Abstract:
A tunable optical waveguide is enclosed in an enclosure containing a controllably moveable region of fluid with a refractive index greater than the optical fiber such that at least a first. transmission property of the waveguide is modified when the region of fluid is moved. In a first embodiment, the optical device comprises a Bragg grating that is tuned by moving the fluid over the grating to vary the amplitude of desired wavelengths that are reflected back through the core of the fiber. In a second embodiment, the optical device comprises a long-period grating that is tuned by moving the fluid over the grating to vary the amplitude of desired wavelengths that are transferred into the cladding of the fiber and, as a result, to decrease the amplitude of those desired wavelengths that are transmitted through the core of the fiber.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates to optical waveguide devices and, in particular, to optical waveguides tunable by electrowetting actuation of fluids in proximity to those devices.  
         BACKGROUND OF THE INVENTION  
         [0002]    Optical fibers are useful for many applications in modern communications systems. A typical optical communications system comprises a transmitter of optical signals (e.g., a laser-based transmitter that generates a desirable wavelength of light, such as 1550 nm), a length of transmission optical fiber coupled to the source, and a receiver coupled to the fiber for receiving the signals. Optical fiber useful in such systems typically comprises a strand of wave-guiding glass with an inner core region and an outer cladding region that surrounds the core. As long as the refractive index of the core exceeds that of the cladding, a light beam can be guided along the length of the core by total internal reflection. One or more amplifying systems may be disposed along the fiber for amplifying the transmitted signal.  
           [0003]    Filters and attenuators, such as those comprising an optical fiber grating, are required in these systems to change the power levels and characteristics of various signals or portions of signals propagating through an optical fiber. An optical fiber grating typically comprises a length of fiber including a plurality of optical grating elements such as index of refraction perturbations, slits or grooves. These elements may or may not be substantially equally spaced. Illustrative examples of such gratings include Bragg gratings and long-period gratings.  
           [0004]    A fiber Bragg grating comprises a length of optical fiber including a plurality of perturbations in the index of refraction. These perturbations selectively reflect light of wavelength λ equal to twice the distance Λ′ between successive perturbations times the effective refractive index, i.e.:  
           λ R =2 n   eff-core Λ  (Equation 1)  
           [0005]    where λ R  is the vacuum wavelength and n eff-core  is the effective refractive index of the propagating mode. The remaining wavelengths pass through the grating essentially unimpeded. Bragg gratings have found use in a variety of applications including filtering, adding and dropping signal channels, stabilization of semiconductor lasers, reflection of fiber amplifier pump energy, and compensation for waveguide dispersion.  
           [0006]    A long period grating couples optical power between two copropagating modes with very low back reflections. It typically comprises a length of optical waveguide wherein the refractive index perturbations are spaced by a periodic distance Λ that is large compared to the wavelength λ of the transmitted light. In contrast with Bragg gratings, long-period gratings use a periodic distance Λ which is typically at least 10 times larger than the transmitted wavelength, i.e., !≧10λ. Typically Λ is in the range of 15-1500 micrometers, and the width of a perturbation is in the range of ⅕ Λ to ⅘ Λ. In some applications, such as chirped gratings, the spacing Λ can vary along the length of the grating. Long-period gratings are particularly useful in optical communication systems for equalizing amplifier gain at different wavelengths. See, for example, U.S. Pat. No. 5,430,817 issued to A. M. Vengsarkar on Jul. 4, 1995.  
           [0007]    Many potential applications require optical gratings wherein light propagation behavior through the grating is tunable. A tunable long period grating, for example, can provide dynamic gain compensation. On the other hand, a tunable Bragg grating can permit dynamic control over which wavelength will pass through the grating and which will be reflected or diverted. While this tunability is desired, light is confined mostly in the core region of an optical fiber and, therefore, the ability to externally effect propagation behavior of the light is significantly limited. With conventional fibers, one is essentially limited to the application of strain and/or temperature changes to the fiber to change the propagation behavior of light in the core. Alternatively, specially designed microstructured fibers have been developed whereby small quantities of fluid are pumped into channels disposed within the structure of the fiber itself. Such fibers are the subject of copending U.S. patent application Ser. No. 10/094093, entitled “Tunable Microfluidic Optical Fiber Devices And Systems,” which is hereby incorporated by reference herein. While prior tunable optical devices are acceptable for many uses, they tend to be limited in their effect on light propagation behavior and can be expensive to manufacture.  
           [0008]    As optical communications systems become more advanced, there is a growing need for new, cost-effective tunable optical devices and methods of using those devices for changing the propagation behavior of light signals through optical waveguides.  
         SUMMARY OF THE INVENTION  
         [0009]    A tunable optical waveguide device is enclosed in an enclosure containing a region of fluid with a refractive index different than the optical waveguide. The region of fluid is controllably moved within the enclosure to modify at least a first transmission property of the device in the region to which or from which the fluid is moved in order to variably attenuate the wavelengths of the signal transmitted through the waveguide. In a first embodiment, the optical waveguide device comprises an optical fiber long-period grating that is tuned by moving the fluid over the grating to vary the amplitude of desired wavelengths that are transferred into the cladding of the fiber and, as a result, to decrease the amplitude of those desired wavelengths that are transmitted through the core of the fiber. In a second embodiment, the optical waveguide device comprises an optical fiber Bragg grating that is tuned by moving the fluid over the grating to vary the amplitude of desired wavelengths that are reflected back through the core of the fiber. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWING  
       [0010]    [0010]FIG. 1A shows a conventional prior art fiber with a Bragg grating;  
         [0011]    [0011]FIG. 1B shows the fiber of FIG. 1A wherein a portion of the cladding corresponding to the Bragg grating has been etched away;  
         [0012]    [0012]FIG. 1C shows the fiber of FIG. 1B wherein a liquid is moved over the exposed core such that it overlaps with the core;  
         [0013]    [0013]FIG. 2 shows cross-section view of a prior art electro-wetting based liquid microlens;  
         [0014]    [0014]FIG. 3 shows a cross-section view of an optical device of the present invention wherein an optical fiber with a grating is disposed within a liquid filled enclosure;  
         [0015]    [0015]FIG. 4A shows the device of FIG. 2 wherein a fiber is contained within the liquid-filled enclosure;  
         [0016]    [0016]FIG. 4B shows the device of FIG. 4A wherein a the liquid is moved over a Bragg grating by varying the voltages on electrodes in proximity to the droplet;  
         [0017]    [0017]FIG. 5 shows a recirculating pump of one embodiment of the present invention wherein a liquid droplet is capable of being reversibly moved over a grating by varying the voltages on electrodes in proximity to the droplet;  
         [0018]    [0018]FIG. 6 shows an illustrative graph of the fiber transmission characteristics of the recirculating pump of FIG. 5;  
         [0019]    [0019]FIG. 7 shows the variation of signal amplitude for varying amounts of overlap of the liquid droplet of FIG. 5 with a ˜2 cm long fiber Bragg grating;  
         [0020]    [0020]FIG. 8 shows a recirculating pump of one embodiment of the present invention wherein a liquid droplet is capable of being reversibly moved over an etched fiber by varying the voltages on electrodes in proximity to the droplet;  
         [0021]    [0021]FIG. 9 shows an illustrative graph representing the attenuation of a transmitted signal that results from various amounts of overlap of the droplet of FIG. 8 with the long-period grating of FIG. 8;  
         [0022]    [0022]FIG. 10 shows an example of using the attenuation resulting from a long-period grating to equalize the output from an erbium doped fiber amplifier; and  
         [0023]    [0023]FIG. 11 shows another example of using the attenuation resulting from multiple long-period gratings to equalize the output from an erbium doped fiber amplifier. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0024]    As illustrated in FIGS. 1A, 1B, and  1 C, the inventors have discovered that tunable optical fiber devices may be created by moving a liquid over an active region of a fiber, such as a Bragg grating (or, alternatively, a long-period grating, a planar waveguide or other device). FIG. 1A shows a conventional prior art fiber  101  with core  103 , cladding  102  (with a refractive index greater than the refractive index of the core), and Bragg grating  104  having a constant period A, which is typically approximately 0.5 μm. Light  105  propagates through fiber  101  with an amplitude represented by curve  106 . When the light encounters the Bragg grating  104 , a specific wavelength of amplitude represented by curve  107  is reflected back through the fiber  101  in direction  113 . The reflected wavelength λ R  is defined in Equation 1 above where n core-eff  is the effective refractive index of the core of the fiber (which depends upon the refractive index of the core and the refractive index of the cladding) and Λ is the period of the grating.  
         [0025]    [0025]FIG. 1B shows the fiber  101  of FIG. 1A wherein a portion  110  of the cladding  102 , corresponding to the Bragg grating  104  has been etched away (i.e., is uncladded), exposing the core  103 . As before, light  105  with amplitude  106  propagates along fiber  101 . In this case, however, since the cladding  102  has been removed, the refractive index of the core  103  exceeds that of the cladding  102  and, as a result, a substantial portion of the light  105  of amplitude  106  traveling through the fiber  101  exits the core and propagates into the surrounding medium, as represented by arrows  111 .  
         [0026]    [0026]FIG. 1C illustrates the principles of the present invention and shows the fiber of FIG. 1B wherein a liquid  114  with a refractive index greater than the core  103  is moved over the exposed core such that it overlaps with the core. In this case, when the light  105  of amplitude  106  encounters the Bragg grating it remains in the core due to the higher refractive index of the liquid  114  relative to the core  103 . As such, wavelength λ R , determined by Equation 1, is reflected back through the core  103  in direction  113 . The amplitude of the reflected wavelength is directly proportional to the overlap L between the liquid  114  and the core  103  of the fiber. Therefore, by varying the overlap of the liquid  114  with the exposed core  103  and Bragg grating  104 , the amplitude of various wavelenghts propagating through the fiber  101  can be altered, or tuned. This same principle can be applied with equally advantageous results to long-period gratings, planar waveguides, and other optical devices.  
         [0027]    Tunable optical devices which operate in accordance with the principles of the present invention, as discussed above, can be advantageously made by using electrowetting principles. The resulting devices consume little power (e.g., &lt;1 milliwatt in some cases), are latchable in operation (i.e., the fluid remains in a given position when the power is turned off), are relatively inexpensive to produce, and are compatible with conventional optical fibers.  
         [0028]    Electrowetting principles (i.e., using electric fields to variably change the properties of a liquid-based device) have previously been used to change the focal length and position of liquid microlenses. Such electrowetting based microlenses are the subject of copending U.S. patent application Ser. No. 10/135973, entitled “Method and Apparatus for Aligning a Photo-Tunable Microlens” and copending U.S. patent application Ser. No. 10/1391 24, entitled “Method and Apparatus for Calibrating a Tunable Microlens,” both of which are hereby incorporated by reference herein. In their simplest form, electrowetting based microlenses use a transparent droplet of liquid to focus incoming light onto a desired focal spot.  
         [0029]    [0029]FIG. 2 shows one prior art embodiment of a simple liquid microlens  201 , described in the &#39;973 and &#39;124 U.S. patent applications referenced above, whereby the phenomenon of electrowetting may be used to reversibly change the contact angle θ between a droplet  202  of a conducting liquid (which may or may not be transparent) and a dielectric insulating layer  203  having a thickness “d” and a dielectric constant ε r . The contact angle θ between the droplet and the insulating layer is determined by interfacial surface tensions (also known as interfacial energy) “γ”, generally measured in milli-Newtons per meter (mN/m). As used herein, γ S−V  is the interfacial tenson between the insulating layer  203  and the air, gas or other liquid that surrounds the droplet, γ L−V  is the interfacial tension between the droplet  202  and the air, gas or other liquid that surrounds the droplet, and γ S−L  is the interfacial tension between the insulating layer  103  and the droplet  202 . The contact angle θ may is determined by the following relationship:  
               cos                 θ     =         γ     S   -   V       -     γ     S   -   L           γ     L   -   V                 (     Equation                 2     )                               
 
         [0030]    An electrode  204 , such as metal electrode is positioned below the dielectric layer  203  and is insulated from the droplet  202  by that layer. The droplet  202  may be, for example, a water droplet, and the dielectric insulating layer  203  may be, for example, a Teflon/Parylene surface.  
         [0031]    When no voltage difference is present between the droplet  202  and the electrode  204 , the droplet  202  maintains its shape defined by the volume of the droplet and contact angle θ 1 , where θ 1  is determined by the interfacial tensions γ as explained above. When a voltage V is applied to the electrode  204 , the voltage difference betweeen the electrode  204  and the droplet  202  causes the droplet to spread. The dashed line  205  illustrates that the droplet  202  spreads equally across the layer  203  from its central position relative to the electrode  204 . Specifically, the contact angle θ decreases from θ 1  to θ 2  when the voltage is applied between the electrode  204  and the droplet  202 . The voltage V necessary to achieve this spreading may range from several volts to several hundred volts. The amount of spreading, i.e., as determined by the difference between θ 1  and θ 2 , is a function of the applied voltage V. The contact angle θ 2  can be determined by the following relationship:  
               cos                     θ   2          (   V   )         =       cos                     θ   1          (     V   =   0     )         +           ɛ   o          ɛ   r         2      d                   γ     L   -   V                V   2                 (     Equation                 3     )                               
 
         [0032]    where θ 1  is the contact angle between the insulating layer  203  and the droplet  202  when no voltage is applied between the droplet  202  and electrode  204 ; γ L−V  is the droplet interfacial tension described above; ε r  is the dielectric constant of the insulating layer  203 ; and ε 0  is 8.85×10 −12  F/M—the permittivity of a vacuum.  
         [0033]    [0033]FIG. 3 shows an embodiment of a structure  301  in accordance with the principles of the present invention that relies on the electrowetting principles described above to move a droplet of conductive fluid  302  through an enclosure  309  that is, for example, a glass tube of circular cross section with  1  mm thick walls. It will be obvious to one skilled in the art that there are many other enclosures that will accomplish the same function such as, for example, a tube with a square or rectangular cross section or, alternatively, two rigid substrates disposed parallel to each other with no sidewalls. In contrast to FIG. 2, the embodiment of FIG. 3 uses a second rigid substrate on top of a conducting liquid droplet  302  to entirely constrain the movement of the droplet in all directions except for the x-direction. Droplet  302  is, for example, a droplet of aqueous sodium dichromate (Na 2 Cr 2 O 7 .2H 2 O), which is advantageous due to the fact that the concentration of sodium dichromate within the solution may be varied (tuned) in order to achieve a refractive index approximately that of a traditional optical fiber cladding. One skilled in the art will recognize that there are equally advantageous fluids that may be used with equally advantageous refractive indices. A low viscosity, low surface energy lubricating liquid  312  (such as, for example a polydimethylsiloxane, DMS-TOO, manufactured by Gelest, Inc.) surrounds the droplet of conducting liquid to facilitate movement of the droplet. This liquid  312  is immiscible with the aqueous sodium dichromate droplet. A dielectric insulating layer  306  is disposed on a first surface of enclosure  309  and serves to separate two electrodes,  304  and  305  respectively, from the surface of enclosure  309 . The dielectric layer is, for example, a 6 μm thick layer of polyimide. Electrodes  304  and  305  are separated from each other by a dielectric spacer  311  (such as, e.g., a spacer made from Teflon or, alternatively, simply a gap between the electrodes). A third unpatterned ground electrode  308  is disposed on another portion of the outer surface of enclosure  309  such that it is not in contact with either electrodes  304  or  305 . The inner surface of the portion of enclosure  309  corresponding to dielectric layer  306  may be coated with a thin film of low surface energy fluoropolymer (such as, e.g., a˜2 μm thick layer of Cytop obtained from Asahi Glass). In addition, the inner surface of the portion of enclosure  309  corresponding to electrode  308  may be coated with, for example, a ˜50 nm thick layer of this fluoropolymer, which is thin enough that it does not provide electrical isolation.  
         [0034]    Electrowetting principles, such as those above, are used to reversibly change the contact angle θ between the liquid and the surface of enclosure  309 . The contact angle θ between the droplet and the insulating layer is, once again, determined by interfacial surface tensions and can be calculated by referring to Equation 2. When no voltage difference is present between the droplet  302  and the electrode  305 , the droplet  302  maintains its position within the enclosure  309  with contact angle θ 1 =θ 2  where θ 1  is determined by the interfacial tensions γ as explained above. When a voltage V is applied to the electrode  305 , the voltage difference between the electrode  305  and the droplet  302  causes the droplet to attempt to spread, as in the case represented by FIG. 2. Specifically, the contact angle where boundary  303 A meets the surface of enclosure  309  increases from θ 1  to θ 2  when the voltage is applied between the electrode  305  and the droplet  302 . The voltage V necessary to achieve this change may range from several volts to several hundred volts. The amount of movement, i.e., as determined by the difference between θ 1  and θ 2 , is a function of the applied voltage V. The contact angle θ 2  can be determined by, once again, referring to Equation 3, where θ 1  is the contact angle between the surface of enclosure  309  and the droplet  302  when no voltage is applied between the droplet  302  and electrode  305 ; γ L−V  is the droplet interfacial tension; ε r  is the dielectric constant of the insulating layer  306 ; and ε 0  is 8.85×10 −12  F/M—the permittivity of a vacuum. Since the droplet of FIG. 3 is constrained in its movement in all directions except the x-direction, a difference in contact angle caused by the applied voltage V leads to a force imbalance between the opposite sides  303 A and  303 B of the fluid droplet. As a result, the fluid droplet moves in direction  310  toward the side of the droplet under higher applied voltage  
         [0035]    [0035]FIGS. 4A and 4B show a schematic cross section of a structure  401  (such as a glass tube or other suitable structure) that controls fluid motion via electrowetting principles as described above. In this embodiment, referring to FIG. 4A, an optical fiber  403  is disposed within the structure  401  in a way such that the movement of a droplet of conducting liquid (such as an aqueous solution of sodium dichromate)  402  varies the optical properties of the fiber  403 . The application of a voltage bias between the two underlying electrodes  404  and  405 , respectfully, and the droplet  402  leads to a contact angle change that drives the droplet of conducting fluid  402  in direction  410  into increased overlap with the electrode  405  with a higher voltage. Referring to FIG. 4B, the resulting overlap of the fluid with a predefined “active” section  406  of fiber  403 , such as, for example, a Bragg grating or a long-period grating, alters the fiber&#39;s transmission properties, as described below. The diameter of fiber  403  is small compared to the spacer  411  thickness and fluid channel width, and the contact of the fiber with the fluid does not significantly change the relevant flow behaviors of the conducting liquid.  
         [0036]    [0036]FIG. 5 shows a cross-sectional view of one embodiment of a recirculating pump  501  in accordance with the principles of the present invention as described above. A droplet of conductive fluid  502  (e.g., aqueous sodium dichromate) is constrained to a recirculating channel  512 . The oval part of the channel  512  is completely filled with fluid of which a small segment is the droplet of conducting liquid  502  and the remainder is lubricant  509  (of, e.g., polydimethylsiloxane), as described above. An optical fiber  503  with an active region  506  (for example a Bragg grating) is positioned within a part of the channel  512 . The optical fiber  503  is, illustratively, a conventional single mode fiber for 1.5 micrometer wavelengths with, for example, a core diameter of ˜8 micrometers, a cladding diameter ˜125 micrometers, and a refractive index ratio εn=(n core −n clad )/n core ˜0.4%. Electrodes  504 ,  505  and  508  are patterned so that there is no voltage across electrodes  504  and  508  (and hence there is no voltage across the droplet of conducting liquid). When a voltage of V±0 is passed across electrode  505 , the motion of the conductive droplet  502  in direction  510  from electrode  504  to electrode  505  leads to overlap (represented by cross-hatched area  513 ) with the active fiber segment  506 . The recirculating geometry of the channel  512  ensures that the motion of the droplet of conducting liquid  502  does not lead to any resistive back-pressure. The velocity of the droplet is defined by the relationship:  
               v   Liquid     ∝         ɛ   o          ɛ   r          DV   2         η                 d                 L               (     Equation                 4     )                               
 
         [0037]    where η is the viscosity of the conducting fluid, D is the channel cross-sectional dimension, and L is the length of the “racetrack” segment over which the droplet of conducting liquid moves.  
         [0038]    [0038]FIG. 6 shows an illustrative graph  601  of the fiber transmission characteristics of the recirculating pump of FIG. 5 wherein the active region  506  of the optical fiber  503  is a ˜2 cm long fiber Bragg grating. Plot  602  represents the transmission of different wavelengths through the fiber when air is the medium surrounding the grating. In contrast, plot  603  shows the transmission of those same wavelengths when a conducting droplet of liquid (e.g., aqueous sodium dichromate) entirely overlaps the grating. A fiber Bragg grating exhibits mode resonance in the cladding and, therefore, the transmitted amplitude of certain wavelengths where such resonance occurs is significantly reduced. These reductions in signal amplitude are represented by the resonance “spikes,” such as spikes  607  of plot  602 . However, the transmission characteristics of the fiber are significantly altered by varying the index of refraction of the surrounding medium. As such, as shown in plot  603  relative to plot  602 , the cladding mode loss resonances, represented by the spikes  607  in plot  602 , can be significantly suppressed when the droplet of conducting fluid  502  in FIG. 5, as opposed to air, is the medium surrounding the Bragg grating  506 . As a result, the transmission amplitude losses shown in plot  602  when air surrounds the grating are suppressed when the droplet of fluid  502  surrounds the grating.  
         [0039]    [0039]FIG. 7 shows the variation of signal amplitude for varying amounts of overlap of an aqueous sodium dichromate liquid droplet with a ˜2 cm long fiber Bragg grating. Since the refractive index of refraction of the sodium dichromate solution is tuned to be approximately equivalent to that of a silica cladding, this overlap effectively shortens the length of the Bragg grating. Plot  707  shows a close-up view of area  604  in FIG. 6 and, in particular, of the resonance spike  605  in FIG. 6 that results when air is the medium surrounding the Bragg grating. Plots  701  through  706  in FIG. 7 show the resonance spikes that result for varying amounts of overlap of the liquid droplet with the grating, with plot  706  being minimal overlap and plot  701  representing the case of full overlap. Plot  701  corresponds to the portion  606  (in FIG. 6) of plot  603  that lies within area  604 . These plots show that the signal amplitude for a particular signal wavelength passing through a Bragg grating can be variably tuned, for example, to variably filter amplitudes of certain wavelengths. While the filtering effect represented by FIG. 7 is small in terms of absolute attenuation adjustment (˜0.5 dBm in the graph in FIG. 7), this limitation is due only to the inefficient cladding mode excitation obtained from the Bragg grating. Electrowetting-actuated tuning can be identically applied to long-period gratings to achieve filter tuning over larger dynamic ranges.  
         [0040]    [0040]FIG. 8 shows an illustrative recirulating pump with a droplet  802  of conductive fluid (e.g., a droplet of aqueous sodium dichromate having a refractive index exceeding that of fiber  803 ) that is constrained to a recirculating channel  812 . Once again, similar to the pump of FIG. 5, the oval part of the channel  812  is completely filled with fluid of which a small segment is the droplet  802  of conducting liquid, and the remainder is lubricant (of, e.g., polydimethylsiloxane), as described above. Optical fiber  803  having an active region  806  is positioned within a part of the channel  812 . In this case, however, in contrast to the fiber of FIG. 5, the region  806  of fiber  803  is etched with hydrofluoric acid to a diameter of ˜15 micrometers over a 5 mm length. As the fluid droplet  802  moves in direction  810  to position  813  and, thus, overlaps with the etched region  806  of the fiber, it causes specific wavelengths of light, dependent upon the period of the grating, to irreversibly couple out of the core. The strength of the attenuation that is associated with this coupling is directly proportional to the extent of overlap of the fluid droplet  802  with the etched region  806  of the fiber and can achieve a 40 dBm or greater reduction in the transmitted amplitude across a wide wavelength spectrum.  
         [0041]    [0041]FIG. 9 is an illustrative graph  901  representing various amounts of overlap of the droplet  802  in FIG. 8 with the active region  806  of fiber  803  in FIG. 8. Line  902  shows the amplitude of wavelengths between 1535 and 1560 nanometers transmitted through the fiber when there is no overlap between the droplet  802  in FIG. 8 and the etched fiber segment  806 . While line  902  shows an approximate 2-3 dBm loss, even though the droplet does not overlap with the etched segment, this loss can be largely attributed to the connections used in connecting the fiber  803  in FIG. 8 to the light source and/or to other components (e.g., a spectrum analyzer). One skilled in the art will recognize that the use of low loss fusion fiber splices can reduce insertion losses to &lt;0.1 dB. Lines  903 ,  904 ,  905  and  906  represent respective increases in the overlap of the fluid droplet  802  with region  806  in FIG. 8 until, as represented by line  906 , an overlap of approximately 2 mm is obtained between the droplet  802  and region  806  in FIG. 8. Thus, line  906  shows that a greater than 40 dBm reduction in transmitted amplitude over a broad wavelength range may be achieved by increasing the overlap of the droplet with the active region of the fiber.  
         [0042]    [0042]FIGS. 10 and 11 represent the transmission characteristics of one potential use of the tunable fiber devices described herein in photonic systems, exemplarily a dynamic gain equalizer for an erbium doped fiber amplifier (EDFA). One skilled in the art will recognize that there are many other potential uses of these devices. Referring to FIG. 10, graph  1001  shows a simple representative gain profile  1004  of a particular EDFA as a function of wavelength. As is typical, profile  1004  shows a relatively narrow peak  1005  about a particular wavelength. One skilled in the art will recognize that it is often desirable to have an EDFA profile, such as profile  1006  in graph  1003 , with a relatively constant peak over a broader range of wavelengths. Graph  1002  represents a tunable fiber device (such as the aforementioned device combining the etched fiber  101  of FIGS. 1B and 1C with the pump  501  of FIG. 5) where the grating is a long-period grating embodying the above described principles. The shape of the gain (attenuation) profile  1007  exhibits a maximum attenuation profile at peak  1008 . Transmitting the signal from the EDFA with gain profile  1004  through the fiber and the long-period grating with attenuation profile  1007 , results in profile  1006  with a relatively broad, constant amplitude over a relatively wide range of wavelengths.  
         [0043]    While FIG. 10 shows a simple example of altering the gain profile output from an EDFA, in real-world applications, the gain profile of such an amplifier is more complex and, thus, it is usually not possible to use one grating to achieve the desired gain profile. Thus, FIG. 11 shows a representative graph  1101  illustrating how a more complex signal profile from an EDFA may be attenuated to provide the broader, constant gain profile represented by profile  1003  in FIG. 10. Specifically, a relatively complex attenuation profile  1105  can be achieved by incorporating multiple tunable long-period gratings into an equalizer. Lines  1102 ,  1103  and  1104  each represent individual attenuation profiles of individual tunable gratings that, when used in conjunction with one another, produce the overall attenuation profile  1105 . Any number of such gratings can be used to create attenuation profiles of varying complexity to achieve the desired EDFA gain profile.  
         [0044]    The foregoing merely illustrates the principles of the invention. It will thus be appreciated that those skilled in the art will be able to devise various arrangements which, although not explicitly described or shown herein, embody the principles of the invention and are within its spirit and scope. Furthermore, all examples and conditional language recited herein are intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting aspects and embodiments of the invention, as well as specific examples thereof, are intended to encompass functional equivalents thereof.