Abstract:
The present disclosure relates to an optical cavity, comprising a first non-concave reflector positioned at a first end of the optical cavity and a second non-concave reflector positioned at a second end of the optical cavity that receives and reflects light reflected from the first non-concave reflector. The first non-concave reflector is configured to focus light that reflects off of the reflector back upon itself to avoid diffraction losses from the optical cavity. In one embodiment of the invention, the first non-concave reflector includes a layer of material that has a thickness that vanes as a function of radial distance out from an axial center of the layer. In another embodiment of the invention, the first non-concave reflector includes a layer of material that has an index of refraction that varies as a function of radial distance out from an axial center of the layer.

Description:
FIELD OF THE INVENTION  
         [0001]    The present disclosure relates to optical cavities for optical devices. More particularly, the disclosure relates to optical cavities for semiconductor and/or dielectric optical devices incorporating a focusing reflector.  
         BACKGROUND OF THE INVENTION  
         [0002]    Semiconductor fabrication techniques have enabled the construction of miniaturized optical devices. Two examples of such devices are semiconductor lasers, e.g., vertical cavity surface emitting lasers (VCSELs), and semiconductor optical filters. Through these techniques, optical devices can be constructed having dimensions on the order of only a few microns. Applications for such devices are many and include optical communications as well as the construction of optical circuits.  
           [0003]    Semiconductor lasers and filters comprise optical cavities through which light passes before being emitted from the devices. Such optical cavities normally include highly reflective, flat mirrors positioned at opposed ends of the cavities that reflect light back and forth within the cavity. The cavities often include an air gap positioned between the mirrors and, in the case of semiconductor lasers, a gain medium that increases the intensity of the light.  
           [0004]    In early designs, semiconductor lasers and filters were only capable of emitting fixed frequencies of optical radiation. More recent semiconductor lasers and filters have been constructed with displaceable mirrors to provide for frequency tuning. Displacement of a mirror at an end of an optical cavity changes the relative spacing of the mirrors and therefore the length of the cavity. As is known in the art, adjustment of the cavity length alters the frequency at which the laser or filter emits radiation.  
           [0005]    Optical cavities formed with flat mirrors present significant disadvantages. For instance, flat mirror optical cavities are highly susceptible to losses due to misalignment of the mirrors. This misalignment can be magnified when one or both of the mirrors is displaced during tuning. In addition, even where the mirrors are aligned correctly, diffraction losses can occur. To reduce such losses, recent semiconductor lasers and filters have been constructed with a concave, semispherical mirror at one end of the optical cavity. With such a configuration, light is reflected back on itself within the device cavity to prevent the light from escaping.  
           [0006]    [0006]FIGS. 1 and 2 illustrate an example prior art semiconductor laser  100  and filter  200 , respectively. As indicated in FIG. 1, the semiconductor laser  100  comprises an optical cavity  102 . At one end of the cavity  102  is a first mirror  104  and at the other end of the cavity is a second mirror  106 . Below the second mirror  106  is a substrate  108  constructed of a semiconductor material. Formed on the substrate  108  is a first current injection layer  110  that is used to provide current to the laser  100  during operation. Disposed within the optical cavity  102  is an active region  112  that is responsible for generating the light that is emitted out of the laser  100 . In contact with the active region  112  is a second current injection layer  114  that, like the first current injection layer  110 , is used to provide current to the laser  100 . Formed on top of the second current injection layer  114  are support posts  116  that, together with support tethers  118 , suspend the first mirror  104  above the active region  112 . Normally formed on the support tethers  118  are tuning electrodes  120  that are used to deliver voltage to the first mirror  104  that displaces it when the laser  100  is tuned. As is evident from FIG. 1, the first mirror  104  is arranged in a concave, semispherical orientation such that light incident on the first mirror is focused inwardly on itself to prevent diffraction losses.  
           [0007]    [0007]FIG. 2 illustrates the semiconductor filter  200 . As is apparent from this figure, the semiconductor filter  200  is similar in construction to the semiconductor laser  100  shown in FIG. 1. Accordingly, the filter  200  comprises an optical cavity  202  that is defined by a first mirror  204  and a second mirror  206 . In addition, the semiconductor filter  200  includes a substrate  208 , first tuning electrode  210 , support posts  212 , support tethers  214 , and second tuning electrodes  216 . Accordingly, the semiconductor filter  200  primarily differs from the semiconductor laser  100  of FIG. 1 in the omission of the active region  112 .  
           [0008]    Although capable of providing for reduced losses, optical cavities having a concave, semispherical mirror are difficult to manufacture. As is known in the art, it is difficult to form a precise concave surface on a very small scale (e.g., 10 μm in diameter) through present semiconductor fabrication techniques. Accordingly, it can be appreciated that it would be desirable to have a tunable, low-loss optical cavity for semiconductor lasers and filters that does not require a concave, semispherical mirror.  
         SUMMARY OF THE INVENTION  
         [0009]    The present disclosure relates to an optical cavity, comprising a first non-concave reflector positioned at a first end of the optical cavity and a second non-concave reflector positioned at a second end of the optical cavity that receives and reflects light reflected from the first non-concave reflector. The first non-concave reflector is configured to focus light that reflects off of the reflector back upon itself to avoid diffraction losses from the optical cavity.  
           [0010]    In one embodiment of the invention, the first non-concave reflector includes a layer of material that has a thickness that varies as a function of radial distance out from an axial center of the layer. By way of example, the outer layer can include a substantially convex, semispherical outer surface and a substantially planar inner surface.  
           [0011]    In another embodiment of the invention, the first non-concave reflector includes a layer of material that has an index of refraction that varies as a function of radial distance out from an axial center of the layer.  
           [0012]    The features and advantages of the invention will become apparent upon reading the following specification, when taken in conjunction with the accompanying drawings.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0013]    The invention can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present invention.  
         [0014]    [0014]FIG. 1 is a schematic of a prior art semiconductor laser.  
         [0015]    [0015]FIG. 2 is a schematic of a prior art semiconductor filter.  
         [0016]    [0016]FIG. 3 is a schematic of a prior art optical cavity.  
         [0017]    [0017]FIG. 4 is a schematic of an optical cavity incorporating a focusing lens.  
         [0018]    [0018]FIG. 5 is a schematic of a first optical cavity of the invention.  
         [0019]    [0019]FIG. 6 is a graph plotting phase delay versus outer layer thickness.  
         [0020]    [0020]FIG. 7 is a schematic of a laser that incorporates the optical cavity shown in FIG.  
         [0021]    [0021]FIG. 8 is a schematic of a filter that incorporates the optical cavity shown in FIG.  
         [0022]    [0022]FIG. 9 is a schematic of a second optical cavity of the invention.  
         [0023]    [0023]FIG. 10 is a graph plotting refractive index as a function of outer layer radius.  
         [0024]    [0024]FIG. 11 is a schematic of a laser that incorporates the optical cavity shown in FIG. 9.  
         [0025]    [0025]FIG. 12 is a schematic of a filter that incorporates the optical cavity shown in FIG. 9.  
     
    
     DETAILED DESCRIPTION  
       [0026]    Referring now in more detail to the drawings, in which like numerals indicate corresponding parts throughout the several views, FIG. 3 provides a schematic representation of a prior art optical cavity  300  that incorporates a concave, semispherical mirror  302 . As indicated in this figure, the mirror  302  is centered about an axis of symmetry  304  and faces a planar mirror  306  at the other end of the cavity  300 . The concave, semispherical mirror  302  has a radius of curvature, σ. Distances outward from the axis of symmetry  304  to points on the surface of the concave, semispherical mirror  302  are represented by the distance, ρ.  
         [0027]    As is known in the art, the arrangement shown in FIG. 3 provides a focusing effect such that a beam of light  308  can travel back and forth between the mirrors  302 ,  306  without a significant portion of the light being lost through diffraction. In particular, the provision of a concave, semispherical mirror  302  counteracts the natural tendency for a light beam to continuously expand as it travels. The optical cavity  300 , the focusing power of the mirror  302 , the separation of the mirrors  302  and  306 , and the beam diameter can each be selected so that little light leaks out past the edges of the mirrors as the light travels back and forth within the cavity  300 .  
         [0028]    Due to the difficulty associated with the construction of small scale concave mirrors identified above, alternative means for focusing light between two mirrors are needed. FIG. 4 illustrates one such alternative. As indicated in this figure, an optical cavity  400  can be constructed with first and second planar mirrors  402  and  404 . To focus the light beam  406 , a lens  408  (e.g., a ground and polished glass lens) can be positioned in the cavity  400  adjacent one of the mirrors (e.g., mirror  402 ). In such an arrangement, the lens  408  comprises a relatively flat, positive lens capable of focusing light back on itself.  
         [0029]    Although theoretically possible to construct an optical cavity  400  as that shown in FIG. 4, it would be impractical to do so. First, the lens  408  must be produced with very high precision and would need to be supported within the cavity  400  in a very precise manner. Such precision requires fabrication and mechanical complexity that could render the design impractical for repeatable production. In addition, the lens  408  would most likely need an antireflection coating on both its top and bottom surfaces to reduce undesired reflections. Inclusion of such antireflection coatings would degrade the performance of the optical cavity  400  by increasing the length of the cavity. As is known in the art, the best performance is normally achieved when the length of the optical cavity is kept very small, for instance, on the order of several light wavelengths. Accordingly, it would be desirable to obtain the focusing effect provided by a lens without actually using a lens within the optical cavity.  
         [0030]    [0030]FIG. 5 illustrates a first optical cavity  500  of the invention. As is illustrated in this figure, the optical cavity  500  includes a first reflector  502  and a second reflector  504  that are positioned at opposite ends of the cavity. Each of the reflectors  502 ,  504  is normally constructed as a distributed Bragg reflector (DBR) comprising a plurality of semi-conductor and/or dielectric layers  506  in a stacked configuration. Although the reflectors  502 ,  504  could alternatively be constructed of known metal materials, semiconductor and/or dielectric materials are preferred in that reflectors can be made with greater precision when constructed of these materials, especially where the scale of the reflectors is very small. Typically, each reflector  502 ,  504  comprises alternating semiconductor or dielectric materials having different indices of refraction. The difference in the refraction indices gives rise to partial reflection of light at each layer interface  508 . Although the reflection from each interface  508  is relatively small, a total reflectivity of greater than 99% can be achieved with this alternating, stacked configuration. For maximum reflectivity, each layer  506  has a wave thickness equal to λ/4n (i.e., quarter wave optical thickness) where λ is the wavelength of the light and n is the refractive index of the material.  
         [0031]    As is indicated in FIG. 5, the semiconductor or dielectric layers  506  can also alternate between relatively thick layers  510  and relatively thin layers  512 . By way of example, the relatively thick layers  510  can comprise silicon dioxide (SiO 2 ) and the relatively thin layers can comprise titanium dioxide (TiO 2 ). Moreover, although the layers  506  are shown and described herein as being relatively thick and thin, each normally is near quarter wave optical thickness due to their differences in index of refraction. Although a specific number of layers  506  is shown for each of the reflectors  502 ,  504  it is to be understood that alternative configurations are feasible.  
         [0032]    The first reflector  502  includes a convex outer layer  514  that comprises a convex, semispherical surface  516 . Accordingly, the first reflector  502  can be designated a convex reflector. As will be appreciated by persons having ordinary skill in the art, the convex, semispherical shape of the surface  516  provides a focusing effect similar to that of the lens  408  shown in FIG. 4 and to that of the concave, semispherical mirror  302  shown in FIG. 3. In particular, the convex, semispherical shape introduces a reflection delay that is radially symmetric from the center of the reflector  502 . This delay creates a focusing effect that reflects light  518  back on itself to reduce diffraction losses.  
         [0033]    To achieve the desired focusing effect, the convex outer layer  514  can be constructed with a particular thickness, t, that varies as a function of a distance, ρ, from the axis of symmetry  520  of the first reflector  502 . This thickness can be determined through normal experimentation by persons having ordinary skill in the art. Alternatively, this thickness can be estimated by analogy to existing optical cavities that use concave, semispherical mirrors. One concave arrangement that has been shown to be effective is that proposed by Vakhshoori, et al. in an article entitled “Microelectromechanical Tunable Filter with Stable Path Symmetric Cavity,” which appeared in  Electronics Letters  on May 27, 1999. In this article, Vakhshoori, et al. describe a single mode, 1550 nanometer (nm), vertical cavity surface emitting laser (VCSEL) having a 50 nm tuning range. The VCSEL described in the article comprises a concave, semispherical mirror having a radius of curvature, σ, of 300 μm.  
         [0034]    The thickness, t, of the convex outer layer  514  can be chosen to emulate a concave, semispherical mirror such as that of the Vakhshoori, et al. VCSEL. In particular, the thickness, t, of the layer  514  can be selected to provide a phase delay, Δφ, representative of the delay in phase between two light rays L 0  and L 1  reflected off of the first reflector  502  and separated by a distance, ρ(see FIG. 5) that is equal to the phase delay, Δφ, between two light rays L 0  and L 1  reflected off of the first mirror  302  and separated by the same distance, ρ(see FIG. 3). The phase delay, Δφ, for the concave arrangement (i.e., FIG. 3) is given by  
         Δφ=− kΔL   [Equation 1] 
         [0035]    where k is the propagation constant equal to 2π/λ, ΔL is the difference in the lengths L 0  and L 1  traveled by a light ray along the axis of symmetry  304  and a light ray traveling parallel to the axis of symmetry but spaced therefrom a distance, ρ, to the reference plane  310 , and λ is the wavelength of the light. The length difference, ΔL, is given by  
         ΔL=ρ 2 /σ  [Equation 2] 
         [0036]    where σ is the radius of curvature of the concave, semispherical mirror  302 . By substituting ρ 2 /σ into Equation 1, the phase delay, Δφ, between the two rays can be defined as a function of σ 
         Δφ=−kρ 2 /σ[Equation 3] 
         [0037]    For purposes of example, a wavelength of λ=1.5 μm and a distance ρ=6 μm from the axis of symmetry  304  can be assumed to determine the phase delay, Δφ, between the two rays at a distance of ρ=6 μm. By inserting these parameters into Equation 3, the phase delay, Δφ, at this distance is equal to −0.16 π.  
         [0038]    As identified above, the thickness, t, of the convex outer layer  514  can be constructed to emulate this phase delay, Δφ, to obtain the same focusing effect of the concave arrangement of FIG. 3. This can be accomplished by first calculating the phase, φ, of a light ray that travels parallel to the axis of symmetry  520  through a given thickness, t, of semiconductor or dielectric material. Although light is reflected multiple times at each layer interface  508 , the details for the planar layers  506  of the first reflector  502  need not be considered if it is assumed that the stack comprising these layers is thick enough to reflect nearly all the light. In that case, the total effect of the stack can be approximated by R planar stack =|r planar stack   2 =1, where R planar stack  is the optical power reflectivity of the light beam and r planar stack  is the optical field reflectivity of the light beam. The reflectivity of the composite structure comprising the planar stack and the convex outer layer  514 , r comp , is given by  
         r comp =(r+e −iφ )/(1+re −iφ )  [Equation 4] 
         [0039]    By inserting an r value that closely approximates the optical field reflectivity at the convex, semispherical surface/air interface, r comp  can be calculated. If the outer layer  514  is assumed to be constructed of SiO 2 , r=−0.18.  
         [0040]    The phase, φ, for a light beam traveling down and back from the convex, semispherical surface  516  to a planar surface  524  of the outer layer  514  is  
         φ= k (2 t )  [Equation 5] 
         [0041]    where t is the thickness of the layer  514  at the distance, ρ, outward from the axis of symmetry  520 . The constant, k, is given by  
           k= 2 πn/λ   [Equation 6] 
         [0042]    where n is the refractive index of the material used to construct the convex outer layer  514  and λ is the free space wavelength of the light. In Equation 4, the phase of r comp  is that of the composite reflector  502  comprising the convex outer layer  514  and the planar layers  506 . More useful, however, is the phase of the reflected light at the reference plane  522  (see FIG. 5) in that the degree to which the light is being focused can be more easily seen at this plane. To determine this, the quantity ((4πt/λ)−π/n) is added to the phase of r comp  to account for the difference between the phase at the convex, semispherical surface  516  and at the reference plane  522 .  
         [0043]    [0043]FIG. 6 provides a graph of the phase delay, Δφ, of the light reflected at the reference plane  522  versus the layer thickness, t, using Equations 5 and 6. Specifically, the graph of FIG. 6 plots ((4t/λ)−1/n))+Arg(r comp(φ(t))/π versus the rescaled thickness, t( 2n/λ), where Arg(r comp )=Arctan(Im(r comp )/Re(r comp ))). The quantity t(2n/λ) is used to permit reference to a single graph irrespective of refractive index, n, and wavelength, λ. If n and λ are known, the graph can be used to relate phase delay, Δφ, to the thickness, t, of the convex outer layer  514 . For example, the thickness at a distance ρ=6 μm away from the axis of symmetry  520  can be determined. For maximum reflectivity, the thickness at the center of the convex outer layer  514  can be the quarter wave optical thickness, namely  
           t= 0.25 λ/n   [Equation 7] 
         [0044]    As identified above, a phase delay, Δφ, of −0.16 results with the concave arrangement shown in FIG. 3 at a distance ρ=6 μm from the axis of symmetry  304 . With reference to the graph of FIG. 6, this phase delay pertains to a thickness value (i.e., t(2n/λ)) of 0.14. By solving for t, the thickness can be determined to be 0.07λ/n. Therefore, the thickness, t, at a distance from the axis of symmetry of ρ=6 μm is 0.07 λ/n. The thickness, t, of the outer layer  514  can be determined in this manner for any distance, ρ, through relation of the phase delay, Δφ, with thickness. It is to be noted that FIG. 6 is quantitative in nature and was generated assuming a variable thickness outer layer  514  that terminated a quarter wave layered stack. Persons having ordinary skill will appreciate that the thickness, t, of the convex outer layer  514  can alternatively be derived as a function of the distance, ρ, through conventional mathematics.  
         [0045]    [0045]FIG. 7 illustrates an example laser  700  incorporating the optical cavity  500  shown in FIG. 5. This laser is shown and described herein to provide an example application of the inventive optical cavity  500 . Therefore, it is to be understood that the laser could have alternative construction, if desired. As shown FIG. 7, the laser  700  includes a substrate  702 . By way of example, the substrate  702  can comprise an n-type doped semiconductor material. Where the laser  700  is a photo-pumped laser, the substrate  702  is adapted to receive light from a separate light source (not shown).  
         [0046]    Disposed within the optical cavity  500  is an active region  706  where electrons and holes are recombined to produce laser light. This region  706  can include a plurality of quantum wells (not shown). By way of example, the active region  706  can comprise an intrinsic (i.e., undoped or lightly doped) semiconductor layer. Formed on top of the active region  706  are support posts  710  that are used to suspend the first reflector  502  above the active region  706 . Although posts  710  are shown, it will be understood that alternative support means could be provided, if desired. By way of example, the support posts  710  can be formed of a dielectric material such as a polymeric material. Mounted on the support posts  710  are support tethers  712  that directly support the first reflector  502 . As with the support posts  710 , it will be understood that alternative support means could be used to suspend the first reflector  502 . Formed on the support tethers  712  are tuning electrodes  714  that are used to deliver voltage to the first reflector  502 . When voltage is applied to the tuning electrodes  714 , the first reflector  502  is displaced downwardly toward the second reflector  504  to adjust (i.e., reduce) the length of the optical cavity  500  to change the frequency of emission of the laser  700 .  
         [0047]    In use, light is delivered to the laser  700 , for example, through the substrate  702 . This light reflects back and forth off of the first and second reflectors  502  and  504  until its intensity increases to the point at which light is transmitted through one of the reflectors, normally the first reflector  502 . To adjust the frequency of this light, voltage can be provided to the first reflector  502  to cause it to be displaced in the manner described above.  
         [0048]    [0048]FIG. 8 illustrates an example filter  800  that incorporates the optical cavity  500  shown in FIG. 5. As with the laser  700  shown in FIG. 7, this filter  800  is shown and described as an example application of the optical cavity  500 . Therefore, it is to be appreciated that alternative constructions are feasible. As is apparent from FIG. 8, the filter  800  is similar in design to the laser  700 . Accordingly, the filter  800  can include a substrate  802 , a first tuning electrode  804 , support posts  806 , support tethers  808 , and second tuning electrodes  810 . In that the filter  800  is used to filter light as opposed to generate light, the filter  800  does not include a gain medium such as active region  706 .  
         [0049]    In use, light is provided to the filter  800  through either its top or bottom such that the light reaches the optical cavity  500 . Within the cavity  500 , the light travels back and forth between the reflectors  502 ,  504  and ultimately is transmitted through one of the reflectors  502 ,  504  (the reflector opposite to that through which the light entered the filter  800 ) at a desired optical frequency. The frequency of light that is emitted from the filter  800  is controlled by adjusting the displacement of the first reflector  502  by provided an appropriate voltage to the reflector with the tuning electrodes  804 ,  810 .  
         [0050]    [0050]FIG. 9 illustrates a second optical cavity  900  of the invention. This optical cavity  900  is similar in many ways to the first optical cavity  500  shown in FIG. 5. Accordingly, the optical cavity  900  includes a first reflector  902  and a second reflector  904  that are positioned at opposite ends of the cavity. Furthermore, each of the reflectors  902 ,  904  is normally constructed as a DBR comprising a plurality of semi-conductor and/or dielectric layers  906  having quarter wave optical thicknesses and different indices of refraction.  
         [0051]    As is with the optical cavity  500  of FIG. 5, the reflector layers  906  of the second optical cavity  900  can alternate between relatively thick layers  908  and relatively thin layers  910 . By way of example, the relatively thick layers  908  can comprise silicon carbide (SiCx) or SiO 2  and the thin layers can comprise TiO 2 . However, instead of having a convex, semispherical outer layer, the first reflector  902  of the second optical cavity  900  comprises a planar outer layer  912  having an index of refraction that varies radially outward from the central axis  914  of the reflector. More particularly, the index of refraction of the outer layer  912  is largest at its axial center and decreases outwardly therefrom. As will be appreciated by persons having ordinary skill in the art, this varied index of refraction provides a focusing effect on light  916  reflected back and forth between the reflectors  902 ,  904 . This focusing effect occurs because, due to the difference in index of refraction, the optical distance traveled through the outer layer  912  by a light ray along the axis of symmetry  914  is longer than that traveled by a parallel light ray separated a distance, ρ, from this axis.  
         [0052]    To achieve the desired focusing effect, the planar outer layer  912  is constructed to have a refractive index, n, that varies as a function of the distance, p, from the axis of symmetry  914 . This refractive index can be determined through normal experimentation by persons having ordinary skill in the art. In addition, this refractive index can be estimated in similar manner to that described above with regard to the first optical cavity  500  by analogy to an optical cavity having a concave, semispherical mirror. By way of example, the refractive index, n, of the outer layer  912  can be chosen to emulate a convex, semispherical mirror having a radius of curvature, σ, of 300 μm (see FIG. 3). Again, the focusing effect can be quantified by evaluating the optical phase, φ, along paths parallel to the axis of symmetry  914 . The phase, φ, of light passing through the outer layer  912  along any one path is given by φ=−2kl, where k is the propagation constant of the material at that point and l is the thickness of the material. In this calculation, k=(2πn)/λ, where n is the local index of refraction of the material and λ is the free space wavelength of light. The field reflectivity, r, is given by  
                 r   l     +     exp        [       -   2k     ·   l     ]           1   +     r   l     +     exp        [       -   2k     ·   l     ]                 [     Equation                 8     ]                               
 
         [0053]    where r l  is the reflectivity of the interface between the outer layer  912  and the free space, and r is the reflectivity of the first reflector  902  as a whole. The phase of light reflected from the structure is given by  
             φ   =     a                   tan        [       Im        [   r   ]         Re        [   r   ]         ]                 [     Equation                 9     ]                               
 
         [0054]    As the index of refraction, n, varies, so does r l  such that  
               r   l     =       1   -   n       1   +   n               [     Equation                 10     ]                               
 
         [0055]    and =−i2kl. For a concave, spherical mirror, the phase, φ, is given by  
             φ   =       2        πρ   2       λσ             [     Equation                 11     ]                               
 
         [0056]    where σ is the radius of curvature of the mirror. By inserting various values for ρ in Equation 11, the index of refraction, n, at each value of ρ can be determined from Equations 8-10. These calculations result in the curve shown in FIG. 10. In particular, FIG. 1O is a refractive index profile for the outer layer  912 . As is apparent from this figure, the refractive index of the outer layer  912  was approximated to be between 1.85 and 1.90 at the axis of symmetry  914  (i.e., ρ=0), and about 1.45 at a position 6 μm outward from the axis (i.e., ρ=6 μm).  
         [0057]    To achieve the index profile shown in FIG. 10, the composition of the outer layer  912  can likewise be varied as a function of radius. By way of example, the composition can be varied to primarily comprise SiC X  at the center of the outer layer  912  and SiO 2  adjacent the edges of the layer. As known in the art, SiC X  has a refractive index of approximately 2.5, while SiO 2  has a refractive index of approximately 1.5. To fabricate such a layer of material, a layer of SiC X  can first be formed through conventional material deposition techniques. Once the layer is formed, its composition can be modified through a selective oxidation process, e.g., using oxygen (excited to a plasma or ionic form) to transform portions of the SiCX into SiO 2 . To achieve the desired radial composition variance, a selective mask structure can be used, for instance, a structure having a larger amount of mask material in the center of the composition layer that decreases radially therefrom.  
         [0058]    [0058]FIG. 11 illustrates an example laser  1100  incorporating the optical cavity  900  shown in FIG. 9. This laser is shown and described herein to provide an example application of the second optical cavity  900 . Therefore, it is to be understood that the laser could have alternative construction, if desired. The laser  1100  includes a substrate  1102  that can comprise an n-type doped semiconductor material. Disposed within the optical cavity  900  is an active region  1106  that can comprise an intrinsic (i.e., undoped or lightly doped) semiconductor layer. Like the laser  700  shown in FIG. 7, the laser  1100  includes support posts  1110  and support tethers that are used to suspend the first reflector  902  above the active region  1106 . Although posts  1110  and tethers are shown, it will be understood that alternative support means could be provided, if desired. Formed on the support tethers  1112  are tuning electrodes  1114  that are used to deliver voltage to the first reflector  902  and displace it downwardly toward the second reflector  904  to adjust (i.e., reduce) the length of the optical cavity  900 .  
         [0059]    [0059]FIG. 12 illustrates an example filter  1200  that incorporates the optical cavity  900  shown in FIG. 9. As with the laser  1100  shown in FIG. 11, the filter  1200  is shown and described as an example application of the optical cavity  900 . Therefore, it is to be appreciated that alternative constructions are feasible. As indicated in FIG. 12, the filter  1200  can include a substrate  1202 , a first tuning electrode  1204 , support posts  1206 , support tethers  1208 , and second tuning electrodes  1210 . In that the filter  1200  is used to filter light as opposed to generate light, the filter  1200  does not include a gain medium such as active region  1106 .  
         [0060]    While particular embodiments of the invention have been disclosed in detail in the foregoing description and drawings for purposes of example, it will be understood by those skilled in the art that variations and modifications thereof can be made without departing from the scope of the invention as set forth in the following claims. For instance, although the focusing effect is described as being made possible by an outer layer having a varying thickness or varying refractive index, it will be appreciated that these two means of focusing can be combined in designing the optical cavity.