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 fig1 a , 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 fig1 a , 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 fig1 b , 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 fig1 c , 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 fig2 , 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 , ncore , greater than the refractive index , ncladding , 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 fig2 , 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 element 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 , λp , 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 λp , 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 , λp , from the forward core - guided mode 114 into a forward cladding mode . thereby , reducing the intensity of the light , centered about λp , 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 fig3 , 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 } in the grating element 112 can be given by 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 perturbations ( phase change ) or can be restricted to optical absorption perturbations . 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 perturbation 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 fig3 is only an exemplary illustration of an embodiment of the invention . other , non - limiting examples of grating elements having azimuthal asymmetry are illustrated in fig4 a – 4o . briefly described , the grating elements 312 ( a ), shown in fig4 a , 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 fig4 b , 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 fig4 c , 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 fig4 d , 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 fig4 e , 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 fig4 f , 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 fig4 g , 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 fig4 h , 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 fig4 , 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 fig4 j , 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 fig4 k , includes a pair of generally pie shaped perturbations 318 ( k ) extending generally inward from the outer surface 302 into the core 306 . the perturbations 318 ( k ) are approximately linearly aligned . the grating element 312 ( l ), shown in fig4 l , 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 fig4 m , 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 fig4 n , 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 fig4 , 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 fig4 k 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 fig5 , 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 fig5 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 fig6 , 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 10 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 . fig6 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 co2 laser . details of this simulation can be found in “ axial rotation dependence of resonances in curved co2 - 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 co2 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 fig4 a – 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 fig7 a and 7b . in fig7 a , 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 element 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 element 112 ( c ) could be rotated by 60 degrees relative to grating element 112 ( a ). in fig7 b , 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 fig8 – 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 co2 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 fig4 . 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 fig8 , 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 . fig8 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 fig7 a – 7b . the grating elements had the same general azimuthal symmetry as the grating element shown in fig6 . 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 co2 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 φ , desired characteristics such as wavelength tuning at constant attenuation and variable attenuation at constant wavelength can be achieved . referring now to fig9 – 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 fig9 . 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 fig9 and 10 , are given in table 1 . the six transmission spectra shown in fig9 are representative of the spectra for the 30 curvatures applied . the tuning of the center wavelength with curvature is shown in fig1 . a total of 38 spectra are summarized in fig1 . 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 fig1 . referring now to fig1 , 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 fig1 and 12 , are given in table 2 . the nine transmission spectra shown in fig1 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 fig1 . as curvature was increased beyond c 9 = 1 . 61 m − 1 ( overall minimum transmission ) the transmission increased ( attenuation decreased ) as shown in fig1 . for axial orientations other than those used in fig9 – 12 , both the wavelength and the transmission simultaneously change when the lpfg region was flexed . a wide variety of wavelength transmission characteristics were observed . as wavelength tuners ( fig9 ) and as variable attenuators / switches / modulators ( fig1 ), 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 electromechanical 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 fig1 , 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 co2 laser . the horizontal axis is the axial direction of the optical fiber , and the vertical axis is the relative index difference , which is given by where n0 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 n0 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 fig1 a – 14f . optical fiber grating 1300 ( a ), shown in fig1 a , 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 fig1 b , 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 fig1 c , 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 fig1 d , 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 fig1 e , 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 fig1 f , 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 fig1 a – 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 fig1 a – 15e , fig1 a 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 fig1 b , shown is a cutaway prospective view of tuning device 1400 , as seen when viewed along line i — i of fig1 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 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 fig1 a 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 fig1 a , 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 fig1 c , 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 fig1 b . when the actuator 1412 is contracted to its first configuration , shown in fig1 a , 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 electromechanical 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 . fig1 d 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 fig1 e , 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 .