CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority to copending U.S. provisional application entitled, “Long Period Fiber Grating Wavelength Tuners/Modulators/Switches,” having Ser. No. 60/205,990, filed May 19, 2000, which is entirely incorporated herein by reference. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     The U.S. government may have a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of grant no. EEC-94-02723 awarded by the National Science Foundation. 
    
    
     FIELD OF THE INVENTION 
     The present invention is directed, in general, to optical fiber gratings, to their fabrication, and to their use as devices in optical systems. 
     BACKGROUND OF THE INVENTION 
     Optical gratings are useful in controlling the paths of propagating light, particularly light composed of multiple wavelengths. Optical gratings are useful in manipulating the transmittance and/or the propagation direction of particular wavelengths within an optical signal. Since optical signals propagate inside optical waveguides, an optical grating consists of a periodic perturbation (variation) of an optical-waveguide parameter such as the real and/or imaginary part of its refractive index or its thickness. One of the most important types of optical waveguides is the optical fiber. Basically, optical fibers are thin strands of glass capable of transmitting information-containing optical signals over long distances with very low loss. In essence, an optical fiber is a small diameter waveguide comprising a core having a first index of refraction surrounded by a cladding having a second (lower) index of refraction. Provided the refractive index of the core exceeds that of the cladding, a light beam propagated within the core may exhibit total internal reflection, and is guided along the length of the core. Typical optical fibers are made of high purity silica with various concentrations of dopants added to control the index of refraction. Optical fibers that have gratings, perturbations in the refractive index, are of particular interest as components in modern multi-wavelength communication systems, such as wavelength-division-multiplexed optical communication systems. 
     In-fiber optical gratings are important elements for selectively controlling specific wavelengths of light transmitted within optical systems such as wavelength-division-multiplexed optical communication systems. Such gratings may include short-period fiber Bragg gratings and long-period fiber gratings. These gratings typically comprise a body of material with a plurality of spaced-apart optical grating elements disposed in the material. Often, the grating elements comprise substantially equally-spaced refractive index or optical absorption perturbations. For all types of gratings, it would be highly useful to be able to reconfigure the grating to adjust selectively the controlled wavelengths. 
     A cladding mode is a mode of light that is not confined to the core, but rather, is confined by the entire waveguide structure. Long-period fiber grating devices selectively forward-diffract light at specific wavelengths by providing coupling between core modes and cladding modes. In general, short-period fiber Bragg gratings can also diffract light into cladding modes. In this case, the cladding modes are back-diffracted. The period, Λ, of the perturbations is chosen to shift transmitted light in the region of a selected peak wavelength, λ p , from a core guided mode into a cladding mode, thereby reducing in intensity a band of light having wavelengths centered about the peak wavelength λ p . In other words, the fiber grating acts as a band-stop optical spectral filter. In addition, since fiber cladding-modes are weakly-guided modes, their power can be easily dissipated by scattering, bending, stretching, and/or rotating the optical fiber. Such devices are particularly useful for equalizing amplifier gains across a band of wavelengths used in optical communications systems. 
     Typically, the spacing between the periodic perturbations in a long-period grating is large compared to the freespace wavelength λ of the transmitted light. In contrast with conventional short-period fiber Bragg gratings, long-period gratings use a periodic spacing Λ that is typically about a hundred times larger than the transmitted freespace wavelength. In some applications, such as chirped gratings, the spacing Λ can vary along the length of the grating. 
     A difficulty with conventional short-period fiber gratings and long-period fiber gratings, however, is their inability to change (tune) dynamically their spectral characteristics. Each short-period fiber grating and each long-period grating with a given periodicity (Λ) selectively filters light with an unchanging attenuation and in an unchanging narrow bandwidth centered around the peak wavelength of coupling, λ p . This wavelength is determined by λ p =(N core ±N cladding ) Λ, where N core  and N cladding  are the guided-mode effective indices of the core and the cladding modes, respectively. The “+” sign is valid for the case of backward-diffracted light by short-period gratings and the “−” sign is valid for forward-diffracted light by long-period gratings. The value of N core  and N cladding  depend on the wavelength, on the core, cladding, and surrounding medium refractive indices, and on the core and cladding radii. 
     Various techniques have been developed to extract light from the core of an optical fiber so that the light may be modulated or filtered. In one approach, part of the cladding surrounding the core of the optical fiber is polished away on one side of the fiber so that a portion of the light in the core can be coupled into the cladding. In another approach, disclosed in U.S. Pat. No. 6,058,226, which is hereby incorporated by reference, a voltage is applied to an electrically sensitive material coupled to the exterior an optical fiber. The applied voltage is used for modulating the light being transmitted through the optical fiber. In yet still another approach, disclosed in U.S. Pat. No. 6,055,348, which is hereby incorporated by reference, a longitudinal strain is applied to a fiber grating so that the spacing between the grating elements are changed to shift the wavelength response of the device to provide a tunable optical grating device. 
     Multi-wavelength communication systems require continuous adjustment of the signal levels. If the signal adjustment is wavelength independent then these devices are called variable optical attenuators (VOA), while for the case of wavelength dependent attenuation they are called variable gain flattening filters. As a first example, in pre-emphasis filtering, some wavelength channels need to be equalized in intensity before they are combined in the fiber. As a second example, the reconfiguration and reallocation of wavelengths among the various nodes of a network by add/drop filtering requires these wavelength channels to be balanced in intensity with the optical network. As a third example, the gain of optical amplifiers, such as erbium-doped optical amplifiers, needs to be the same for all wavelengths, thus requiring wavelength-by-wavelength control of the optical gain. Optical amplifiers have deleterious peaks in their gain spectra that need to be flattened. As a fourth example, an adjustable wavelength and attenuation filter is needed for suppressing amplifier spontaneous emission (ASE) in optical amplifiers. As a fifth example, in a related application, there is a need to control the output power of tunable lasers to be constant over multiple wavelength ranges in order to provide a constant output power over any selected wavelength range. 
     Multi-wavelength communication systems also require network control functions to be available. As a first example, each wavelength channel should be tagged or labeled. This can be accomplished by modulating each channel wavelength with a slightly different kilohertz frequency. As a second example, network supervisory information needs to be distributed within the existing optical network (without resorting to external wire-based communications) and without affecting any of the data channels within the optical network. This can be done by modulating the existing data channels at kilohertz frequencies with the supervisory information to be distributed. 
     All of the above needs require a device whose transmission can be controlled in wavelength and amplitude. Adjusting the fiber grating as described in this invention allows tuning of the center wavelength or the adjustment of the attenuation at a fixed wavelength or a combination of these. As such, an adjustable fiber grating is capable of fulfilling all of the above listed application needs. Generally, prior art optical fiber gratings have grating elements that are typically disposed in the optical fiber core and perpendicular to the longitudinal centerline of the optical fiber. However, there are also optical fiber gratings that have grating elements that are slanted, instead of perpendicular, with respect to the centerline of the optical fiber. Several patents also exemplify fiber gratings with slanted refractive-index variation, which are U.S. Pat. No. 5,430,817 to A. M. Vengsarkar, U.S. Pat. No. 5,764,829 to J. Boyd et al. It is accordingly an object of the present invention to provide a new class of fiber gratings. 
     SUMMARY OF THE INVENTION 
     The present invention provides an apparatus and method for tuning, attenuating, switching, and modulating optical signals in a waveguide. 
     Briefly described, in architecture, one embodiment of the apparatus, among others, can be implemented as follows. A length of optical comprising a core region with a refractive index distribution and a cladding region with a refractive index distribution, the cladding region disposed on the core region. The optical fiber includes an azimuthally varying grating element. The optical properties of the optical fiber are changed by physical manipulation of the optical fiber. 
     The present invention can also be viewed as providing methods for selecting the coupling between modes in an optical fiber. In this regard, one embodiment of such a method, among others, can be broadly summarized by the following steps: an optical fiber having a grating region, which includes at least one azimuthally varying grating element, is disposed in an optical network; and the optical fiber is oriented in a predetermined position. The coupling between optical modes in the optical fiber are related to the positioning of the optical fiber. 
     The present invention can also be viewed as providing methods for making grating elements that have azimuthal variation in an optical fiber. In this regard, one embodiment of such a method, among others, can be broadly summarized by the following steps: disposing a length of optical fiber in a predetermined position; and heating a portion of the optical fiber. The heating of the optical fiber produces a perturbation in the refractive index of the heated portion of the optical. An alternative embodiment for making a grating element having an azimuthal variation can be broadly summarized by the following steps: disposing a dopant in a non-uniform pattern in an optical fiber; and irradiating the dopant with a laser beam. The irradiation by the laser beam of the dopant in the optical fiber produces a perturbation in the refractive index in the portion of the optical fiber having the dopant. disposed therein. 
     Other systems, methods, features, and advantages of the present invention will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description, be within the scope of the present invention, and be protected by the accompanying claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present invention. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. 
     FIG. 1A shows a schematic illustration of a fiber grating having slanted refractive index variation in the form of a slanted-fringe grating. 
     FIG.  1 B and FIG. 1C show two ways to fabricate fiber gratings. 
     FIG. 2 shows a schematic view of an optical fiber having a grating region disposed there. 
     FIG. 3 is a cross sectional view of a grating element. 
     FIGS. 4A-4O are cross sectional views of exemplary grating elements. 
     FIG. 5 shows a bent optical fiber having a grating region disposed therein. 
     FIG. 6 shows a cross sectional view of normalized intensity of a transversely applied beam in an optical fiber. 
     FIGS. 7A and 7B show exemplary grating element configurations. 
     FIG. 8 shows rotational dependence of the transmission characteristics of a grating region that includes grating elements, which were written into the optical fiber by a CO 2  laser beam. 
     FIG. 9 shows transmission spectral characteristics with bending curvature as a parameter for a glass optical fiber having a grating region that includes grating elements, which were written into the optical fiber by a CO 2  laser beam. 
     FIG. 10 shows the center wavelength as a function of bending curvature for a glass optical fiber having a grating region that includes grating elements, which were written into the optical fiber by a CO 2  laser beam. 
     FIG. 11 shows transmission spectral characteristics with bending curvature as a parameter for a glass optical fiber having a grating region that includes grating elements, which were written into the optical fiber by a CO 2  laser beam. 
     FIG. 12 shows the transmission spectral characteristics as a function of bending curvature for a glass optical fiber having a grating region that includes grating elements, which were written into the optical fiber by a CO 2  laser beam. 
     FIG. 13 shows longitudinal relative index difference in an optical fiber. 
     FIGS. 14A-14B show exemplary configurations of fiber gratings in optical fibers. 
     FIGS. 15A-15C show an exemplary device for configuring an optical fiber. 
     FIGS. 15D and 15E show another exemplary device for configuring an optical fiber. 
    
    
     DETAILED DESCRIPTION 
     The present invention is directed to an improved type of fiber grating possessing a general azimuthal refractive index variation, as well as a fabrication method, and optical devices for adjusting the optical characteristics of the grating. The optical adjustment device provides a means for tuning, attenuating, switching, and modulating optical signals in the waveguide. For the purposes of this disclosure, a preferred embodiment is discussed with the optical adjustment device disposed in an optical fiber containing a long-period fiber grating (LPFG). It is to be understood that the invention includes, but is not limited to, in-fiber gratings, such as LPFGs and short-period fiber Bragg gratings. 
     In FIG. 1A, the grating has a refractive index variation  10 , which varies from the refractive index of the core, inside the core  11  of a single-mode fiber  15 . In the preferred embodiment, the refractive index variations  10  have a periodicity of Λ and form an angle θ  13  with respect to the longitudinal fiber axis  25 . This type of structure is called a “slanted” grating. In a conventional optical fiber grating, the refractive index variation  10  is uniform within the slanted grating and within “unslanted” gratings, i.e., gratings that are perpendicular with respect to the centerline. In other words, the variation of the refractive index of the core is uniform for all values of Ψ angular rotations about centerline  25  in the plane of the refractive index variation  10 . In the preferred embodiment, the refractive index variation  10  is rotationally non-uniform in the plane defining the refractive index variation. For the purposes of this disclosure azimuthal angles and rotations are measured in the plane defined by the refractive index variation. In the embodiment illustrated in FIG. 1A, there is no index perturbation in the fiber cladding-region  12 . A method of developing these gratings is via direct illumination of the fiber by a UV excimer laser. In FIG. 1B, the fiber  15  comprised by the cladding region  12  and the core region  11  is illuminated by the laser beam  22 . The amplitude mask  20  controls the shape of the laser beam incident upon the fiber. The laser is turned on and laser-light passes through the slit  21  and impinges on the fiber. After the laser is turned off, the fiber  15  is then translated by distance Λ and then the laser is turned on again. The same process is repeated many times such that the formed grating has the desired number of periods Λ. In an alternative approach shown in FIG. 1C, the amplitude mask  23  has several thin slits and an interference intensity pattern impinges the fiber. This method can be used for the development of short-period fiber Bragg gratings. 
     Referring to FIG. 2, the optical fiber  100  is a conventional single-mode optical fiber used in transmitting light signals in a network, such as a telecommunications network. Light is transmitted through the optical fiber  100  in a guided mode through the core  106 , the core having a refractive index, n core , greater than the refractive index, n cladding , of the cladding  108 . Although, the core  106  has been illustrated as a single region having symmetry about the centerline  110 , those skilled in the art are familiar with cores that have a plurality of concentric annular regions disposed therein, non-limiting examples of which are dispersion shifted optical fibers. The scope of the invention includes cores that have a generally uniform index of refraction and cores that have a plurality of regions with differing indices of refraction. 
     In one embodiment, the optical fiber  100  is a glass optical fiber. Those skilled in the art recognize that there are many glass optical fibers such as fluoride glass, doped glasses, and co-doped glasses. Examples of dopants used in glass optical fibers include, but are not limited to, germanium, boron, and hydrogen. Furthermore, optical fibers are also made from plastic materials and/or polymer materials, and are also included within the scope of the invention. Most, if not all, optical fibers having cores and/or claddings in which the magnitude of the refractive index of the core/claddings can be irreversibly or reversibly changed are intended to be included within the scope of the present invention. 
     Referring to FIG. 2, the optical fiber  100  includes one or more fiber gratings  104 , each comprising a plurality of grating elements  112  of width W. For the purposes of this disclosure, a grating element  112  is generally a planar portion of width W of the optical fiber  100 . The grating element  112  includes a perturbation  118  in the index of refraction of the optical fiber. The perturbation  118  can be in the index of refraction of the core  106 , as shown for grating element  112 (A), or in the cladding  108 , as shown for the grating element  112 (B), or the perturbation can extend from the core  106  into the cladding  108 , as shown for the grating element  112 (C), or the perturbation can extend across the width of the optical fiber  100 , as shown for the grating element  112 (D). Although the grating elements  112  are generally shown as being of uniform width, it should be noted that this is for illustrative purposes only and that the width of each perturbation can vary. For example, the grating elements  112 (C) is illustrated as having a width that is twice the width of grating element  112 (A). In addition, the width of the perturbation can be non-uniform, for example, wide at one place and narrow in another part of the grating element. The width of the grating element is such that two generally parallel planes separated by a width W surround the perturbation. 
     It should also be noted that although the grating elements  112  are illustrated as being generally parallel to each other and generally perpendicular to centerline  110  that this configuration is for illustrative purposes. In an alternative embodiment, the grating elements  112  are obliquely aligned with respect to the centerline  110 . In yet another embodiment, the grating elements are obliquely aligned with respect to each other. 
     In a short-period fiber Bragg grating, the spacing between the grating elements  112  which is typically in the range 0.1 to 15 microns is chosen to shift the transmitted light in the region of the selected wavelength, λ p , from the forward core-guided mode  114  into a backward core-guided or backward cladding mode. Thereby, reducing the intensity of the light, centered about λ p , transmitted through the core  106 . 
     In an LPFG, the spacing between the grating elements  112  which is typically in the range 15 to 1,500 microns is chosen to shift the transmitted light in the region of the selected wavelength, λ p , from the forward core-guided mode  114  into a forward cladding mode. Thereby, reducing the intensity of the light, centered about λ p , transmitted through the core  106 . 
     In the preferred embodiment, the fiber grating  104  is a LPFG having grating elements  112  that are separated with a periodicity of Λ and a width, W, that is typically in the range of (1/10)Λ&lt;W&lt;(9/10)Λ. The width of the perturbation in the refractive index defines the width, W, of the grating element  112 . Generally, the perturbation in the refractive index varies smoothly across the width of the grating element and the variation can be represented as a Gaussian shape or other shape. It should be noted that the periodicity and the width are design parameters, and those skilled in the art will recognize the periodicity, Λ, and/or width, W, can be adjusted to fit design considerations. 
     Refer now to FIG. 3, which shows a cross-sectional view of an exemplary grating element  112 , the core  106  is generally cylindrical and centered around the centerline  110  (not shown) and has a radius of R 1 , and the cladding  108  is generally annular with an inner radius of R 1  and an outer radius of R 2 . In the preferred embodiment the grating element  112  is azimuthally varying about the centerline  110 . The grating element  112  includes a perturbation  118 , which includes cladding perturbation  120  and core perturbation  122  and an unperturbed region  124 . The index of refraction at a point, given in polar coordinates (r,φ), in the grating element  112  can be given by the following equation:          n        (     r   ,   φ     )       =     {               n   core          (     r   ,   φ     )       ,     0   &lt;   r   ≤     R   1       ,     α   &lt;   φ   ≤       2                 π     -   α                         n   core          (     r   ,   φ     )       +       Φ   1          (     r   ,   φ     )         ,     0   &lt;   r   ≤     R   1       ,       -   α     &lt;   φ   ≤   α                     n   cladding          (     r   ,   φ     )       ,       R   1     &lt;   r   ≤     R   2       ,     α   &lt;   φ   ≤       2                 π     -   α                         n   cladding          (     r   ,   φ     )       +       Φ   2          (     r   ,   φ     )         ,       R   1     &lt;   r   ≤     R   2       ,       -   α     &lt;   φ   ≤   α             }                            
     where the perturbation in the core and the cladding is given by Φ 1  and Φ 2 , respectively. The quantities Φ 1  and Φ 2  can be restricted to refractive index pertubations (phase change) or can be restricted to optical absorption pertubations. In the latter case, Φ 1  and Φ 2  represent perturbations in the imaginary part of the refractive index. In the general case, Φ 1  and Φ 2  can represent perturbations in both the real and imaginary parts of the refractive index. It should be noted that the pertubation in the core  106  may be different from, or the same as, the perturbation in the cladding  108 . 
     In the simplest case, the index of refraction of the grating element  112  is given by the following equation:          n        (     r   ,   φ     )       =     {             n   core     ,     0   &lt;   r   ≤     R   1       ,     α   &lt;   φ   ≤       2                 π     -   α                       n   core     +     Φ   1       ,     0   &lt;   r   ≤     R   1       ,       -   α     &lt;   φ   ≤   α                   n   cladding     ,       R   1     &lt;   r   ≤     R   2       ,     α   &lt;   φ   ≤       2                 π     -   α                       n   cladding     +     Φ   2       ,       R   1     &lt;   r   ≤     R   2       ,       -   α     &lt;   φ   ≤   α             }                            
     where the core  106  and the cladding each have uniform index of refraction, and the perturbations in the core  106 , Φ 1 , and the cladding  108 , Φ 2 , are also uniform. However, even in the simplest case, the index of refraction varies as the azimuthal angle crosses the boundary between the perturbation region  118  and the unperturbed region  124 . 
     It should be noted that FIG. 3 is only an exemplary illustration of an embodiment of the invention. Other, non-limiting examples of grating elements having azimuthal asymmetry are illustrated in FIGS. 4A-4O. Briefly described, the grating elements  312 (A), shown in FIG. 4A, includes a perturbation  318 (A) that extends generally inward from the outer surface  302  into the cladding  308 . The perturbation  318 (A) is relatively small, extending only a portion of the way from the outer surface  302  towards the core  306 , and is generally a pie shaped wedge having a generally acute angle at its vertex  314 (A). 
     The grating element  312 (B), shown in FIG. 4B, includes a perturbation  318 (B) extending generally inward from the outer surface  302  into the core  306 . The perturbation  318  is approximately pie shaped with an acute angle at its vertex  314 (B). 
     The grating element  312 (C), shown in FIG. 4C, includes a perturbation  318 (C) extending generally inward from the outer surface  302  beyond the core  306  into the distal region of the cladding  308 . The perturbation  318 (C) is approximately pie shaped with an acute angle at its vertex  314 (C). 
     The grating element  312 (D), shown in FIG. 4D, includes a perturbation  318 (D) that extends generally inward from the outer surface  302  into the cladding  308 . The perturbation  318 (D) extends from the outer surface  302  towards the core  306  and defines an acute angle, which is in the approximate range of 30 to 90 degrees at its vertex  314 (D). 
     The grating element  312 (E), shown in FIG. 4E, includes a perturbation  318 (E) that extends generally inward from the outer surface  302  into the core  306 . The vertex  314 (E) of the perturbation  318 (E) has an acute angle, which is in the approximate range of 30 to 90 degrees. 
     The grating element  312 (F), shown in FIG. 4F, includes a perturbation  318 (F) that extends generally inward from the outer surface  302  beyond the core  306  into the distal region of the cladding  308 . The vertex  314 (F) of the perturbation  318 (F) defines an acute angle, which is in the approximate range of 30 to 90 degrees. 
     The grating element  312 (G), shown in FIG. 4G, includes a perturbation  318 (G) that extends generally inward from the outer surface  302  and to the cladding  308 . An arc  316 (A), the center of which is not shown and which is outside of the grating element  312 (G), defines the perturbation  318 (G). 
     The grating element  312 (H), shown in FIG. 4H, includes a perturbation  318 (H) that extends generally inward from the outer surface  302  into the core  306 . An arc  316 (B), the center of which is not shown and which is outside of the grating element  312 (H), defines the perturbation  318 (H). 
     The grating element  312 (I), shown in FIG. 4I, includes a perturbation  318 (I) that extends generally inward from the outer surface  302  past the core  306  and into the distal region of cladding  308 . An arc  316 (C), the center of which is not shown and which is outside of the grating element  312 (I), defines the perturbation  318 (I). 
     The grating element  312 (J), shown in FIG. 4J, includes at least one perturbation  318 (J). The perturbation  318 (J) can be of any arbitrary shape and size and can be located anywhere in the grating element  312 (J), provided the azimuthal symmetry about the center of the core is broken. It should be noted that if the perturbation  318 (J) extends across the entire grating element  312 (J), then the perturbation  318 (J) has azimuthal asymmetry, otherwise, the perturbation could be uniform. In the preferred embodiment, the perturbation  318 (J) has azimuthal asymmetry about the center of the core  306 . 
     The grating elements  312 (K), shown in FIG. 4K, includes a pair of generally pie shaped perturbations  318 (K) extending generally inward from the outer surface  302  into the core  306 . The perturbation is  318 (K) are approximately linearly aligned. 
     The grating element  312 (L), shown in FIG. 4L, includes three generally pie shaped perturbations  318 (L), each perturbation  318 (L) extends generally inward from the outer surface  302  into the core  306 . The perturbations  318 (L) are approximately equally spaced from each other. 
     The grating element  312 (M), shown in FIG. 4M, includes four approximately pie shaped perturbations  318 (M) each of which extends generally inward from the outer surface  302  into the core  306 . The perturbations  318 (M) are approximately equally spaced from each other. 
     The grating element  312 (N), shown in FIG. 4N, includes five approximately pie shaped perturbations  318 (N), each of which extends generally inward from the outer surface  302  into the core  306 . The perturbations  318 (N) are approximately equally spaced from each other. 
     The grating element  312 (O), shown in FIG. 40, includes four approximately pie shaped perturbations  318 (O), each of which extends generally inward from the outer surface  302  into the core  306 . In contrast to FIGS. 4K through 4N, the perturbations  318 (O) are not approximately equally spaced from each other. 
     It should be noted that the grating elements  312  are non-limiting examples of embodiments of the grating elements having azimuthal asymmetry. All grating elements having azimuthal asymmetry are intended to be within the scope of the invention. 
     Referring now to FIG. 5, an optical fiber  400  having a fiber grating  404 , which includes a plurality of azimuthally varying grating elements  412 , is configured such that the centerline  410  is curved. In this example, the optical fiber  400  is bent into an arc having an arbitrary radius of curvature. Generally, the optical characteristics, such as the coupling between core mode  414  which propagates into the fiber core and cladding mode  416 , of the fiber grating  404  are a function of the alignment of the azimuthally varying grating elements  412 . The coupling between the core mode  414  and the cladding mode  416  can be tuned by changing the relative orientation of the azimuthally varying grating elements  412 . It will be demonstrated hereinbelow that with appropriately bending of the fiber grating  404  the coupling between the core modes  414  and the cladding modes  416  can be tuned at desired frequencies. 
     Although FIG. 5 illustrates changing the optical path by smoothly bending the optical fiber, any method of changing the relative orientations of the grating elements including but not limited to, kinking, micro-bending, are intended to be included within the scope of the invention. Furthermore, when the optical fiber grating  404  is axially twisted about centerline  410 , the relative orientations of the perturbations in the grating elements  412  are changed. Consequently, the fiber grating  404  can be tuned to couple to desired frequencies with appropriate twisting of the fiber grating  404 . The coupling between modes can also be tuned by a combination of rotation of the optical fiber  400  and deformation of the fiber grating  404 . 
     Referring to FIG. 6, in one embodiment, an azimuthally varying grating element  112  is produced by illuminating a portion of an optical fiber  100  by a laser beam. To make the grating element  112 , incident light  502  of intensity I 0  is transversely applied to a region of the optical fiber  100 . The wavelength of the incident light is chosen such that it is highly absorbed by optical fiber  100 , thereby heating the region of the optical fiber  100  that absorbs the incident light  502 . An amplitude mask can be used with one slit or multiple slits to control the light pattern impinging on the fiber. 
     FIG. 6 also represents simulated results of normalized incident light intensity in optical fiber  100 . In this experiment optical fiber  100  is a standard telecommunications matched-clad glass fiber and the incident light is a laser beam from a CO 2  laser. Details of this simulation can be found in “Axial Rotation Dependence of Resonances in Curved CO 2 —Laser-Induced Long-Period Fibre Gratings,” Electronic Letters, vol. 36, pp. 1354-1355, Aug. 3, 2000, which is hereby incorporated by reference. 
     For the purposes of this disclosure, we shall define a top surface region  504  as being the portion of the grating element  112  in which the normalized intensity is approximately between 0.2 and 1, and we shall define a bottom surface region  506  as being the portion of the grating element  112  that is radially distal from the top surface region  504 . Clearly, almost all of the incident light is absorbed by the optical fiber  100  within approximately 20 microns from the incident surface. The incident light  502  is used for creating a temperature gradient between the upper surface  504  and the bottom surface  506 . 
     A perturbation in the refractive index of the optical fiber  100  is produced in the portion of the optical fiber  100  that is heated by the incident light  502 . Generally, the magnitude of the perturbation in the refractive index is related to the temperature of the heated portion. Thus, the incident light  502  produces a grating element  112  having a given perturbation in the refractive index in the upper surface region  504  and a smaller perturbation in the bottom surface region  506 . Likewise, the perturbation in the refractive index of the core  106  is generally greatest in the region of the core proximal to the top surface region  504  and least in the region distal from the top surface region  504 . It is also understood that the magnitude of the refractive-index perturbation can be controlled by the laser beam intensity. 
     While the top surface region  504  absorbs more energy than does the bottom surface region, the absorption is generally symmetric about a vertical line (not shown) at x=0. Thus, when the optical fiber  100  is initially symmetric about a vertical line at x=0, the perturbation in the refractive index caused by heating from incident laser light  502  is also symmetric about a vertical line at x=0, and consequently, the optical characteristics of the grating element  112  are symmetric about a vertical line at x=0. 
     In the preferred embodiment, a first grating element  112  of the fiber grating  104  is produced by applying the incident light  502  to a portion of the optical fiber for a predetermined duration and at a predetermined intensity. A subsequent grating element, which is a predetermined distance from the first grating element, is produced by applying the incident light  502  for a predetermined duration and intensity to a subsequent portion of the optical fiber  100 . In the preferred embodiment, the optical fiber  100  is positioned in a given orientation relative to the incident laser beam and the relative orientation of the top surface region  504  for each subsequent grating element  112  is predetermined. 
     Although, the preferred embodiment uses a CO 2  laser as a heat source to produce the azimuthally varying grating elements  112  in the optical fiber  100 , other embodiments include but are not limited to heat sources such as plasma arcs, ultraviolet lasers, visible lasers, narrow flames, etc. 
     In another embodiment, azimuthally varying grating elements are produced by including dopants, such as, but not limited to, germanium, boron, and hydrogen in optical fiber  100  and exposing the dopants to light sources, such as an UV laser. In this embodiment, during the fabrication of the optical fiber  100 , the dopants are disposed in the optical fiber according to a predetermined or a random azimuthally varying pattern, non-limiting examples of which are shown in FIGS. 4A-4O. It is to be understood that a plurality of dopants can be disposed in a azimuthally varying grating element. In one embodiment, a first region has a first dopant disposed therein and a second region has a second dopant disposed therein. In another embodiment, a plurality of dopants are disposed in a region of the azimuthally varying grating element. In yet another embodiment, a dopant or a plurality of dopants are disposed in one or several regions of the azimuthally varying grating element and the concentration of the dopant or dopants is varied. 
     Typically, the grating elements  112  are configured such that each top surface region  504  is approximately linearly aligned. In alternative embodiments, the top surface regions  504  of the grating elements  112  are aligned according to a predetermined scheme. Non-limiting examples of two alignment schemes are shown in FIGS. 7A and 7B. In FIG. 7A, fiber grating  104  includes a plurality of grating elements  112 (A)- 112 (F). In this exemplary fiber grating  104 , the grating elements  112  are rotationally aligned such that each grating element is offset by a predetermined amount. For example, grating elements  112 (B) is azimuthally rotated about the centerline (not shown) by 30 degrees relative to the orientation of the grating element  112 (A). In this example, except for being rotated with respect to each other, the grating elements are essentially the same. All of the perturbations  118  were produced by absorbing essentially the same amount of energy, with each incident top surface region being rotationally offset. Thus, equivalent portions of the grating elements are rotationally offset. For example, region  120  of the perturbation  118  is essentially the same in each grating element  112 . It should be clear that the amount of rotation of each grating element  112  is a design choice, and that each grating element  112  need not be rotated by a multiple of a predetermined amount. For example, the grating element  112 (B) could be rotated by 11 degrees and the grating elements  112 (C) could be rotated by 60 degrees relative to grating element  112 (A). 
     In FIG. 7B, the grating elements  112 (of exemplary fiber grating  104  are periodically rotationally offset. In this example, grating elements  112 (B),  112 (D) and  112 (F) are rotationally offset by 90 degrees with respect to grating elements  112 ((A),  112 (C) and  112 (E). It should be clear that the amount of rotation is a design choice, as is the periodicity of the rotated gratings. For example, in another embodiment, the grating elements could be grouped into three sets, each of the three sets having different rotational orientation. 
     Referring now to FIGS. 8-12, shown are transmission characteristics of two exemplary LPFG (LPFG). The two exemplary LPFG&#39;s were fabricated period by period using carbon dioxide laser pulses. Gratings were written into standard matched-clad single-mode fiber (Corning SMF 28) with no hydrogen loading or special treatment of any kind. The experimental configuration, details of which can be found in “Tuning, Attenuating, and Switching by Controlled Flexure of Long-Period Fiber Gratings,” Optics Letters, vol. 25, pp. 61-63, Jan. 15, 2001, which is incorporated herein by reference, included a computer-controlled translation stage that positioned the fibers so that single pulses of CO 2  laser light of 10.6 μm wavelengths could be focused onto the fiber at desired positions along the fiber axis. The grating period, Λ, was 480 μm. For LPFG No. 1, the number of periods, N, was 40 and the incident writing energy was 88 mJ/period (0.40 watts for 0.22 seconds). For LPFG No. 2, the number of periods, N, was 50 and the incident writing energy was 100 mJ/period (0.40 watts for 0.25 seconds). The transmission spectra of these LPFG&#39;s were measured from 1000 nm to 1600 nm using an optical spectrum analyzer (Hewlett Packard Model 70951B). For the measurements presented herein the fibers containing the LPFG&#39;s were placed on top of a horizontal plastic optical fiber platform and held there under slight tension (a tensile force of 25 milli-Newtons). Beneath the horizontal plastic optical fiber platform, at approximately the center, a micropositioner was used to deflect upwardly the plastic optical fiber platform and the LPFG&#39;s, which were correspondingly flexed as shown in FIG.  4 . The radius of curvature could be varied from R=infinity to 0.2 meters (curvature varied from C=1/R=0 m −1  to 5 m −1 ). 
     Referring now to FIG. 8, shown is the transmission characteristic for the long period optical fiber grating number 1 having 40 grating elements  112  (with a periodicity of 480 μm. FIG. 8 demonstrates the strong dependence of the transmission on the axial rotational orientation of the optical fiber  100 , where φ′ denotes the azimuthal rotation of the optical fiber from the configuration illustrated in FIGS. 7A-7B. The grating elements had the same general azimuthal symmetry as the grating element shown in FIG.  6 . From symmetry arguments, the transmission at φ′=90° and φ′=270° should be the same and this was observed experimentally to a close approximation. The diffraction of the core modes  114  into the cladding modes  116  as illustrated by transmission magnitude, τ, is sensitive to the axial rotational orientation of the fiber. 
     The strong axial rotation orientation dependence observed in CO 2  laser induced LPFG&#39;s provides an important additional degree of freedom for tailoring the transmission characteristics of wavelength tuners, attenuators, switches, and modulators. This degree of freedom is not present in symmetric gratings, such as conventional UV induced grating. By proper choice of axial rotation angle A, desired characteristics such as wavelength tuning at constant attenuation and variable attenuation at constant wavelength can be achieved. 
     Referring now to FIGS. 9-12, six to ten distinct resonances were typically observed in the wavelength range from 1,000 to 1,600 nanometers. Varying the curvature, C, of the LPFG&#39;s caused the resonance to change both in attenuation and in wavelength. Also, the resonance changed significantly with axial rotation of the fiber. Consequently, the evolution of the resonance with increasing curvature depends sensitively on the axial orientation of the LPFG with respect to the plane of curvature. Orienting LPFG No. 1 appropriately on the flexing optical fiber platform enabled wavelength tuning at a constant attenuation as shown in FIG.  9 . In this particular case, an attenuation of 21 dB was tuned over a wavelength range of 20 nanometers from 1,472 nanometers to 1,452 nanometers by changing the curvature of the LPFG No. 1 from C 1 =2.23 m −1  to C 6 =3.85 m −1 , thereby demonstrating constant attenuation tuning with an LPFG. The radius of curvature for each of the labeled curves shown in FIGS. 9 and 10, are given in Table 1. 
     
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Bending curvatures for optical characteristics shown in FIGS. 9 and 10. 
               
             
          
           
               
                 C 1   
                 C 2   
                 C 3   
                 C 4   
                 C 5   
                 C 6   
               
               
                   
               
               
                 2.23 m −1   
                 2.61 m −1   
                 2.98 m −1   
                 3.23 m −1   
                 3.48 m −1   
                 3.85 m −1   
               
               
                   
               
             
          
         
       
     
     The six transmission spectra shown in FIG. 9 are representative of the spectra for the 30 curvatures applied. The tuning of the center wavelength with curvature is shown in FIG. 10. A total of 38 spectra are summarized in FIG.  10 . The wavelength tuning is linear with curvature and has a tuning sensitivity of 11.92 nanometers/m −1  over most of the range. It should be noted that the transmission increases (attenuation decreases) at the high and low curvature ends for the 30 curvatures shown in FIG.  10 . 
     Referring now to FIG. 11, shown are the transmission characteristics of an exemplary LPFG 2. The transmission characteristics demonstrate variable attenuation/switching/modulation at a constant wavelength by appropriate axial rotation of the LPFG No. 2 coupled with bending the LPFG No. 2. In this case, the attenuation at a wavelength of 1,422 nanometers was varied over a 19 dB range by changing the curvature of the LPFG No. 2 from C 1 =0.0 m −1  to C 9 =1.61 m −1 . The radius of curvatures for C 1  through C 9 , shown in FIGS. 11 and 12, are given in Table 2. The nine transmission spectra shown in FIG. 10 are representative of the spectra for 21 curvatures (a total of 22 spectra) applied in this experiment. The transmission (attenuation) as a function of curvature is shown in FIG.  11 . As curvature was increased beyond C 9 =1.61 m −1  (overall minimum transmission) the transmission increased (attenuation decreased) as shown in FIG.  12 . For axial orientations other than those used in FIGS. 9-12, both the wavelength and the transmission simultaneously change when the LPFG region was flexed. A wide variety of wavelength transmission characteristics were observed. 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Bending curvatures for optical characteristics shown in FIGS. 11 and 12. 
               
             
          
           
               
                 C 1   
                 C 2   
                 C 3   
                 C 4   
                 C 5   
                 C 6   
                 C 7   
                 C 8   
                 C 9   
               
               
                   
               
               
                 0.0 m −1   
                 0.25 m −1   
                 0.73 m −1   
                 0.98 m −1   
                 1.17 m −1   
                 1.29 m −1   
                 1.42 m −1   
                 1.48 m −1   
                 1.61 m −1   
               
               
                   
               
             
          
         
       
     
     As wavelength tuners (FIG. 9) and as variable attenuators/switches/modulators (FIG.  11 ), these grating devices have significant potential for application to fiber optic network telecommunications. A major advantage is that the modulating device is contained within the fiber as opposed to being external to the fiber. Piezoelectric, electromechanical or similar transducers, including but not limited to a microelectronic apparatus, mechanical-apparatus, an electro-mechanical solenoid, a linear motor, a stepping motor and mechanical cam, a hydraulic apparatus, a pneumatic apparatus, a thermomechanical apparatus, a photoelastic apparatus, an acoustic apparatus, a magnetostrictive apparatus, a electrostrictive apparatus, and a piezo-electric ceramic platform can be attached to the fiber to make the tuning, attenuation, switching, and modulation electrically controllable by controlling the positioning of the fiber. The wavelength tuning and variable attenuation effects can be applied in sensor applications, and other applications. 
     Referring now to FIG. 13, shown is a relative index difference profile for the cladding region of a hydrogen-loaded optical fiber that has had a plurality of grating elements with periodicity of 480 μm written into the optical fiber by a CO 2  laser. The horizontal is the axial direction of the optical fiber, and the vertical axis is the relative index difference, which is given by 
     
       
         Δ=[ n ( r,z )− n   0   ]/n   0 , 
       
     
     where n 0  is the index of refraction of an index matching oil chosen to match the index of refraction of the unperturbed cladding region and where n(r,z) is the index of refraction of the radial region measured from the centerline at positions along the centerline. Using transverse interferometry, the relative index difference was measured on the side of the optical fiber upon which the laser beam was incident. The peaks in the relative index difference, which are about 0.05%, correspond to the grating elements and have the appropriate periodicity. The value of n o  was 1.458, so the increase in the refractive index of the cladding region upon which the laser beam was incident upon was about 1.5×10 −3 . 
     Although the experimental results given hereinabove were for LPFGs, it is to be understood that they were exemplary fiber grating, which were not intended to limit the scope of the invention. Other fiber gratings included in the scope of the invention include, but are not limited to, short-period fiber Bragg gratings. Other exemplary fiber gratings are shown in FIGS. 14A-14F. 
     Optical fiber grating  1300 (A), shown in FIG. 14A, has a fiber grating  1304  disposed therein. The fiber grating  1304  includes a plurality of approximately equally spaced grating elements  1312  extending from the cladding into the core. 
     Optical fiber grating  1300 (B), shown in FIG. 14B, has a pair of fiber gratings  1304 (A) and  1304 (B) disposed therein. Each fiber grating  1304  includes a plurality of approximately equally spaced grating elements  1312  extending from the cladding into the core. The periodicity of the grating elements  1312  included in the fiber grating element  1304 (A) is approximately the same as the periodicity of the grating elements  1312  in the fiber grating  1304 (B). 
     Optical fiber grating  1300 (C), shown in FIG. 14C, has a pair of fiber gratings  1304 (c) and  1304 (D) disposed therein. Each fiber grating  1304  includes a plurality of approximately equally spaced grating elements  1312  extending from the cladding into the core. The periodicity of the grating elements  1312  included in the fiber grating element  1304 (D) is approximately greater than the periodicity of the grating elements  1312  in the fiber grating  1304 (C). The difference in the periodicity is a design choice, as is the relative positions of fiber gratings  1304 (C) and  1304 (D). 
     Optical fiber grating  1300 (D), shown in FIG. 14D, has a chirped fiber grating  1304  disposed therein, which includes a plurality of grating elements  1312  having non-uniform longitudinal spacing extending from the cladding into the core. The spacing between grating elements  1312  in fiber grating  1304  of optical fiber  1310 (D) is a design choice. In an alternative embodiment, the spacing between grating elements can conform to any predetermined or random pattern. 
     Optical fiber grating  1300 (E), shown in FIG. 14E, has a pair of chirped fiber gratings  1304 (E) and  1304 (F) disposed therein. Each fiber grating  1304 (E) and  1304 (F) includes a plurality of grating elements  1312  extending from the cladding into the core. The spacing of the grating elements  1312  included in the chirped fiber grating element  1304 (E) is approximately the same as the spacing of the grating elements  1312  included in the chirped fiber grating  1304 (F), and the spacing generally decreases from left to right in both of the fiber gratings,  1304 (E) and  1304 (F). 
     Optical fiber grating  1300 (F), shown in FIG. 14F, has a pair of chirped fiber gratings  1304 (G) and  1304 (H) disposed therein. Each fiber grating  1304 (G) and  1304 (H) includes a plurality of grating elements  1312  extending from the cladding into the core. The spacing of the grating elements  1312  included in the chirped fiber grating element  1304 (G) is approximately the same as the spacing of the grating elements  1312  included in the chirped fiber grating  1304 (H). However, the spacing of the grating elements included in the chirped fiber grating  1304 (G) decreases from left to right and the spacing of the grating elements  1312  included in the chirped fiber grating  1310 (H) increases from left to right. 
     The embodiments shown in FIGS. 14A-14F are non-limiting examples of possible configurations of azimuthally varying grating elements. Other non-limiting configurations include, but are not limited to, disposing the azimuthally grating elements  1312  in a portion of the core or in a portion of the cladding or across the core and cladding. 
     Referring now to FIGS. 15A-15E, FIG. 15A is a side view of tuning/attenuating/switching/modulating fiber grating device  1400 , hereinafter collectively referred to as “tuning device.” Tuning device  1400  includes a housing  1402  having opposed ends  1404  that are adapted to be coupled to devices and/or fibers within an optical network. Extending between the opposed ends  1404  are opposed sidewalls  1406  that have bottom wall  1408  and top wall  1410  extending there between. Housing  1402  has a generally hollow interior extending between the opposed ends  1404 . 
     Tuning device  1400  further includes, disposed within the generally hollow interior of the housing  1402 , a tuning actuator  1412 , a plurality of posts  1414 , an optical fiber platform  1416  and an optical fiber  100  having opposed ends  102 . The opposed ends  1404  of housing  1402  include aligned openings  1418  for receiving the opposed optical fiber ends  102 . In the preferred embodiment, the openings are vertically aligned approximately half way between the bottom wall  1408  and the top wall  1410  and extending between the openings  1418  is optical fiber  100 , which includes a plurality of azimuthally varying grating elements in the grating element  104 . The openings  1418  are typically contained within standard commercial fiber optic connectors. 
     Referring now to FIG. 15B, shown is a cutaway prospective view of tuning device  1400 , as seen when viewed along line I-I of FIG.  15 A. Fixedly attached to the bottom wall  1408 , approximately half way between opposed ends  1404  and extending at least partially between opposed sidewalls  1406 , is tuning actuator  1412 . Disposed on tuning actuator  1412  is optical fiber platform  1416 , which in the preferred embodiment is generally a rectangular sheet of resilient material such as plastic or metal defined by opposed ends  1420  and opposed sides  1422 , for positioning the optical fiber. The optical fiber platform  1416  further includes a bottom surface  1424 , which engages tuning actuator  1412 , and a generally flat top surface  1426  that has a generally V-shaped groove  1428  formed therein. The V-shaped groove  1428  extends between opposed platform ends  1420  and is aligned with optical fiber  100 , which is disposed therein. In the preferred embodiment, each of the posts includes a generally V-shaped groove  1430  for receiving a portion of the optical fiber  100 . The generally V-shaped grooves formed in the posts  1414 l are aligned with the platform V-shaped groove  1428 , straddling the optical fiber  100 , and the optical fiber  100  is affixed to the optical fiber platform  1416 , proximal to opposed platform ends  1420 , by means such as adhesive. In an alternative embodiment, the optical fiber  100  is disposed directly on the tuning actuator  1412 , thus the tuning actuator can also be used for positioning the optical fiber  100  in a given orientation between opposed ends  1404  of housing  1402  and for flexing or bending the optical fiber  100 . 
     Rigidly affixed to sidewalls  1406  and extending therein, are the plurality of posts  1414  made from a rigid material such as metal or hard plastic. The posts are vertically aligned such that the posts engage the top surface  1426  of the optical fiber platform  1416  proximal to the opposed platform ends  1420 . 
     Referring now to FIGS. 15A and 15C, the optical fiber  100  is disposed in the groove of the optical fiber platform  1416  and fixedly attached thereto, such that the grating region  104  extends at least partially between the posts  1414 . In FIG. 15A, tuning actuator  1412  is shown coupled to the bottom wall  1408  of housing  1402  in a first configuration engaging the bottom surface  1424  of optical fiber platform  1416 . 
     The tuning actuator  1412 , the posts  1414 , the optical fiber platform  1416  and the housing  1402  cooperate to deform optical fiber  100 . The tuning actuator  1412 , which is rigidly coupled to bottom wall  1408  and in contact with optical fiber platform  1416 , is adapted to vertically extend and contract. Referring now to FIG. 15C, shown is tuning actuator  1412  in a second configuration in which the tuning actuator  1412  is partially extended upwards, thereby pressing optical fiber platform  1416  upwards. The plurality of posts  1414  engage the top surface  1426  of the optical fiber platform  1416  proximal to opposed platform ends  1420 , thereby preventing the end portions of the optical fiber platform from being vertically raised by the extension of actuator  1412 . In response to the extension of actuator  1412  the portion of the optical fiber platform extending between the posts  1414 (A) and  1414 (B) becomes curved, as shown in FIG.  15 B. When the actuator  1412  is contracted to its first configuration, shown in FIG. 15A, the optical fiber platform, which is made from a resilient material, returns to its generally flat shape. 
     In the preferred embodiment, the optical fiber  100  is disposed in groove  1428  and fixedly attached thereto by means such as adhesive. The optical fiber  100  is positioned such that at least a portion of the grating region  104  of the optical fiber is disposed between posts  1414 (A) and  1414 (B). Thus, when the tuning actuator  1412  is extended or contracted, thereby changing the curvature of the optical fiber platform  1416 , the curvature of the grating region of the optical fiber changes correspondingly. The optical fiber platform  1416 , with the optical fiber disposed thereon, can be bent or flexed by a variety of devices such as, but are not limited to, a piezoelectric apparatus, a micro-electro-mechanical apparatus, an electro-mechanical solenoid, a linear motor, a stepping motor and mechanical cam, a hydraulic apparatus, a pneumatic apparatus, a thermomechanical apparatus, a photoelastic apparatus, an acoustic apparatus, a magnetostrictive apparatus, and a electrostrictive apparatus. 
     In an alternative, non-limiting, embodiment, optical fiber  100  is fixedly clamped to optical fiber platform  1416  such that changes in the curvature of the optical fiber  100  correspond to changes in the contraction/expansion of the tuning actuator. In yet another non-limiting embodiment, optical fiber  100  is coupled to opposed ends  1404  such that the optical fiber extending therebetween engages the optical fiber platform, and such that changes in the curvature of the optical fiber correspond to changes in the expansion/contraction of tuning actuator  1412 . 
     In another non-limiting embodiment, the opposed optical fiber ends  102  of the optical fiber  100  are rotatably mounted to opposed ends  1404  of tuning device  1400 . Each opposed optical fiber end  102  of optical fiber  100  is independently axially rotatable. In this embodiment, the optical fiber, extending between the opposed ends  1404  of the tuning device, is not adhered to the optical fiber platform  1416 . Rather, the optical fiber  100  is disposed in the platform groove  1428  and is rotatable therein. Thus, the grating region  104  of the optical fiber  100  is rotated by rotating the optical fiber ends  102 . The grating region  104  can also be axially twisted about the centerline by counter rotating the opposed optical fiber ends  102 , or by rotating just one of the opposed optical fiber ends, or by rotating one of the optical fiber ends. It should be noted that the optical fiber  100  is axially rotatable/twistable even when the optical fiber is not linearly aligned between the opposed ends  1404 , e.g., even when the optical fiber region is curved in response to curvature of optical fiber platform  1416 . 
     FIGS. 15D and 15E show an alternative embodiment of the tuning device  1400 . In this embodiment, the optical fiber  100  is disposed on an optical fiber platform  1430  that is a commercially available piezo-ceramic layer, which are known to those skilled in the art. The piezo-ceramic layer includes opposed electrodes  1432  disposed on intermediate layers  1434 , which sandwich a piezo-ceramic layer  1436  such as barium titanate or lead lanthanum zirconate titanate. The optical fiber platform  1430  curves in response to a voltage applied to the opposed electrodes  1432 , as illustrated in FIG. 15E, thereby inducing a change in curvature of the optical fiber  100  disposed thereon. Thus, optical fiber platform  1430  positions the optical fiber  100  extending between opposed ends  1404  of housing  1402  and flexes to change the curvature of the grating region  104  of optical fiber  100  disposed thereon. 
     As previously demonstrated hereinabove, small changes in the curvature of the grating region may produce dramatic changes in the optical transmission characteristics of the optical fiber. Those skilled in the art will recognize that other embodiments, different than those disclosed hereinabove, exist for changing the relative orientation of the grating region, and all such embodiments are intended to be within the scope of the invention. The above-cited embodiments are intended to be non-limiting examples for positioning and flexing the optical fiber having azimuthally varying grating elements disposed therein. 
     From the above discussion of the current invention it should be understood by those skilled in the art that many implementations of the current invention are possible. It should be emphasized that the above-described embodiments of the present invention, particularly, any “preferred” embodiments, are merely possible examples of implementations, merely set forth for a clear understanding of the principles of the invention. Many variations and modifications may be made to the above-described embodiment(s) of the invention without departing substantially from the spirit and principles of the invention. All such modifications and variations are intended to be included herein within the scope of this disclosure and the present invention and protected by the following claims.
The present invention relates to a type of optical fiber grating having an azimuthal refractive-index perturbation. The optical fiber includes a fiber grating that has a plurality of grating elements formed therein. At least one of the grating elements has a spatially varying index of refraction that varies azimuthally about the centerline of the optical fiber. The fiber grating acts as a band-stop optical spectral filter. In addition, since fiber-cladding modes are weakly-guided modes, their power can be easily dissipated by scattering, bending, stretching, and/or rotating the optical fiber. Multiple configurations of these gratings within an optical fiber are given. Methodologies are given for the fabrication of these gratings. Devices are presented which can dynamically attenuate, tune, switch, or modulate the wavelength spectral characteristics of an optical signal.