Abstract:
An apparatus and method for thermal compensation of an optical waveguide grating includes a temperature compensating package attached to the optical waveguide at two attachment points encompassing the grating. The distance between the two attachment points varies non-linearly with temperature over an operating temperature range for the apparatus.

Description:
FIELD  
         [0001]    This invention generally relates to optical waveguide diffraction gratings. More particularly, this invention relates to apparatuses and methods for compensating for thermally induced changes in the reflected wavelength of optical waveguide diffraction gratings.  
         BACKGROUND  
         [0002]    An optical filter may be placed in a selected region of an optical fiber device to reflect a particular wavelength of incident light. One such filtering device is the Bragg grating, in which a diffraction grating is impressed into the core of an optical fiber. A conventional Bragg grating comprises an optical fiber in which the index of refraction undergoes periodic perturbations along its length. The refractive index perturbations create a diffraction grating that reflects a known spectrum of light from an incident spectrum while allowing the rest of the incident spectrum to pass unaltered. The reflected wavelength of light is centered around a wavelength equal to twice the spacing between successive perturbations multiplied by the refractive index of the fiber core. Such Bragg gratings are employed in a variety of applications including signal filtration, laser source stabilization in Dense Wavelength Division Multiplexing (DWDM) networks, reflection of fiber amplifier pump energy, compensation for chromatic dispersion of the fiber, and strain and temperature measurement, to name a few.  
           [0003]    These applications demand very tight tolerances on the bandwidth and stability of the reflected signal over wide temperature ranges. As more communications wavelengths are crowded into single fibers, performance demands of fiber Bragg gratings (FBGs) will continue to increase.  
           [0004]    Unfortunately, both the refractive index of the grating and the distance between successive perturbations of the grating are temperature dependent. As a result, the spectrum of light reflected by the grating is also temperature dependent. In many cases, however, it is desirable to provide a stabilized wavelength reflection spectrum that is substantially temperature independent. Shifts in the reflected wavelength reflection spectrum that occur over the operating temperature range of the FBG device are typically an order of magnitude larger than the desired tolerances for current applications. Therefore, specialized packaging of the grating is needed to compensate for the thermally induced material changes, and thereby maintain a spectrum output that is constant with changes in temperature.  
           [0005]    One method of reducing the influence of temperature variations is to apply an axial strain on the grating that changes with temperature. Axial strain also causes shifts in the reflected spectrum, and application of the appropriate strain with temperature will effectively cancel the wavelength drift caused by optical fiber material changes, thus stabilizing the grating.  
           [0006]    The amount of strain needed to compensate a FBG is determined using the equation:  
           Δλ=λ 0 (ζ+α f )( T−T   0 )+λ 0 (1− P   e )ε  (1)  
           [0007]    where Δλ is the change in reflected wavelength, λ, of the FBG at temperature T; λ 0  is the reflected wavelength of the unstrained FBG at reference temperature T 0 ; and ε is the amount of axial strain imposed on the FBG by the package at applied temperature T. The terms α f , ζ and P e  are the thermal expansion coefficient, thermo-optic coefficient, and strain optic coefficient, respectively, of the FBG.  
           [0008]    The strain required to compensate a FBG is determined by setting αλ to 0 in equation (1) then solving for the strain as follows:  
             ɛ   =       -       (     ζ   +     α   f       )       (     1   -     P   e       )              (     T   -     T   0       )               (   2   )                               
 
           [0009]    The FBG properties α, ζ and P e  are typically treated as being temperature independent. Commonly assigned values are α=0.55 ppm/° C., ζ=6.7 ppm/° C. and P e =0.22. (The term ppm is commonly used to indicate parts per million or ×10 −6 .) Using equation (2) and the commonly assigned FBG parameters, it is apparent that the strain applied by the package on the grating (ε applied ) must change with temperature by a rate of −9.3 ppm/° C. In other words, the package must impose an effective thermal expansion on the FBG of −9.3 ppm/° C. The negative value of ε applied  indicates that the package must cause the FBG to become shorter as temperature increases.  
           [0010]    Current devices and methods used to thermally compensate gratings are based on either attaching the FBG to materials with negative thermal expansion coefficients (e.g. zirconia tungstate or β-eucryptite) or attaching the FBG to a package composed of two or more materials with different thermal expansion coefficients arranged in a particular design to impose the appropriate effective thermal expansion on the FBG. These devices and methods provide linear compensation to the FBG in that they produce negative effective thermal expansion coefficients that are constant or nearly constant over the temperature range of the device.  
           [0011]    However, contrary to the typical assumption in the design of thermal compensating FBG devices, the FBG properties α, ζ and P e  are not constant with temperature. Therefore, the reflected wavelength of the FBG changes with temperature in a slightly non-linear fashion. Thus, when an FBG is mounted in a perfectly tuned linear package, the reflected wavelength will still change slightly (i.e., drift) with temperature. The thermally induced wavelength drift can produce changes in the reflected wavelength on the order of 0.02 nm to 0.08 nm, which is significant when compared to the application tolerances for these devices. A need exists for thermal compensating devices employing non-linear effects to effectively reduce or eliminate the thermal component of the wavelength drift, thereby improving the accuracy of the devices and greatly opening tolerances on manufacturing specifications for the devices.  
         SUMMARY  
         [0012]    Aspects of the invention described herein include apparatuses and methods that compensates for thermally induced non-linear and linear changes in the reflected wavelength of optical waveguide gratings, such as fiber Bragg gratings (FBGs).  
           [0013]    In one aspect, an embodiment according to the invention includes a temperature compensating package attached to an optical waveguide having a grating. The temperature compensating package is attached to the optical waveguide at two attachment points encompassing the grating. The distance between the two attachment points varies non-linearly with temperature over an operating temperature range of the device.  
           [0014]    In another aspect, an embodiment according to the invention includes a temperature compensating package having two attachment points configured for attachment to an optical waveguide. The operating temperature range of the device is divided into a plurality of segments. The distance between the attachment points varies linearly with temperature within each of the plurality of temperature range segments. The linear variations with temperature are different within each temperature range segment, such that the distance between the attachment points varies non-linearly across the operating temperature range of the device.  
           [0015]    In another aspect, an embodiment according to the invention includes a temperature compensating package having an asymmetric layered composite substrate. The asymmetric layered composite substrate is composed of two or more materials with different coefficients of thermal expansion arranged asymmetrically about a neutral axis of the substrate, causing the substrate to bend towards the optical waveguide when heated.  
           [0016]    In another aspect, an embodiment according to the invention includes a compression member attached to the optical waveguide. The compression member is positioned within a frame. The compression member and frame have different coefficients of thermal expansion, such that compression of the optical waveguide attached to the compression member varies non-linearly with temperature.  
           [0017]    In another aspect, an embodiment according to the invention includes an optical fiber equipped with a Bragg grating having a characteristic wavelength, λ, in the unstressed state that is about equal to  
           λ 0 [1+β( T−T   0 )+γ( T−T   0 ) 2 ] 
           [0018]    where λ 0  is the characteristic wavelength of the grating at reference temperature, T 0 , T is the applied temperature, β is the first-order thermo-optic optic coefficient of the fiber and γ is the second-order thermo-optic optic coefficient of the fiber; and a temperature compensating package attached to the fiber at two attachment points encompassing the grating, where the distance between the two attachment points, L g , varies non-linearly with temperature and is about equal to  
         L   g0          [     1   +       (       λ   1     -     λ   0       )         λ   0          (     1   -     P   e       )         +       (       α   f     -     β     (     1   -     P   e       )         )          (     T   -     T   0       )       -       γ     (     1   -     P   e       )              (     T   -     T   0       )     2         ]                           
 
           [0019]    where L g0  is the distance between the attachment points at the reference temperature, λ 1  is the wavelength of the Bragg grating at the reference temperature T 0  when attached to the package, α f  is the coefficient of thermal expansion of the fiber, and P e  is the strain optic coefficient of the fiber.  
           [0020]    In another aspect, an embodiment according to the invention includes a temperature compensating package having two attachment points configured for attachment to the optical fiber, wherein the distance between the attachment points varies linearly with temperature within each of at least two temperature ranges, and wherein the linear variation of the distance with temperature is different for each of the at least two temperature ranges to substantially compensate for non-linear temperature behavior of the optical fiber.  
           [0021]    In another aspect, an embodiment according to the invention includes an apparatus for temperature compensation of a region of an optical fiber with a frame having a first end and a second end; a longitudinal compression member for axially compressing the optical fiber, the compression member positioned within the frame and extending from the first end of the frame toward the second end of the frame, wherein the compression member has a coefficient of thermal expansion larger than a coefficient of thermal expansion of the frame.  
           [0022]    In another aspect, an embodiment according to the invention includes a method for thermal compensation of an optical waveguide grating comprising securing an optical waveguide equipped with an optical grating at two attachment points of a thermal compensation package; and varying the distance between the attachment points non-linearly with temperature over an operating temperature range. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0023]    [0023]FIG. 1 is one embodiment according to invention of an asymmetric layered composite substrate package for non-linear thermal compensation of optical waveguide gratings.  
         [0024]    [0024]FIG. 2 is one embodiment according to the invention of a support beam compression package for non-linear thermal compensation of optical waveguide gratings.  
         [0025]    [0025]FIG. 3 is another embodiment according to the invention of a support beam compression package for non-linear thermal compensation of optical waveguide gratings.  
         [0026]    [0026]FIG. 4 is another embodiment according to the invention of a support beam compression package for non-linear thermal compensation of optical waveguide gratings.  
         [0027]    [0027]FIG. 5 is another embodiment according to the invention of a support beam compression package for non-linear thermal compensation of optical waveguide gratings.  
         [0028]    [0028]FIG. 6 is an embodiment according to the invention of a non-linear retrofit device for converting linear thermal compensation packages to non-linear thermal compensation packages.  
         [0029]    [0029]FIG. 7A is an exemplary embodiment of a linear thermal compensation package.  
         [0030]    [0030]FIG. 7B is an illustration of the non-linear retrofit device of FIG. 6 incorporated into the linear thermal compensation device of FIG. 7A.  
         [0031]    [0031]FIG. 8 is one embodiment according to invention of a fiber composite substrate package for non-linear thermal compensation of optical waveguide gratings. 
     
    
     DETAILED DESCRIPTION  
       [0032]    In the following detailed description of the preferred embodiments, reference is made to the accompanying drawings, which form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced. It is to be understood that other embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present invention. The following detailed description, therefore, is not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims.  
         [0033]    FBG properties are not constant with temperature. Thus, the effective thermal expansion α effective  imposed on an FBG must not only be negative but must also change with temperature. In most applications, it is necessary for the effective CTE to decrease (become more negative) with increasing temperature. However, in other applications it is necessary for the effective CTE to increase with increasing temperature instead.  
         [0034]    Some embodiments of thermal compensation devices according to the present invention (referred to as continuous non-linear compensation devices) impart a continuously changing effective thermal expansion. The effective thermal expansion required to compensate a FBG with this approach can be estimated using the following relation:  
               α   effective     =       -     β     (     1   -     P   e       )         -         2      γ       (     1   -     P   e       )            (     T   -     T   0       )                 (   3   )                               
 
         [0035]    where β and γ are experimentally determined first and second order parameters describing the change in reflected wavelength of an unstrained FBG with temperature as follows:  
         Δλ=λ 0 [β( T−T   0 )+γ( T−T   0 ) 2 ]  (4)  
         [0036]    Additional higher order terms may also be added to equations (3) and (4) for even further accuracy. It should be noted that the coefficients β and γ are properties of the fiber and not the grating, while λ 0  is a characteristic of the grating.  
         [0037]    Experimental measurements of FBGs in a non-commercial, high numerical aperture germano-silicate photosensitive fiber (designated TF-19), manufactured by 3M Company, of Saint Paul, Minn., U.S.A., yield exemplary values of β and γ to be 6.61±0.18 ppm/° C. and 5.3±1.7 ppb/° C. 2 , respectively, for 18 mm long FBGs with room temperature reflected wavelengths written at 1555 nm (ppb indicates parts per billion or ×10 −9 ). The experimentally measured values are representative of most commercially available optical fibers in this wavelength range. The experimentally measured values mean that a compensating device based on this approach must impose effective thermal expansions on FBGs around −8.5 ppm/° C. at room temperature, and change at a rate of −13.6 ppb/° C. 2  with increasing temperature to be useful in compensating both linear and non-linear temperature sensitivities in FBGs written in this fiber.  
         [0038]    Embodiments of thermal compensation devices according to the present invention based on a continuous non-linear approach employ several different non-linear mechanical effects, such as changes in material properties with temperature, Hertzian contact, and/or geometric non-linearities.  
         [0039]    Other embodiments of thermal compensation devices according to the present invention (referred to as multi-linear compensation devices) impose constant effective thermal expansions on FBGs over incremental temperature ranges within the overall temperature range of the device, but change from one incremental range to another as temperature changes. An exemplary bi-linear device would impose an effective thermal expansion on the FBG that could be described with the following equation:  
               α   effective     =     {               -       β   1       (     1   -     P   e       )                       for                 T     ≤     T   a                     -       β   2       (     1   -     P   e       )                       for                 T     ≥     T   a                       (   5   )                               
 
         [0040]    where β 1  and β 2  are experimentally determined parameters describing the linear change in reflected wavelength above and below a particular temperature, T a  as follows:  
             λ   =     {                 λ   0          [     1   +       β   1          (     T   -     T   0       )         ]                     for                 T     ≤     T   a                       λ   0          [     1   +       β   2          (     T   -     T   0       )         ]                     for                 T     ≥     T   a                       (   6   )                               
 
         [0041]    Additional incremental temperature ranges may also be included to equations (5) and (6) for a more accurate multi-linear approach. It should be noted that the coefficients β 1  and β 2  are properties of the fiber and not the grating, while λ 0  is a characteristic of the grating.  
         [0042]    Experimental measurements of FBGs in a non-commercial, high numerical aperture germano-silicate photosensitive fiber (designated TF-19), manufactured by 3M Company, of Saint Paul, Minn., U.S.A., yield exemplary values of β 1 , β 2  and T 0  to be 6.26±0.24 ppm/° C., 6.94±0.21 ppm/° C., and 22±5° C., respectively, for 18 mm long FBGs with room temperature reflected wavelengths written at 1555 nm. The experimentally measured values are representative of most commercially available optical fibers in this wavelength range. The experimentally measured values mean that a bi-linear package must have an effective coefficient of thermal expansion of −8.0 ppm/° C. below 22° C. and −8.9 ppm/° C. above 22° C. to compensate these FBGs.  
         [0043]    Embodiments of thermal compensation devices according to the present invention based on a multi-linear approach can employ discontinuous, non-linear mechanical effects such as contact and buckling.  
         [0044]    In accordance with the present invention, the characteristic wavelength λ of a fiber grating can be described with respect to temperature and applied strain as follows:  
         λ=λ 0 [1+β( T−T   0 )+γ( T−T   0 ) 2 ]+λ 0 (1 −P   e )ε  (7) 
         [0045]    where:  
         [0046]    T 0  is the reference temperature;  
         [0047]    T is the applied temperature;  
         [0048]    ε is the applied strain;  
         [0049]    λ 0  is the characteristic wavelength measured at the reference temperature under zero stress;  
         [0050]    β is the 1st order thermo-optic optic coefficient of the unstressed wavelength versus temperature behavior;  
         [0051]    γ is the 2nd order thermo-optic optic coefficient of the unstressed wavelength versus temperature behavior; and  
         [0052]    P e  is the strain optic coefficient of the fiber.  
         [0053]    The coefficients β, γ and P e  are properties of the fiber. This analysis differs from most in that the second order term γ is included, and that the coefficients β and γ include both thermal expansion and refractive index effects on the wavelength shift.  
         [0054]    The applied strain is:  
             ɛ   =         L   g       L   g0       -   1   -       α   f          (     T   -     T   0       )                 (   8   )                               
 
         [0055]    where:  
         [0056]    L g0  is the unstressed grating length measured at the reference temperature;  
         [0057]    L g  is the stressed grating length measured at the applied temperature; and  
         [0058]    α f  is the coefficient of thermal expansion (CTE) of the fiber.  
         [0059]    To determine the length behavior needed to thermally compensate a fiber grating, equation (8) is substituted into equation (7) and solved for L g  as follows:  
               L   g     =       L   g0          [     1   +       (       λ   1     -     λ   0       )         λ   0          (     1   -     P   e       )         +       (       α   f     -     β     (     1   -     P   e       )         )          (     T   -     T   0       )       -       γ     (     1   -     P   e       )              (     T   -     T   0       )     2         ]               (   9   )                               
 
         [0060]    where λ 1  is the stressed wavelength of the grating at the reference temperature (i.e., the wavelength of the grating when attached to the thermal compensation package at the reference temperature).  
         [0061]    Asymmetric Layered Composite Substrate Package  
         [0062]    A simple non-linear thermal compensation device  50  can be made for an FBG comprising an optical fiber  52  equipped with a fiber Bragg grating (FBG)  54  by attaching the fiber  52  and FBG  54  to an asymmetric layered composite substrate  56  as shown in FIG. 1. The asymmetric layered composite substrate  56  is composed of two or more materials with different coefficients of thermal expansion arranged in an asymmetric manner about neutral axis  62  so as to cause the substrate  56  to bend towards the FBG  54  when heated. When this occurs the length L of the FBG  54  between the bonding points  58  decreases, thus providing an effective negative thermal expansion as required for thermal compensation of the FBG  54 . The posts  60  located between the fiber  52  and the asymmetric layered composite substrate  56  hold the fiber a distance above the substrate and serve to amplify the strain effect imposed by the device on the FBG  54 . As used herein, the neutral axis is the line or plane in a member under transverse pressure, at which the member is neither stretched nor compressed (i.e., where the longitudinal stress is zero).  
         [0063]    Under certain circumstances the effective thermal expansion imposed by the asymmetric layered composite substrate  56  on the FBG  54  changes with temperature to a degree that it can be useful for compensating the linear and non-linear changes in FBG reflected wavelengths with temperature.  
         [0064]    For an asymmetric layered composite substrate package with posts, the length of the FBG  54  between the posts  60  at any temperature will be:  
               L   g     =     2        (       1   κ     -   h     )          sin        (       1   2        κ                 L     )                 (   10   )                               
 
         [0065]    where:  
         [0066]    κ is the curvature of the bimetallic substrate (e.g., 1/radius of curvature);  
         [0067]    L is the length of the substrate as measured along the curved neutral axis of the substrate; and  
         [0068]    h is the distance between the fiber and the neutral axis  62  of the substrate at the attachment points.  
         [0069]    The parameters, κ, L and h will change with temperature as follows:  
                   L   =       L   0          [     1   +       α   L          (     T   -     T   0       )         ]                   h   =       h   0          [     1   +       α   h          (     T   -     T   0       )         ]                   κ   =         κ   0     +       f   t          (     T   -     T   0       )         =       κ   0     +     F        (     T   -     T   0       )                         (   11   )                               
 
         [0070]    where:  
         [0071]    L 0  is the substrate length measured at the reference temperature;  
         [0072]    h 0  is the fiber to neutral axis distance measured at the reference temperature;  
         [0073]    κ 0  is the substrate curvature measured at the reference temperature;  
         [0074]    α L  is the CTE of the substrate along the neutral axis;  
         [0075]    α h  is the effective CTE of the combined materials between the substrate neutral axis and fiber;  
         [0076]    t is the thickness of the substrate;  
         [0077]    ƒ is the change in substrate curvature with temperature, or “flexivity” of the substrate.  
         [0078]    In equation (11), the term  
       f   t                         
 
         [0079]    is replaced with F to simplify the analysis.  
         [0080]    Usually the material properties α L , α h  and ƒ are constant with temperature but in some cases ƒ may vary slightly with temperature over a desired operating range. This variation of ƒ has an impact on the thermal compensation package design.  
         [0081]    An asymmetric layered composite substrate thermal compensation package according to the invention is designed by first measuring the fiber properties and determining the required grating length. Next, for the grating length needed, the available bimetallic materials are determined. A combination of equations (9), (10) and (11) is used to determine the required values of h and t to thermally compensate the fiber.  
         [0082]    In some embodiments according to the invention, additional design limitations are put in place to ensure a reasonable manufacturing yield. Specifically, h is required to be greater than ½ t to ensure the fiber sits above the top surface of the bimetallic material. When using some bimetallic materials, it is possible for h to be less than ½ t. In this embodiment according to the invention, a groove is required in the bimetallic material substrate to accommodate the fiber (rather than securing the fiber to posts extending above the bimetallic material substrate).  
         [0083]    A more direct but less accurate calculation of thermal compensation package parameters may be determined by using the approximation:  
               sin        (   x   )       ≈     x   -       1   6          x   3                 (   12   )                               
 
         [0084]    in equation (10). Most analysis of bimetallic material substrates use the approximation sin(x)=x and thus do not recognize the nonlinear capabilities of this device. Substituting equation (12) into equation (10):  
               L   g     =       L        (     1   -     κ                 h       )            (     1   -       1   24          κ   2          L   2         )               (   13   )                               
 
         [0085]    Setting κ 0 =0 (e.g., the reference temperature is the temperature at which the bimetallic substrate is flat) and substituting equation (11) directly into equation (13):  
               L   g     =       L   0     [     1   +       (       α   L     +       h   0        F       )          (     T   -     T   0       )       -       (         h   0          F        (       α   L     +     α   h       )         +       1   24          L   0   2          F   2         )            (     T   -     T   0       )     2       +     O        [       (     T   -     T   0       )     3     ]                   (   14   )                               
 
         [0086]    where O[(T−T 0 ) 3 ] represents all of the terms containing (T−T 0 ) 3  and higher order. These terms will be small and can be neglected.  
         [0087]    Setting equation (14) for the thermal compensation package equal to equation (9) for the fiber, and grouping all terms with respect to (T−T 0 ) i  to separate out the different package parameters:  
                     L   0     =       L   g0          [     1   +       (       λ   1     -     λ   0       )         λ   0          (     1   -     P   e       )           ]                       L   0          (       α   L     +       h   0        F       )       =       L   g0          (       α   f     -     β     (     1   -     P   e       )         )                       L   0          [         h   0          F        (       α   L     +     α   h       )         +       1   24          L   0   2          F   2         ]       =       L   g0          γ     (     1   -     P   e       )                       (   15   )                               
 
         [0088]    Solving for L 0 , h 0  and F:  
                                  L   0     =       L   g0          [     1   +       (       λ   1     -     λ   0       )         λ   0          (     1   -     P   e       )           ]                                  F   =       f   t     =         24     L   0   2            [           L   g0       L   0            γ     (     1   -     P   e       )         +       (       α   L     +     α   h       )          (           L   g0       L   0            (       α   f     -     β     (     1   -     P   e       )         )       -     α   L       )         ]                                        h   0     =       1   F          [       α   L     -         L   g0       L   0            (       α   f     -     β     (     1   -     P   e       )         )         ]                       (   16   )                               
 
         [0089]    The assumptions used to arrive at equations (16) are: 1) the curvature, κ, is zero at the reference temperature T 0 ; and 2) all the material properties are constant with respect to temperature.  
         [0090]    Support Beam Compression Package  
         [0091]    Another exemplary embodiment of a non-linear thermal compensation device  100  is shown in FIG. 2. This embodiment provides a bilinear FBG thermal compensation. The thermal compensation device  100  consists of a slender or small diameter support beam  102  and a larger diameter plunger  104  fitted inside a rigid frame  106 . The plunger  104  is made from a material with a high coefficient of thermal expansion (CTE) while the frame  106  is made from a material with a low CTE. In one embodiment according to the invention, the support beam  102  may be made out of materials with a range of CTEs equal to or less than the CTE of the plunger  104  material. However, lower CTE materials are preferred. The diameter of the support beam  102  is of sufficient diameter and rigidity to prevent buckling under compressive axial loading.  
         [0092]    When the thermal compensation package is heated, the support beam  102  and plunger  104  expand at a greater rate than the frame  106  and eventually start pushing on the ends  108 ,  110  of the frame  106 . As the support beam  102  and plunger  104  push on the frame  106 , an axial compressive force is generated within the support beam  102  and plunger  104 . The average compressive forces in the support beam  102  and plunger  104  are equal. However, the smaller diameter of the support beam  102  relative to the diameter of the plunger  104  produces a higher compressive stress (force per unit area) in the support beam  102  than in the plunger  104 . The higher compressive stress translates into a higher compressive strain in the support beam  102 . If the compressive strain is large enough, the compressive strain will overcome the thermal expansion of the support beam  102 , thus forcing the support beam  102  to become shorter as the temperature increases. If an FBG  54  is mounted on the support beam  102 , an effective negative CTE is imposed on the FBG  54 . If the frame  106  and plunger  104  are infinitely rigid compared to the support beam  102 , then the effective thermal expansion imposed on the support beam  102  can be estimated using the following equation:  
               α   effective     =       α   fr     +         L   p       L   s            (       α   fr     -     α   p       )                 (   17   )                               
 
         [0093]    where:  
         [0094]    L s  is the length of the support beam;  
         [0095]    L p  is the length of the plunger (Note: L p1  is the length when T≦T a  and L p2  is the length when T≧T a );  
         [0096]    α fr  is the CTE of the frame;  
         [0097]    α p  is the CTE of the plunger.  
         [0098]    The thermal compensation package  100  is made non-linear by creating a “stepped contact” interface  112  between the plunger  104  and frame  106 . At low temperatures, the plunger  104  and frame  106  come into contact at an intermediate step position  114  giving the plunger  104  an effective length of L plunger(low)  as shown in FIG. 2. As the package  100  is heated, the end  116  of the plunger  104  will continue to expand until it comes into contact with the end  110  of the frame  106 , increasing the length of the plunger  104  to L plunger(high) . As can be seen from equation (17), if the plunger  104  has a higher CTE than the frame  106 , then increasing the plunger  104  length will cause the effective CTE imposed on the support beam  102  to become more negative. The temperature at which the transition occurs will be dictated by the thickness of the gap  118  between the end  116  of the plunger  104  and end  110  of the frame  106 .  
         [0099]    The thermal compensation package of FIG. 2 can be assembled by cooling the support beam  102  and plunger  104  and/or heating the frame  106  until the support beam  102  and plunger  104  fit inside the frame  106 . The entire assembly will hold itself together at room temperature by the compressive forces created in the support beam  102  and plunger  104 . The temperature at which the device can be assembled is dictated by the difference in length between the frame  106  measured to the step  114  and the length of the support beam  102  plus the length of the plunger  106 . Tuning of the assembly and transition temperatures could be achieved by the appropriate positioning of a set screw (not shown) or other means of adjusting the gap  118  thickness. The effective CTE of the device  100  would be set by the relative lengths of the various components in the device. The FBG  54  can be mounted to the support beam  102  either at two points on either side of the grating  54  or continuously along the grating  54 . In one embodiment according to the invention, the support beam  102  has an axial bore  103  (illustrated by dashed lines in FIG. 2) in which the FBG  54  is secured. Such a configuration would be beneficial in protecting the FBG from the environment.  
         [0100]    Another embodiment of a non-linear thermal compensation package  150  according to the invention is shown in FIG. 3. The thermal compensation package  150  of FIG. 3 provides multi-linear thermal compensation by incorporating additional steps  114 ′,  114 ″ between the plunger  104 ′ and frame  106 ′, in contrast to the bilinear device of FIG. 2. The effective CTE of the thermal compensation package  150  of FIG. 3 is determined in the same manner described above with respect to the bilinear device  100  of FIG. 2.  
         [0101]    Yet another embodiment of a non-linear thermal compensation package  200  according to the invention is shown in FIG. 4. The thermal compensation package  200  of FIG. 4 provides a curved interface  212  between the end  216  of the plunger  104 ″ and the end  210  of frame  106 ″. The curved interface  212  allows a continuous length change, rather than a stepped length change as provided in the embodiments  100 ,  150  of FIGS. 2 and 3.  
         [0102]    Yet another embodiment of a non-linear thermal compensation package  250  according to the invention is shown in FIG. 5. The thermal compensation package  250  of FIG. 5 includes a curved end  212  on the plunger  104 ″, and a flat end  10  on the frame  106 ′″. This thermal compensation package  250  functions differently from the previously illustrated embodiments  100 ,  150 ,  200  in that the non-linearity results from the force-displacement relationship from Hertzian contact problems. As the plunger  104 ″ is pushed harder into the frame  106 , the contact area between the plunger  104 ″ and frame  106  increases and the contact stiffness increases. This means that increasingly larger forces are required to push the plunger  104 ″ further into the frame  106 , and the axial compressive force on the plunger  104 ″ and support beam  102  increases with temperature in a non-linear manner.  
         [0103]    Bilinear Retrofit Device  
         [0104]    Linear thermal compensation packages may be converted to bilinear thermal compensation packages by incorporation of a retrofit device, as shown in FIG. 6. The retrofit device  300  consists of a beam  302  that fits inside the cavity  304  of an outer frame  306 . The beam  302  and the frame  306  are composed of different materials with different coefficients of thermal expansion (CTE&#39;s). The length of the beam  302  is selected so that over part of the operating temperature range of the device  300 , the beam  302  is shorter than the length of the cavity  304 . As indicated at  308 , one end of the beam  302  is attached to one end of the cavity  304  inside the frame  306 . Depending upon the temperature, there is either a gap  312  between the free end  310  of the beam  302  and the end of the cavity  304  (as illustrated in solid lines in FIG. 6) or the free end  310  of the beam  302  and frame  306  are in compressive contact (as illustrated by dashed line  310 ′ in FIG. 6).  
         [0105]    When the free end  310  of the beam  302  and frame  306  are not in contact, the effective CTE of the frame  306  (and thus device  300 ) will be determined solely by the CTE of the frame material. When the free end  310  of the beam  302  and frame  306  are in contact, the device  300  will display a different effective CTE that is largely determined by the CTE&#39;s, moduli and cross-sectional areas of the frame  306  and beam  302 . The temperature at which contact between beam  302  and frame  306  first occurs is determined by the lengths and CTE&#39;s of the beam  302  and cavity  304 . If the beam  302  is composed of a material with a lower CTE than the CTE of the frame material, then the device  300  will exhibit a step decrease in its effective CTE from the frame material CTE to the composite CTE as the temperature drops through the contact temperature. If the beam  302  is composed of a material with a higher CTE than the frame material, then the device  300  will also exhibit a step decrease in its effective CTE, but from the composite CTE to the frame material CTE as the temperature drops through the contact temperature.  
         [0106]    The utility of the retrofit thermal compensation device  300  of FIG. 6 is demonstrated by incorporating the retrofit device  300  into an existing linear thermal compensation device  320 , as shown in FIG. 7A. The linear compensation device  320  of FIG. 7A includes a low CTE rod  322  equipped with two high CTE end caps  324  and high CTE cantilevers  326 . The end caps  324  and cantilevers  326  are designed so that cantilevers  326  extend back over the rod  322 . An FBG  54  is attached at bond points  328  near the ends of the two cantilevers  326  as shown in FIG. 7A. As the temperature of the package  320  is heated, the low CTE rod  322  increases in length by a small amount, while the high CTE end caps  324  and cantilevers  326  increase in length by a larger amount, thereby causing the distance between the two bond points  328  on the cantilevers  326  to decrease with increasing temperature.  
         [0107]    The effective CTE imposed on the FBG  54  is largely a function of the lengths and CTEs of the rod  322  and cantilevers  326  and the distance between bond points  328 .  
         [0108]    [0108]FIG. 7B illustrates the incorporation of the retrofit thermal compensation device  300  of FIG. 6 into the cantilever  326  of FIG. 7A, thereby converting the linear thermal compensation package  320  of FIG. 7A to a bilinear thermal compensation package  350 . In the embodiment illustrated in FIG. 7B, the retrofit device  300  consists of a high CTE outer component  306  with a low CTE inner component  302 . At temperatures above the contact temperature, T 0 , for the retrofit device, the cantilever  326  would have a CTE dictated by the CTE of the outer component  306 . At temperatures below the contact temperature, T 0 , the inner and outer components  302 ,  306  are in contact with each other, resulting in a lower effective CTE for the cantilever  326 . Thus, the effective CTE imposed on the FBG by the thermal compensation package  350  of FIG. 7B is larger at lower temperatures.  
         [0109]    Fiber Composite Material Package  
         [0110]    Another embodiment of a thermal compensation device according to the invention for use in a bilinear or continuous non-linear compensation approach is illustrated in FIG. 8. The device  370  of FIG. 8 includes an optical fiber  52  equipped with a Bragg grating  54  attached to a substrate  372  at attachment points  374 . Substrate  372  is comprised of a continuous fiber composite surrounded by an organic matrix. As one example, substrate  372  comprises a polymer fiber available under the name Spectra® (available from Honeywell, of Morristown, N.J., U.S.A.) in an epoxy matrix. Spectra® fiber has a CTE lower than the effective CTE typically required to thermally compensate FBGs. When the fiber is incorporated into an epoxy matrix, the CTE of the fiber/epoxy composite is raised to a value closer to what is required for FBG thermal compensation. Different types of fibers, such as carbon fiber, may optionally be added to the composite to further tune the CTE to the requirements of the FBG. If the tensile modulus of the matrix material drops rapidly (as often occurs near the glass transition temperature of epoxies), the properties of the fiber will dominate the properties of the composite along the direction parallel to the composite fiber axes, and the effective thermal expansion of the composite substrate  372  in the fiber axie direction will become lower with increasing temperature. The magnitude of the CTE change can be controlled by controlling the amount that the matrix modulus decreases with temperature and by controlling the glass transition temperature of the epoxy.  
         [0111]    Although specific embodiments have been illustrated and described herein, upon reading and understanding of this disclosure it will be appreciated by those of ordinary skill in the art that a wide variety of alternate and/or equivalent implementations and embodiments may be substituted for the specific embodiments shown and described without departing from the scope of the present invention. Those with skill in the optical, mechanical, electro-mechanical and opto-mechanical arts will readily appreciate that the present invention may be implemented in a very wide variety of embodiments. This application is intended to cover any adaptations or variations of the embodiments discussed herein.