diodes can be angularly positioned around the area of the semiconductor stack being pumped to increase the total pump power. In a second embodiment, the semiconductor laser includes a broad-area diode laser/amplifier. Anamorphic optics couple the asymmetric output of the optical diode to the single-mode fiber. In a third embodiment, a laser diode pumps a solid-state rod composed of an optically active material such as YAG. One end of the rod is coated with a mirror, and the other end is optically coupled to the single-mode fiber having the Bragg grating written thereon. The invention can be advantageously used to optically pump an erbium-doped fiber amplifier.
1. A laser system comprising:
an optically active medium having a first and a second end, the optically active medium having sufficiently large lateral dimensions to support multiple transverse lasing modes;
a back mirror attached to said first end to reflect light at a predetermined frequency;
a mode-discriminating front mirror comprising
an optical fiber having a core diameter sufficiently small to support only a single fundamental zero-order transverse mode, and
a Bragg grating written in said optical fiber partially reflecting light at said predetermined frequency; and
fiber coupling optics coupling light from said second end of said optically active medium to said optical fiber by reducing the width of a light beam from the width corresponding to the lateral dimensions of said optically active medium to the width corresponding to the core diameter of said optical fiber and compensating for beam divergence difference;
wherein light at said predetermined frequency lases in an optical laser cavity defined between said back mirror and said mode-discriminating front mirror, and the optical feedback from said Bragg grating discriminates against lasing of higher-order transverse modes to stabilize high power lasing only at the fundamental zero-order transverse mode, and
wherein said fiber coupling optics comprise anamorphic optics focusing light upon an input mirror formed on an input end of a solid-state rod having an output end coated with an anti-reflective coating.
2. The laser system of
3. The laser system of
4. The laser system of
5. The laser system of
6. The laser system of
7. The laser system of
8. The laser system of
9. The laser system of
10. A laser system comprising:
a mode-discriminating front mirror comprising
an optical fiber having a core diameter sufficiently small to support only a single fundamental zero-order transverse mode, and
a Bragg grating written in said optical fiber having a period corresponding to a predetermined wavelength;
a solid medium configured as a transversely multi-mode optical waveguide and comprising an optically active material;
a back mirror reflective at said predetermined wavelength coated on a first end of said optical waveguide, an optical cavity being formed between said mode-discriminating front mirror and said back mirror for lasing light at said predetermined wavelength, and the optical feedback from said Bragg grating discriminating against lasing of higher-order transverse modes to stabilize high power lasing only at the fundamental zero-order transverse mode; and
fiber coupling optics optically coupling a second end of said optical waveguide to an input end of said optical fiber by reducing the width of a light beam from the width corresponding to the lateral dimensions of said transversely multi-mode optical waveguide to the width corresponding to the core diameter of said optical fiber and compensating for beam divergence difference, and
wherein said fiber coupling optics comprises anamorphic optics focusing light upon an input mirror formed on an input end of a solid-state rod having an output end coated with an anti-reflective coating.
11. The laser system of
12. The laser system of
13. The laser system of
14. The laser system of
15. The laser system of
16. The laser system of
17. A semiconductor pump laser system, comprising:
an optically active semiconductor device capable of amplifying an optical signal within an optical wavelength band including a desired lasing wavelength, the optically active semiconductor device having sufficiently large lateral dimensions to provide an optical output of said semiconductor device being a transversely multi-mode output at said lasing wavelength, wherein said semiconductor device comprises an edge-emitting diode optical amplifier;
a mode-discriminating front mirror comprising
an optical fiber including an input end and having a core diameter sufficiently small to support only a single fundamental zero-order transverse mode, and
a Bragg grating written on said optical fiber having a period corresponding to said lasing wavelength, wherein an optical cavity producing light of said lasing wavelength is defined on one end by said mode-discriminating front mirror and extends within said optically active semiconductor device; and
fiber coupling optics coupling said multi-mode output of said semiconductor device to said input end of said optical fiber by reducing the width of a light beam from the width corresponding to the lateral dimensions of said optically active semiconductor device to the width corresponding to the core diameter of said optical fiber and compensating for beam divergence difference, whereby the optical feedback from said Bragg grating determines said lasing wavelength of said optically active semiconductor device and discriminates against lasing of higher-order transverse modes to stabilize high power lasing only at the fundamental zero-order transverse mode, and
wherein said fiber coupling optics comprises anamorphic optics focusing light upon an input mirror formed on an input end of a solid-state rod having an output end coated with an anti-reflective coating.
18. The laser system of
19. The laser system of
20. The laser system of
a mirror disposed on said first end of said optical cavity; and
an anti-reflective coating disposed on said second end of said optical cavity.
21. The laser system of
a highly reflective mirror disposed on said first end of said optical cavity; and
a partially transmissive mirror disposed on said second end of said optical cavity.
22. The laser system of
23. The laser system of
24. The laser system of
25. The laser system of
26. The laser system of
27. The laser system of
28. The laser system of
29. The laser system of
30. The laser system of
31. The semiconductor pump laser system of
32. The laser system of
33. The semiconductor pump laser system of
34. The semiconductor pump laser system of
35. The semiconductor pump laser system of
1. Field of The Invention
The invention relates generally to semiconductor lasers. In particular, the invention relates to a laser having a resonant cavity including both a semiconductor amplifier and an optical fiber upon which is written a Bragg grating providing the frequency and mode discrimination of the laser.
2. Technical Background
Optical amplifiers, in particular doped fiber amplifiers, have become increasingly incorporated into the backbone of the telecommunications network when it is necessary to amplify optical signals without the need to first reconvert them to electrical form. Instead, the optical signal itself is amplified regardless of its coding format. As illustrated schematically in FIG. 1, a digital optical signal being transmitted across the telecommunications network is received on a single-mode optical fiber 10 and is combined in an optical combiner 12 with an optical pump signal from an optical pump source 14. The combined signals traverse an optical amplifier 16, preferably constituted of an erbium-doped fiber amplifier (EDFA), that is, a silica fiber doped with optically active erbium ions Er3+. In an EDFA, an optical pump signal excites the erbium ions, which can then amplify another optical signal at a lower frequency than the pump frequency. In a telecommunications system, the pump signal amplifies the input data signal, and the EDFA outputs the amplified data signal to a single-mode output fiber 18. Other configurations are possible, for example, the data and pump signal may counter-propagate, and further components such as isolators and stabilization circuits may be included. These variations are not important to the invention and will not be further discussed.
For optical communications, the optical carrier for data signals is typically in the 1300 to 1350 nm or 1525 to 1610 nm ranges while the pump signal is advantageously in the 950 to 1000 nm range, but other wavelength ranges are possible.
For long-range transmission, it is greatly desired that not only the transmission fibers 10, 18 be single mode but that the elements associated with the EDFA 16 also be single mode so as to maintain the integrity of the data signal being amplified. In particular, it is advantageous that a single-mode fiber 19 link the optical pump source 14 and the optical combiner 12 and other parts of the EDFA.
Modern optical fiber communication systems have placed increasingly difficult requirements on the systems illustrated in FIG. 1, in particular the need for increasing levels of amplification. Not unexpectedly, it is desired to amplify a single optical signal as much as possible so as to maximize the distance between required amplification stations. Not so apparent is the increased power requirement necessitated by wavelength division multiplexing (WDM). In this fiber optic transmission technology, a number of closely space optical channels carry different data channels and are simultaneously amplified by the single EDFA 16. The number of WDM channels is increasing from 4 and 16 to 64 and considerably beyond. Each of the multiple channels requires its own fraction of optical pump power. Furthermore, for channel separation, high data rates, and efficiency, it is greatly desired that the data signal be carried only on a single-mode fiber and be combined with a pump signal carried on a single mode fiber. That is, the optical pump source 14 is being expected to provide ever higher amounts of optical power while maintaining its single-mode characteristics.
The prevalent types of single-mode fiber (SMF) systems include semiconductor laser sources based on either narrow single-stripe laser diodes or flared master oscillator-power amplifier (MOPA) configurations. Single-stripe lasers have been reported with output powers of 700 mW, and MOPA with output powers in excess of 1 W. The best currently commercially available SMF coupled pump source provide only about 200 mW of optical pump power at 980 nm. The apparent reasons for this low number include stability and reliability problems produced by the very high optical power densities on the laser mirrors.
A broad-area laser diode has a width considerably larger than that associated with single-mode operation, for example, a stripe width of 100 μm, so that broad-area laser diodes produce multi-moded optical outputs. Their large size allows them to generate higher optical power while still operating at a fairly low power density. However, it is extremely difficult to achieve stable operation with a fundamental (zero-order) transverse mode, the mode of use in pumping a single-mode fiber amplifier. Adequate mode selectivity can be achieved with a narrow slit and an external mirror defining one end of the cavity. However, stability is achieved only by the continued precise alignment of the external elements.
Another approach in the design of high-power lasers uses a multiple quantum-well (MQW) structure in a surface-emitting configuration (that is, a vertical-cavity surface-emitting laser, VCSEL) with an external spherical mirror defining one end of the cavity. This approach produces high performance, but the alignment of the external mirror must be precisely maintained, and at higher pump power the mode selectivity may not be strong enough to ensure operation only in the zero-order mode. These structures typically rely upon either semiconductor interference mirrors formed on a face of the VCSEL or upon the length of the vertical optical cavity formed on the chip to provide the frequency discrimination required of a laser. Such mirrors, particularly when formed of semiconductors, require a large number of layers whose thicknesses must be precisely controlled, contributing to both increased cost and optical loss. Frequency-discrimination based upon cavity length of a semiconductor structure introduces large thermal drift in the lasing frequency because of the large thermal dependence of the effective dielectric constants in semiconductors.
All these solutions further do not effectively address the added problem of coupling the lasing light into a single-mode optical fiber, as required for many applications including the preferred optical pump source for an EDFA.
The invention includes a semiconductor optical amplifier coupled to a single-mode optical fiber upon which is written a Bragg grating having a period corresponding to the desired lasing wavelength. The Bragg grating defines one end, preferably the output end, of an optical cavity which includes the semiconductor amplifier.
The semiconductor laser of the invention is advantageously used as an optical pump source for a doped fiber amplifier, such as an erbium-doped fiber amplifier requiring pump light around 980 nm.
In one set of embodiments of the invention, the semiconductor amplifier includes a wide-area stacked structures of semiconductor layers generally corresponding to the structure of a vertical-cavity surface-emitting laser. Preferably, the active region includes a plurality of strained quantum wells spaced at the nodes the desired lasing wavelength.
The semiconductor stack can be optically pumped either from the front side or the back side.
A plurality of optical pump sources can be directed at inclined angles toward the beam area of the semiconductor stack.
Advantageously, a partially transmissive mirror may be coated on the side of the semiconductor stack facing the fiber so as to create a coupled cavity laser in which the amplification occurs in one cavity and the wavelength selection predominantly occurs in the other cavity.
In another set of embodiments of the invention, the semiconductor amplifier includes an edge-emitting diode laser operating as an amplifier with a mirror on one side and which is electrically pumped.
In yet a further set of embodiments, the optical amplifier includes an solid-state laser rod optically pumped by a diode laser.
FIG. 1 is a schematic diagram of fiber communication network including an erbium-doped fiber amplifier with which the semiconductor laser of the invention can be used.
FIG. 2 is a schematic, cross-sectional view of a first embodiment of the invention that is optically pumped from the front surface of the semiconductor stack.
FIG. 3 is a cross-sectional view of an example of the semiconductor stack of FIG. 2.
FIG. 4 is an isometric view of a multi-source embodiment of the invention.
FIG. 5 is a schematic, cross-sectional view of another embodiment of the invention that is optically pumped from the back surface of the semiconductor stack.
FIG. 6 is a schematic, cross-sectional view of an embodiment of the invention utilizing coupled optical cavities in the laser.
FIG. 7 is graph demonstrating the increased quantum efficiency achievable with the coupled-cavity laser of FIG. 6.
FIG. 8 is an isometric view of an embodiment of the invention using a broad-area laser diode and anamorphic optics.
FIG. 9 is an orthographic view of another embodiment of the invention using a wide-area laser diode and a taper section on the end of the single-mode fiber.
FIG. 10 is a schematic orthographic view of an embodiment of the invention using a solid-state laser rod.
A Bragg grating written into a single-mode optical fiber (that is, a fiber Bragg grating—FBG) can be used as a frequency-discriminating and mode-discriminating mirror defining one end of an optical cavity including a large area optical gain region and optics coupling the multi-mode optical gain region and the single-mode fiber. The fiber, unlike an erbium-doped fiber amplifier, is undoped and is not optically active. The single-mode fiber can be directly and efficiently coupled to a single-mode fiber receiving the output of the laser system. The invention is applicable to both optically and electrically pumped semiconductor lasers.
A first embodiment of the invention illustrated in the schematic cross-sectional view of FIG. 2 uses top-surface optical pumping of a vertically arranged optical-gain structure 20, hereafter referred to as the semiconductor stack 20. Advantageously, the semiconductor stack 20 has large lateral dimensions, typically of the order of at least 100 μm up to a few millimeters allowing the generation of large amount of laser power at relatively low power densities. A variety of solid-state materials, prepared in the form of a relatively thin disk or layer, can be used for the active part of the semiconductor stack 10. For use as a pump source for an EDFA, the operating wavelength needs to be near 980 nm. The preferred structure of the stack at this time for this spectral range includes strained multiple quantum wells (MQWs) of InGaAs/GaAs. This structure is typically epitaxially grown on a GaAs substrate to produce, as shown schematically in FIG. 2, a bottom interference mirror 22, spacers 24, 26, and an active region 28 sandwiched between the spacers 24, 26. A more detailed vertical structure will be discussed later with reference to FIG. 3. Because the structure 10 is optically pumped and being essentially undoped, does not involve a p-n junction, the active region 28 can be made relatively thick. The semiconductor stack 20 is coated with an anti-reflection coating 30, as is well known in such vertical structures.
The active region 28 of the semiconductor stack 20 is optically pumped by one or more pump beams 32 obliquely oriented with respect to the normal of the semiconductor stack 20, for example, at an angle of 45�. The diameter of the pump beam 32 is made relatively large, for example, the 100 :m to 3 mm of the semiconductor stack 20 to allow optical generation in the larger volume of the optical gain structure 20. A 100 :m spot size is approximately optimized for a 2 W optical pump. Such widths are substantially greater than the lateral dimensions associated with confined radiation having a single transverse mode. It is noted that because of the higher refractive index inside the semiconductor stack 20, the pump beam 32 produces a somewhat more vertically oriented beam inside the stack 20. However, because the width of the pump beams 32 is usually considerably larger than the depth of interaction within the semiconductor stack 10, the beam inclination assumes little significance beyond surface reflection coefficients and beam ellipticity. For generating 980 nm light in InGaAs MQWs, the pump light should be in the range of 800 to 850 nm. Intense optical diode laser bars emitting at 808 nm are commercially available for use in pumping solid-state lasers and can be easily adapted for pumping the semiconductor lasers of the invention.
The intense light from the optical pump beam 32 causes the active region 28 to emit light in an optical band near 980 nm. The emitted light is strongly reflected by the back mirror 22 but is efficiently transmitted through the anti-reflection coating 30 into a forward directed beam 34.
A lens system 36 focuses the output beam 34 onto an input end 38 of a single-mode optical fiber 40. The lens system 36, which in this embodiment may be composed of one or more simple lenses, reduces the size of the beam 34 from the multi-moded width of the pumped region of the semiconductor stack 20 to a single-moded width associated with the single-mode optical fiber 40 as well as taking into account the beam divergences associated with both.
The single-mode optical fiber 40 is typically composed of silica materials. Such a fiber 40 is closely related to single-mode optical fibers extensively used in communications networks. The diameter of its circular core is sufficiently small, on the order of 4 to 6 μm, to support only a single transverse mode. However, more complex fiber structures, such as a graded core-cladding, are possible.
According to the invention, a fiber Bragg grating (FBG) 42 is written into the fiber 40 close to its input end 38. The grating 42 is only schematically illustrated in FIG. 2. Its size and location and possible multiplicity of gratings are not limited by the illustration. It is well known how to write the Bragg grating into silica fiber by exposing the fiber to ultraviolet light through an appropriate mask. The periodicity of the fiber Bragg grating 42 causes it to serve as a wavelength selector since the grating periodicity causes a narrowly defined band of wavelengths to be reflected back toward the semiconductor stack 20. Other wavelengths are transmitted through the grating 42. The light reflected back to the semiconductor stack 20 has a total round trip gain less loss of greater than unity, thereby permitting it to self-amplify. The optical signal becomes coherent as it intensifies, and upon stable lasing gain and loss are exactly equal. As is well known, the gain in a lasing structure is concentrated in the optical mode having a wavelength with the least loss. Thereby, the fiber Bragg grating 42 defines the lasing wavelength λL or equivalently the lasing frequency of the semiconductor laser of FIG. 2. A fiber Bragg grating has at least two advantages. It requires only minimal optical alignment, and its thermal sensitivity is low.
Furthermore, the Bragg grating 42 is written on a single-mode fiber 40 which will support only a single optical mode. In fact, there are two degenerate fundamental modes in the circular geometry assumed for the fiber 40, but these can be considered to be a single mode of indeterminate polarization unless other means are used to suppress one of the two orthogonal fundamental modes. Thereby, the single-mode Bragg grating 42 discriminates against lasing of higher-order transverse modes.
The Bragg grating 42, however, is not 100% reflective at its center wavelength λL, a 90% reflectivity being typical. A small fraction of the lasing light is transmitted through the partially transmissive Bragg grating 42 to form the laser output beam. An advantage of the Bragg grating 42 being written into the single-mode fiber 40 is that the entire optical output of the laser is already impressed on a single-mode fiber 40. This fiber 40 can either be directly used as the pump input fiber 19 in the EDFA of FIG. 1, or alternatively a highly efficient splice may be made between the single-mode pump fiber 40 of FIG. 2 and another single-mode fiber used for routing the 980 nm pump signal.
Thus, the fiber Bragg grating 42 simultaneously achieves three advantages. It serves as a thermally insensitive wavelength selector. It suppresses all but the zero-order transverse modes. Its lasing output is already carried on a single-mode fiber.
A detailed example of the vertical structure of the semiconductor stack 20 providing the required optical gain is illustrated in FIG. 3. The active region 28 includes a large odd number, preferably greater than 10, of sets of thin InGaAs strained quantum-well layers 46, relatively thin InGaP strain compensating layers 48, and relatively thick InGaAsP or AlGaAs light-absorbing layers 50. The sets of layers 46, 48, 50 are arranged on a period having an optical length of λL/2, where λL is the desired lasing wavelength, here 980 nm. As is well known, the quantum-wall layers 46 have very small thicknesses, of the order of nanometers, and are strained to produce well defined energy levels within the quantum wells having an energy separation corresponding to the desired emission wavelength λL. The strain compensating layers 48 have the opposite strain so as to prevent strain from accumulating to the point that dislocations would form. The relatively thick light-absorbing layers 50 provide the desired periodicity and are made optically absorbing at the pump wavelength so that the active region 28 efficiently absorbs the pump light. Electrons and holes generated in the light-absorbing layers 50 can diffuse to the much thinner quantum-well layers 46. An additional thicker InGaAsP light-absorbing layer 52 having an optical thickness λL may be grown above the active region 28. A transparent aluminum-free InGaP window layer 54 having an optical thickness of 3λL/4 may be grown at the top of the semiconductor stack. The indicated optical thicknesses have the advantage of placing the maxima of the standing wave at the quantum wells.
The anti-reflection coating 30 is deposited over the semiconductor stack and typically includes a half-wavelength thickness of a dielectric material so as to couple light into and out of the stack 20 with reduced reflection. The anti-reflection coating is important not only on the semiconductor stack 20 but also on other components included within the semiconductor laser cavity so as to reduce the internal cavity loss. The described active region 28 produces a round-trip gain of about 0.1. A 90% reflectivity of the fiber Bragg grating 42 translates to a top mirror loss in logarithmic units of 0.053. Therefore, lasing is possible only if the total of other internal round-trip loss in the laser cavity does not exceed 0.047, including scattering, absorption, and fiber coupling.
The bottom mirror 22 may be formed of a large number, for example 30, pairs of alternating GaAs layers 56 and AlGaAs layers 58, each layer 56, 58 having an optical thickness of λL/4. The dielectric contrast between the large number of paired quarter-wavelength layers 56, 58 produces a semiconductor interference mirror with a reflectivity of at least 99.5% and preferably greater than 99.8%. It is typical for the illustrated structure 20, with the exception of the interference mirror 30, to be grown in a single growth cycle of epitaxial deposition upon an unillustrated GaAs wafer, for example, by chemical vapor deposition or molecular beam epitaxy. In the top-pumped embodiment of FIG. 2, the continued presence of the growth substrate presents no problem. The bottom mirror 22 need not be transparent to the pump light, and various types of thermal heat sinking may be applied to the bottom surface without regards to the pump light.
It is possible to replace the bottom semiconductor interference mirror 22 with a dielectric interference stack or, in the case of the top-pumped embodiment of FIG. 2, even a metallic mirror, for example, of silver or gold. The dielectric stack is composed of layers, for example of SiO2 and Si3N4, exhibiting much higher dielectric contrast with very low optical loss and, as a result can offer reflectivities of up to 99.8% compared to about 98% for a metallic mirror. In either case of the alternative mirrors, however, the growth substrate must be at least locally removed to expose the top or bottom of the illustrated semiconductor structure.
The previously described diode lasers are currently available with optical output powers in the range of 2 W, which should be sufficient to achieve an optical output of about 700 mW in the optically pumped configuration of FIG. 2. However, the optically top-pumped configuration has the further advantage of permitting multiple angularly offset laser pump sources. As illustrated in the isometric view of FIG. 4, four laser pump sources 66 are disposed at 90� intervals about a normal to the semiconductor stack 20. They output respective pump beams 68 inclined at 45� to the surface of the semiconductor stack 20. The number of pump sources 66 may be fewer or greater depending on the power multiplication desired.
Broad-area lasers typically produce generally rectangular or asymmetrically conical optical beams. Anamorphic optics should be included within the laser pump source 66 so that all of them produce a same symmetric beam profile 70 at the surface of the semiconductor stack 20. If the diffusion of charge carriers excited by the pump beams within the semiconductor stack is taken into account, the maximum overlap between the gain and optical field profiles can be achieved if the circular gaussian pumping spot 70 is slightly smaller in size than the circular mode field 72 determined by the output beam optics 36 of FIG. 2 and is positioned at the center of the mode field 72.
If multiple pumping sources are used, they should be rotated at their respective positions to produce the same polarization direction at the surface of the semiconductor stack 20. In all cases, the displacement of the fiber Bragg grating 42 from the fiber input end 38 should not be long enough to permit significant scrambling of the polarization state of the lasing standing wave, that is, not more than several centimeters, for example, 5 cm.
On the other hand, in order to minimize power instability and noise associated with mode hopping, it is desirable to have several longitudinal modes lase simultaneously. Therefore, the wavelength spacing of the modes determined by the length of the external cavity should be smaller than the reflection bandwidth. This condition is relatively easy to satisfy, as shown by the following estimate. For a typical fiber Bragg grating having a reflection bandwidth of about 0.2 nm to have three longitudinal modes in the output spectrum, the mode spacing Δλ needs to be about 0.05 nm. Including the semiconductor chip, lens, air spacing, and some length of the fiber and taking into account both the round trip and the local refractive index, the total effective cavity length Leff needs to be at least
which is about 2 cm for 0.05 nm spacing of a 980 nm signal. Thus, for a reasonable packaging scheme having an air spacing of 2 cm, the fiber Bragg grating may be placed directly adjacent (closer than 1 cm) to the cleaved end 38 of the fiber 40, which necessarily satisfies the polarization scrambling condition as well. The calculation can be somewhat generalized to require a minimum optical cavity length of 1 cm.
An optically bottom-pumped embodiment of the invention is illustrated in the schematic cross-sectional view of FIG. 5. It differs primarily from the front-pumped embodiment of FIG. 2 in that its optical pump beam 70 is positioned on the side of the gain-structure 20 having the bottom mirror 22. The optical pump beam 70 may be aligned in parallel with the output beam 34. The configuration is optically and structurally simpler. However, it imposes several constraints. The bottom mirror 22 must be transmissive to the pump wavelength but highly reflective to the lasing wavelength. Therefore, a metallic bottom mirror cannot be used. Furthermore, the substrate supporting the semiconductor stack 20 and perhaps its epitaxial growth substrate needs to be considered. A GaAs substrate cannot be made transmissive at 810 nm so that, to allow a bottom window, the illustrated semiconductor stack 20 may be lifted off its growth substrate or a window may be etched in the back of the growth substrate and a dielectric window deposited in the window.
As mentioned before, the optically pumped external-cavity semiconductor laser relying upon a fiber Bragg grating requires very low cavity loss to achieve round-trip gain of greater than unity. A coupled-cavity embodiment illustrated in the schematic cross-sectional view of FIG. 6 relaxes the loss constraints. This embodiment is similar to those of FIGS. 2 and 5. However, instead of an anti-reflection coating disposed between the active region 28 and the fiber 40, a partially reflective mirror 80 is placed on the output face of the semiconductor portions of an semiconductor stack 82.
The partially reflective mirror 80 is preferably composed of a relatively few periods of a dielectric stack or of a semiconductor interference mirror grown on the semiconductor stack 82. The partially reflective mirror 80 is designed to have a significant but sub-unity reflectivity rs at the lasing wavelength λL. Its reflectivity rs is high enough that a significant amount of the standing wave excited by the active region 28 is reflected back towards the active region without exiting the semiconductor stack 82. However, the reflectivity is low enough that the light internally reflected from the partially reflecting mirror 80 is insufficient to support lasing. However, the wavelength-selected portions of the spectrum reflected from the fiber Bragg reflector 42 through the partially reflective mirror 80 do contribute sufficient intensity to support the lasing condition of unity gain.
The described structure is in fact a coupled cavity laser. One cavity including the semiconductor stack 20 provides the optical gain. Another cavity including the fiber Bragg grating 42 provides the frequency selection. The two cavities are partially coupled through the partially transmissive mirror 80.
Such a partially reflective mirror also improves the quantum efficiency of the device. Calculations have been performed based upon a realistic set of parameters. First, as shown by line 86 in the graph of FIG. 7 referenced to the right ordinate, as the reflectivity rs of the top mirror 80 increases from 1% to 81%, the minimum reflectivity rext of the fiber Bragg grating 42 required to achieve lasing decreases in a substantially linear fashion. For each pair of these reflectivities rs, rext, the device output quantum efficiency was estimated, as shown by line 88. The quantum efficiency increases with increasing reflectivity rs of the top mirror 80 but quickly saturates at about 60%. A top mirror reflectivity rs of 30% increases the quantum efficiency to about 50% from a value of about 32% for no top mirror, that is, a perfect anti-reflection coating. This calculation indicates that 2 W of optical pumping power from a diode laser can produce 1 W of single-mode optical power on the fiber 40. The very high efficiency can be explained in terms of the top mirror 80 recycling part of the laser emission back to the amplifying medium without subjecting the recycled part to the relatively high loss of fiber coupling.
However, an excessively reflective top mirror 80 should be avoided. An increase of the top mirror reflectivity rs above 40% yields little improvement in quantum efficiency and is likely to degrade mode selectivity because it lowers the threshold almost equally for all transverse modes. Hence, the preferred range for top mirror reflectivity rs is between 25 and 40% at the lasing wavelength λL. If the device is optically pumped from the front surface, the top mirror 80 should also be substantially transparent at the pump wavelength.
It should be noted however that a significant reflection at the top mirror 80 requires that the reflection from the fiber Bragg grating 42 be spectrally matched with the internal Fabry-Perot resonance of the semiconductor stack 82. Not only should the reflectivity be near its maximum at the resonant wavelength of the semiconductor cavity, the reflection should be in phase with the resonance. These conditions are generally easily met because of the relatively broad resonance of the cavity.
The optics associated with the optically pumped embodiments can be easily accomplished with conventional A/R coated lenses, and in particular by A/R coated graded index (GRIN) lenses. So called collimators are commercially available in which a ferrule grasps the fiber and is fixed within a glass tube. A cylindrically shaped GRIN lens is also fixed within the glass tube at a fixed orientation and separation from the fiber end. Commonly known procedures are available for performing the alignment and fixing such that the optical beam on the side of the GRIN lens opposite the fiber is centered on the tube axis and has a waist at a predetermined distance from the GRIN lens. The glass tube with attached fiber and GRIN lens can then be fixed inside a larger metal tube or other support structure. The semiconductor stack is placed in the support structure at the location of the beam waist. The semiconductor stack is rotated at different inclinations to the beam axis to achieve maximum reflectance, which can be measured at the other end of the single-mode fiber bearing the Bragg grating. The semiconductor stack is then fixed at the angle producing the highest reflectance.
Thus, at each of the two alignment steps, there are only two elements, and in each step only one relative dimension or angle is being adjusted. Maintaining a precise separation between the fiber or GRIN lens and the semiconductor stack structure or its front mirror is not critical because, as was explained above, the laser is designed to have a relatively long external cavity so as to emit several longitudinal modes.
In the above embodiments, one or more light sources optically pump the semiconductor stack, which is essentially undoped. It is well known to fabricate such a stack as a electrically driven vertical-cavity surface-emitting diode laser, and this design could be changed to an optical amplifier usable with the invention by doping the two vertical sides to opposite conductivity types, thus forming a p-n junction about the quantum wells, and by suitably changing the output mirror to an anti-reflective coating or partially transmissive mirror. However, the vertical-cavity diode configuration presents difficulties with forming a low-resistance contact over a large area.
The invention can also be advantageously applied to edge-emitting semiconductor diode lasers, particularly broad-area devices in which an active waveguide is supporting and amplifying a large number of modes. The fiber Bragg grating can be characterized as stabilizing the operation of a broad-area diode laser to its zero-order transverse mode.
A first embodiment utilizing a broad-area diode laser and anamorphic optics is illustrated in the schematic isometric view of FIG. 8. The figure illustrates a ridge waveguide diode laser having a ridge 90 formed on a substrate 92. Other edge-emitting diode laser structures, such as buried heterostructures, are more prevalent in power applications, but the ridge structure more easily illustrates the operation. The ridge 90 defines an optical waveguide underneath the ridge 90 and, through electrical contacts applied to the top of the ridge 90, also laterally defines an optical gain region. The vertical semiconductor structure below the ridge 90 includes a p-n junction and a vertical waveguiding structure. A high reflectivity coating is applied to a back facet 94. In normal edge-emitting laser diodes, a cleaved front facet 96 provides sufficient reflectance to define the end of the cavity and keep the round-trip gain equal to unity. For the present invention in which the fiber Bragg grating 42 provides the wavelength discrimination, the front facet 96 needs to be made highly transmissive, for example, by applying an anti-reflection coating onto it. Many diode waveguide lasers include a distributed Bragg grating impressed into or below the ridge 90 to define the lasing wavelength although other rely upon the shape of the gain curve of the active material. However, in the illustrated diode laser, the wavelength selection is provided by the fiber Bragg grating 42, and no significant wavelength selection occurs within the diode itself. That is, the diode itself is acting as an amplifier, not a laser, with the exception of the highly reflective mirror applied to the back facet 94.
The structure emits light from an emission area 98 on the front facet 96 below the ridge 90. In broad-area lasers, the width of the ridge 90 or other waveguide defining structure is made relatively large. The large area increases the power handling capabilities of the laser but also causes the waveguide to support numerous transverse modes. The emission area 98 has a similar width, and can emit the multiple transverse modes. On the other hand, the emission area 98 is relatively thin in the vertical direction, and its vertical emission pattern is diffraction limited. As a result, the pattern of an emission beam 100 emitted from the emission area 98 under lasing conditions is highly asymmetric and generally rectangular. In this embodiment, anamorphic optics are used to focus the emission beam 100 onto the input end 38 of the single-mode fiber 40 impressed with the fiber Bragg grating 42. The anamorphic optics must convert the large rectangular beam 100 to a small, generally symmetric beam having lateral dimensions of the order of the fiber core. The anamorphic optics may include two cylindrical lenses 102, 104 of different focal lengths and oriented perpendicularly to each other, but other types of anamorphic optics are known.
A second embodiment utilizing a broad-area diode laser and a fiber taper is illustrated in the schematic cross-sectional view of FIG. 9. The end of the fiber 40 with the Bragg grating 42 includes an adiabatic taper section 108 having an input end 110 closely matched to the emission beam 100 from the emission area 98. Preferably, the taper section 108 has a rectangular or asymmetric pyramidal shape. Its smaller end 112 is closely matched to the single-mode input of the single-mode fiber 40. The taper is gradual enough as to be adiabatic, that is, does not mix modes but only rejects the higher-order modes which it cannot support at its narrow end.
Broad-area and other edge-emitting diode lasers typically have sufficient gain so that lasing can occur in higher-order transverse modes even without feedback from the fiber Bragg grating. To suppress the higher-order modes, additional measures are likely to be necessary. For example, the output facet may be coated with an AIR coating having an extremely low reflectivity, for example. 0.1% or less. The length of the active area of the diode laser may be made shorter than usual, for example, 100 μm or less.
If the wavelength-selected light reflected back from the fiber Bragg grating 42 is to significantly affect the gain vs. loss in the diode laser, any excess loss due to coupling optics needs to be minimized. Furthermore, the elongate emission area 98 presents a high numerical-aperture source with attendant spherical aberrations in the emission beam 100. The optics need to account for the spherical aberrations as well as to correct some of the internal astigmatism produced within the laser diode.
The invention may also be applied to solid-state lasers composed, for example, of a rod of optically active material that is optically pumped. Such optically active materials include Nd:YAG, where Nd is the optically active neodymium dopant and YAG is yttrium aluminum garnet, but other suitably doped crystals and glasses are possible for achieving different optical wavelengths. The dopant is almost always an optically active ion having a metastable excited state and which is incorporated into the host, here the YAG. When sufficiently pumped with radiation at 800 to 820 nm, Nd:YAG can be made to lase at about 1064 nm. However, solid-state rods are typically of substantial diameter, for example, a few millimeters, and thus act as multi-mode waveguides. As a result, a solid-state laser is not directly suitable as a laser driving a single-mode fiber.
An embodiment of an end-pumped solid-state laser incorporating the invention is illustrated in FIG. 10. A broad-area (alternatively called broad-stripe) diode laser 120 emits laser pump radiation from a wide emission area 122. The diode laser 120 is similar in design to the semiconductor amplifiers and lasers of the previous embodiments, but it has a semiconductor composition appropriate for emitting the desired pump wavelength. Furthermore, it is designed as a complete laser with its own end mirrors and frequency selection. Optics 124, preferably anamorphic optics, focus the pump radiation upon an input mirror 126 formed on the input end of a rod 128 of an optically active material. The input mirror 126 is designed to pass light at the pump wavelength but to be highly reflective at the lasing wavelength so as to form one end of the optical cavity. Side-pumped configurations are also possible.
The output end of the rod 128 is coated with an anti-reflective coating 130 as determined at the lasing wavelength to maximize transmission across the interface. Optics 132 focus the light from the rod 126 to the input end 38 of the single-mode optical fiber 40 written with the Bragg grating 42. The optics 132 may include free-standing lenses or graded-index (GRIN) lenses among many possibilities. An adiabatically tapered fiber input is also possible for the optics 132, but the rod size is generally too large relative to the core of a single-mode fiber.
The Bragg grating 42 defines the second end of the laser cavity and also defines the precise lasing wavelength consistent with the gain bandwidth of the active medium. It further selects only the lowest-order transverse modes for lasing within the rod 126.
The semiconductor or solid-state laser of the various embodiments of the invention presents several advantages.
The input end of the single-mode fiber effectively serves as a very efficient mode filter, thus providing strong mode selectivity. Because the fiber is a single-mode fiber, the coupling for higher-order modes is significantly less than for the zero-order mode. Consequently, the feedback provided by the fiber Bragg grating for the higher-order modes is insufficient to support lasing of those modes, at least in the optically pumped embodiments and also in well designed edge-emitting electrically pumped embodiments. The stability of single-mode operation is not degraded at higher pumping intensities, even in the presence of spatial hole burning because the modal gain for higher-order modes cannot increase enough to compensate for the higher coupling losses of those modes.
The optical alignment becomes non-critical. After initial positioning, it is not necessary to precisely maintain the distance between the fiber and the semiconductor stack, the edge-emitting laser, or the active rod since the external cavity is intentionally made long enough to support multiple longitudinal modes.
The precise lasing wavelength is determined by the Bragg grating written into the fiber although it needs to be consistent with the relatively broad gain maximum of the semiconductor chip or otherwise optically active material and, in the case of a vertical structure, correspond to the internal Fabry-Perot resonance. The fiber Bragg reflection is highly frequency selective. The gain bandwidths of optical gain media are relatively wide and can accommodate many different lasing wavelengths set by the fiber Bragg grating.
Coupling lasing light to single-mode device, such as fiber amplifiers, is greatly simplified since the laser output is already carried on a single-mode fiber.
The thermal stability is determined by the relatively thermally insensitive silica fiber, which can be further thermally isolated from the active and hot semiconductor regions or devices.
For purposes of the claims, the following points are noted. A semiconductor laser diode constitutes an optically active material because of its interaction between electrons and photons. Even an undoped semiconductor stack, particularly one incorporating quantum wells, constitutes an optically active material in which pump light excites carriers to upper levels and the carriers relax at a different wavelength. A solid-state rod acts as an active optical amplifier for light having a wavelength selected by the Bragg grating.
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The Carlit hotel had a very good location in the city of Barcelona you can move around the city and...
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The Carlit hotel had a very good location in the city of Barcelona you can move around the city and...
I'm definitely going to stay at Hotel Carlit next time I'm in Barcelona. It's within walking...
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I'm definitely going to stay at Hotel Carlit next time I'm in Barcelona. It's within walking...
Customers who viewed Hotel Sehrs Carlit also booked these hotels.
Rates quoted in currencies other than the hotel's base currency are subject to the rate of the international exchange. Rate may change throughout stay. Rate may reflect average nightly rate. Extra charges may apply. Incidental charges, such as room service, are not included in the rate.
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Overall score
would recommend to a friend.
Reviewer score
Would recommend
vacation trip
The Carlit hotel had a very good location in the city of Barcelona you can move around the city and the servicies was nice and their staff were always friendly and helpful. They have the best value for your money.
the only thing a don't recommend
is the breakfast because it was the same every day and you can find a nice place near the hotel to have it a good price.
Enjoy the beutiful Barcelona
fine trip
ı lıke the hotel .ıt ıs cloce to familiar placec in barcelona
Great location
I'm definitely going to stay at Hotel Carlit next time I'm in Barcelona. It's within walking distance of all the main sights (la sagrada familia, la ramblas, casa batllo, la pedrera, guell park etc) It's close to 2 metro stations (Girona will take
you to the beach in less than 10 mins). The hotel was very comfortable and the staff were extremely friendly and helpful. The reason I only gave the staff 4 stars is because I asked for a wake up call for the morning of my flight and didn't get one, so it was a good job I set my own alarm as well. Overall, the perfect place to stay for the price.
Would not recommend
The guys at front desk were amazing, but that is all. Location was just ok. Rooms very small and they never clean the bathrooms, the towels was a joke.
Sagrada Familia
great easy stay
24 hour staff, very friend, excellent English. Great location to Sagrada Familia. Terrific value for money. Breakfast is optional, which is fine.
Frequent travellar
staffs were excellant ,room was small but manageble
bathroom window needs dark shade ,it was keeping bedroom bright at night
very close to Sagrada familia only 10 minutes walk
I asked for the coffee in the morning and they gave me cofffee and cake
and did not charge for it
I have nothing to complaint and would highly recommend
Good deal
The hotel was comfortable, safe, and a good value.
hotel prior to cruise
Good value for a hotel in Barcelona. Close to transportation and centrally located. Took metro to cruise port. Convenience store next door and cafes in area.
It was a nice 4 nights stay.
Everithing was just fine, the bad is nice, and the room is clean and neat. perfect combination for money/quality you can get.
Sagrada de Familia
Convenient for Barcelona Break
Arrived before check-in time and room not available, but we able to leave luggage while we took car to parking garage. Parking outside hotel not possible, but can double park for short time at next corner, 20yds away. Room adequate but rather
basic and just large enough. WiFi not strong enough for room (3rd floor) but available free in lobby.
Reasonably convenient for central attractions if ok to walk reasonable distances. Metro station short walk away.
Metro ticket for 10 trips good value at less than 1/2 price of single trip. The ticket can be used by more than one person and is OK for buses as well.
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A mother has spoken of her heartache at the betrayal by a party-loving former friend who seduced her 14-year-old son in their home.
The mother, who cannot be named for legal reasons, was sickened to discover Karen Ackland, 44, had taken advantage of her son - who is 30 years her junior.
Divorced mother-of-two Ackland was at an event celebrating the youngster's football achievements when she first set eyes on him.
After hours of drinking, the boy's mother offered Ackland a bed at their home.
Ackland pounced on the boy as he got ready for bed and used him as her "sex object" - only to be rumbled when his older brother heard her making sex noises.
She was sentenced to a nine-month jail sentence - suspended for a year - at Canterbury Crown Court.
Judge Simon James said Ackland had "immediately regretted" her behaviour and although committed in drink he said "that does not afford you any real excuses".
"She was always a party animal and when she had too many drinks she completely loses all self-respect and embarrasses herself..." - victim's mother
He added the law was to protect teenagers from doing things they might later regret.
The youngster's distraught mother called for harsher sentences for female sex offenders.
She said: "I never expected her to do this, you trust your friends. And he was just a child.
"She was always a party animal and when she had too many drinks she completely loses all self-respect and embarrasses herself.
"She used to always say 'I'm a nightmare when I've had a drink' and she'd always have a few men on the go.
"But I was a great friend to her and I stood by her. I never expected this.
"When my son was interviewed I was welling up. He looked exhausted, he was emotionally drained. It was absolutely harrowing to hear.
"She was very domineering and my son said as soon as it happened that he'd wished he'd never done it."
Ex-sailor Ackland was heard demanding the youngster spit in her mouth during their sex session in April 2013.
She was also heard to say "I can't believe I'm doing this with a 15-year-old!"
But the court heard the boy, who is now 16, was just 14 at the time.
Ackland, of Cavell Square, changed her plea to guilty just before the victim was due to give evidence - admitting three charges of sexual activity with a child.
After the boy's brother burst into the room, Ackland ran out the family's home and kept what she had done from the his mother.
The boy later told a friend: "I went to get into my trackies and she stripped naked in front of me.
"Yeah we had sex but it was really weird. She kept asking me to spit on her and all these weird things."
Mr Espley said within days, the incident was the talk of the school and teachers were forced to report the incident to police.
Ackland told a friend: "He tried to kiss me. I'm a 40 year old woman what am I supposed to do?"
Domini Webber, defending, said the Tesco shelf-stacker grew up in Germany as the daughter of a father who was in the military.
She married in 1993 but is now divorced with two teenage children.
Mr Webber said: "She accepts that this was extremely irresponsible behaviour
and she admits to being a binge drinker."
Ackland was also ordered to sign the Sex Offenders' Register and pay £500 in court costs.
Director of children's charity Kidscape Claude Knights yesterday said the sentence "sends out a very weak message".
She said: "The suspended nine month custodial sentence does not reflect the severity of this crime and sends out a very weak message.
"Despite many advances in our understanding the true extent of female sexual abuse remains a hidden picture. One has to ask how this crime would have been perceived had it been committed by a man.
"The response to such despicable crimes against children should be very robust regardless of the gender of the perpetrator."
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Spreadsheet Modeling & Decision Analysis A Practical Introduction to Management Science 5th edition Cliff T. Ragsdale Chapter 12 Introduction to Simulation Using Crystal Ball On Uncertainty and Decision-Making… "Uncertainty is the most difficult thing about decision-making. In the face of uncertainty, some people react with paralysis, or they do exhaustive research to avoid making a decision. The best decision-making happens when the mental environment is focused. …That fined-tuned focus doesn't leave room for fears and doubts to enter. Doubts knock at the door of our consciousness, but you don't have to have them in for tea and crumpets." -- Timothy Gallwey, author of The Inner Game of Tennis and The Inner Game of Work. Introduction to Simulation § In many spreadsheets, the value for one or more cells representing independent variables is unknown or uncertain. § As a result, there is uncertainty about the value the dependent variable will assume: Y = f(X1, X2, …, Xk) § Simulation can be used to analyze these types of models. Random Variables & Risk § A random variable is any variable whose value cannot be predicted or set with certainty. § Many "input cells" in spreadsheet models are actually random variables. – the future cost of raw materials – future interest rates – future number of employees in a firm – expected product demand § Decisions made on the basis of uncertain information often involve risk. § "Risk" implies the potential for loss. Why Analyze Risk? § Plugging in expected values for uncertain cells tells us nothing about the variability of the performance measure we base decisions on. § Suppose an $1,000 investment is expected to return $10,000 in two years. Would you invest if... – the outcomes could range from $9,000 to $11,000? – the outcomes could range from -$30,000 to $50,000? § Alternatives with the same expected value may involve different levels of risk. Methods of Risk Analysis § Best-Case/Worst-Case Analysis § What-if Analysis § Simulation Best-Case/Worst-Case Analysis § Best case - plug in the most optimistic values for each of the uncertain cells. § Worst case - plug in the most pessimistic values for each of the uncertain cells. § This is easy to do but tells us nothing about the distribution of possible outcomes within the best and worst-case limits. Possible Performance Measure Distributions Within a Range worst case best case worst case best case worst case best case worst case best case What-If Analysis § Plug in different values for the uncertain cells and see what happens. § This is easy to do with spreadsheets. § Problems: – Values may be chosen in a biased way. – Hundreds or thousands of scenarios may be required to generate a representative distribution. – Does not supply the tangible evidence (facts and figures) needed to justify decisions to management. Simulation § Resembles automated what-if analysis. § Values for uncertain cells are selected in an unbiased manner. § The computer generates hundreds (or thousands) of scenarios. § We analyze the results of these scenarios to better understand the behavior of the performance measure. § This allows us to make decisions using solid empirical evidence. Example: Hungry Dawg Restaurants § Hungry Dawg is a growing restaurant chain with a self-insured employee health plan. § Covered employees contribute $125 per month to the plan, Hungry Dawg pays the rest. § The number of covered employees changes from month to month. § The number of covered employees was 18,533 last month and this is expected to increase by 2% per month. § The average claim per employee was $250 last month and is expected to increase at a rate of 1% per month. Implementing the Model See file Fig12-2.xls Questions About the Model § Will the number of covered employees really increase by exactly 2% each month? § Will the average health claim per employee really increase by exactly 1% each month? § How likely is it that the total company cost will be exactly $36,125,850 in the coming year? § What is the probability that the total company cost will exceed, say, $38,000,000? Simulation § To properly assess the risk inherent in the model we need to use simulation. § Simulation is a 4 step process: 1) Identify the uncertain cells in the model. 2) Implement appropriate RNGs for each uncertain cell. 3) Replicate the model n times, and record the value of the bottom-line performance measure. 4) Analyze the sample values collected on the performance measure. What is Crystal Ball? § Crystal Ball is a spreadsheet add-in that simplifies spreadsheet simulation. § A limited life trial version of Crystal Ball is on the CD-ROM accompanying this book. § It provides: – dialogs & functions for generating random numbers – commands for running simulations – graphical & statistical summaries of simulation data § For more info see:http://www.decisioneering.com Random Number Generators (RNGs) § A RNG is a mathematical function that randomly generates (returns) a value from a particular probability distribution. § We can implement RNGs for uncertain cells to allow us to sample from the distribution of values expected for different cells. How RNGs Work § The RAND( ) function returns uniformly distributed random numbers between 0.0 and 0.9999999. § Suppose we want to simulate the act of tossing a fair coin. § Let 1 represent "heads" and 2 represent "tails". § Consider the following RNG: =IF(RAND( )<0.5,1,2) Simulating the Roll of a Die § We want the values 1, 2, 3, 4, 5 & 6 to occur randomly with equal probability of occurrence. § Consider the following RNG: =INT(6*RAND())+1 If 6*RAND( ) falls INT(6*RAND( ))+1 in the interval: returns the value: 0.0 to 0.999 1 1.0 to 1.999 2 2.0 to 2.999 3 3.0 to 3.999 4 4.0 to 4.999 5 5.0 to 5.999 6 Generating Random Numbers With Crystal Ball § Crystal Ball provides two different ways for creating RNGs in spreadsheets – CB functions Ø Used in formulas like any other Excel function Ø But require CB to be installed on the machine displaying the spreadsheet & do not support all CB functionality – The Distribution Gallery Ø Display a number (not a formula) in a cell but generates random numbers for that cell when simulating the model Ø Does not require CB to be installed on the machine to display the spreadsheet & supports all CB functionality § Both techniques useful in different situations Some of the RNGs Provided By Crystal Ball Distribution RNG Function Binomial CB.Binomial(p,n) Custom CB.Custom(range) Gamma CB.Gamma(loc,shape,scale,min,max) Poisson CB.Poisson(l) Continuous Uniform CB.Uniform(min,max) Exponential CB.Exponential(l) Normal CB.Normal(m,s,min,max) Triangular CB.Triang(min, most likely, max) Using CB RNG Functions Click Insert Function icon Select CB option Select RNG function Using the Distribution Gallery Click Define Assumption icon Select distirbution Specify parameters Examples of Discrete Probability Distributions Examples of Continuous Probability Distributions Discrete vs. Continuous Random Variables § A discrete random variable may assume one of a fixed set of (usually integer) values. – Example: The number of defective tires on a new car can be 0, 1, 2, 3, or 4. § A continuous random variable may assume one of an infinite number of values in a specified range. – Example: The amount of gasoline in a new car can be any value between 0 and the maximum capacity of the fuel tank. Preparing the Model for Simulation § Suppose we analyzed historical data and found that: – The change in the number of covered employees each month is uniformly distributed between a 3% decrease and a 7% increase. – The average claim per employee follows a normal distribution with mean increasing by 1% per month and a standard deviation of $3. Revising & Simulating the Model See file Fig12-9.xls The Uncertainty of Sampling § The replications of our model represent a sample from the (infinite) population of all possible replications. § Suppose we repeated the simulation and obtained a new sample of the same size. Q: Would the statistical results be the same? A: No! § As the sample size (# of replications) increases, the sample statistics converge to the true population values. § We can also construct confidence intervals for a number of statistics... Constructing a Confidence Interval for the True Population Mean where: Note that as n increases, the width of the confidence interval decreases. Constructing a Confidence Interval for the True Population Proportion where: Note again that as n increases, the width of the confidence interval decreases. Additional Uses of Simulation § Simulation is used to describe the behavior, distribution and/or characteristics of some bottom-line performance measure when values of one or more input variables are uncertain. § Often, some input variables are under the decision makers control. § We can use simulation to assist in finding the values of the controllable variables that cause the system to operate optimally. § The following examples illustrate this process. An Reservation Management Example: Piedmont Commuter Airlines § PCA Flight 343 flies between a small regional airport and a major hub. § The plane has 19 seats & several are often vacant. § Tickets cost $150 per seat. § There is a 0.10 probability of a sold seat being vacant. § If PCA overbooks, it must pay an average of $325 for any passengers that get "bumped". § Demand for seats is random, as follows: Demand 14 15 16 17 18 19 20 21 22 23 24 25 Probability .03 .05 .07 .09 .11 .15 .18 .14 .08 .05 .03 .02 § What is the optimal number of seats to sell? Random Number Seeds § RNGs can be "seeded" with an initial value that causes the same series of "random" numbers to generated repeatedly. § This is very useful when searching for the optimal value of a controllable parameter in a simulation model (e.g., # of seats to sell). § By using the same seed, the same exact scenarios can be used when evaluating different values for the controllable parameter. § Differences in the simulation results then solely reflect the differences in the controllable parameter – not random variation in the scenarios used. Implementing & Simulating the Model See file Fig12-20.xls Using an Overlay Chart to Compare Alternatives… 21 Reservations 27 Reservations Inventory Control Example: Millennium Computer Corporation (MCC) § MCC is a retail computer store facing fierce competition. § Stock outs are occurring on a popular monitor. § The current reorder point (ROP) is 28. § The current order size is 50. § Daily demand and order lead times vary randomly, viz.: Units Demanded: 0 1 2 3 4 5 6 7 8 9 10 Probability: 0.01 0.02 0.04 0.06 0.09 0.14 0.18 0.22 0.16 0.06 0.02 Lead Time (days): 3 4 5 Probability: 0.2 0.6 0.2 § MCC's owner wants to determine the ROP and order size that will provide a 98% service level while minimizing average inventory. Implementing & Simulating the Model See file Fig12-30.xls Using Trends Charts to Compare Reorder Policies… Original Optimal A Project Selection Example: TRC Technologies § TRC has $2 million to invest in the following new R&D projects. Revenue Potential Initial Cost Prob. Of ($1,000s) Project ($1,000s) Success Min Likely Max 1 $250 0.9 $600 $750 $900 2 $650 0.7 $1250 $1500 $1600 3 $250 0.6 $500 $600 $750 4 $500 0.4 $1600 $1800 $1900 5 $700 0.8 $1150 $1200 $1400 6 $30 0.6 $150 $180 $250 7 $350 0.7 $750 $900 $1000 8 $70 0.9 $220 $250 $320 § TRC wants to select the projects that will maximize the firm's expected profit. Implementing & Simulating the Model See file Fig12-40.xls Risk Management § The solution that maximizes the expected profit also poses a significant (»9%) risk of losing money. § Suppose TRC would prefer a solution that maximizes the chances of earning at least $1 million while incurring at most a 9% chance of losing money. § We can use OptQuest to find such a solution... A Portfolio Optimization Example: The McDaniel Group § $1 billion available to invest in merchant power plants Generation Capacity per Million $ Invested Fuel Gas Coal Oil Nuclear Wind MWs 2.0 1.2 3.5 1.0 0.5 Normal Dist'n Return Parameters Fuel Gas Coal Oil Nuclear Wind Mean 16% 12% 10% 9% 8% St Dev 12% 6% 4% 3% 1% A Portfolio Optimization Example: The McDaniel Group § Returns from different types of plants are correlated Return Correlations by Fuel Fuel Gas Coal Oil Nuclear Wind Gas 1 -0.49 -0.31 -0.16 0.12 Coal 1 -0.41 0.11 0.07 Oil 1 0.13 0.09 Nuclear 1 0.04 Wind 1 § How much should be invested in each type of plant? § What is the efficient frontier? Implementing & Simulating the Model See file Fig12-49.xls Efficient Frontier Obtained Using OptQuest End of Chapter 12
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Fork oil strangeness
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Location: Idiotville, OR
Oddometer: 4,241
The problem is you're starting from the end. The oil level is measured with the forks fully compressed and the spring removed, however the actual air chamber is created with the spring and spring guide installed and the forks at full extension. In your/creeper's analysis, you're starting from full compression and compressing even more, which isn't possible.
If the oil level is set to 100mm, the initial height of the air chamber is 300mm. That's 100mm + 275mm (suspension travel) - 75mm (spring and guide volume). At full compression, the air height is 25mm. So the air pressure is now 14.7 * (300/25 - 1) or 161 psi.
Repeat for 150mm oil height and you get 75mm compressed, 350mm extended for a compressed pressure of 53 psi.
These numbers aren't quite right because they ignore the volume of the damper rod and the gap between the fork lowers and uppers.
But, to take these numbers further....
The area of the lower fork tube is 2.8 square inches, so the force on the wheel from 161psi is 450# in each leg. In comparison, the force from the spring is 319# (.5kg/mm rate, 15mm preload) With the stock oil level of 150mm, the force is 151#
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September 18, 2012
This recipe is so simple to make, and you can change up the filling to suit your family's taste. Try it as a Reuben, then a pizza loaf, or a chicken and Swiss loaf.
It is pretty filling, so plan on serving a crowd with the slices. We like it with fruit and yogurt parfaits. Enjoy!
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Beer League Goons...Why?
Recreational hockey goons, why do people feel the absolute need to fight?
I generally play a very clean game, I'm talking averaging maybe 2 Penalty Minutes a season, but there is one game I recall where the other team probably thought I was a goon.
The first period started fine, but as it went on it became apparent that the refs were either not paying attention or were allowing it to get more physical than most games in the league. This lead to increased trash talk and other signs of general disrespect from both teams towards each other [snow showers on the goalie, unnecessary physicality completely away from the puck].
Things were getting out of hand and in the 2nd period it all came to a head. In a short sequence while I was out on the ice playing defense, our goalie made a save, got mildly clipped but I was able to pass the puck out of the zone to one of our wingers. I checked on our goalie and he seemed okay and I'm slowly heading up ice to join the offensive push. For some reason one of their forwards was hanging back with me, he was immensely behind the play [we're at the tops of the faceoff dots as the puck is crossing the line into their zone].
He didn't say anything to me but proceeded to skate up next to me and try to slow me down by leaning into me/cutting me off. It was a silly, worthless dick move. I have no problem with people playing physical, but why bother doing something like that when neither of us are in the play. The puck is nowhere near us, it was just dumb. So I gave him a little chop to the back of the leg to signal that I did not appreciate what he was trying to do. Not too hard, but not too light. He turned around and looked like he was about to throw down. The only thing that stopped this was the outcry of our entire bench.
I didn't get to see what happened but I look up and our best forward is laying on the ice on his back with a WTF look in his eyes, staring at the ref. You know that look, when someone OBVIOUSLY did something illegal in full sight of the refs and they didn't call it? Yeah, that was the look he had. Of course it was the best skater too. He was getting hacked and slashed, tripped and checked [in a non-checking league] in pretty much every game I saw him in over the 4 seasons we played together. I'd seen him get multiple concussions in our non-checking rec league.
At this point I had made my way to the opposing blue line and I had enough. The guy who was our general hothead [goon if you prefer] wasn't on the ice and the way the game was going things were already out of hand. The puck bounced to one of their players, right in line with me, and I skated up and planted him with a straight shoulder-to-sternum check. Didn't care that it was 2 minutes, it seemed like it needed to be done.
After that the game was a whole lot cleaner. Less physical, more respect. It's hard to regret what I did that night even though I know it was wrong. The game was getting out of hand, I took an obvious penalty, the game was back under control after that. That's the story of how I became a goon for 15 minutes.
Doing things like rocking someone with a bomb of a check tend to escalate tense games even more. If i was the captain i would go to the refs and say this **** is getting out of hand, either you start making calls or this game ends here. Nobody needs to get hurt.
There needs to be a separate division for people who feel like they need to play dirty and fight during recreational hockey.
I'm all for watching that kind of behavior at the highest competitive levels, but when I'm out there trying to work on my shot I don't need some Matthew Barnaby wannabe out there stirring the pot with everybody. The worst is a grown man who pulls that crap. Grow the **** up, you don't have fans, the championship trophy of your obscure beer league is a plastic trinket. All you're doing is agitating strangers who are carrying weapons.
Only time i would understand fighting in recreational hockey is when someone makes a very dangerous play such as boarding or the most obvious knee.
When someone tries to hurt someone really badly, they should answer with fists if they have to.
Refs play a huge role in this, but you can tell that some players are just bad apples and should be scorned by teammates as much as by other teams. I hate having to "deal" with other teams anger just because one of my teammates was being stupid.
My team was winning 8-1 and in the final 3 minutes i got hit from behind going into a corner to chase down a loose puck.
The defenseman hit me from behind and the only reason i didn't get severely hurt or maybe paralyzed was because i was able to put my hands up just in time to avoid going completely head first in the boards.
After everything calmed down I asked the guy WTF he was thinking. He told me he had to send a message because we beat them badly.
These questions basically ran inside my head as i sat on the bench...
WTF? What message are you sending? I don't even know who you are? Are we playing each other again?
I started playing ball hockey after that season. I can't sacrifice my livelihood and go into debt and put a burdon on my family because a knuckle dragger needs to send a message to me in a meaningless beer league game.
That was my second penalty all year.
rec goons are stupid. most of the time it doesn't amount to much in my experience. However, if people get caught up in the BS I'll say something to the refs about it.
Most of the time I'll just get physical with goons and try and draw some PIM's. I dont' really get riled up by that sort of thing. I'm also little so it's not like I can intimidate or deter goonery.
I've only taken matters into my own hands a few times and then it's because it's a 2nd or 3rd offense. The last time was some ****** going into the boards with me with is elbow in my head. First time I said watch the elbow thinking it may have have been incidental. 2nd time I told him he does it again we're "going" and then I yelled at the ref and said he does it again and Im going to instigate. So when it happened the 3rd time I slashed the guy in the back of the leg , un-snapped my lid and called him out. I got a 2 for slashing, 2 for unsporstmanlike and a warning about unsnapping the lid. Had I dropped the lid or gloves I would have been gone. The lid would have been a lengthy suspension or something? I guess that's a newish USA Hockey rule.
A two handed slash across the top of a helmet? Talk about disrespect for the game and the players who play it. That's not fighting, that's assault.
I'm fortunate enough to play on ice that's in a Park District. Fighting will not only get you ejected from the game, but the police will be called and escort you to their car.
Most goon it up because they need attention. If you want to fight in Beer League, schedule a date in the parking lot or at a local bar. Otherwise, quit wasting peoples time who want to actually play the game.
In a playoff game, a girl on our team bumped into a girl on their team. But of these girls are damn solid players even in a "men's" league. The cop chick two handed our check across the back of the neck. The cop chick was a vice-cop. Smoking hot, though. But still not an excuse for assault. maybe some chick wrestling,though. I'd have enjoyed that.
A couple of years ago, my team was running up the score in a playoff game and we could see the other team was starting to get frustrated. We starting backing off a little because we had the game in hand and their season was effectively over, but I had a feeling that something was going to happen. What I didn't know was that some guy on the other team (he was probably about 6'3" 250 lbs, I am 6'1" 210 lbs) was going to randomly grab me by the earloops and start using my skull like a heavy bag. Unprovoked? Yes. Unfair? You betcha. But I'll tell you what, the ref certainly wasn't about to step in front of this guy whether fighting was legal or not.
Whether on the ice or in every day life, crimes are commited because some people do not have any regard for the rules in the heat of the moment.
There have been several times where a team is running it up on us and I was looking for an excuse to bounce someone around a little... but in the end I have never been able to do it because it would have required taking a cheap shot on someone. I wanted to do it... I just could not pull the trigger. In the end, I always feel better afterward for not doing it, but it would be a lie to say that I wasn't looking for a triggering action at times. Just a competitive nature/frustration thing.
There have been a few games where the whole team wanted to drop the gloves with me. I dont consider myself a goon, Im just a physical D-man who works hard, knows how to use the body and knows a million little tricks to get guys off their game and out of position, especially in front of the net. I dont chirp and dont hunt heads but theres something about my game that gets under guys skin, and I love it :P
Recently I played a few games for a full check mens rec league and to my surprise, the games were much less chippy than a no-contact game. The guys police themselves out there, and there is a level of mutual respect among the players. Not to mention its 25x more fun.
Why are there Beer league goons? Well there are D-bags in all aspects in life and even though most hockey people are good people that doesn't make Rec hockey the exception to the rule. Luckily for me I would say in all the leagues I have played in I would say 95%+ of all players are logical and understand how to play hard but not dirty.
When the other 5% starts doing there thing if you have competent refs that care it usually gets resolved before anything crazy happens. However once in a blue moon I will see the combo of an incredibly stupid player and a ref who doesn't give a **** and won't control the game.
Here is where the debate ensues. Should you stoop to the other guys level? Protect yourself? Should you just try to ignore the guy?
IMO at a certain point you have to stand up for yourself and/or your teammates. The thing is a lot of these goons are the same type of person who was a relentless bully as an adolescent or the same type of guy who will pick on you at work. History has shown that ignoring these people doesn't necessarily make them stop. At a certain point you have to stand up for yourself. This is true in life period not just in hockey.
These situations are so rare I don't worry about them. I can only think of 2 incidences in the past 5-7 years and when I think about how many games I've played in that time period it has to be around 250-350. Both times I have had incidences it had to do with one of these goons spearing/slashing me or my teammate in the crotch. I simply do not tolerate stuff like that.
For another example if somebody two hand tomahawk chopped me across the head like the video in the link posted by the OP. Someone would have to physically restrain me because I would literally try hurt that guy.
I should qualify this by saying I'm not a goon, I've never actually fought. But as horrible as it sounds, I kind of enjoy when my beer league team gets into it with the other team. Its kind of like that school yard crap when there is a fight.
I switch between C and LW a lot, but when I go in front of the net, I fully expect contact in our no-contact league. However, there's a fine line between some contact, some battling for position with the occasional shove, and some out of shape hack who thinks he's Paul Bunyan and is trying to chop my short legs down like I'm a **** redwood.
The message sending also applies to the beginning of games too. We had a game about 2-3 years ago where I started and scored about 30 seconds in on a shot that hit crossbar before going in. After scoring I get shoved by one of their players into the boards, yelling at me for shooting high and headhunting their goalie, who was easily a few inches shorter than me. Told this dude that if I was going for his **** head I would have hit him (probably not true :laugh:) Long story short, found out later that he did this a few more times later in the season and was later suspended.
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To read the full review and learn more about Eduard Ezeanu's book, visit the Vkool website at: http://vkool.com/conversation-confidence/
To download Conversation Confidence book, visit the official website
About Bryant Johnson: Bryant Johnson is an editor of the website Vkool.com. In this website, Bryant Johnson provides people with a series of communication tips and advice.
Read the full story at http://www.prweb.com/releases/conversation-confidence/review/prweb12021988.htm.
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Learn more about LG N2B1D 1 2 Bay Super-Multi Network Attached Storage with Blu-Ray Disc ReWriter:
|Super-Multi NAS N2B1D is a data storage that is attached to a network rather than to a PC. It is perfect for both home and small business users such as doctors and photo studios who need scalable storage solution as they manage a large amount of data such as pictures, documents, video, etc. The storage capacity is drive dependent meaning whatever size hard drives that are available in the markets, you can add two of those hard drives to our NAS.
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This NAS is very fast. Much better than slow cheap NAS devices. It can be a bit of a bear to setup with drives previously formatted using GUID partition tables. Had to remove the drives and repartition them before they could be recognized. The manual is horrible but other than the GUID table drives I have had very few issues. I have two Seagate 1.5TB drives in the box. Pretty sure any SATA drive will work. The feature list on this NAS is unreal (FTP, Time Capsule, WebDAV / Web Server, AFP support, AD Support, mySQL etc..) especially for the price.


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text: Publications Search Results Users may wish to consult What's Included in the Bibliography. Results 1 - 1 Results per page: 25 50 100 Sort by: Pub Date (newest) Title Recent Additions Author Clear All Pub. Year Citation 2011 Young, J. Kenneth, Beaujean, A. Alexander . Measuring personality in Wave I of the National Longitudinal Study of Adolescent Health. Frontiers in Psychology. 2, (Article 158), Full Text Options: DOI Worldcat Google Scholar Export Options: RIS EndNote XML [1]


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1856-S 25C XF45 PCGS. CAC. Briggs 3-D....
2013 January 9-14 US Coin FUN Signature Auction - Orlando #1181
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1856-S Seated Quarter, XF451856-S 25C XF45 PCGS. CAC. Briggs 3-D. This variety is characterized by the unusually high placement of the date, and on the reverse the mintmark is partially imbedded in the feather above. In spite of the generous mintage of more than a quarter-million coins, the 1856-S is seldom located in AU or Uncirculated grades. The surfaces of this piece show medium gray patina overall with contrasting near-brilliant high points. The fields are slightly roughened from circulation, but the only singularly mentionable defect is a planchet flake out of the right obverse field. Population: 8 in 45, 20 finer (11/12).(Registry values: P7) (NGC ID# 23TD, PCGS# 5440)
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