Fiber optic mode selector

Abstract: An all-fiber mode selector comprises a single-mode opti­ cal fiber (100) and a double-mode optical fiber (110), each having a facing surface (144, 154) formed on one side of the cladding The facing surfaces (144, 154) are juxtaposed in close facing relationship. The fibers are selected so that an optical signal propagating in the LP₁₁ propagation mode of the double-mode optical fiber (110) propagates at substanti­ ally the same phase velocity as an optical signal propagating in the LP₀₁ propagation mode of the single-mode optical fiber (100). The evanescent fields of the two fibers interact to couple optical energy from the LP₁₁ mode of the double-­ mode optical fiber (110) to the LP₀₁ mode of the single-mode optical fiber (100) and vice versa.

Description: Field of the Invention The present invention relates generally to fiber optic coupling devices, and more specifically to devices that couple light energy between selected modes of two dissimilar optical fibers. Background of the Invention In fiber optic systems, it is frequently desirable to remove, select, or suppress certain propagation modes of an optical signal. For example, in a two-mode optical fiber having an optical signal propagating therein in the first and second order spatial propagation modes, it is known that the light propagating in the second order mode can be "stripped" from the optical signal within the fiber by forming a segment of the fiber's length into a coil having a suitably selected coil diameter. The coil diameter is selected to perturb the second order mode without substantially affecting the first order mode, such that light propagating in the second order mode of the fiber enters the cladding of the optical fiber and escapes therefrom. The portion propagating in the first order mode is guided by the fiber and remains within the fiber's core. This light in the first order mode does not ordinarily couple to the second order mode due to the difference in propagation constants between the first order and second order modes of the fiber. Thus, after passing through the length of coil fiber, the optical signal propagates substantially solely in the first order propagation mode. Thus, the "mode stripper" allows the selection of the light propagating in the first order mode through removal of the light in the second order mode. Although a mode stripper is an advantageous device, its uses are limited, since the light that is stripped from the fiber merely radiates into free space. The mode stripper does not have the capability of coupling selected modes of two different optical fibers. The ability to couple a selected spatial mode of one optical fiber to a selected spatial mode of another optical fiber has many uses in a fiber optic system. For example, in a fiber optic frequency shifter wherein light propagating in a first order mode is coupled to a second order mode and is shifted in frequency, it is desirable that the portion of the frequency shifted light in the second order mode be coupled to a selected mode of a different fiber so as to be able to transmit the light at the shifted frequency. Thus, a need exists for a mode selector which can, for example, separate lower order modes (e.g., a first order mode) from higher order modes (e.g., a second order mode) and provide the higher order mode as an output for further use in the fiber optic system. There is disclosed in an article by R. G. Lamont, et al., "Tuned-Port Twin Biconical-Fiber Splitters, Fabrication From Dissimilar Low-Mode-Number Fibers," Optics Letters , No. 1, Vol. 10, January 1985, pp. 46-48, a tuned port twin biconical-fiber splitter wherein coupling occurs between a chosen pair of modes of two dissimilar monomode or quasi-monomode fibers. In that reference, the etched sections of two fibers are placed side-by-side and brought into contact in the coupler-fabrication jig. Heat is applied at the contact point with an O₂/H₂ microtorch, thereby fusing the strands. Finally, under tension, the splitter is pulled into its completely fused biconical-taper shape. In a fused splitter, the cross section of the cores of each of said fused fibers is substantially lesser in the interaction region than outside that region. The Lamont article mention possible use of a technique involving an evanescent-wave polished splitter. However, this reference does not disclose anything pertaining to this technique in connection with optical coupling of propagation modes in optical fibers. Furthermore, it characterizes a recourse to evanescent-wave polished splitter as being difficult, complex and inflexible. it finally states that compensating for the mismatch in mode propagation constants would raise a problem and that possible mistuning of the device by the index-matching oil usually placed between the two splitter flats to facilitate their free movement would also have to be considered. In another article by Whalen et al, "Effectively nonreciprocal evanescent-wave optical fibre directional coupler," Electronics Letters , Vol. 21, No. 5, p. 175-176, there is disclosed a nonreciprocal directional coupler using evanescent coupling between a single-mode and a multimode optical fiber. The coupler disclosed in the Whalen article couples between low order modes and high order modes. However, no selective coupling is accomplished between the fundamental mode of the second optical fiber and the first order mode of the first optical fiber. In the Whalen article, coupling occurs between the fundamental mode of a single mode fiber and a number of high-order modes of a multimode fiber. Summary of the Invention The present invention comprises a mode selector which provides a means for separating light propagating in two or more modes in a multimode fiber and coupling light from a selected one of these modes to a selected mode of a separate optical fiber. The present invention thus operates as a fiber optic mode filter; it is defined in Claim 1. The present invention includes first and second dissimilar optical fibers. The first optical fiber has at least one propagation mode and the second optical fiber has at least two propagation modes and an elliptical core. Only two of the propagation modes have matching propagation velocities. One of the modes having a matching propagation velocity is in the first fiber and the other of the modes having the matching propagation velocity is one of the two modes in the second fiber. In the preferred embodiment, each of the two fibers is arcuately mounted in a supporting structure, and a portion of the cladding is removed from one side of each of the fibers to form oval cladding surfaces which are juxtaposed to form an interaction region. The cores of the fibers have substantially the same cross section inside the interaction region as outside the interaction region, and the proximity of cores at the interaction region is selected such that light propagating in one of the matching propagation modes in one of the fibers is coupled to the other of the matching modes in the other of the fibers. The length of the interaction region is selected to cause substantially complete coupling between the two propagation modes having the matched propagation velocities. The remainder of the propagation modes in both of the fibers have mismatched propagation velocities such that the propagation velocity of each of the mismatched propagation modes differs sufficiently from the propagation velocities of all of the other propagation modes to prevent substantial optical coupling between any of the mismatched modes. In the preferred embodiment, the second fiber has an inner core which has a diameter greater than the inner core of the first fiber. More specifically, the first fiber of this embodiment is a single-mode fiber which propagates light exclusively in the first order mode, while the second fiber is a double-mode (two-mode) fiber which propagates light exclusively in the first and second order modes. Also, in the preferred embodiment, one of the two propagation modes having the matching propagation velocities is a higher order mode than the other of the two modes having the matching propagation velocities. This embodiment may additionally include means for controlling the orientation of the energy distribution pattern in the higher order mode to thereby control the coupling between the two modes. Preferably, the cladding is removed from each of the two fibers so that only a small amount of cladding remains between the oval cladding surfaces of each fiber and the core of each fiber. Thus, the coupling between the two fibers is accomplished through evanescent field interaction between the matched modes of the two fibers. Brief Description of the Drawings Figure 1 is a cross sectional view of the apparatus of the present invention showing a double-mode fiber and a single mode fiber juxtaposed in a directional coupler. Figure 2 is a perspective view of the coupler halves which comprise the present invention, and shows the facing surfaces formed on the fibers mounted in each coupler half. Figure 3 is a cross-sectional end view taken along the lines 3-3 in Figure 1 showing the positional relationship between the cores and the claddings of the two fibers in Figure 1. Figure 4a is a cross-sectional view of the single-mode optical fiber taken along the lines 4a-4a in Figure 1. Figure 4b is a graphical representation of the electric field energy distribution of an optical signal propagating in the LP₀₁ mode of the single-mode optical fiber in Figure 4a. Figure 5a is a cross-sectional view of the double mode fiber taken along the lines 5a-5a in Figure 1. Figure 5b is a graphical representation of the electrical field energy distribution of the LP₀₁ propagation mode and the LP₁₁ propagation mode of an optical signal propagating in the double-mode fiber of Figure 5a. Figure 6a shows the single-mode optical fiber and the double-mode optical fiber in juxtaposed relationship at their facing surfaces. Figure 6b graphically illustrates the interaction of the evanescent fields of the LP₁₁ propagation mode of the double-mode optical fiber with the LP₀₁ propagation mode of the single-mode optical fiber. Figure 7a is a graphical representation of the waveform of an optical signal propagating in the LP₀₁ mode of the single-mode optical fiber. Figure 7b is a graphical representation of the waveform of an optical signal propagating in the LP₀₁ mode of the double-mode optical fiber. Figure 7c is a graphical representation of the waveform of an optical signal propagating in the LP₁₁ mode of the double-mode optical fiber. Figure 8a pictorially illustrates mismatched phase propagation velocities of the single-mode and double-mode optical fibers when the core axes are parallel. Figure 8b pictorially illustrates the matching of phase propagation velocities by positioning one of the optical fibers at an angle with respect to the core axis of the other optical fiber. Figure 9 is a pictorial illustration of an inter-mode modulator that uses the apparatus of the present invention to separate frequency-shifted light in the LP₁₁ propagation mode from unshifted light in the LP₀₁ propagation mode. Figure 10 is a system incorporating the device of the present invention to verify the modal selection capability of the device. Figure 11 is a system incorporating the present invention and an evanescent field grating reflector that separates light propagating at a particular frequency from light at other frequencies. Description of the Preferred Embodiment As shown in Figures 1-5b, the present invention comprises a first optical fiber 100 and a second fiber 110. The first optical fiber 100 has an inner core 102 and an outer cladding 104. The second optical fiber 110 has an inner core 112 and a outer cladding 114. The core 102 of the first optical fiber 100 has a core refractive index n core1 , and the cladding 104 has a cladding refractive index n cladding1 . The core refractive index and the cladding refractive index of the first fiber 100 are chosen such that the core refractive index is greater than the cladding refractive index (i.e., n core1 > n cladding1 ). Therefore, light propagating in the core 102 will propagate at a slower phase velocity than light propagating in the cladding 104. In like manner, the core 112 of the second optical fiber 110 has a core refractive index n core2 and the cladding 114 has a cladding refractive index cladding n cladding2 which are selected so that the core refractive index is greater than the cladding refractive index (i.e., n core2 > n cladding2 ). In the preferred embodiment, the core refractive index, the cladding refractive index, and the diameter of the core of the first optical fiber 100 are selected so that the first optical fiber 100 is a single-mode optical fiber at a selected optical frequency f o . The core refractive index, the cladding refractive index, and the diameter of the core of the second optical optical fiber 110 are selected so that the second optical fiber 110 is a double-mode (i.e. a two-mode) optical fiber at the same selected optical frequency f o . Thus, the first optical fiber 100 will propagate only light in the first order LP₀₁ mode at the selected optical frequency. The second optical fiber 110 will propagate light in the first order LP₀₁ mode and will also propagate light in a higher order mode, namely, the second order LP₁₁ propagation mode. The first optical fiber 100 is arcuately mounted in a first mounting block 120. The second optical fiber is arcuately mounted in a second mounting block 130. In the preferred embodiment, the first and second mounting blocks 120, 130 are constructed in accordance with the teachings of U.S. Patent No. 4,536,058, which is incorporated herein by reference. The first mounting block 120 has a flat mounting surface 140 into which an arcuate slot 142 is cut to provide a guide for the first optical fiber 100. As described in U.S. Patent No. 4,536,058, the slot 142 has a depth with respect to the mounting surface 140 at each of two ends of the first mounting block 120 that is greater than the depth at the middle of the mounting surface 140 so that when the first optical fiber 100 is positioned in the slot 142, a portion of the cladding 104 on one side of the first optical fiber 100 is proximate to the mounting surface 140. The mounting surface 140 is polished so that the cladding 104 of the first optical fiber 100 is gradually removed with the surface 140 to form a facing surface 144 on the cladding 104 which has a general oval shape that is coplanar with the surface 140, as illustrated in Figure 2. The polishing is continued until a sufficient amount of the cladding 104 is removed so that the facing surface 144 is within a few microns of the core 102 of the first optical fiber 100. In like manner, an arcuate slot 152 is formed in a mounting surface 150 of the second mounting block 130 and the second optical fiber 110 is positioned in the slot 152. The mounting surface 150 and the cladding 114 of the second fiber 110 are polished in the above-described manner to form a facing surface 154. As illustrated in Figure 3, the facing surface 144 of the first optical fiber 100 is positioned in juxtaposed relationship with the facing surface 154 of the second optical fiber 110 to form an interaction region 156 for transferring light between the fibers. The core 102 of the first optical fiber 100 and the core 112 of the second optical fiber 110 are spaced apart by the thin layer of the cladding 104 remaining between the facing surface 144 and the core 102, and the thin layer of the cladding 114 remaining between the facing surface 154 and the core 112. The removal of the cladding is preferably performed in accordance with the method described in U.S. Patent No. 4,536,058. The oil drop test described in U.S. Patent No. 4,536,058 is advantageously used to determine the amount of cladding removed and the proximity of the facing surfaces 144, 154 to the cores 102, 112 respectively. As discussed hereinafter, cladding is removed from the first fiber 100 and the second fiber 110 until the evanescent field penetration of the facing surfaces 144,154 for the selected guided modes of the fibers is sufficient to cause coupling of light between the two guided modes. When the facing surface 144 and the facing surface 154 are superimposed, as illustrated in Figure 1, the first fiber 100 and the second fiber 110 converge near the center of the mounting blocks 120 and 130 and diverge gradually as the distance away from the center of the blocks 120 and 130 increases. The rate of convergence and divergence of the two fibers is determined by the radius of curvature of the two arcuate grooves, which, in one preferred embodiment, is selected to be 25 centimeters. This radius of curvature permits the cores of the two fibers to be positioned in close proximity to permit the evanescent fields to interact while limiting the length of the interaction region 156. As explained in detail by Digonnet, et al, in "Analysis of Tunable Single Mode Optical Fiber Coupler," IEEE Journal of Quantum Electronics , Vol QE-18, No. 4, April 1982, pp. 746-754, and in U.S. Patent No. 4,556,279, the teachings of which are incorporated herein by reference, the length of an interaction region of two juxtaposed fibers is defined principally by the radii of curvature of the fibers, while the strength of coupling is defined principally by the proximity of the cores in the interaction region, particularly the minimum core spacing (i.e., the distance between the cores at the centers of the facing surfaces 144 and 154). The length of the interaction region is preferably at least an order of magnitude larger than the core diameter of either of said fibers so that there is a substantial amount of light transferred, and preferably a complete transfer of light between the two fibers. The interaction region length increases with increasing radii of curvature and the strength of coupling increases with decreasing core spacing. The radii of curvature are preferably selected to be sufficiently large so that little, if any bending effect is introduced into the fibers. Further, the core spacing is preferably no less than zero so that the diameters of the cores 102, 112 are uniform throughout the length of the apparatus of the invention, and, thus, no modal perturbations are introduced by changes in the characteristics of the fiber. The operation of the present invention can be more fully understood by referring to Figures 4a-b, 5a-b, 6a-b, 7a-c, and 8a-b. Figures 4a and 4b illustrate the electric field intensity distribution for the LP₀₁ propagation mode of an optical signal propagating in the single-mode optical fiber 100. As illustrated in Figure 4b, the field intensity distribution is defined by an electric field intensity distribution graph 200 which has a maximum 202 substantially in the center of the core 102. The intensity decreases as the distance from the center of the core 102 increases. Most of the electric field energy of the LP₀₁ propagation mode is concentrated in the core 102 of the fiber 100. However, a portion of the electric field energy extends into the cladding 104, as illustrated by a field portion 204 and a field portion 206 of the graph 200. The portion of the electric field energy outside the core 102 is referred to as the evanescent field. The interaction of the evanescent fields of two guided modes within the interaction region 156 provides the means for coupling optical energy between the two fibers 100, 110, as described in U.S. Patent No. 4,536,058. The amount of coupling is determined principally by the length of the interaction region and the distance between the respective cores of the two fibers. Figures 5a and 5b illustrate the electric field intensity distribution for light propagating in the LP₀₁ and LP₁₁ modes of the double-mode fiber 110 at the selected frequency. The electric field intensity distribution of the LP₀₁ propagation mode is illustrated by a graph 220, and the electric field distribution of the LP₁₁ propagation mode is illustrated by graph 222. As discussed above with regard to the graph 200 in Figure 4b, the electric field of an optical signal propagating in the LP₀₁ propagation mode is concentrated in the core 112 near the center of the fiber 110, as illustrated by a maximum 224, and the intensity diminishes as the distance from the center of the core 112 increases. A portion of the electric field intensity distribution of the LP₀₁ propagation mode extends into the cladding 114 as an evanescent field, designated as portions 226 and 228. The electric field intensity distribution graph 222 for the light propagating in the LP₁₁ propagation mode has a minimum intensity 230 near the center of the core 112 and the intensity increases gradually as the distance from the core 112 increases. The maximum electric field intensity occurs at maxima 232 and 234 which are proximate to the interface between the core 112 and the cladding 114 of the optical fiber 110. Thus, the evanescent field of an optical signal propagating in the LP₁₁ propagation mode, represented by electric field energy distribution portions 236 and 238, extends further into the cladding than the evanescent field of the portion of an optical signal propagating in the LP₀₁ mode of the second optical fiber 110. As illustrated in Figure 5b, the optical signal propagating in the LP₀₁ propagation mode of the second optical fiber 110 has very little evanescent field extending beyond the core 112 of the fiber 110 (see the portions 226 and 227 of the graph 220). In contrast, the evanescent field of an optical signal propagating in the LP₁₁ propagation mode extends well into the cladding 114 of the second optical fiber 110 (see the portions 236 and 238 of the graph 222). Thus, when a portion of the cladding is removed from each of the two optical fibers so that the cores 112 and 102 can be closely juxtaposed, there is a relatively large evanescent field intensity for the LP₁₁ propagation mode available to interact with the core 102 of the first optical fiber 100. This is illustrated in Figures 6a and 6b, wherein the electric field intensity distribution graphs 220 and 222 of the second optical fiber 110 are shown in relation to the electric field intensity distribution graph 200 of the first optical fiber 100 when the two fibers are juxtaposed at their respective facing surfaces 154 and 144. As illustrated, there is substantially no overlap of the LP₀₁ electric field intensity distribution 220 of the second optical fiber 110 with the LP₀₁ electric field intensity distribution 200 for of the first optical fiber 100. However, there is relatively large overlap of the evanescent field portion 238 of the LP₁₁ electric field intensity distribution 222 of the second optical fiber 110 with the evanescent field portion 204 of the LP₀₁ electric field intensity distribution 200 of the first optical fiber 100. Thus, the LP₁₁ propagation mode of the second optical fiber 110 and the LP₀₁ propagation mode of the first optical fiber 110 interact strongly as compared to the interaction between the LP₀₁ modes of the two fibers. It has been found that, in one embodiment, when the spacing between the cores of the two fibers is selected to be approximately 2.5 times the radius of the core 112 of the second optical fiber 110, the electric field amplitude of the LP₁₁ mode is greater than 10 times the electric field amplitude of the LP₀₁ mode of the second optical fiber 110 at a normalized frequency of V = 2.6. Due to the strong interaction between the LP₁₁ mode of the double-mode fiber 110 and the LP₀₁ mode of the single-mode fiber 100, a relatively large amount of optical energy is coupled between the LP₁₁ propagation mode of the fiber 110 and the LP₀₁ propagation mode of the fiber 100. However, since there is substantially no interaction between the LP₀₁ modes of the two fibers 100, 110, there is substantially no optical energy coupled between the LP₀₁ propagation mode of the fiber 110 and the LP₀₁ mode of the fiber 100. As discussed hereinafter, coupling between the LP₁₁ mode of the fiber 110 and the LP₀₁ mode of the fiber 100 is enhanced by selecting the fibers such that the propagation constants of these two modes are the same. Similarly, coupling between the LP₀₁ modes of the fibers is inhibited by ensuring that the LP₀₁ modes of the fibers have substantially different propagation constants. One skilled in the art will recognize that the electric field intensity distribution of the LP₁₁ propagation has a lobe pattern which varies with the orientation of the double-mode optical fiber 110. In order to obtain maximum coupling, one of the lobes should be oriented to be adjacent to the facing surface 154 so that the lobe is proximate to the single-mode optical fiber 100. One means of orienting the lobes for maximum coupling is to use a fiber phase shifter (not shown) to adjust the phase of the four true eigenmodes that make up the LP₁₁ mode approximation. In a preferred embodiment, the double-mode optical fiber 110 is an elliptical core double-mode fiber in which the true eigenmodes are lobe-like in shape. The eigenmodes propagate down the fiber without changing so that the lobe pattern for the LP₁₁ propagation mode can be oriented to allow for maximum coupling to the single-mode fiber 100. The lobe pattern for the LP₁₁ mode is adjusted, using a polarization controller or the like, for maximum coupling while passing through the evanescent coupling region. As discussed above, the energy of an optical signal propagating in the LP₀₁ mode of a fiber is confined mostly within the core of the fiber. Thus, an optical signal in the LP₀₁ propagation mode propagates at a phase propagation velocity which is largely determined by the refractive index of the core of the fiber. The effective refractive index seen by the light propagating in the LP₀₁ propagation mode has a value close to the value of the refractive index of the core. In contrast to the LP₀₁ mode, the LP₁₁ propagation mode propagates a larger fraction of optical energy in the cladding of the fiber. Thus, the phase propagation velocity of an optical signal propagating in the LP₁₁ propagation mode is determined by an effective refractive index which has a value less than the refractive index of the core and greater than the refractive index of the cladding. Accordingly, the effective refractive index for light in the LP₁₁ propagation mode has a value which is less than that for light in the LP₀₁ propagation mode. Thus, the phase propagation velocity of an optical signal propagating in the LP₁₁ propagation mode is faster than the phase propagation velocity of an optical signal propagating in the LP₀₁ mode. Due to the difference in phase velocities of the LP₀₁ and LP₁₁ modes, these modes do not easily couple; rather, they tend to function as two independent optical paths. In the preferred embodiment, selective coupling between the LP₁₁ mode of the fiber 110 and the LP₀₁ mode of the fiber 100 is accomplished by utilizing dissimilar fibers such that the phase propagation velocity of the LP₁₁ mode of the fiber 110 matches the phase propagation velocity of the LP₀₁ mode of the fiber 100, while the phase propagation velocities of all other pairs of modes are not matched. From the foregoing, it will be understood that the propagation velocity of an optical signal propagating in the LP₀₁ mode of the first (single-mode) optical fiber 100 is determined in part by a combination of the refractive index of the core 102, the refractive index of the cladding 104, and the diameter of the core 102. Similarly, the phase propagation velocities of optical signals propagating in the LP₀₁ mode and the LP₁₁ mode of the second (double-mode) optical fiber 110 are determined by the combination of the refractive index of the core 122, the refractive index of the cladding 124, and the diameter of the core 122. As set forth above, the phase propagation velocity of an optical signal propagating in the LP₁₁ mode in the optical fiber 110 will be greater than the phase propagation velocity of an optical signal propagating in the LP₀₁ mode of the optical fiber 110. In the present invention, the first optical fiber 100 and the second optical fiber 110 are selected to have characteristics (i.e., refractive indices and core diameters) such that the phase propagation velocity of an optical signal in the LP₁₁ propagation mode of the second optical fiber 110 is matched to the phase propagation velocity of an optical signal in the LP₀₁ propagation mode of the first optical fiber 100. Thus, the phase propagation velocity of an optical signal propagating in the LP₀₁ mode in the second optical fiber will be slower than the phase propagation velocity of an optical signal propagating in the LP₁₁ mode of the second optical fiber 110 and will also be slower than the phase propagation velocity of an optical signal propagating in the LP₀₁ mode of the first optical fiber 100. The relationship among the phase propagation velocities is illustrated in Figures 7a, 7b, and 7c. In Figure 7a, a traveling wave 250 represents the phase propagation of a signal propagating in the LP₀₁ propagation mode of the first (single-mode) optical fiber 100. The traveling wave 250 has a first wavelength L₁ which is defined by a velocity V₁ of the optical signal in the LP₀₁ propagation mode of the fiber 100 and the selected optical frequency f o (i.e., L₁ = V₁/f o ). Similarly, Figure 7b illustrates a traveling wave 252 that represents the phase propagation of a signal traveling in the LP₀₁ propagation mode of the second (double-mode) optical fiber 110 at the selected optical frequency f o . The traveling wave 252 has a wavelength L₂ which is defined by a velocity V₂ of the optical signal in the LP₀₁ propagation mode of the second optical fiber 110 and the selected optical frequency f o (i.e., L₂ = V₂/f o ). Figure 7c illustrates a traveling wave 254 which represents the phase propagation of a signal traveling in the LP₁₁ propagation mode of the optical fiber 110 at the selected optical frequency f o . The travelling wave 254 has a wavelength L₂ which is defined by a velocity V₃ of the optical signal in the LP₁₁ propagation mode of the second optical fiber 110 and the selected optical frequency f o (i.e., L₃ = V₃/f o ). As set forth above, the characteristics of the first optical fiber 100 and the second optical fiber 110 are chosen so that the velocity V₁ is substantially equal to the velocity V₃. Thus, the velocity V₂, which must be less than the velocity V₃, is less than the velocity V₁. Therefore, the wavelength L₃ matches the wavelength L₁ and the wavelength L₂ does not match the wavelength L₁. Accordingly, as illustrated in Figures 7a and 7c, light travelling in the LP₁₁ propagation mode of the second optical fiber 110 will have a substantially fixed phase relation to light travelling in the LP₀₁ propagation mode of the first optical fiber 100. On the other hand, as illustrated in Figures 7a and 7b, light traveling in the LP₀₁ propagation mode of the second optical fiber 110 will have a continually varying phase relation to light travelling in the LP₀₁ propagation mode of the first optical fiber 100. It has been shown that to couple light from a mode of one fiber to a mode of another fiber, the modes should interact through their evanescent fields over an interaction length and the phase propagation velocities of the two optical signals should be substantially equal. In the preferred embodiment, the phase propagation velocity V₃ of the LP₁₁ propagation mode of the second optical fiber 110 at the selected frequency is substantially equal to the phase propagation velocity V₁ of the LP₀₁ propagation mode of the first optical fiber 100. Thus, the apparatus of the present invention provides a means for coupling optical energy between the LP₁₁ propagation mode in the second optical fiber 110 and the LP₀₁ propagation mode in the first optical fiber 100. An optical signal propagating in the LP₀₁ propagation mode in the second optical fiber 110 is not coupled to the first optical fiber 100 because the phase propagation velocity V₂ for light propagating in the LP₀₁ mode in the second optical fiber 110 does not match the phase propagation velocity V₂ for light propagating in the LP₀₁ propagation mode of the first optical fiber 100. Thus, the apparatus of the present invention provides selection between optical energy propagating in the LP₀₁ mode of the second optical fiber 110 and optical signal propagating in the LP₁₁ mode of the second optical fiber 110. Accordingly, as shown in Figure 1, when optical energy is input into a first end 300 of the second optical fiber 110 in the LP₀₁ propagation mode, represented by an arrow 302, and in the LP₁₁ propagation mode, represented by an arrow 304, the optical energy in the LP₁₁ propagation mode will be coupled to the first optical fiber 100 and will exit from an end 310 of the first optical fiber 100 in the LP₀₁ propagation mode of the first optical fiber 100, as represented by an arrow 312. In contrast, the optical energy in the LP₀₁ propagation mode of the second optical fiber 110 will remain in the second optical fiber 110 and will exit from a second end 320 of the second optical fiber 110, as represented by an arrow 322. The first optical fiber 100 therefore provides an output signal which corresponds to the optical signal incident to the interaction region 156 of the two fibers propagating in the LP₁₁ propagation mode of the second optical fiber 110. The foregoing properties of the present invention are reciprocal in that an optical signal introduced into an end of the first optical fiber 100 in the LP₀₁ propagation mode of the first optical fiber 100 interacts with the LP₁₁ propagation mode of the second optical fiber 110 in the interaction region between the first facing surface 144 and the second facing surface 154 to couple optical energy into the LP₁₁ propagation mode of the second optical fiber 110. This reciprocal effect has advantages in many applications. The apparatus of the present invention can be fine-tuned by orienting the two fibers 100, 110 so that the longitudinal axes of the two fibers are not exactly parallel. Thus, if the phase propagation velocities V₁ and V₃ are not precisely the same at the selected frequency, the second optical fiber 110, for example, can be positioned so that the longitudinal axis of the core 112 of the second optical fiber 110 is at an angle with respect to the longitudinal axis of the core 102 of the first optical fiber 100 such that the magnitude of the component of the phase velocity V₃ in the direction of the longitudinal axis of the core 102 of the first optical fiber 100 is the same as the phase velocity V₁ along the longitudinal axis of the core 102 of the first optical fiber 100. This is illustrated in Figures 8a and 8b, wherein a vector 402 represents the phase propagation velocity V₃ of the LP₁₁ propagation mode of the second optical fiber 110 (shown in phantom) and a vector 400 represents the phase propagation velocity V₁ of the propagation mode LP₀₁ in the first optical fiber 100 (shown in phantom). In Figure 8a, the two vectors are positioned in parallel and the magnitude of the vector 400 is smaller than the magnitude of the vector 402. Thus, the phase propagation velocities V₃ and V₁ do not match and efficient coupling cannot occur. In Figure 8b, the second optical fiber 110 is oriented at a small angle with respect to the first optical fiber 100 so that the phase propagation velocity vector 400 is oriented at a small angle with respect to the phase propagation velocity vector 402. The component of the phase propagation velocity vector 402 in the direction of the phase propagation velocity vector 400 is shown in dashed lines as a vector 402′ that represents a velocity V₃′. The vector 402′ has substantially the same magnitude as the vector 400 and thus the phase propagation velocities V₃′ and V₁, represented by the vectors 402′ and 400, match at the angle shown. Thus, efficient coupling can occur from the LP₁₁ propagation mode of the second optical fiber 110 to the LP₀₁ propagation mode of the first optical fiber 100. Although, for clarity of illustration, the angle between the fibers is shown as a significant angle in Figure 8b, it is preferable that the angle between the two fibers 100 and 110 be very small so that the fibers are substantially parallel at the interaction region 156. In the present invention, it is desirable to avoid large angles between the fibers to prevent a significant reduction in the interaction length. As used herein, the interaction length means the length in the direction of the fiber axis of one of the fibers (e.g., the fiber 100) through which the core of the one fiber (e.g., the fiber 100) is positioned within the evanescent field of the other fiber (e.g., the fiber 110). An exemplary application for the present invention is illustrated for an inter-mode frequency shifter 500 in Figure 9. The inter-mode frequency shifter 500 preferably includes an input optical fiber 600 which is advantageously a single-mode optical fiber. The input optical fiber 600 is butt-spliced to a double-mode optical fiber 602. A first portion of the double-mode optical fiber 602 is formed into a coil 604 which operates as a mode stripper in a manner known to the art. A second portion of the double-mode optical fiber 602 interconnects the mode stripper 604 with an inter-mode frequency shifter 606. The inter-mode frequency shifter 606 is preferably constructed in accordance with copending Patent Application Serial No. 820,513, entitled "Fiber Optic Inter-mode Coupling Single Side Band Frequency Shifter," filed on the same day as the instant application, and assigned to the assignee of the instant application, the disclosure of which is hereby incorporated by reference. A transducer 610 induces vibrations into the fiber 602 which propagate in a single direction 614 away from the transducer 610 as a flexure wave comprising a series of traveling microbends. The inter-mode frequency shifter 606 operates to couple light from a first propagation mode (e.g., the LP₀₁ mode) to a second propagation mode (e.g., the LP₁₁ mode) and to cause the light to be shifted in frequency by an amount determined by a modulation signal applied to the transducer 610 of the frequency shifter 606 from a modulation source 612. After passing through the frequency shifter 606, the double-mode optical fiber 602 interconnects the frequency shifter 606 with a mode selector 640 constructed in accordance with the present invention. In the mode selector 640, the double-mode optical fiber 602 is juxtaposed with a single mode optical fiber 650 at an interaction region 652 in the manner described above. The double-mode optical fiber 602 has an output end portion 654. The single mode optical fiber 650 has an output end portion 656. The inter-mode frequency modulator operates in the following manner. An optical signal, represented by an arrow 660, is introduced into the input optical fiber 600. Preferably, the optical signal is propagating solely within the LP₀₁ propagation mode for the input optical fiber 600. The optical signal propagates through the input optical fiber 600 and is coupled to the double-mode optical fiber 602 and propagates within the double-mode optical fiber 602 in the LP₀₁ propagation mode. Any optical signal propagating in the LP₁₁ propagation mode in the fiber 602 is stripped from the double-mode optical fiber 602 in the mode stripper 604 in a manner known to the art. Thus, after passing through the mode stripper 604, the optical signal remaining in the double-mode optical fiber 602 is propagating solely in the LP₀₁ propagation mode. The optical signal propagates in the LP₀₁ propagation mode through the double-mode optical fiber 602 to the frequency shifter 606. In the frequency shifter 606, the optical signal propagating in the LP₀₁ propagation mode is coupled to the LP₁₁ propagation mode and is shifted in frequency by an amount determined by the frequency of the modulation source 612. As set forth in the above-referenced copending Application Serial No. 820,513 the optical signal coupled to the LP₁₁ propagation mode can be shifted upward in frequency or downward in frequency in accordance with the direction of propagation of traveling flexure waves in the frequency shifter 606. The frequency shifted light in the LP₁₁ propagation mode and any light remaining in the LP₀₁ propagation mode propagates from the frequency shifter 606 to the mode selector 640 through the double-mode optical fiber 602. Within the mode selector 640, the light propagating in the LP₁₁ propagation mode is coupled to the LP₀₁ propagation mode of the single-mode optical fiber 650 and propagates to the end portion 656 where it exits as frequency shifted light, represented by the arrow 662. The light propagating in the LP₀₁ mode in the fiber 602 at the original unshifted frequency propagates to the end portion 654 of the double-mode optical fiber 602 and exits as unshifted light, represented by an arrow 654. As set forth above, the mode selector 640 of the present invention is reciprocal so that an optical signal can be input into the end portion 656 of the optical fiber 650 in the LP₀₁ propagation mode. The light in the LP₀₁ propagation mode of the single-mode optical fiber 650 is coupled to the LP₁₁ propagation mode of the double-mode optical fiber 602 within the mode selector 640. Thereafter, the light propagates through the optical fiber 602 to the frequency shifter 606 where it is shifted in frequency and is coupled to the LP₀₁ mode of the optical fiber 602. The optical signal propagates from the frequency shifter 602 through the the optical fiber 602 to the mode stripper 604 wherein any optical signal remaining in the LP₁₁ propagation mode is stripped from the optical fiber 602. Thus, the optical signal propagating from the mode stripper 604 to the single-mode optical fiber 600 (which now operates as an output optical fiber) is propagated solely in the LP₀₁ propagation mode and is shifted in frequency from the optical signal input at the end portion 656 of the optical fiber 650. Although described above with regard to a single-mode fiber and a double-mode fiber, the present invention can also be used to selectively couple optical energy between modes in two dissimilar multimode fibers. For example, optical energy can be coupled from the LP₀₁ mode of a first double-mode fiber to the LP₁₁ mode of a second double-mode optical fiber. This is illustrated in Figure 10 for a first double-mode fiber 700 and a second multimode fiber 710. The fibers 700, 710 are selected such that the phase propagation velocity of an optical signal in the LP₀₁ mode of the first double-mode fiber 700 is substantially equal to the phase propagation velocity of the LP₁₁ propagation mode of the second double-mode fiber 710. The first fiber 700 and the second fiber 710 are constructed in accordance with the present invention, as described above, by positioning the two fibers in a first coupler half 720 and a second coupler half 730, forming first and second facing surfaces on the two fibers, and juxtaposing the two fibers at the facing surfaces, as illustrated pictorially in Figure 10. In one embodiment, the two fibers are made by ITT. The first fiber 700 has a core with a diameter of approximately 3.8 microns and has a numerical aperture of 0.12. The second fiber has a core diameter of 5.6 microns and has a numerical aperture of approximately 0.08. Both fibers have cutoff wavelengths on the order of 580 nanometers, An Argon Ion laser 740 is used as a source of optical energy at a wavelength of 4,880 Angstroms. At that wavelength, both the first fiber 700 and the second fiber 710 propagate optical energy in both the first and second order modes. The optical signal from the laser 740 is provided as an input signal to a first end 750 of the first fiber 700. In order to operate the first fiber 700 in accordance with the present invention, a portion of the first optical fiber 700 is formed into a mode stripper 752, which employs tight bends to remove any energy propagating in the second order LP₁₁ mode. Thus, the only energy propagating to the portion of the first fiber 700 in the coupler half 720 is in the LP₀₁ propagation mode. The embodiment of Figure 10 preferably includes a polarization controller 754 between the mode stripper 752 and the coupler half 720 so that the polarization of the optical energy in the LP₀₁ propagation mode incident to the coupler half 720 is controllable. As described above, the light incident to the portion of the first fiber 700 in the coupler 720 in the LP₀₁ propagation mode is coupled to the second fiber 710 in the LP₁₁ propagation mode. The phase velocity of the LP₀₁ propagation mode in the second fiber 710 does not match the phase propagation velocity of the optical energy in the LP₀₁ propagation mode of the first optical fiber 700. Thus, substantially no optical energy is transferred to the LP₀₁ propagation mode of the second optical fiber 710. The light propagating in the first optical fiber 700 after passing through the coupler half 720 is output from a second end 760 of the first optical fiber 700, as indicated by an arrow 762, and is projected onto a screen 764 where the field pattern of the output light can be observed. Similarly, the light coupled to the second optical fiber 710 is output from an end 770 of the second optical fiber 710, as indicated by an arrow 772, and is also projected onto the screen 764. Observations of the field patterns thus projected onto the screen 764 in embodiments constructed in accordance with Figure 10 show that the field pattern generated by the light output from the end 760 of the first optical fiber 700 corresponds to the LP₀₁ mode pattern. Similarly, the light projected onto the screen 764 from the end 770 of the second optical fiber 710 corresponds to the field pattern for an LP₁₁ propagation mode. Measurement of the power from the light output from the second end 760 of the first optical fiber 700 and the light output from the end 770 of the second optical fiber 710 has shown that a coupling efficiency of at least 97% can be obtained. This coupling efficiency is calculated by dividing the coupled power (i.e., the power output from the end 770 of the second multimode optical fiber 710) by the sum of the coupled power and the uncoupled power (i.e., the power of the light output from the second end 760 of the first multimode optical fiber 700). The distance between the fiber cores can be adjusted, by laterally displacing the fibers, as described in U.S. Patent No. 4,536,058, to adjust the coupling efficiency from zero to 97%. Figure 11 illustrates a system which incorporates a mode selector built in accordance with the present invention into a system that separates light propagating at a plurality of frequencies in one fiber into a plurality of light signals at discrete frequencies propagating in separate fibers. The system includes a first optical fiber 800 which, in the embodiment shown, has only two propagation modes. This fiber 800 includes a first end 802 which receives input light, represented by an arrow 804. The input light 804 is comprised of a plurality of optical signals having discrete optical wavelengths λ₁, λ₂, . . . λ n . Preferably, the optical signals are propagating in the LP₀₁ propagation mode of the fiber. A portion of the optical fiber 800 is positioned in a coupler half 806 constructed in accordance with the present invention. A second optical fiber 810, which is preferably a single-mode optical fiber, is positioned in a second coupler half 812, also constructed in accordance with the present invention. The two coupler halves 806, 812 are positioned so that facing surfaces formed on the fibers 800 and 810 are juxtaposed to provide coupling between the propagation modes of the two fibers and thereby form a mode selector 814 of the present invention. A second portion of the first optical fiber 800 is incorporated into an evanescent field grating reflector 820, constructed in accordance with copending U.S. Patent Application Serial No. 754,271, entitled "Optical Fiber Evanescent Grating Reflector," filed on July 15, 1985, and assigned to the assignee of the instant application. This application is incorporated herein by reference. As disclosed in the copending application, by properly selecting the periodicity of the grating of the grating reflector 820, light incident on the grating reflector in the LP₀₁ propagation mode of the optical fiber 800 as represented by an arrow 830, is reflected by the grating reflector 820 and is caused to propagate in the reverse direction in the LP₁₁ propagation mode, as illustrated by an arrow 840. As set forth in the copending patent application, the grating reflector 820 can be constructed to have a series of periodic gratings with a periodicity of Λ, (wherein Λ is the distance between parallel lines forming the grating) so that light incident upon the grating reflector 820 in the LP₀₁ mode with a wavelength of λ₀₁ (wherein λ₀₁ refers to the wavelength at the input frequency in the LP₀₁ propagation mode) will be reflected back into the fiber 802 in the opposite direction at a wavelength λ₁₁ which corresponds to the wavelength of a signal at the same frequency in the LP₁₁ propagation mode. In order to achieve this reflection characteristic, the periodicity Λ of the grating reflector 820 is selected in accordance with the following equation: 1 Λ = 1 λ₀₁ + 1 λ₁₁ As set forth in the copending patent application, the grating reflector 820 acts as an inter-mode coupler when the periodicity of the grating is selected in accordance with Equation 1. The grating reflector 820 is particularly advantageous in that it is frequency selective and can separate light propagating in a plurality of frequencies such that the light propagating in the reverse direction, represented by the arrow 806, will only have a selected one of the plurality of frequencies. That frequency (having a wavelength λ₁, representing the freespace wavelength of an optical signal at the selected frequency) is the frequency wherein the LP₀₁ mode wavelength λ₀₁ and the LP₁₁ mode wavelength λ₁₁ satisfy Equation 1 for the periodicity Λ of the grating reflector 820. Thus, although the input light signal incident upon the first end 802 of the first multimode optical fiber 800, as represented by the arrow 804, has a plurality of optical frequencies (i.e., λ₁, λ₂, λ₃ . . . λ n ) only the optical signal having the wavelength λ₁, having propagation mode wavelengths λ₀₁ and λ₁₁ satisfying the equation 1, will be reflected by the grating reflector 800. The system in Figure 11 operates as follows. The light incident to the first end 802 of the first optical fiber 800 in the LP₀₁ mode propagates to the mode selector 814. The mode selector 814 is constructed with the fibers 800 and 810 selected so that the phase propagation velocities are matched only for coupling from the LP₁₁ mode of the first optical fiber 800 to the second LP₀₁ mode of the second optical fiber 810. Thus, optical signals propagating in the LP₀₁ mode of the first optical fiber 810 pass through the interaction region of the mode selector 814 with little coupling to the second optical fiber 810. The light incident to the grating reflector 820, represented by the arrow 830, thus comprises substantially all of the input light at the input frequencies λ₁, λ₂, λ₃, . . . λ n in the LP₀₁ mode. At the grating reflector 820 the input light at the frequency λ₁, which satisfies the equation (1) for the wavelength λ₀₁ for the LP₀₁ propagation mode and the wavelength λ₁₁ for the LP₁₁ propagation mode is reflected by the grating reflector 820 and propagates in the reverse direction in the LP₁₁ propagation mode as indicated by an arrow 840. When this light is incident upon the mode selector 814, the optical signal in the LP₁₁ propagation mode of the first optical fiber 800 is coupled to the LP₀₁ propagation mode of the second optical fiber 810 and is provided as an output signal, represented by an arrow 850, from an end 852 of the second optical fiber 810. The input optical signals at the other frequencies (represented by λ₂, λ₃. . . λ n are not reflected by the grating reflector 820 and continue to propagate in the LP₀₁ propagation mode of the first optical fiber 800 in the original forward direction as indicated by an arrow 860. Thus, the mode selector 814 and the grating reflector 820 act together to select the optical signal at the frequency corresponding to the wavelength λ₁, and provide it as a discrete output signal from the end 852 of the second optical fiber 810 in the LP₀₁ propagation mode. Additional pairs of mode selectors and grating reflectors (not shown) constructed for the other wavelengths (i.e., λ₂, λ₃, . . . λ n ) can be formed on the first optical fiber 800 to select the other wavelengths and provide them as discrete output signals. Thus, the embodiment of Figure 11 provides an advantageous means for separating optical frequencies from an input light having a plurality of input frequencies. From the discussions relating to the embodiments set forth above, it will be understood that the mode selector of the present invention utilizes two dissimilar optical fibers, one of which is multimode, while the other may be either single-mode or multimode. The multimode fibers of the present invention, however, are a special class of multimode fibers, referred to herein as "few-mode fibers," which propagate light in no more than about five to ten spatial modes. Those skilled in the art will recognize that it is difficult to accomplish the propagation velocity matching and mismatching discussed above in fibers that have more than about five to ten modes, since the difference between the propagation velocities decreases as the number of modes increases. Further, the propagation velocity difference for higher order modes is ordinarily less than for lower order modes. For example, the propagation velocity difference between the 99th order mode and the 100th order mode of a hundred mode fiber is very small compared to the propagation velocity difference between the first and second order modes of a double mode fiber. Thus, it is particularly advantageous to use few mode fibers in the present invention. While preferred embodiments of this invention have been disclosed herein, those skilled in the art will appreciate that changes and modifications may be made therein without departing from the scope of this invention, as defined in the appended claims.

Claims: A fiber optic mode selector, comprising: first and second dissimilar optical fibers (100, 110) which are juxtaposed to form an interaction region (156), said first fiber (100) having a core and a cladding which provide at least one propagation mode (LP₀₁) for light of a wavelength, said second fiber (110) having a core and a cladding which provide at least two propagation modes (LP₀₁, LP₁₁) for light of said wavelength, only two of said modes having matching propagation velocities such that light propagating in the matching mode in one of said fibers is efficiently coupled to the matching mode in the other of said fibers, one of the matching modes being in said first fiber (100) and the other being in said second fiber (110), said selector being characterized in that the cores (102, 112) of said fibers (100, 110) have substantially the same cross section inside said interaction region (156) as outside said interaction region (156), in that said second optical fiber (110) has an elliptical core (112), and in that the propagation velocity of each of the mismatched modes differs sufficiently from all of the other modes to prevent substantial optical coupling between any of the mismatched modes. A fiber optic mode selector, as defined by Claim 1, characterized in that said second fiber (110) has a core (112) which has a diameter greater than that of said first fiber (100). A fiber optic mode selector, as defined by either Claim 1 or 2, characterized in that said first fiber (100) is a single-mode fiber which propagates light exclusively in the first order mode (LP₀₁). A fiber optic mode selector, as defined by any one of Claims 1-3, characterized in that said second fiber (110) is a two-mode fiber which propagates light exclusively in first and second order modes (LP₀₁, LP₁₁). A fiber optic mode selector, as defined by any one of Claims 1-4, characterized in that said fibers are juxtaposed over an interaction region (156), the length of said interaction region (156) selected to cause substantially complete coupling between the two modes having matched propagation velocities. A fiber optic mode selector, as defined by any one of Claims 1-5, characterized in that one of said modes having matching propagation velocities is a higher order mode than the other of said modes having matching propagation velocities. A fiber optic mode selector, as defined by any one of Claims 1-6, characterized in that said mode selector additionally comprises means for controlling the orientation of the energy distribution pattern in said higher order mode to control the coupling between said modes having matching propagation velocities. A fiber optic mode selector, as defined by any one of Claims 1-7, characterized in that each of said fibers (100, 110) is arcuately mounted in a supporting structure (120, 130). A fiber optic mode selector, as defined by any one of Claims 1-8, characterized in that each of said fibers (100, 110) has cladding (104, 114) removed from one side thereof to form an oval cladding surface (144, 154). A fiber optic mode selector, as defined by any one of Claims 1-9, characterized in that said fibers (100, 110) are substantially parallel throughout said interaction region (156). A fiber optic mode selector, as defined by any one of Claims 1-10, characterized in that the light is coupled between said two fibers (100, 110) by evanescent field interaction between said matching modes. A fiber optic mode selector, as defined by any one of Claims 1-11, characterized in that the length of said interaction region (156) is at least an order of magnitude larger than the core diameter of either of said fibers. The fiber optic mode selector, as defined by any one of Claims 1-12, characterized in that one of the propagation modes of said second optical fiber (110) includes eigenmodes which have a lobe-like pattern, the optical fiber (110) causing the eigenmodes to propagate down the second optical fiber without changing, thereby allowing the lobe-like pattern to be oriented for maximum coupling between said second optical fiber (110) and said first optical fiber (100). The fiber optic mode selector, as defined by any one of Claims 1-13, further comprising a grating reflector (820), disposed at a location on said first fiber (800) for coupling light between the two propagation modes of the first fiber (800). A method of separating plural light signals having respective plural frequencies, comprising the steps of: selectively coupling one of said plural light signals from a first propagation mode (LP₀₁) of a first optical fiber (800) to a second propagation mode (LP₁₁) of said first optical fiber (800), each of said propagation modes of said first optical fiber (800) having different propagation velocities; optically coupling said second mode (LP₁₁) of said first optical fiber (800) to a propagation mode of a dissimilar second optical fiber (810), said fibers being juxtaposed to form an interaction region (156) and the cores (102, 112) of said fibers (100, 110) having substantially the same cross section inside said interaction region (156) as outside said interaction region (156), said first and second fibers forming a reciprocal mode selector comprising an input port and an output port, said mode of said dissimilar optical fiber (810) having a propagation velocity which matches the propagation velocity of said second mode to cause transfer of light therebetween, without causing substantial transfer of light between said first mode and said dissimilar optical fiber mode; and outputting said one of said plural light signals at said output port of said mode selector. A method of selectively coupling light signals by launching them into a fiber optic mode selector according to any of Claims 1 to 14.

Inventors: KIM BYOUNG Y, SHAW HERBERT J, SORIN WAYNE V, KIM, BYOUNG Y., SHAW, HERBERT J., SORIN, WAYNE V.
Applicants: UNIV LELAND STANFORD JUNIOR, THE BOARD OF TRUSTEES OF THE LELAND STANFORD JUNIOR UNIVERSITY
Application year: 1987
Main classification: G02B6
IPC codes: G02B6