Fiber optic inter-mode coupling single side band frequency shifter

Abstract: An optical fiber (300) is subjected to a series of traveling flexural waves or microbends propagating along a length of the fiber. At least a portion of an optical signal propagating within the optical fiber in a first propagation mode is coupled to a second propagation mode. The optical signal in the second propagation mode has a frequency which is equal to either the sum of or the difference between the frequency of the optical signal in the first propagation mode and the frequency of the traveling flexural waves or microbends. The frequency of the optical signal in the second propagation mode is shifted upward or downward from the frequency of the optical signal in the first propagation mode as determined by the direction of propagation of the first optical signal with respect to the direction of propagation of the traveling flexural waves or microbends, and as also determined by whether the phase propagation velocity of the optical signal in the first propagation mode is greater than or less than the propagation velocity of the optical signal in the second propagation mode.

Description: Field of the Invention The present invention relates generally to fiber optic devices, and, more specifically, to devices which couple light energy from an optical signal input into an optical fiber in one mode at one frequency to a different mode at a shifted frequency. Background of the Invention Fiber optic frequency shifters are useful devices for a variety of fiber optic sensor and signal processing applications, such as in fiber optic gyros and the like. It has been shown, for example in European patent application number 84308010.2, filed November 20, 1984, published on June 12, 1985 under Publication Number 0144190 and assigned to the assignee of the present application, that light launched in one propagation mode of a fiber can be coupled to another propagation mode and shifted in frequency by propagating an acoustic wave along the length of the fiber to cause a periodic stress of the fiber. The light is shifted in frequency by an amount equal to the frequency of the acoustic wave. The European patent application number 84308010.2 is incorporated herein by reference. As set forth in the above-referenced copending application, if the acoustic wave propagates along the fiber in the same direction as an optical signal propagates through the fiber, light traveling in a first propagation mode in the fiber at a first phase velocity and at a first frequency is coupled to a second propagation mode at a second phase velocity higher than the first phase velocity and is shifted downward in frequency. Similarly, if the light is originally propagating in the fiber in a faster propagation mode, the light is coupled to a slower propagation mode at a higher frequency. On the other hand, if the acoustic wave propagates along the fiber in a direction opposite the direction that an optical signal is propagating through the fiber, light traveling in a slower propagation mode is coupled to a faster propagation mode and is shifted upward in frequency. Similarly, light traveling in a faster propagation mode opposite the direction of propagation of an acoustic wave is coupled to a slower propagation mode and is shifted downward in frequency. For optimal coupling to occur in the frequency shifter described in the above-referenced copending application, the acoustic wavelengths in the direction of propagation of the optical signal through the fiber should be substantially equal to the beat length of an optical signal traveling through the fiber. As is well known, when light travels through a fiber in more than one propagation mode, the light travels through the fiber at a different phase velocity for each of the different propagation modes. Light traveling in the slower propagation mode travels at a lower phase velocity than light in a faster propagation mode. Thus, a light signal having a fixed frequency will have a longer wavelength in the faster propagation mode than it has in the slower propagation mode. As the light propagates down the length of the fiber, a phase difference will thus develop between the light in the two modes. At spatially periodic distances, the light in the two modes will be in phase. The distance between successive locations where the light is in phase is referred to as the beat length of the fiber for the two modes at a specified frequency. For the devices discussed in the above-mentioned co-pending application, this is the beat length that must match the acoustic wavelength in order to achieve optical coupling of energy, between the modes. The light propagating along a fiber in one propagation mode is converted to light propagating in a second propagation mode by applying a periodic, travelling wave, compressive force along a segment of the length of the fibers. A more complete description of this technique is found in "Single-Sideband Frequency Shifting in Birefringent Optical Fiber", W. P. Risk, et al., SPIE Volume 478 - Fiber Optic and Laser Sensors II (1984), pp. 91-97, which is incorporated herein by reference. Another example of a prior art fiber optic frequency shifter is shown in European Patent Application No. 85300904.1, filed February 11, 1985, published on August 28, 1985 under Publication No. 0153124 and assigned to the assignee of the present application. In the above-referenced prior art, a fiber optic frequency shifter comprises an optical fiber for guiding a lightwave and an acoustic transducer for generating an acoustic wave. The acoustic transducer is positioned relative to the fiber to cause the wave front of the acoustic wave to acoustically contact the fiber at an angle which is less than 90 degrees. The angle can be adjusted to match the beat length of the optical fiber to the wavelength of the acoustic wave. The present invention is a coupling apparatus as defined in Claim 1, and a coupling method as defined in Claim 31. It is an improvement over known methods of shifting the frequency of an optical signal propagating in an optical fiber, and it provides for more efficient utilization of the energy input into fiber to cause the coupling. The present invention also has a broader optical bandwidth and is thus usable over a broader range of frequencies. The additive effect of the microbends comprising the microbend wave causes an optical signal input into the optical fiber at a first frequency in one of the two propagation modes to be coupled to an optical signal in the other of the two propagation modes at a second frequency which is either the sum of or the difference between the first frequency and the frequency of the traveling microbend wave. In preferred embodiment, the optical signal is input into the optical fiber in the first order LP₀₁ propagation mode at a first phase velocity. When the periodic microbend wave is propagating along the length of the fiber in the same direction as the optical signal is propagating in the fiber, the optical energy in the first order LP₀₁ mode is coupled to a high order mode (e.g., the LP₁₁ mode) at a higher phase velocity and is shifted downward in frequency from the first frequency to a second frequency which is lower than the first frequency. The second frequency is equal to the difference between the first frequency and the frequency of the periodic microbend wave. When the optical energy is input into the fiber in the second order LP₁₁ mode and propagates in the same direction as the propagation of the periodic microbend wave, optical energy is coupled from the second order LP₁₁ mode to the first order LP₀₁ mode with a shift upward in frequency to a second frequency and a corresponding decrease in phase velocity. The second frequency in this case is equal to the sum of the first frequency and the frequency of the periodic microbend wave. On the other hand, if the optical energy is input into the fiber and propagates in the opposite direction as the direction of propagation of the periodic microbend wave, optical energy input into the higher order LP₁₁ mode at a first frequency is coupled to the first order LP₀₁ mode at a second frequency lower than the first frequency and the phase velocity decreases. The second frequency is equal to the first frequency minus the frequency of the traveling periodic microbend wave. Similarly, optical energy input into the fiber at a first frequency in the first order LP₀₁ mode and propagated in a direction opposite the direction of propagation of the traveling microbend wave is coupled from the first order LP₀₁ mode to the second order LP₁₁ mode and is shifted upward in frequency from the first frequency to a second frequency equal to the sum of the first frequency and the frequency of the periodic microbending, and the phase velocity is increased. The present invention is particularly advantageous in that it employs a multimode optical fiber rather than a single-mode birefringent fiber as used in the prior art frequency shifters that couple light between the polarization modes of an optical signal. Exemplary prior art devices require precise alignment of the birefringent axes of a birefringent fiber with the transmission axes of polarizers at both the input end and the output end of the birefringent fiber to assure that the light is input to the fiber and received from the fiber in the proper polarization mode. The present device does not require precise alignment since it does not critically depend upon the polarization of the light input to it. Furthermore, since the propagating microbend wave is confined to the fiber, the fiber does not have to be precisely straight as in other prior art devices to maintain the proper relationship between the beat length of the optical signal and the wavelength of the propagating microbend wave. Therefore, the present invention is substantially easier to construct than prior art devices. The present invention is particularly advantageous in that it operates over a broad range of optical frequencies and over a broad range of modulation frequencies. The broad range of optical frequencies results from the coupling of optical energy between spatial propagation modes. The beat length of two spatial propagation modes for an optical signal does not vary significantly over a relatively large frequency range. The broad range of modulation frequencies results from the fact that the modulation energy is concentrated in the traveling microbend wave in the fiber and thus a large amount of energy is available to effectuate coupling from one spatial propagation mode to the other spatial propagation mode in a relatively few number of beat lengths. Thus, the modulation wavelength can deviate by a relatively large percentage from the wavelength corresponding to the beat length without causing a large accumulation of phase error between the optical beat lengths and the traveling microbend wave. The combined effect of the large absolute frequency of modulation corresponding to the beat length of the optical signal propagation modes and the acceptable deviation from the frequency provides a relatively broad absolute range of modulation frequencies. No compressive forces are required to cause the coupling of light between the two propagation modes. Thus, no error is introduced into the optical signals by static coupling which can cause an output signal in the coupled propagation mode in the absence of a modulation signal. The periodic microbending is introduced into the fiber by a transducer which is bonded to a portion of the fiber. The transducer is caused to vibrate at a frequency which is selected to generate a series of periodic microbends having a propagation constant substantially equal to the difference in the propagation constants of the two propagation modes in the optical fiber. In one preferred embodiment, the transducer is an acoustic transducer which is coupled to the optical fiber via a fused quartz rod. The fused quartz rod has a first end which has substantially the same diameter as the optical fiber and which is fused to only one side of the optical fiber. The quartz rod has a second end which is substantially larger than the first end and which has an piezoelectric acoustic transducer bonded to it. When an electrical signal is applied to the piezoelectric transducer, an acoustic wave propagates from the second end of the quartz rod to the first end and thus causes a vibration to be induced in the optical fiber. The vibration propagates away from the first end of the quartz rod as a series of periodic microbends in the optical fiber. The propagation velocity of the acoustic wave along the length of the fiber is dependent upon the cross-sectional dimensions of the optical fiber. Thus, the wavelength of an acoustic wave is dependent upon the cross-sectional dimensions of the fiber as well as dependent upon the acoustic frequency. In alternative embodiments of the present invention, the optical fiber in the frequency shifter has cross-sectional dimensions that vary along the length of the fiber. The fiber thus provides a plurality of different locations wherein the frequency of the acoustic wave having a wavelength that matches the optical beat length varies in accordance with the cross-sectional dimensions. This enables the acoustic frequency to be varied while providing a region on the fiber where substantial coupling occurs for each of the frequencies. The cross-sectional dimensions of the optical fiber can advantageously be varied in discrete steps to provide a plurality of fiber portions that define coupling regions. A first portion preferably has a larger outer diameter than a second portion so that a traveling flexural wave at a first acoustic frequency has a first acoustic velocity in the first portion corresponding to an acoustic wavelength that matches the optical beat length in the fiber, and so that a traveling flexural wave at a second frequency has substantially the same acoustic wavelength in the second portion of the fiber and thus also matches the optical beat length. An optical signal in the fiber can be selectively shifted in frequency by selecting the acoustic frequency of the traveling flexural waves. The traveling flexural waves are preferably generated by an acoustic transducer. The acoustic transducer is preferably an elongated member having a first small end mechanically coupled to the optical fiber and a larger end having an electrically driven transducer, such as a piezoelectric transducer, disposed thereon. Application of an electrical signal to the electrically driven transducer generates an acoustic wave at the large end of the elongated member that propagates to the smaller end where it induces a flexural wave in the fiber. In preferred embodiments of the invention, the elongated member has a cavity proximate to the larger end to suppress propagation of bulk acoustic waves in the elongated member. The cavity can advantageously be filled with an acoustic damping material. In preferred embodiments of the invention, the optical fiber of the frequency shifter is a two-mode optical fiber having a core with an elliptical cross section such that the lobe orientations of one of the higher order propagation modes of the fiber is non-degenerate with the orthogonal lobe orientation of the same mode. In one embodiment of a system incorporating the present invention, the system includes a first segment of a multimode optical fiber which receives light from a single-mode optical fiber. The light entering this first segment of multimode optical fiber is preferably propagating substantially entirely within the fundamental or first order LP₀₁ mode. The optical signal has a wavelength which will propagate through the multimode fiber in both the first and second order propagation modes. A mode stripper is preferably provided at the first segment of multimode fiber to suppress further propagation of any light energy which may be traveling in the second order LP₁₁ propagation mode. The mode stripper may be advantageously produced by forming a portion of the first segment of the multimode fiber into a coil sized to have a proper coil diameter to strip light propagating in the second order mode from the fiber without affecting the light propagating in the first order mode. Alternatively, the mode stripper may comprise one-half of a directional coupler. The light from the second order mode is stripped from the fiber by applying a liquid, having an appropriate index of refraction, to the exposed segment of fiber to cause the light traveling in the second order propagation mode to be lost from the fiber. The light leaving the mode stripper, which contains only light traveling in the first order LP₁₀ propagation mode, then enters a second segment of the multimode optical fiber. The second multimode fiber segment is part of an inter-propagation mode, frequency shifter build in accordance with the present invention. Accordingly, a periodic, traveling microbend or flexural wave is induced in the second segment such that it propagates along the length of the second segment of the multimode fiber. The wavelength of the traveling microbend or flexural wave is matched to the beat length of the optical signal traveling in the fiber. The periodic, traveling microbend or flexural wave causes light energy in the first order LP₀₁ propagation mode to be coupled to the second order LP₁₁ propagation mode because of the periodically repeating series of bends which the wave causes in the multimode optical fiber. The traveling microbends also cause the light so coupled to be frequency shifted by an amount equal to the frequency of the periodic, traveling microbend or flexural wave. After the frequency shifter, the second segment of the multimode optical fiber is connected to a fiber optic mode selector for multimode signals. The mode selector is configured to couple only that light which is propagating in the second order LP₁₁ propagation mode from the multimode fiber to an immediately adjacent single-mode fiber. Thus, the only light transmitted from the fiber optic mode selector is that light which has been coupled to the second order LP₁₁ propagation mode and shifted in frequency. The fiber optic mode selector is constructed in accordance with the description set forth in a copending U.S. Patent Application Serial No. 820,411, entitled "Fiber Optic Mode Selector," filed on the same date as the present application, and assigned to the assignee of the instant application. The copending application is incorporated herein by reference. The present invention may be more fully understood from the following detailed description, taken in conjunction with the drawings. Brief Description of the Drawings Figure 1a is a graphical illustration of the electric field distribution for the LP₀₁ optical propagation mode. Figure 1b is a graphical representation of the electric field distribution for the LP₁₁ optical propagation mode. Figure 2 is a partial cross sectional view of a bend in an optical fiber pictorially illustrating the coupling effect from the LP₀₁ optical mode to the LP₁₁ optical mode. Figure 3 is a pictorial illustration of the phase relationships between the optical signals traveling in the two propagation modes. Figure 4 is a pictorial representation of an optical fiber formed into a series of static microbends. Figure 5 is a perspective illustration of the present invention showing an optical fiber and a transducer mechanically connected to the optical fiber to induce a series of traveling microbends in the optical fiber. Figure 5a is a cross sectional view taken along the lines 5a-5a in Figure 5 showing the attachment of the optical fiber to the transducer. Figures 6a-6e are partial elevational views showing the operation of the transducer to generate the traveling microbends in the optical fiber. Figure 7a is a graphical representation of the coupling between the propagation modes when the optical signal is traveling in the same direction as the direction of propagation of the traveling microbends. Figure 7b is a graphical representation of the coupling between the propagation modes when the optical signal is traveling in the opposite direction as the direction of propagation of the traveling microbends. Figure 8 is a perspective illustration of a preferred embodiment of a transducer to generate the traveling microbends in the optical fiber. Figure 9 is a pictorial illustration of the present invention in combination with a fiber optic mode selector to produce an optical output signal from the mode selector which is shifted in frequency from an optical signal input into the combination. Figure 10a is an illustration of an embodiment of the present invention showing the acoustic horn and the optical fiber. Figure 10b is an illustration of an alternative embodiment of the present invention showing an acoustic horn with a cavity for suppressing bulk acoustic waves. Figure 11 is a perspective view of a cylindrical rod showing the coordinate system used to mathematically define the acoustic wave propagation in the present invention. Figures 12a, 12b, 12c, and 12d are plots of longitudinal mode dispersion curves for values of Poisson's ratio of 0.1, 0.2, 0.3 and 0.4, respectively. Figure 13 is a plot of longitudinal mode group and phase velocity in fused silica as a function of fa/c t . Figures 14a and 14b are graphs of longitudinal mode characteristics in a cylinder in terms of the cylinder radius with fa/c t as a parameter for axial and radial displacements, respectively. Figure 15 is a graph of phase velocity as a function of fa/c t for the five lowest circumferential modes of a cylindrical rod. Figures 16a, 16b, 16c and 16d are graphs of dispersion curves for the first five flexural wave modes in a cylinder for Poisson's ratio of 0.1, 0.2, 0.3 and 0.4, respectively. Figures 17a, 17b, 17c and 17d are graphs of phase velocity versus fa/c t for flexural waves where the mode number n is equal to 2 for Poisson's ratio of 0.1, 0.2, 0.3, and 0.4, respectively. Figure 18 is a graph of the calculated phase velocity (solid lines) and the group velocity (dashed line) as a function of the cylinder radius with fa/c t as a parameter for the lowest order flexural mode in fused silica. Figures 19a, 19b and 19c are graphs illustrating the flexural wave mode pattern variation as a function of the fa/c t parameter in the radial, azimuthal and axial directions, respectively. Figure 20 is a graph of the maximum displacement amplitude as a function of fa/c t for the three lowest modes in fused silica showing the graph for the flexural mode as a solid line, the graph for the longitudinal mode as a dashed line, and the graph of the torsional mode as a phantom line. Figure 21a is a graph of the coupling efficiency k e as a functional of a/L b for the coupling of light from one mode into the other mode through interaction with a traveling acoustic wave propagating in the fiber. Figure 21b is a graph of the normalized frequency (synchronous frequency) fL b /C ext as a function of a/L b . Figure 22a illustrates an alternative embodiment of the present invention utilizing an optical fiber having a plurality of portions with differing radii to provide interaction regions responsive to a plurality of acoustic frequencies. Figure 22b illustrates an alternative embodiment of the present invention in which the radius of the optical fiber varies gradually. Figure 23 is an illustration of the LP₁₁ mode degeneracy in circular core fiber showing the LP₀₁ and LP₁₁ modes plotted in terms of their relative propagation constants. Figure 24 illustrates two far-field radiation patterns from the end of a double-mode fiber. Figure 25 illustrates three far-field radiation patterns of light from an elliptical core fiber. Detailed Description of the Preferred Embodiments A multimode fiber is a fiber which can support more than one spatial propagation mode for an optical signal. Typically, such fibers comprise an inner core of relatively large refractive index surrounded by an outer core of relatively low refractive index. As is well known in the art, the fundamental, first order LP₀₁ propagation mode, or even mode, has the slowest phase propagation velocity of the spatial propagation modes. Figure 1a illustrates an amplitude diagram for the electric field distribution of the LP₀₁ mode with respect to the core of the optical fiber. The portion of an optical signal traveling in the LP₀₁ mode has its optical energy concentrated near the center of the core of the optical fiber as illustrated by the maximum 10 in the amplitude diagram in Figure 1a. As the distance from the center of the core increases, the amplitude of the light decreases. In contrast to the lower order LP₀₁ mode, light traveling in the second order LP₁₁ mode or odd mode, has an electrical field amplitude distribution having two maxima 20 and 22 displaced away from the center of the core as illustrated Figure 1b. As also illustrated in Figure 1b, the amplitude of the optical energy in the fiber at diametrically opposed locations in the core are 180° (π radians) out of phase with each other. In a substantially straight, unstressed optical fiber, the LP₀₁ mode and the LP₁₁ mode are considered to be orthogonal propagation modes such that light traveling in one of the modes is not ordinarily coupled to the other mode. This non-coupling condition is a maintained so long as the amplitude distribution is symmetrical about the center of the core, as illustrated by the LP₀₁ mode in Figure 1a, or substantially 180° out of phase about the center of the core as illustrated by the odd mode in Figure 1b. While these conditions are maintained, there is no overlap between the two modes and thus no coupling between the modes. Since the first order LP₀₁ mode has its energy concentrated near the center of the core, substantially all of the optical energy travels in the core. In contrast, the second order, LP₁₁ mode has a substantially larger portion of its energy distributed near the cladding. Since the cladding has a lower refractive index than the core, the phase velocity of the second order LP₁₁ mode is higher than the phase velocity of the first order LP₀₁ mode. It has been found that if a fiber 100, having a core 102 and a cladding 104, is bent, as illustrated in cross section in Figure 2, a portion of the optical energy entering the bent portion of the fiber in one mode (e.g., the first order LP₀₁ mode) is coupled to the orthogonal mode (e.g., the second order LP₁₁ mode) as the optical energy propagates through the bent portion of the fiber 100. One explanation for this effect is that the optical energy traveling through the core 102 of the fiber 100 on the inside of the bend has a shorter path then the light traveling on the outside of the bend. Referring to Figure 2, location 106 designates the beginning of the bent portion of the fiber 100. Location 108 designates the end of the bent portion of the fiber 100. An electric field amplitude distribution curve 110 is superimposed upon the cross section of the fiber 100 at the location 106 and illustrates that the optical energy is in the LP₀₁ mode (i.e., the electric field amplitude distribution is symmetrical about the center of the fiber). A second optical amplitude curve 112 illustrates the amplitude of the optical energy in the LP₁₁ mode. In this example, it will be assumed that there is no light in the second order LP₁₁ mode at the location 106, and thus, the electric field distribution amplitude curve 112 is shown as having zero magnitude. Thus, all of the optical energy is concentrated in the LP₀₁ mode at the location 106 of the fiber 100. In the straight portion of the optical fiber before the location 106, the LP₀₁ and LP₁₁ modes are orthogonal and no coupling occurs. As the optical signal travels from the location 106 to the location 108, a portion of the optical signals traveling along the center of the core, illustrated in phantom lines by a path 120. A portion of the optical signal also travels along an inner path 122, illustrated in dashed lines, which has a shorter radius than the path 120 in the center of the fiber core and thus has a shorter path length. Additionally, a portion of the optical signal travels along a path 124, also illustrated by dashed lines, which has a larger radius than the path 120 and thus has a longer path length. Thus, an optical signal traveling along the path 122 or any other path having a radius smaller than the radius of the center of the core will travel a shorter distance from the location 106 to the location 108 than an optical signal traveling along the path 124 or any other path having a radius greater than the radius of the path 120. Because of the difference in the lengths of the paths from the location 106 to the location 108, the optical signal which was in phase across a cross-section of the fiber 100 at the location 106, is no longer in phase when it reaches the location 108. Thus, the amplitude distribution of the optical signal at the location 108 does not correspond to the symmetrical distribution shown in Figure 1a. Therefore, the optical signal is no longer entirely orthogonal to the LP₁₁ mode, and a portion of the optical signal is coupled to the LP₁₁ mode. As illustrated in Figure 2, at location 108 the amplitude of the signal in the LP₀₁ mode, depicted by a curve 110′ has been reduced in amplitude. Furthermore, a curve 112′, representing the optical amplitude in the LP₁₁ mode, no longer has a zero magnitude. Thus, a portion of the optical energy is transferred from the LP₀₁ mode to the LP₁₁ mode. The fraction of energy transferred from the LP₀₁ mode to the LP₁₁ mode depends upon the radius of the bend of the fiber core 102 and upon the length of the fiber core 102 which is so bent. The foregoing effect is reciprocal in that light energy input into the fiber such that it is traveling in the LP₁₁ mode is coupled to the LP₀₁ mode. When an optical signal is traveling in the core 102 of the fiber 100 in two different propagation modes, light traveling in the first order LP₀₁ mode travels at a slower phase propagation velocity than light traveling in the second order LP₁₁ mode. Thus, if the light in the two modes is from the same source and has the same frequency, light traveling a distance L in the first order LP₀₁ mode will take more time to travel the distance L than the light traveling the same distance in the second order LP₁₁ mode. Thus, the phase of the light in the LP₀₁ mode will lag the phase of the light in the LP₁₁ mode through the distance L. This is pictorially illustrated in Figure 3. The light traveling in the LP₁₁ mode is represented as a series of waves 150 and the light traveling in the LP₀₁ mode is represented as a series of waves 152. The length L is selected such that if an optical wavefront traveling in the LP₀₁ mode completes exactly n cycles in traveling the distance L, the light traveling in the LP₁₁ mode will complete exactly n-1 cycles. This is illustrated in Figure 3. Thus, when the light in the LP₁₁ mode is exactly in phase with the light in the LP₀₁ mode at the beginning of the distance L, designated as the locations 154 and 156 on the curves 150 and 152, respectively, the light will also be in phase at the end of a distance L, illustrated as locations 158 and 160 on the curves 150 and 152, respectively. Similarly, when the light has traveled a distance of L/2, the light in the LP₁₁ mode is 180° (π radians) out of phase with the light in the LP₀₁ mode, as illustrated by the locations 162 and 164 on the curves 150 and 152, respectively. The distance L is referred to as the beat length of the fiber 100 for the two propagation modes at a selected frequency. The distance L is calculated as L = 2π Δk (1) where Δk is the difference in the propagation constants of the two modes along the fiber. As is well known, the propagation constant, k, is 2π times the number of cycles of a signal in a unit length, and is calculated as follows: k = 2π λ (2) where λ is the wave length in the medium in which the signal is propagating. As set forth above, a signal propagating in the first order LP₀₁ mode propagates at a lower velocity and thus has more cycles per unit length than the second order or LP₁₁ mode. Thus, a given signal at a given frequency propagating in the first order LP₀₁ mode will have a higher propagation constant k₀₁ than a signal than a propagation constant k₁₁ of the same signal propagating at the same frequency in the second order LP₁₁ mode. Returning to Equation (1), above, the beat length L is thus inversely proportional to the difference (Δk=k₀₁-k₁₁) in the propagation constants in the two modes. A greater difference Δk in the propagation constant results in a smaller beat length, and vice versa. Typically, the difference in the propagation constants between the first order LP₀₁ propagation mode and the second order LP₁₁ propagation mode is greater than the differences in the propagation constants between two polarization modes of a signal in a birefringent fiber. Thus, the beat lengths of the two spatial propagation modes are shorter than the beat lengths of the two polarization modes. It has been found that if an optical frequency, referred to as a center frequency, is selected to provide a minimum beat length for the first and second order propagation modes, the frequency of the optical signal can be varied substantially above and below the center frequency without causing a significant change in the difference between the propagation constants of the two modes. Thus, the beat length of the two propagation modes does not vary significantly at frequencies near the center frequency. Therefore, the beat length is relatively insensitive to changes in optical frequency over a relatively broad optical frequency range in comparison to the sensitivity of the beat length between two polarization modes of a birefringent fiber. It has been discovered that when an optical fiber is formed into a series of periodic bends which are spaced by a beat length, then the coupling between the two spatial propagation modes of an optical signal traveling through the fiber will have a cumulative effect. As illustrated in Figure 4, a length of a fiber 200 has a series of small bends 202, 204, 206, 208, 210, 212 and 214, referred to as microbends, which are spaced apart such that the distance between corresponding bends (i.e., between bends in the same direction) is substantially equal to L, the beat length of an optical signal passing through the fiber 200. The effect of each section having a length of L is cumulative with each other section having an length of L to cause a cumulative coupling of optical energy from one mode to another mode in the fiber 200. This effect was demonstrated in theory in "Bending Effects in Optical Fibers," Henry F. Taylor, Journal of Lightwave Technology , Vol. LT-2, Pages 616-633 (1984). In that paper, the periodic microbends were introduced by statically positioning the fiber between opposing periodic structures. Thus, the coupling between the modes was a static coupling which did not effect any change in the frequency of the optical signal in the coupled mode. Figure 5 illustrates an embodiment of the present invention in which a traveling periodic microbend is introduced into a multimode fiber to cause light to be coupled from one mode to another and to be shifted in frequency. The present invention comprises an optical fiber 300, having a first end portion 302 into which an optical signal, represented by an arrow 304, is introduced at a first angular frequency ω₀. The fiber 300 is secured to a transducer 310. The transducer 310 is preferably a shear transducer comprising PZT (lead-zirconium-titanate), lithium niobate (LiNbO₃) or another piezoelectric material. As shown in Figure 5a, the fiber 300 may advantageously have a small portion of its outer cladding removed to form a flat surface 312 which rests on a top surface 314 of the transducer 310 to thereby provide additional mechanical contact between the transducer 310 and the fiber 300. The fiber 300 can be secured to the transducer 310 by epoxy 316 or other securing means. The transducer 310 is driven by an electrical signal source 320 (shown schematically), which, in the preferred embodiment, is an a.c. source. When activated by the source 320, the transducer 310 operates in the shear mode as illustrated in Figures 6a-6e. The transducer 310 is shown in cross section in Figure 6a with the fiber 300 mounted to the top surface 314 of the transducer 310. The transducer 310 has a first side 324 and a second side 326. At rest, the cross section of the transducer 310 is substantially rectangular. When the electrical signal 320 is applied to the transducer 310 with a first polarity, the transducer 310 operates in the shear mode causing the first side 324 and the second side 326 to be displaced in opposite directions indicated by the arrows 328 and 330, respectively, in Figure 6b. This causes the fiber 300 to be displaced at an angle with respect to the rest position shown in Figure 6a. When the a.c. electrical signal applied to the transducer 310 reaches a zero crossing, the first side 324 and second side 326 return to their rest positions as illustrated in Figure 6c, thus returning the fiber 300 to its rest position. When the a.c. electrical signal is applied to the transducer 310 with the opposite polarity to the polarity applied in Figure 6b, the first side 324 and the second side 326 are displaced in directions indicated by the arrows 332, 334 in Figure 6d. This displacement is opposite to the displacement illustrated in Figure 6b. Thus, the fiber 300 is displaced at an angle opposite the angle of displacement in Figure 6b. When the a.c. electrical signal again reaches zero crossing, the first side 324 and the second side 326 again return to their rest positions and the fiber 300 thus returns to its rest position as illustrated in Figure 6e. In the preferred embodiment, the a.c. electrical signal is applied to the transducer 310 so that the fiber 300 is periodically displaced to thereby induce a flexural wave in the fiber 300 which propagates as a series of traveling microbends along the length of the fiber 300 away from the transducer 310. The traveling microbends have a frequency that is determined by frequency of the a.c. source 320. The present invention preferably includes a first damper 336 formed of damping material which surrounds the fiber 300 at a location proximate to the side 324 of the transducer 310. Thus, any flexural wave which travels away from the transducer 310 in the direction towards the damper 336 is suppressed. Therefore, the flexural waves travel away from the transducer 310 in one direction only, as indicated by an arrow 340 in Figure 5. The damper 336 can advantageously be supported by a first support block 342. The first support block 342 can also serve as a mounting block for the transducer 310 to hold the transducer 310 in a fixed relationship to the damper 336. The present invention also preferably includes a second damper 344, formed of damping material through which the fiber 300 passes to thereby suppress any further propagation of the traveling microbends so that the microbends have no further effect beyond the second damper 344. The second damper 344 is preferably supported by a second support block 346. The second damper 344 is positioned so that only a selected length of the optical fiber 300 is affected by the traveling microbends. In some applications, in which a long interaction length may be desired, the second damper 344 may not be necessary as the traveling microbend wave will be attenuated by the length of the fiber 300. The optical fiber 300 can be suspended by air, vacuum, or another medium between the first support block 342 and the second support block 346. The medium can be any material which does not attenuate the traveling microbend waves and which does not conduct any of the energy away from the optical fiber 300. It is not necessary that the fiber 300 be taut between the first and second support blocks 342, 346, nor is it necessary that the fiber be straight so long as the fiber 300 is not bent with a radius sufficiently small so that the optical signal in the fiber 300 is perturbed by the bend. The frequency of the electrical signal applied to the transducer 310 is chosen so that the flexural wave thus produced has a wave length along the fiber which is substantially equal to the beat length L as indicated in Figure 5. Thus, as discussed above, the coupling of optical energy from one propagation mode to the other propagation mode will be reinforced in each section of the fiber. However, unlike the previously discussed static microbend device, the microbends in the fiber 300 propagate along the length of the fiber 300 at a velocity v p . The propagation velocity v p is determined by the particular characteristics of the fiber 300. The frequency of the electrical signal applied to the transducer 310 (referred to hereinafter as f a ) is selected so that the wave length (referred to hereinafter as λ a ) of the propagating microbend is substantially equal to the beat length L. Since the frequency f a is equal to the velocity v p divided by the wave length λ a , then the frequency f a is determined by: The angular frequency ω a of the electrical signal is ω a = 2πf a . It has been shown that when a propagating acoustic wave causes a periodic, traveling stress on an optical fiber, the effect of the traveling acoustic wave is to cause light to be coupled from one polarization mode to another polarization mode and be shifted in frequency. See for example "Single-Sideband Frequency Shifting in Birefringent Optical Fiber," W. P. Risk, et al., SPIE Vol. 478 - Fiber Optic and Laser Sensors II (1984), pp. 91-97, in which this effect is discussed with respect to coupling between polarization modes in a birefringent fiber. A similar effect has been described for multimode fibers for an externally applied stress to the fiber. See, for example, co-pending U.S. Application Serial No. 556,636, "Single-mode Fiber Optic Single-sideband Modulator" filed November 30, 1983, and assigned to the same assignee as the present application. Thus, an optical signal, illustrated as an arrow 350, exiting from a second end portion 352 of the fiber 300 exits at an angular frequency ω s , which is shifted in frequency from the angular frequency ω₀ which was input at the first end portion 302 of the fiber 300. As will be shown below, the frequency ω s is equal to the angular frequency ω₀ plus or minus the angular frequency ω a of the signal applied to the transducer 310 (i.e., ω s =ω O ±ω a ). Whether the frequency ω a is added to or subtracted from the frequency ω₀ is determined by whether the signal is input in the first order LP₀₁ mode or the second order LP₁₁ mode and whether or not the optical signal is propagating in the same direction as the propagating microbend. The embodiment of Figure 5 is bidirectional in that the optical signal ω₀ can be introduced into the second end portion 352 and thereby be caused to propagate towards the first end portion 302 in a direction opposite the direction of propagation of the traveling microbend. The frequency shifting referred to above can be understood further by referring to Figures 7a and 7b which illustrate ω-k diagrams that help explain the frequency shifting effect of the invention illustrated in Figure 5. Figure 7a is an ω-k diagram for an optical signal which propagates through the fiber 300 in the same direction as the propagation of the traveling flexural wave or microbend generated by the transducer 310. The horizontal axis represents the phase propagation constant k of the optical signal. The vertical axis represents the angular frequency ω of the optical signal. As illustrated, the phase propagation constant varies with the frequency (i.e., as the frequency ω increases, the propagation constant k increases). As is well known, the relationship between the phase propagation constant and the frequency varies with the phase propagation velocity through the optical fiber 300. This is illustrated by a first graph 400 corresponding to the LP₁₁ mode and a second graph 402 corresponding to the LP₀₁ mode. At any particular frequency, the slope of a line from a location on one of the graphs 400 or 402 to the origin represents the phase propagation velocity at that frequency in the respective mode (i.e., velocity = slope = ω/k = (radians/ sec) ÷ (radians/meter) = (meters/sec) . The first and second graphs 400 and 402 are bounded by a dashed line 404 representing the velocity of a signal propagating through a medium having the same refractive index as the cladding and bounded by a dashed line 406 representing the velocity of a signal propagating through a medium having the same refractive index as the core. Since the optical energy propagating in the LP₀₁ mode is concentrated in the core of the fiber, the second graph 402 is shown to be asymptotic to the line 406 at higher frequencies. Similarly, since the optical energy propagating in the LP₁₁ mode is dispersed more towards the cladding, the graph 400 is offset from the graph 402 towards the line 404. In other words, the phase velocity of the LP₁₁ mode is greater than the phase velocity of the LP₀₁ mode. The phase velocity of the LP₁₁ mode at the angular frequency ω o is shown as a line 408 that represents the slope of the LP₁₁ ω-k graph 400 at that frequency. As illustrated, the line 408 has a greater slope than the slope of the LP₀₁ ω-k graph 402 at that frequency. One skilled in the art will recognize that the graphs 400 and 402 converge asymptotically at very large optical frequencies although they are shown as essentially parallel lines at the frequencies of interest in Figures 7a and 7b. First consider a light signal input into the optical fiber 300 at a first frequency ω₀ in the slow LP₀₁ optical mode. Referring to the graph 402, the frequency ω₀ at a location 412 corresponds to a propagation constant k₀₁. On the other hand, if the optical signal is introduced into the optical fiber 300 at the frequency ω₀ in the fast LP₁₁ optical mode, the frequency ω₀ intersects the graph 400 at a location 414 corresponding to a propagation constant of k₁₁, which is less than the propagation constant k₀₁. As set forth in the above-referenced paper, "Single-Sideband Frequency Shifting in Birefringent Optical Fiber," by W. P. Risk et al., when a traveling acoustic wave stresses an optical fiber having an optical signal propagating therein in the same direction as the traveling acoustic wave, the frequency of the traveling acoustic wave will be subtracted from the frequency of the optical signal if the optical signal is initially traveling in the slow optical mode (a first polarization mode in the Risk paper). On the other hand, if the optical signal is initially traveling in the fast optical mode (a second polarization mode in the Risk paper), the frequency of the acoustic wave is added to the original frequency ω₀ of the optical signal. A similar effect occurs when the fiber is flexed by the traveling microbend having a frequency ω a in the present invention. This effect is illustrated in Figure 7a as a first shift along a line 420 from the location 412 on the LP₀₁ graph 402 to a location 422 on the LP₁₁ graph 400. Thus, the light input on the slow LP₀₁ optical mode at the frequency ω₀ is coupled from the slow LP₀₁ optical mode to the fast LP₁₁ optical mode and is downshifted in frequency by an amount of ω a to a frequency shown as ω₁₁ (i.e., ω₁₁ = ω o - ω a ). On the other hand, light initially input at the frequency ω₀ in the fast LP₁₁ optical mode, illustrated at the location 414 on the LP₁₁ graph 400, is upshifted in frequency along a line 424 to a location 426 on the LP₀₁ graph 402. Thus, the light input in the fast LP₁₁ optical mode at the frequency ω₀ is shifted upward in frequency by an amount ω a to a frequency ω₀₁ (i.e., ω₀₁ = ω o +ω a ) in the LP₀₁ optical mode. In Figure 7a, the slope of the line 420 and the slope of the line 424 represent the velocity v p of the traveling microbend which propagates along the fiber 300 (i.e., v p =ω a /k a ). Thus, as illustrated in Figure 7a, the slope (i.e., the velocity) of the traveling microbend is shown as positive (i.e., in the same direction) with respect to the slopes (i.e., the velocities) of the two propagation modes illustrated by the graphs 400 and 402. The effect of the traveling microbend on the optical signal when the traveling microbend propagates in the opposite direction as the optical signal is illustrated in Figure 7b. In Figure 7b, the graphs 400 and 402 again represent the relationships between the frequency and the propagation constant for the last LP₁₁ optical mode and the slow LP₀₁ optical mode, respectively, as in Figure 7a. An optical signal input at a frequency ω₀ in the fast LP₁₁ optical mode, corresponding to a location 450 on the LP₁₁ graph 400, will be shifted to the slow LP₀₁ optical mode at a location 452 on the LP₀₁ graph 402. This coupling is represented by the addition of a line 454, corresponding to the velocity of the traveling microbends in the fiber 300. The slope of the line 454 is in the opposite direction to the slopes representing the velocities of the optical modes because the microbends are traveling in the opposite direction as optical propagations. When the acoustic wave is traveling in the opposite direction of the light wave, the coupling from the fast LP₁₁ optical mode to the slow LP₀₁ optical mode causes a downshift in the frequency from the original frequency ω₀ to a new frequency ω₀₁ (i.e., ω₀₁=ω o -ω a ). This is the opposite effect from the frequency shift that occurs when the optical signal and the microbends are propagating in the same direction, as illustrated by Figure 7a. Similarly, when the light initially travels in the slow LP₀₁ optical mode, represented by a location 460 on the LP₀₁ graph 402, the light is coupled to the fast LP₁₁ optical mode, illustrated by a location 462 on the LP₁₁ graph 400. The coupling is represented by the addition of a line 464, representing the velocity of the traveling microbend, to the location 460 on the LP₀₁ graph 402. As illustrated, the coupled light has a frequency ω₀ (i.e., ω₁₁=ω o +ω a ). The foregoing can also be considered in terms of the summation of the propagation constants of the two optical modes and the traveling microbends. As illustrated in Figures 7a and 7b, for proper phase matching between the traveling microbends and the optical signal, the propagation constants must satisfy the following mathematical relationship: k₁₁ + k a = k₀₁ (4) Thus, when the optical signal is initially traveling in the LP₁₁ mode, the propagation constant k a of the traveling microbends is added to the propagation constant k₁₁ of the optical signal in the LP₁₁ optical mode to obtain the propagation constant k₀₁ of the LP₀₁ optical mode as set forth in Equation (4) above. Similarly, when the optical signal is initially traveling in the LP₀₁ optical mode, the propagation constant k a of the traveling microbends is subtracted from the propagation constant k₀₁ of the LP₀₁ mode to obtain the propagation constant k₁₁ of the LP₁₁ optical mode as follows: k₀₁ - k a = k₁₁ (5) The resulting frequency of the coupled optical signal depends upon whether the velocity of the traveling microbends is in the same direction as the direction of propagation of the optical signal, as illustrated in Figure 7a, or in the opposite direction if the propagation of the optical signal, as illustrated in Figure 7b. The frequency shifting can be expressed mathematically by representing the light in the fast LP₁₁ optical mode as cos(ω₀t-k₁₁Z) , where ω₀ is the initial frequency of the input light, t is time, and Z is the distance in the direction of propagation 340 of the traveling microbends along the fiber 300. The traveling microbends may be represented as cos(ω a t-k a Z) , where ω a is the frequency of the traveling microbends, k a is the propagation constant of the traveling microbends and Z is the distance along the axis of the fiber 300 in the direction of propagation of the microbends. The interaction of the optical signal with the traveling microbends leads to a product term proportional to the following expression: 1/2{cos[(ω₀+ω a )t-(k₁₁+k a )Z]+cos[(ω₀-ω a )t-(k₁₁-k a )Z]} (6) The second term of Expression (6) does not satisfy the phase matching condition of either Equation (4) or Equation (5) above. The first term in the expression is phase matched in accordance with Equation (4). This match explicitly indicates that the optical signal in the LP₀₁ mode is upshifted in frequency to the frequency ω₀₁ = ω₀ + ω a . A similar analysis for interaction of an optical signal in the LP₀₁ mode leads to a product term proportional to the following expression: 1/2{cos[(ω₀-ω a )t-(k₀₁-k a )Z]+cos[(ω₀-ω a )t-(k₀₁+k a )Z]} (7) The second term in Expression (7) is not phase matched in accordance with either Equation (4) or Equation (5) above. The first term does meet the phase matching requirements of Equation (5). This explicitly indicated that the LP₁₁ mode is downshifted in frequency to the frequency ω₁₁ = ω₀ - ω a . One can readily see that Expressions (6) and (7) conform to the frequency shifting illustrated in Figure 7a. If the optical signal propagates in the opposite direction as the traveling microbends, the traveling microbend can be represented as cos(ω a +k a Z) . The interaction of an optical signal in the LP₁₁ mode with the traveling microbend leads to a product term proportional to the following expression: 1/2{cos[(ω₀+ω a )t-(k₁₁-k a )Z]+cos[(ω₀-ω a )t-(k₁₁+k a )Z]} (8) The first term in Expression (8) does not provide proper phase matching in accordance with either Equation (4) or Equation (5). The second term does provide proper phase matching in accordance with Equation (4). Thus, when the optical signal propagates in the opposite direction to the traveling microbends, the light coupled to the LP₀₁ mode is downshifted in frequency from the light input in the LP₁₁ mode to a frequency ω₀₁ = ω₀ - ω a instead of being upshifted as discussed above with regard to Expression (6) for light propagating in the same direction. When the optical signal is initially in the LP₀₁ mode and propagates in the opposite direction as the traveling microbends, the interaction of the optical signal and the microbends leads to a product term proportional to the following expression: 1/2{cos(ω₀-ω a )t-(k₀₁+k a )Z]+cos[(ω₀+ω a )t-(k₀₁-k a )Z]} (9) The first term in Expression (9) is not properly phase matched in accordance with either Equation (4) or Equation (5). The second term is properly phase matched in accordance with Equation (5). Thus, the optical energy coupled from the LP₀₁ mode to the LP₁₁ mode is shifted upward in frequency to a frequency ω₁₁ = ω₀ + ω a . One can see that Expressions (8) and (9) conform to the frequency shifting illustrated in Figure 7b. The present invention has many advantages. For example, the present invention uses a symmetrical multimode fiber rather than a birefringent fiber. Thus, the present invention does not require precise alignment of the birefringent axes of a birefringent fiber with the transmission axes of polarizers at first and second ends of the fiber such as is required by some exemplary devices which couple between polarization modes. The present invention is particularly advantageous in that it operates over a broad range of optical frequencies for the input optical signal. This advantage results from the use of the spatial propagation modes for coupling. As set forth above, the beat length of the two spatial propagation modes (e.g., the LP₀₁ and LP₁₁ modes) does not vary significantly over a broad optical frequency range. Thus, the beat length will match the wavelength of the traveling microbend wave even when the optical frequency of the input optical signal is varied over a broad frequency range about the selected center frequency where the optical beat length and the wavelength of the traveling microbends match exactly. The frequency of the a.c. signal modulation applied to the transducer 310 (Figure 5) can also be varied over a relatively broad range in the present invention. The broad range of modulation frequencies results from two features of the present invention. The first feature of the present invention that provides for operation over a broad modulation frequency range is that it couples optical energy between the spatial propagation modes. The beat length of the two spatial propagation modes is substantially smaller than the beatlength between the polarization modes of an optical signal at the same frequency. Thus, the present invention operates at a higher absolute modulation frequency than an exemplary device which couples optical energy between polarization modes. The present invention operates with optical beat lengths of approximately 200µm to 400µm and thus can operate with a microbend frequency of approximately 10MHz to 20MHz. The second feature of the present invention that provides for operation over a broad modulation frequency range is that the modulation energy from the transducer 310 (Figure 5) is coupled directly into the fiber 300 to induce the traveling, periodic microbend wave. The present invention does not require a substrate or other medium external to the fiber 300 to conduct the modulation energy to the fiber 300. Thus, a relatively large percentage of the modulation energy acts upon the fiber 300 to create the traveling microbend wave. Therefore, for a given modulation energy input, it is believed that a larger percentage of the optical energy is transferred from one spatial propagation mode to the other spatial propagation mode in each beat length. Thus, relatively fewer beatlengths of interaction between the optical signal and the traveling microbend wave are required to couple substantially all of the optical energy from one spatial propagation mode to the other spatial propagation mode. It has been shown that coupling between the spatial propagation modes will occur even when there is a small percentage of deviation from the modulation wavelength which corresponds exactly with the beat length of the two spatial propagation modes so long as the deviation is not allowed to accumulate to a large total percentage of deviation over a large number of beat lengths. Thus, since relatively few beat lengths are required in the present invention to couple the optical energy from one spatial propagation mode to the other spatial propagation mode, the acceptable percentage of deviation in one beatlength can be relatively large (relative to a device requiring a large number of beat lengths). The relatively large percentage of acceptable deviation in wavelength combined with the relatively large absolute modulation frequency results in a relatively broad range for the modulation frequency. The present invention is particularly advantageous in that the energy required to cause the coupling between the modes is concentrated entirely within the fiber 300. Substantially all of the energy applied to the transducer 310 is transferred to the optical fiber 300 to produce the periodic microbends. Thus, very little, if any energy is wasted in the present invention. Thus, the mechanical energy generated by the transducer 310 is utilized very efficiently. Figure 8 illustrates an alternative embodiment of the present invention in which the transducer 310 of Figure 5 is replaced with a transducer 500 particularly adapted to generate the periodic microbends described above. The transducer 500, in the preferred embodiment comprises a rod of fused quartz having a substantially circular cross section throughout its length. A first end 502 of the transducer 500 has a diameter substantially equal to the diameter of the fiber 300. For example, in one embodiment of the present invention, the diameter of the fiber 302 and of the first end 502 of the transducer 500 is approximately equal to 100µm. Preferably, the transducer 500 and the optical fiber 300 are fused together at a location 504 to provide good acoustic contact between the fiber 302 and the second end 502 of the transducer 500. The transducer 500 has a second end 510 which has a diameter which is substantially larger than the diameter of the first end 502. For example, the second end 510 can have a diameter of approximately two millimeters. In the preferred embodiment, the transducer 500 is formed from a rod of solid fused quartz having an initial diameter of two millimeters or larger and by drawing the quartz rod into a form which gradually tapers from the second end 510 to the smaller first end 502. A piezoelectric material 512, such as PZT, is bonded to the second end 510 of the transducer 500 in a manner well-known to the art. When an electrical signal, represented schematically as a signal generator 514, is applied to the piezoelectric material 512, the piezoelectric material 512 expands and contracts in the directions indicated by the double-headed arrow 516 and generates a series of acoustic wavefronts which propagate through the transducer 500 from the second end 510 to the first end 502, as indicated by an arrow 518. At the first end 502, the acoustic energy in the transducer 500 is coupled directly to the optical fiber 300 at the location 504 to cause up and down movement of the fiber 300, thus inducing a vibration in the fiber 300 which propagates away from the location 504 as a traveling flexural wave or traveling microbend as described above with respect to Figure 5. The solid quartz of the transducer 500 acts as an acoustic funnel which concentrates the acoustic energy developed at the second end 510. Thus, in the example presented, when the second end 510 has a diameter of approximately 20 times the diameter of the first end, the acoustic energy per unit area applied to the first end 502 is approximately 400 times the acoustic energy per unit area applied to the second end 510. Furthermore, substantially all of the acoustic energy applied to the second end 510 is conducted to the first end 502 and is used to induce the traveling microbend in the fiber 300. As in Figure 5, the embodiment of Figure 8 further includes the first damper 336, proximate to the location 504, to limit the travel of the microbend in the fiber 302 to one direction, indicated by an arrow 520, away from the damper 336. The embodiment of Figure 8 also preferably includes the second damper 344 to suppress propagation of the microbends beyond a selected length of the fiber 300 as discussed above. While the embodiments of the present invention described above employ light and an optical fiber which are matched to each other to allow propagation only in the first and second order modes, the present invention may alternatively employ light and optical fibers matched to each other to provide coupling between higher order propagation modes. Figure 9 illustrates the present invention in use as an inter-propagation mode frequency shifting modulator. the modulator comprises an input optical fiber 600, which is preferably a single-mode optical fiber which propagates input light only in the first order LP₀₁ propagation mode. The input fiber 600 is coupled to a second fiber 602 by butt-splicing or other known methods. The second fiber 602 is preferably a multimode fiber, and more preferably, a double-mode fiber. The second fiber 602 is formed into a mode stripper 604 which is advantageously a series of tightly wound turns of the fiber 602. As is well-known in the art, a mode stripper formed in this manner will cause any residual light in a higher order mode (e.g., the LP₁₁ mode) to be radiated from the fiber in the turns. Thus, substantially all of any light which may enter the fiber 602 in the LP₁₁ mode from the fiber 600 will be eliminated in the mode stripper 604. Alternative mode strippers can also be advantageously used to remove any optical energy traveling in the LP₁₁ mode. The multimode fiber 602 on the other end of the mode stripper 604 then passes to an inter-mode frequency shifter 606, built in accordance with the present invention. In the embodiment illustrated in Figure 9, the inter-mode frequency shifter comprises the damper 336, described above. The fiber 602 passes through the damper 336 to suppress any vibrations and also to prevent the traveling microbends from traveling in the reverse direction, as described alone in connection with Figures 5 and 8. The inter-mode frequency shifter 606 further comprises a transducer 610 which can be the transducer 500 described above in connection with Figure 8, or the transducer 310, described above in connection with Figure 5. The transducer 610 is driven by an a.c. signal source 612. The optical fiber 602 is connected to the transducer 610 so that mechanical movement of the transducer 610 is coupled to the fiber 602 to cause microbends to propagate in the fiber 602 in a direction, indicated by an arrow 614, away from the damper 336 along a length 620 of the fiber 602. Thus, an optical signal within the fiber 602 in the LP₀₁ mode is coupled to the LP₁₁ mode, as described above. Preferably, the inter-mode frequency shifter 606 also includes the second damper 344 which prevents the vibrations induced into the length 620 of the fiber 602 from passing beyond the length 620. After passing through the inter-mode frequency shifter 606, the fiber 602 then passes through a fiber optic mode selector 640 for multimode signals, such as that described in copending U.S. Patent Application Serial No. 820,411, entitled "Fiber Optic Mode Selector," filed on the same day as the present application, and assigned to the same assignee. As described in the copending application, in the mode selector 640 only that light which is propagating in the second order LP₁₁ mode is coupled out of the double-mode fiber 602 into a juxtaposed adjacent single-mode fiber 650 at an interaction region 652. The fiber 650 is selected so that an optical signal propagating in the LP₀₁ mode in the fiber 650 has a phase propagation velocity which matches the phase propagation velocity of the light propagating in the LP₁₁ mode in the fiber 602. Any light remaining in the first order LP₀₁ mode remains in the fiber 602 and exits from a second end 654 of the fiber 602 as light in the original unshifted frequency. The light coupled to the single-mode optical fiber 650 exits from an end 656 of the fiber 650 as frequency shifted light in the first order LP₀₁ mode of the fiber 650. The frequency of the light which exits from the end 654 of the fiber 650 is equal to the frequency of the light which was input into the single mode fiber 600 in the first order LP₀₁ mode minus the frequency of the acoustic signal applied to the transducer 610 in the inter-mode frequency shifter 606. The downward shift in frequency corresponds to the shift from the location 412 on the graph 402 to the location 422 on the graph 400 in Figure 7a. The a.c. signal applied to the transducer 610 by the a.c. signal source 612 can be varied in frequency, thereby varying the frequency of the optical signal that exits from the end 654 of the fiber 650. The amplitude of the a.c. signal applied to the transducer 610 can be varied to vary the percentage of light coupled from the LP₀₁ mode to the LP₁₁ mode in the frequency shifter 606 and thus vary the amplitude of the optical signal that exits from the end 654 of the fiber 650. The system of Figure 9 is reciprocal. An optical signal can be introduced into the end 654 of the optical fiber 650 so as to propagate towards the interaction region 652 of the mode selector 640 in the LP₀₁ propagation mode. The mode selector 640 operates reciprocally so that the optical signal in the LP₀₁ mode in the fiber 650 is coupled to the LP₁₁ mode in the fiber 602. The optical signal then propagates in the LP₁₁ mode from the interaction region 652 towards the frequency shifter 606 and thus propagates to the length 620 of the fiber 602 in which the traveling microbends are propagating. The optical signal propagates through the length 620 of the fiber 602 in a direction opposite the direction indicated by the arrow 614 and thus propagates in the direction opposite the direction of propagation of the traveling microbends. Thus, referring to Figure 7b, the optical signal traveling in the LP₁₁ mode is coupled to the LP₀₁ mode and is shifted down in frequency (i.e., from the location 450 on the graph 400 to the location 452 on the graph 402). The optical signal then passes through the mode stripper 604 wherein any optical signal remaining in the LP₁₁ mode is stripped from the fiber leaving only the optical signal propagating in the LP₀₁ mode at the shifted frequency to be coupled to the single-mode fiber 600 which, in this example, serves as an output fiber. The embodiment of Figure 9 can be used to shift an optical signal upward in frequency by locating the transducer 610 proximate to the second damper 344 rather than proximate to the first damper 336, thus causing the traveling microbends to travel in the length 620 of the fiber 602 in a direction opposite the direction indicated by the arrow 614. Thus, light input into the single-mode fiber 600 and propagating toward the single-mode fiber 650 will be shifted upward in frequency in accordance with the shift from the location 460 on the graph 402 to the location 462 on the graph 400 in Figure 7b. Light input into the single-mode fiber 650 and propagating towards the single-mode fiber 600 will be shifted upward in frequency in accordance with the shift from the location 414 on the graph 400 to the location 426 on the graph 402. Two alternative embodiments of the present invention are illustrated in Figures 22a and 22b. The frequency shifters of Figures 22a and 22b include an acoustic horn 660 having an end 670 attached to an optical fiber 662a (Figure 22a) or 662b (Figure 22b). Unlike the previously described optical fibers of Figures 1 to 9, the optical fibers 662a and 662b of Figures 22a and 22b do not have uniform outer cladding diameters. Rather, the optical fiber 662a has a plurality of sections having differing outer cladding diameters. For example, the optical fiber 662a is shown as having a first portion 672, having a first outer diameter; a second portion 674, having a second outer diameter; and a third portion 676, having a third outer diameter. In an exemplary embodiment, the first outer diameter is 42.5µm, the second outer diameter is 26.5µm, and the third outer diameter is 16µm. The fiber 662b of Figure 22b has a gradual taper in the outer diameter cladding of the fiber from a relatively large outer diameter (e.g., 42.5µm) to a relatively small outer diameter (e.g., 16µm). The frequency shifters of Figures 22a and 22b provide means for selectively shifting the frequency of an optical signal propagating in the fiber 662a and 662b by one of a plurality of acoustic frequencies while maintaining optimum or near-optimum acousto-optic coupling efficiency in the fibers 662a and 662b. Prior to describing the operation of the embodiments of Figures 22a and 22b, the solutions of the wave equations which describe the characteristics of the propagation and optical interaction of guided waves in two-mode optical fibers will be presented. The discussion is also applicable to the operation of the acoustic horn 660, as well as an improved acoustic horn which will also be presented. The following describes the excitation and propagation of acoustic waves in optical fibers which have no acoustic cladding. As has been shown above, acoustic flexural waves propagating along a two-mode optical fiber provide an efficient coupling of light between the propagation modes of the fiber. The basic arrangement for excitation of flexural waves in an optical fiber is shown in Figure 10a. Excitation of the acoustic waves in an optical fiber 700 in Figure 10a is performed by connecting the optical fiber 700 rigidly to a first small end 702 of an acoustic horn 704, constructed of glass or the like, which propagates acoustic waves of high amplitude. This high amplitude is obtained by exciting lower amplitude waves at a second end 706 of the acoustic horn 704 where the cross section is appreciably larger. The acoustic horn 704 is tapered between the two ends 702 and 706. Acoustic horns have been used to transform low amplitude oscillations into high amplitudes by changing the cross section of the rod. However, they typically have been limited to resonant structures having the length between the small end and the large end equal to multiples of half an acoustic wavelength and with transverse dimensions small compared to an acoustic wavelength. The embodiment of Figure 10b describes a non-resonant acoustic horn structure which does not have these limitations and which functions to convert surface acoustic waves at one end of the structure to longitudinal waves at the opposite end of the structure, which in turn excite flexural waves in the optical fibers. While formal mathematical solutions for acoustic wave propagation in solid cylinders are available in the technical literature, specific solutions are less abundant. Therefore, a more extensive discussion of specific solutions of both dispersion (i.e., the relationship between the velocity of propagation of the acoustic wave and its frequency) and acoustic wave mode behavior is presented below to assist in describing the present invention. It has been shown in Taylor, "Bending Effects in Optical Fibers," Journal of Lightwave Technology , referenced previously, that in a two-mode optical fiber, efficient coupling between the two modes occurs when a static periodic bending of the fiber is introduced. The required periodicity of this bending is determined by the beat length of the fiber for the two modes. As discussed above in connection with Figures 1-9, it has been found that when these periodic bendings travel as an acoustic (flexural) wave through the fiber, the optical frequency is shifted by the frequency of the acoustic wave. In order to more fully understand the properties of the acoustic modes in the previously described frequency shifter, reference is again made to the diagram in Figure 10a. Flexural acoustic waves propagate along a part of the optical fiber 700 where the plastic jacket has been stripped away. In this area, the acoustic waves suffer only insignificant attenuation. The acoustic horn 704 is constructed from fused silica with the small end 702 having a diameter comparable to that of the fiber 700. The small end 702 is rigidly attached to the fiber 700 as shown. The large end 706 of the horn 704 has a much larger diameter and is connected to an acoustic transducer 708. By tapering the horn 704 between the two diameter values over a sufficiently large length, the amplitudes generated at the large end 706 of the horn will be converted into higher amplitudes at the small end 702 because of the much smaller area. Provided there is an efficient transmission of power from the small end 702 to the fiber 700, the longitudinal movement of the small end 702 of the horn 704 will thus create a flexural wave of large amplitude in the optical fiber 700. Due to the symmetrical setup, flexural waves will be excited in both directions, 710 and 712, along the optical fiber 700. If necessary, acoustic waves propagating in one of the directions can be suppressed by applying a strongly absorbing material on one side of the junction, as described above. Although only longitudinal motion of the small end 702 has been discussed so far, flexural and torsional movements at the small end 702 will also couple to flexural waves in the optical fiber 700. Therefore, all of these modes will be considered. As is well known, the optical fiber 700 has a core and cladding for the purpose of light guidance. It will be assumed that the acoustic wavelength of the interest is much larger than the dimension of the core of the fiber 700. It will also be assumed, in the following discussion, that the fiber 700 is a homogeneous rod. Further, the discussion disregards any stretching of the fiber 700 which might be of importance when the acoustic wavelength is very long compared to the rod diameter, i.e., for very low frequencies. In the following discussion, theoretical results are used to calculate numerical relationships between the propagation velocity and the frequency of the acoustic waves propagating in cylindrical rods. For reference purposes, a wide range of material parameters are used, and all three mode groups are considered. Phase velocities for several modes within each mode group are calculated. More detailed results are given for fused silica which is the material of most interest for the present invention. Acoustic Wave Propagation in Cylindrical Rods The general solutions of the acoustic wave equations in solid, circular rods consisting of isotropic, homogeneous material are set forth below. The cylindrical coordinate system being used is shown in Figure 11. For purposes of analysis, the rod is assumed to have a diameter of 2a and an infinite length. Solving the wave equation in cylindrical coordinates according to Figure 11, the general displacement distribution given by u r , u  , and u z can be shown to be Here, ω is the angular frequency, k₀ is the acoustic wave propagation constant in the z direction, and n is an integer describing the circumferential field variation. Either the lower set or the upper set of trigonometric functions is to be used. The radial variations are given by: Here, J n is the Bessel function of the first kind and of order n, J ' / n denotes its derivative with respect to the argument, and k d and k t are given by where the bulk dilatational and transverse wave velocities c d and c t , respectively, are defined in terms of the density ρ of the fiber and Lame's constants λ and µ as: Requiring the three components T rr , T rz , and T r of the stress tensor to be zero for r = a yields the dispersion relation which determines k₀ as well as the relative magnitudes of the constants A, B, and C. These constants can be normalized by imposing suitable requirements. First consider the longitudinal modes, i.e., the modes which are axially symmetric with the cylinder and have no circumferential movement. This is obtained by choosing n = 0 and using the lower set of trigonometric functions in Equation (10), where C, being decoupled from A and B for n = 0, is set independently to zero. Introducing the "normalized" wave numbers q t = k t a , q d = k d a and q₀ = k₀a , the following two equations in A and B are obtained: The dispersion relation is obtained by requiring the determinant of these equations to be zero. Having solved this problem, the relation between A and B can be found by applying one of the equations in (14). In solving these equations, it has been found convenient to normalize the wave velocity c to c ext = (Y/ρ 1/2 , which is the velocity of the fundamental longitudinal mode in the low frequency limit as given by Young's modulus Y = µ(2µ+3λ)/(µ+λ) . Thus, the relative velocity, c rel is defined as: c rel = c/c ext (15) To obtain universal curves, the dimensionless parameter fa/c t is chosen as the independent variable where f = ω/2π . In this way, it is easy to study the acoustic wave propagation parameters as a function of the acoustic wave frequency for a given dimension of the cylinder. Furthermore, with respect to the present invention, the variation of the propagation parameters with varying rod radius for a given frequency can also be obtained. Numerically calculated dispersion curves for longitudinal modes are shown in Figures 12a, 12b, 12c, and 12d for four values of Poisson's ratio σ used as a parameter. Figures 12a, 12b, 12c and 12d are plots of these longitudinal mode dispersion curves for values of Poisson's ratio equal to 0.1, 0.2, 0.3, and 0.4, respectively. For reference, σ = λ/2(µ+λ) has been varied over the range of practical interest, and the five lowest order propagation modes are shown for each of these four values of σ. Only the lowest mode 720 extends to the lowest fa/c t values. Since the present invention functions in this range, the lowest mode is of particular interest. Therefore, only this mode is discussed in detail hereinafter. The calculated phase velocity as a function of fa/c t is shown in more detail in Figure 13 by a line graph 730 for fused silica which has the following characteristics: ρ = 2.20·10³kg/m³, c ext = 5760m/sec, c t = 3764m/sec, σ = 0.71. The group velocity is given by: A plot of c g is shown in Figure 13 as the curve 732. Applying Equations (10), (11), and (14) to the fused silica characteristics, the amplitude distributions of the acoustic wave modes can be obtained. Numerical calculations of the amplitude distributions for fused silica are shown in Figures 14a and 14b where fa/c t has been used as a parameter. The axial (Figure 14a) and radial (Figure 14b) amplitude distributions for the lowest longitudinal mode are shown as functions of the normalized cylinder radius, r/a, for seven values of the parameter fa/c t equal to 0.1, (curves 740 and 747) 0.4 (curves 741 and 748), 0.5 (curves 742 and 749), 0.6 (curves 743 and 750), 1 (curves 744 and 751), 2 (curves 745 and 752), and 4 (curves 746 and 753). Normalization has been performed by requiring that for each value of the parameter fa/c t , the maximum displacement component shall be unity. From line graph 730 in Figure 13, it is clear that the phase velocity 730 for a small rod radius (i.e., for a small value of fa/c t ) approaches that of a slender bar as given by Young's modulus, i.e., c rel = 1.0. Figures 14a and 14b show that the displacement for a small rod radius approaches a purely longitudinal movement. This is illustrated in Figures 14a and 14b by the axial and radial displacement curves 740 and 747, respectively, corresponding to a value of 0.1 for the parameter fa/c t . Comparing these axial and radial displacement amplitudes, it is clear that the axial amplitude represented by the curve 740 is much greater than the radial amplitude represented by the curve 747, and is also nearly uniform over the entire radius of the rod. As fa/c t increases to values large compared to unity, the velocity approaches the velocity of surface waves. This is illustrated at location 734 on the curves 730 and 732 in Figure 13 for values of fa/c t between 1.0 and 1.5. The displacement pattern asymptotically approaches that of surface waves in which case the energy is confined basically to a thin surface layer about one wavelength in thickness. Figures 14a and 14b graphically represent the surface wave characteristics in terms of the displacement amplitudes for large values of fa/c t . Examination and comparison of the axial and radial displacement amplitude curves, 746 and 753, respectively, for fa/c t equals 4 reveals features that are characteristic of surface waves. First, both the axial and radial displacements are approximately zero for the interior regions of the cylinder (e.g., for r/a less than about 0.6). Second, the radial displacement, 753, is much larger near the surface of the rod, (e.g., r/a≃0.7), than the axial displacement 746 in the same radial region. (Note: Negative amplitudes are 180° out of phase with the driving source.) A comparison of Figures 14a and 14b shows that a rod with a gradually varying radius will transform a longitudinal mode propagating in a rod section having a small radius into modes approaching surfaces waves in a rod section having a larger radius. If this tapering of the rod radius is gradual enough, the change in mode pattern from longitudinal to surface will be without noticeable loss due to mode conversion. In other words, transformation from one mode pattern to the other will occur adiabatically. This transition of the propagation mode from a predominantly longitudinal mode to a predominantly surface wave mode as the rod radius becomes progressively larger is shown in Figures 14a and 14b. Examination of the series of curves 740 through 746 of the axial displacement amplitudes reveals that as the radius goes from small values, (e.g., fa/c t = 0.1 represented by the curve 740), to larger values, (e.g., fa/c t = 4 represented by the curve 746), the relative displacement goes from a uniform (i.e., virtually constant) value of approximately 1.0 as a function of r/a to a distribution which is virtually zero up to values of r/a = 0.6 and a peak of a relatively small amplitude of approximately 0.18. Emphasis is put on the relative magnitudes of the two curves as well as the concentration of the fa/c t = 4 amplitude curve 746 near the surface of the rod, (i.e., r/a approximately equal to 0.9). In contrast, a similar comparison of the radial amplitude distributions as a function of r/a, shown in Figure 14b, shows that the fa/c t = 0.1 curve 747 is considerably reduced in magnitude to approximately 0.1 while the fa/c t = 4 curve 753 is nearly zero from the center of the rod, r/a = 0 to r/a = 0.6 and then increases rapidly to a value of approximately 1.0 for r/a = 1, a position corresponding to the surface of the rod. In summary, curves 740 and 747 illustrate a longitudinal wave, i.e., a predominantly axial displacement which is uniform as a function of position along the rod radius, for the small values of fa/c t = 0.1. For the large value of fa/c t = 4, curves 746 and 753 illustrate a surface wave, i.e., a predominantly radial displacement which is concentrated near the surface of the rod, e.g., r/a > 0.8. The plots of axial and radial displacement for intermediate values of fa/c t between 0.1 and 4 show the gradual transition from longitudinal mode to surface wave mode as the rod radius increases. Thus, it is seen that a longitudinal wave excited at the small diameter end of the tapered rod is transformed into a mostly surface-like-wave at the large diameter end of the tapered rod for appropriately selected diameters. By reciprocity, a surface-wave-like wave excited uniformly around the rim at the larger end of the rod is transformed into a mostly longitudinal displacement at the other end if the rod radius is made sufficiently small. This longitudinal displacement pattern is well suited to exciting flexural waves in an optical fiber connected to the small end of the rod. The acoustic horn 704 of Figure 10a constructed from a solid cylindrical section of glass rod has been shown to exhibit the characteristics just described. That is, surface waves excited in the large diameter end 706 of the tapered horn 704 were transformed into longitudinal waves at the small diameter end 702. This horn 704 has been used to excite flexural acoustic waves in an optical fiber by attaching the small end to the fiber as shown in Figures 8 and 10a. The acoustic horn 704, described above, performs well; however, in addition to the desired primary longitudinal mode, resonant modes were also observed at the small end 702 of the horn 704. These resonant modes can be suppressed by drawing the horn from a silica glass tube such that the horn is hollow in the center from the large diameter base to the neck at the end of the transition region. Figure 10b illustrates a hollow acoustic horn 756 having a hollow region 758 in a base 759. The hollow region 758 of the horn 756 terminates in a neck portion 761. The neck portion terminates on a small end 762. The small end 762 is connected to the optical fiber 700 as discussed above. The hollow region 758 suppresses the resonant modes in the horn 756. Suppression of the resonant mode can be further enhanced by filling the hollow region 758 with acoustic damping material. The horns of Figures 10a and 10b have successfully launched flexural acoustic waves with amplitudes of tens of nanometers onto the optical fiber 700. The foregoing discussion relates to the propagation of longitudinal mode acoustic waves in a cylinder and how such modes are useful in the construction of an acoustic horn. Other modes of propagation can exist in a cylindrical rod. Using Equations (10) and (11), one can see that by maintaining n = 0 and using the upper set of trigonometric functions in Equation (10), one can mathematically describe circumferential displacement. In this case A and B can be set equal to zero independently, thus giving a purely circumferential displacement. The dispersion relation is obtained by requiring the component T r of the stress tensor to be zero for r = a which yields: q t J₀(q t )-2J₁(q t )=0 (17) where q t = k t a as before. This equation has one root, q t = 0, as well as an infinite set of roots different from zero. The special case q t = 0 yields a solution c = c t that is nondispersive. This lowest mode propagates with the shear wave velocity and has a displacement distribution given by: The other solutions correspond to displacements as found from Equation (11), i.e., Dispersion relations for the higher modes can be found by solving Equation (17) for values of q t other than zero. Once q t is found, k₀ = ω/c can be substituted in Equation (12) to obtain c/c t = [1 - (q t c t /ωα)²]⁻ 1/2 (20) Thus, the relative velocities of the higher modes are expressed analytically by q t and fa/c t . Calculated universal curves are shown in Figure 15. Only the lowest mode 760 propagates for low fa/c t values. The circumferential displacement of this dispersion-free mode varies proportionally with the radial distance. A third group of modes called flexural waves which are of particular interest in the context of the features of the present invention related to the frequency shifting of light in an optical fiber, is obtained by putting an integer n ≠ 0 in Equation (11). In this case, all three displacement components are present, and the boundary conditions of a stress-free surface leads to a dispersion relation that can be written in determinant form as: In Equation 21, γ n (q) = qJ n-1 (q)/J n (q) , and From these calculations, the relative magnitudes of the constants A, B, and C from Equation (11) can be determined, as before. The choice of the upper or lower set of trigonometric functions in Equation (10) differs only in the choice of direction of the x-axis and y-axis in Figure 11. Figures 16a-d show dispersion curves for the first five flexural wave modes when n is chosen to have its lowest possible value, n = 1. Analogous to the dispersion curves for the longitudinal modes previously discussed in relation to Figures 12a-d, Figures 16a, 16b, 16c, and 16d are plots of the flexural mode dispersion curves representing the lowest order modes for values of Poisson's ratio, σ, equal to 0.1, 0.2, 0.3, and 0.4, respectively. As was seen for the other mode groups, i.e., longitudinal and circumferential, only the lowest mode 770 is propagated for very low values of fa/c t , as illustrated in Figures 16a-d. Additionally, Figures 16a-d show that the phase velocity of the lowest mode goes uniformly to zero approximately as (fa/c t ) 1/2 for small values of this parameter, while for large values of fa/c t , the phase velocity of the lowest mode approaches the surface-wave velocity of a plane surface. The other higher order modes, 772, 774, 776, and 778, likewise approach the transverse wave velocity c t for high fa/c t values. If n is larger than 1, we obtain yet higher order flexural modes. An example is shown in Figures 17a, 17b, 17c and 17d where n = 2 has been considered for Poisson's ratio of 0.1, 0.2, 0.3 and 0.4, respectively. Figures 17a-d demonstrate that all modes are cut off at low fa/c t values and that for large fa/c t , the lowest mode approaches the surface wave velocity while the other modes approach the transverse wave velocity c t . These properties are typical of flexural modes with n larger than 1. Figure 18 shows a graph 800 of the calculated phase velocity and a graph 802 of the group velocity for the lowest mode of the n = 1 group for fused silica. Figures 19a, 19b, and 19c show the flexural wave mode pattern variation as a function of the fa/c t parameter, similar to the wave pattern amplitude distribution for longitudinal waves shown in previously discussed Figures 14a and 14b. Figures 19a, 19b, and 19c illustrate the displacement amplitude distributions of the lowest order flexural mode in the radial, azimuthal, and axial directions, respectively. The four curves in each plot represent values of the parameter fa/c t equal to 0.1, 0.5, 1, and 3, respectively. The calculations represented by Figures 19a, 19b, and 19c, show that in the limit of small fa/c t , e.g., for fa/c t = 0.1, that the radial, azimuthal, and axial amplitude distributions, shown as curves 810, 812, and 814, respectively, approach a purely transverse displacement. Similarly, for higher values of fa/c t , e.g., fa/c t = 3, the radial, azimuthal, and axial amplitude distributions, shown as curves 816, 818, and 820, respectively, approach a displacement corresponding to a surface wave distribution. It should be noted that as opposed to the lowest longitudinal mode, this mode is modulated by a sine function in the circumferential direction. Power Relations In an optical fiber, the lowest flexural mode is of special interest for the acousto-optic interaction. At the thin end of the rod, only the lowest of the longitudinal modes is presently used for excitation of the flexural mode in the fiber. Nevertheless, both the lowest flexural as well as the lowest torsional mode can be used for this purpose. Therefore, in determining the relations between the rod radius and the acoustic amplitude for a given power, all three modes will be considered. The relationship of the coupling strength between the two optical modes coupled by a flexural wave travelling in the fiber and the fiber radius will also be discussed. The (time averaged) energy density E of a travelling wave having displacement components given by Equation (10) is equal to the sum of the peak kinetic energy densities for each displacement component, i.e., E= 1 2 ρω² {|u r |² + |u  |² + |u z |²} (22) The power P flowing through the fiber cross section S is given by: In Equation (23), c g represents the group velocity of the travelling wave. Combining Equations (22) and (23), the power flow can be expressed in terms of the temporal peak displacement components, i.e., where the normalized radius R = r/a has been introduced. The constants on the right-hand side of this equation can be varied through a variation of the parameter fa/c t . This establishes a universal relation between the displacement and the transmitted power in terms of fa/c t . As shown in Figures 14 and 19, distribution and relative magnitudes of the displacement components vary considerably when fa/c t is varied. Accordingly, there may be several choices from among the variables f, a, c t , and combinations thereof, in selecting one particular quantity for describing these amplitude plots. The spatial maximum value of any of the three displacement components, i.e., radial, azimuthal, and axial, for a given cross section and mode has been selected to represent the displacement for that mode. The amplitude curves in Figure 20 were calculated following this selection procedure. The maximum amplitude as a function of fa/c t for the three lowest modes in fused silica, longitudinal, torsional, and flexural represented by curves 840, 842, and 846, respectively, are plotted in Figure 20. These curves all follow the same general trend wherein the amplitude is larger for small values of fa/c t than for larger values of fa/c t . The curves in Figure 20 can be used to determine the variation in amplitude of an acoustic wave traveling through a tapered rod, such as the rod 704 shown in Figure 10a. By way of example, suppose that the acoustic transducer 708 is attached to the tapered glass rod 704 at a location having a diameter corresponding to fa/c t = 4.0. A longitudinal wave excited into the rod at this point would have an amplitude of approximately 0.008µm/W 1/2 , shown at 848 in Figure 20. At a location on the tapered rod having a diameter such that fa/c t = 0.1, the amplitude would be approximately 0.1µm/W 1/2 , shown at 850. If the taper is smooth so that no wave energy is lost between the two points, it is seen that the amplitude at the smaller diameter is approximately 0.1/0.008 = 12.5 times greater than the amplitude excited in the rod at the larger diameter. This rod would thus have an amplitude transformer ratio of 12.5. The transformer ratio is the ratio of the amplitude at the larger diameter to the amplitude at the smaller end of the tapered rod. The longitudinal mode is of most interest for this purpose, but the other two modes have been included for reference. Consider now the efficiency for coupling light between two modes of an optical fiber via an interaction with an acoustic wave propagating in the same fiber. It can be shown that in a two-mode optical fiber, flexural acoustic waves will couple one mode to the other with 100% efficiency over a length L c given by In Equation (25), L c is the coupling length and u t is the transverse amplitude. For an actual two-mode fiber the following data are given when the normalized frequency V = 3.03: L b (optical fiber beat length) = 265µm a c (optical fiber core radius) = 2.3µm C₁ (constant) = 0.908 a (fiber radius) = 42.5µm. The normalized frequency V is defined to be where a c is the fiber core radius, n c and n cl are the indices of refraction of the core and cladding respectively, and λ is the optical wavelength. Since the core radius is small compared to the fiber radius, u t may be equated to the value of |u r | (or |u  |) for r = 0. By means of Equation (24), the relation between the acoustic input power and the optical coupling length is thus obtained. Besides the obvious dependence on power input, the variation of coupling length as a function of the fiber radius can also be obtained from these relationships. Defining the acousto-optic coupling efficiency as k e = C₁µ t (a c √P) , Equation (25) can be rewritten as For the specific core properties given above for V = 3.03, k e has been plotted as a function of fiber radius normalized to the fiber beat length in Figure 21(a). For other core parameters, k e can be calculated by scaling according to its definition as given above. The optical fiber has a core and cladding for the purpose of light guidance. In an exemplary two-mode fiber, this central core is 2.3µm in radius while the total fiber radius is 42.5µm. When the acoustic energy is transmitted through the optical fiber in the flexural wave mode, the acoustic energy will be distributed throughout the entire 42.5µm radius of the fiber, and is not confined to the central core. Since the central core is considerably smaller than the overall radius of the fiber, the model describing the propagation of the flexural waves through the optical fiber may be that of an homogeneous rod. The previous solution of the wave equation in cylindrical coordinates for the flexural modes in solid circular rods comprised of isotropic homogeneous material yields the results presented in Figures 21a and 21b. Figure 21a illustrates the coupling efficiency, k e , for the coupling of light traveling in one mode into the other mode through interaction with a traveling flexural acoustic wave propagating in the fiber. For constant core properties, i.e., a constant beat length L b , Figure 21a shows that the coupling efficiency for a given input power can be increased considerably by reducing the outer radius, a₀, of the fiber. For low values of a/L b , k e is proportional to (a/L b ) -2.5 . Reducing the outer radius of the fiber creates a decrease in the phase velocity of the flexural acoustic wave propagating in the fiber. If the frequency of the acoustic signal is fixed, this decrease in phase velocity creates a corresponding decrease in the acoustic wave length within portions of the fiber having relatively smaller radii. The beat length of the fiber is determined by the properties of the central core. Therefore, reducing the radius of the fiber by removing only the outer cladding portion does not alter the beat length of the fiber. Since substantial cumulative coupling of the optical signal between the two propagation modes of the fiber only occurs when the acoustic wave length is substantially equal to the heat length of the fiber, the acoustic frequency must be decreased accordingly in order to maintain an acoustic wave length which is substantially equal to this beat length. This relationship between the frequency of the acoustic wave, f A , defined as the synchronous frequency, normalized to the beat length (L b ) and the extensional velocity ( c ext = (Y/ρ) 1/2 , where Y is Young's modulus and ρ is the density of the fiber) is illustrated in Figure 21(b). The synchronous frequency f A in linearly proportional to the radius for small values of the normalized radius a/L b . For an exemplary fused silica two-mode fiber, typical values of the extensional velocity (c ext ), beat length (L b ), core radius (a c ), and fiber radius (a₀), are: c ext = 5760 m/sec L b = 265µm a c = 2.3µm a₀ = 42.5µm Using these numbers, it is seen that at the location labelled 900 on Figure 21a, for a fiber radius a = 42.5µm, the coupling efficiency is approximately 0.071 W -1/2 and that at location 910 on Figure 21b that an acoustic frequency f A of approximately 8MHz produces an acoustic wave in the fiber with a wave length approximately equal to the fiber beat length of 265µm. Assuming the fiber outer radius is etched or otherwise reduced to approximately 16µm, it is seen from Figure 21a that at the location marked 920 the coupling efficiency increases to approximately 0.5W -1/2 , about seven times greater than the coupling efficiency of the unetched fiber with a radius of 42.5µm. The curve of Figure 21b shows that the acoustic frequency which produces an acoustic wave with a wave length equal to the fiber beat length is approximately 4.0MHz, illustrated at the location 930. Similarly, for a fiber radius of approximately 26.5µm, Figure 21a shows a coupling efficiency of approximately 0.17W -1/2 at a location 940 and Figure 21b shows that an acoustic frequency of approximately 6.0MHz will produce an acoustic wave length equal to the beat length of the fiber, 265µm at the location 950. Thus, it is clearly illustrated in Figures 21a and 21b that the coupling efficiency and synchronous frequency vary with the radius of the fiber. The present invention utilizes these characteristics of multimode fiber to produce a broad band fiber optic frequency shifter. The invention further uses these characteristics to couple the acoustic wave to the fiber without using external dampers to confine the acoustic wave to the coupling region of the fiber. Coupling of the two optical modes in a two-mode fiber has been shown to be efficient when performed with a flexural acoustic wave propagating along the fiber. The present scheme of excitation of the flexural wave requires the acoustic energy to be propagated from a piezoelectric transducer through a tapered cylindrical rod. The mode at the thin end of the rod has been chosen to be longitudinal for the present invention although both flexural and torsional modes may advantageously be used. Therefore a relatively broad presentation of all mode types has been presented, because the mode shapes change substantially over the parameter range of interest. Calculations have shown that by reducing the fiber radius and keeping the core radius constant, the coupling length can be reduced substantially for a given acoustic power. This means that the bandwidth of the acousto-optic coupling interaction can be increased by reducing the fiber radius. Alternatively, acoustic power can be reduced if the coupling length is kept constant. As the fiber radius is reduced, the operating frequency is reduced to match the beat length. Figure 22a illustrates an alternative embodiment of the present invention in which the dampers 336 and 344 shown in Figure 8 are no longer needed. The acoustic horn 660 couples longitudinal mode acoustic waves to the fiber 662a at the general location indicated by the letter B. A pair of arrows 964, 966, pointing in opposite directions within the fiber portion 672, indicate that flexural acoustic waves are excited in the fiber 662a by the acoustic horn 660 which propagate in both directions along the fiber 662a. The section of optical fiber 662a shown in Figure 22a is comprised of four portions. The first portion 672 between a location A and a location C is the full radius of the fiber a₀. The second portion 674, between a location C and a location D, has been etched to a fiber radius of a₁ which is less than a₀. The portion 676 between a location D and a location E, has been further etched to fiber radius a₂ which is less than a₁. A fourth portion 678, between a location E and a location F, has not been etched and has original fiber radius a₀. Referring to Figure 21a, the coupling efficiency in the first portion 672 is less than the coupling efficiency in the second portion 674 which is in turn less than the coupling efficiency in the third portion 676. The fourth portion 678 with radius a₀ will have the same coupling efficiency as the first portion 672 since these two portions are the same radius. Due to the low coupling efficiency in the first portion 672, the flexural acoustic wave propagating in the direction of the arrow 966 will cause virtually no acousto-optic coupling between modes when the excitation takes place at the location B. Likewise, the flexural acoustic wave propagating in the direction of the arrow 964 will cause virtually no coupling while the flexural acoustic wave is propagating within the first portion 672. When the flexural acoustic wave propagating in the direction 964 reaches the second portions 674 and the third portion 676, the acousto-optic coupling efficiency increases substantially as shown in Figure 21a. The coupling efficiency in the fourth portion 678 will be small compared to that in portions 674 and 676 resulting again in virtually no coupling. The advantage of this configuration is that acoustic wave dampers are no longer needed along the fiber at the ends of the section CDE because no substantial acousto-optic interaction occurs outside the region of the second portion 674 and the third portion 676. A second characteristic of the configuration shown in Figure 22a is that the acoustic frequency required to produce an acoustic wave whose wave length matches the fiber beat length in the second portion 674 with fiber radius a₁, will be different than the frequency required for matching the beat length in the third portion 676. This enables the same apparatus to be used for frequency shifting the light by two or more frequencies. The radius of the fiber in the second portion 674 may be optimized for one frequency, and its length may be selected to achieve 100% coupling at the frequency. To increase the bandwidth of the coupling interaction, the third portion 676 may be optimized in radius and length for a different frequency. Similarly, adding more regions of fiber with different radii and lengths increases the bandwidth of the frequency shifter accordingly. A smooth variation of the fiber radius over the total interaction region is illustrated in Figure 22b. In Figure 22b, the diameter of the fiber 662b gradually varies from a diameter d₁ at a first portion 980 where the fiber 662b is coupled to the acoustic horn 660 to a second diameter d₂ at a location 984, which is smaller than the first diameter d₁. As stated earlier, precise matching of the beat length and the acoustic wave length is not necessary as long as complete coupling is accomplished within a few beat lengths of the fiber. This minimizes the phase mismatch error created by the mismatch in acoustic wavelength with the fiber beat length in the coupling region. Therefore, the taper shown in Figure 22b can be gradual enough so that within a length of fiber wherein 100% coupling occurs, the acoustic wave length does not vary appreciably from the fiber beat length. The configuration of Figure 22b will allow continuous tuning of the frequency shift between a frequency f₁ corresponding to fiber diameter d₁ and a frequency f₂ corresponding to the fiber diameter d₂. The optimum angle of the taper, or rate of change of fiber radius as a function of length along the fiber longitudinal axis, may be determined by an empirical process. The process would include measuring the coupling efficiency for a number of different taper angles for a fixed acoustic frequency and selecting the angle which produces the maximum coupling efficiency. Thus, a broad band fiber optic frequency shifter has been described wherein the frequency shift is tuneable by adjusting the acoustic frequency. Additionally, the frequency shifter is not critically dependent on external dampers for suppression of the undesired sidebands created by the counterpropagating optical and acoustic waves. Description of an Alternative Fiber Embodiment As previously discussed in reference to the mode selector 640 shown in Figure 9, only light which is propagating in the second order LP₁₁ mode is coupled out of the double-mode fiber 602 into the juxtaposed adjacent single-mode fiber 650 at the interaction region 652. An important criteria in the design of this mode selector is the lobe orientation of the LP₁₁ mode as it traverses the coupling region 652. In a circularly symmetric multi-mode fiber, the LP₁₁ modes are actually approximations to the true second order eigenmodes. An exact analysis, however, predicts that the lobe orientation of the LP₁₁ modes will rotate about the fiber axis as they travel along the fiber over a distance of several centimeters. The coupling of the double-mode fiber LP₁₁ mode to the single-mode fiber LP₀₁ mode in the mode selector 640 varies sinusoidally with the LP₁₁ mode lobe orientation. This happens because the antisymmetric LP₁₁ mode evanescent tail fields must generate symmetric LP₀₁ mode fields in the coupled fiber. To have an environmentally stable coupling coefficient between the two fibers, the orientation of the LP₁₁ mode lobes must be controlled. The degeneracy of the orthogonal lobe orientations of the LP₁₁ modes can be resolved by using an elliptical core fiber. Figure 23 illustrates the LP₁₁ mode degeneracy in a circular core fiber where the LP₀₁ and LP₁₁ modes are plotted in terms of their relative propagation constants and the shape of the fiber core. As shown at location 1000, which represents the value of the propagation constant for the LP₁₁ modes in a circular fiber, two orthogonal lobe orientations, 1002 and 1004, exist for the LP₁₁ propagation mode. It can be shown that the LP₁₁ lobes will follow the shape of an elliptical core fiber, thus resolving this degeneracy. This effect is illustrated by the two unequal propagation constant values, shown at locations 1006 and 1008, in Figure 23 for the LP₁₁ modes which exist in an elliptical core fiber. The orthogonal orientation of the two non-degenerate LP₁₁ modes in the elliptical core fiber which were degenerate in the circular core fiber, are shown as 1010 and 1012. Therefore, use of an elliptical core fiber is seen to provide orientational control over the LP₁₁ propagation modes. Since the alignment of the LP₁₁ lobe orientation can be controlled with elliptical fiber, the mode selector 640 in Figure 9, when constructed with an elliptical fiber, can preferentially select either of the non-degenerate LP₁₁ modes. Alignment accuracy is not critical, since the only disadvantage of a misaligned fiber is loss of optical signal by the factor cos²Δ , where Δ is the angular alignment error. Empirical verification of the above described lobe orientations in the LP₁₁ modes in circular and elliptical core fiber was obtained using the frequency shifter shown in Figure 9. In the experimental setup, an LP₁₁ mode selector was not used in the frequency shifter, so the output signal from the acoustic interaction region was the end of the fiber 602 in Figure 9. Figure 24 illustrates the far-field radiation pattern from the end of the double-mode fiber 602 with an acoustic signal applied to the fiber shown at 1024, and without an acoustic signal applied shown at 1020. A complete coupling from the LP₀₁ mode shown at 1020 to the LP₁₁ mode shown at 1024 is seen with an input electrical signal of 100mW at about 8MHz applied to the PZT. Overcoupling was observed when the acoustic power was increased further. The three far-field radiation patterns shown in Figure 25 demonstrate that ellipticity in the shape of the core of the double-mode fiber used for frequency shifting has a marked effect on the output signal from the device. The resolution of the two orthogonal lobe orientations of the LP₁₁ mode can also be observed by using the acousto-optic frequency shifter described previously to selectively couple light travelling in the LP₀₁ mode to either of the two LP₁₁ orthogonal lobe orientation modes. This is accomplished by using acoustic waves of slightly different frequencies for the coupling interaction. Figure 25 shows the far-field radiation pattern from the output of a double-mode fiber with no acoustic signal, shown at 1030; with an acoustic signal or 7.73 MHz, shown at 1050; and with an acoustic signal of 7.93 MHz, shown at 1040 applied to the fiber. As clearly shown, nearly 100% coupling to each LP₁₁ mode orientation was accomplished with little or no coupling to the other LP₁₁ mode for the acoustic signal frequency satisfying the coupling conditions for that transition. 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: An apparatus for coupling optical energy between optical propagation modes in an optical fiber to shift the frequency of an optical signal propagating in the fiber, comprising a multimode optical fiber (300, 500, 602, 662a, 662b, 700) having a first spatial propagation mode and a second spatial propagation mode for optical signals propagating therein; and a generator (310, 500, 610, 660, 704, 756) arranged to directly produce microbends in the fiber so as to form a travelling flexural wave which propagates as travelling microbends in said fiber, the wave length and propagation velocity of said flexural wave being selected to provide a microbend propagation constant which is substantially equal to the difference in the propagation constants of the two propagation modes for the optical signals travelling within the fiber whereby, in use, said travelling microbends will cause a portion of the optical energy propagating in said first propagation mode to be coupled to said second propagation mode and shifted in frequency by a frequency magnitude equal to said frequency of said flexural wave. The apparatus as defined in Claim 1, characterized in that said travelling flexural wave frequency and propagation velocity are selected to cause said wavelength of said flexural wave to be substantially equal to the beat length of said fiber for said optical signal. The apparatus as defined by Claim 1, characterized in that the propagation velocity of said flexural wave is dependent upon the cross sectional dimensions of said fiber and wherein said fiber is tapered to cause said propagation velocity to vary along the length of said fiber. The apparatus as defined in Claim 3, characterized in that said taper is in discrete steps. The apparatus as defined by either Claim 3 or 4, characterized in that said taper is gradual. The apparatus, as defined by any one of Claims 1 to 4, characterized in that said generator (310, 500, 610) includes a device (320, 514, 612) for varying the frequency of said flexural wave. The apparatus as defined by any one of Claims 3 to 6, characterized in that the angle of the taper of said fiber is selected such that the length of the region over which substantial coupling occurs is small compared to the length of said fiber, the location of said region varying along said fiber as the frequency of said flexural wave is varied. The apparatus as defined by Claim 7, characterized in that the length of said fiber is at least about an order of magnitude greater than the length of said coupling region. The apparatus, as defined in Claim 7, characterized in that the length of said coupling region is on the order of a few beat lengths of the first and second propagation modes. The apparatus as defined in any one of Claims 1 to 9, characterized in that said optical fiber (662a) comprises at least first and second portions (674, 676), said first portion (674) having a larger outer diameter than said second portion (676), said traveling flexural wave having a first acoustic propagation velocity and a corresponding first acoustic wavelength in said first portion and having a second acoustic propagation velocity and a corresponding second acoustic wavelength in said second portion, said first acoustic wavelength being substantially equal to a first fiber beat length of a first optical signal at a first optical frequency and said second acoustic wavelength being substantially equal to a second fiber beat length of a second optical signal at a second optical frequency. The apparatus as defined in any one of Claims 1 to 9, characterized in that said optical fiber (662a) comprises at least first and second portions (674, 676), said first portion (674) having a larger outer diameter than said second portion (676), said first portion being sized to cause said traveling flexural wave to have a first acoustic frequency at a first acoustic propagation velocity corresponding to an acoustic wavelength, said second portion sized to cause a traveling flexural wave at a second acoustic frequency and at a second acoustic propagation velocity to have the same acoustic wavelength. The apparatus as defined in Claim 11, characterized in that the length of said first and second portions (674, 676) are substantially equal to the length in which substantially all of the optical energy traveling in said first propagation mode is coupled to said second propagation mode and shifted in frequency by said acoustic frequency. The apparatus as defined in any one of Claims 10 to 12, characterized in that: said fiber (662a) includes a third portion (672) having a diameter larger than the diameter of said first and second portions (674, 676) of said optical fiber; and said diameter of said third portion (672) being sized so that virtually no coupling between said first and second optical propagation modes occurs in said third portion (672) of the fiber. The apparatus as defined in Claim 13, characterized in that said generator (660) of said flexural wave is coupled to said optical fiber (662a) at said third portion (672) of said optical fiber. The apparatus as defined in any one of Claims 1 to 14, characterized in that optical energy traveling in said first propagation mode at a first optical frequency and first phase propagation velocity is coupled to said second propagation mode at a second optical frequency and second propagation velocity so that said second frequency is substantially equal to either the sum or difference of said first optical frequency and said frequency of said flexural wave. The apparatus as defined in Claim 15, characterized in that said second optical frequency is equal to said first optical frequency plus said frequency of said flexural wave when said optical signal propagates in the same direction as said flexural wave and said first phase propagation velocity is greater than said second phase propagation velocity, and said second optical frequency is equal to said first optical frequency minus said frequency of said flexural wave when said optical signal propagates in the same direction as said flexural wave and said first phase velocity is less than said second phase velocity. The apparatus as defined in any one of Claims 1 to 16, characterized in that said generator (500, 704) of said flexural wave comprises an acoustic transducer. The apparatus as defined in Claim 17, characterized in that said acoustic transducer comprises an elongated member having a first end mechanically coupled to said optical fiber and having a second end disposed away from said first end, said second end having a transducer (512, 708) disposed thereon, said transducer being responsive to an electrical signal applied thereto for generating an acoustic wave which propagates from said second end of said member to said first end of said member to thereby induce said flexural waves in said optical fiber. The apparatus as defined in Claim 18, characterized in that said second end of said member is larger than said first end of said member so that the acoustic energy per unit area applied to said optical fiber is greater than the acoustic energy per unit area excited in said second end of said member by said transducer (512, 708). The apparatus as defined in either Claim 18 or 19, characterized in that said first end of said member has a cross-sectional dimension smaller than the wavelength of said acoustic wave. The apparatus as defined in any one of Claims 18 to 20, characterized in that said transducer (512, 708) excites longitudinal, torsional or flexural acoustic waves in said member. The apparatus as defined in any one of Claims 18 to 20, characterized in that said transducer (512, 708) excites surface acoustic waves at said second end, said member converting the energy of said surface waves to provide longitudinal waves at said first end of said member. The apparatus as defined in Claim 22, characterized in that said member comprises a cylinder which is hollow at said second end and is solid at said first end, the transition between said hollow end and said solid end being a smooth and gradual taper. The apparatus as defined in any one of Claims 1 to 23, additionally characterized by a damper, mechanically coupled to said optical fiber, to prevent reflection of said flexural wave traveling in said optical fiber. The apparatus as defined in Claim 1, characterized in that: said optical fiber (662b) includes a tapered portion in which the diameter of the cladding of said optical fiber decreases from a larger diameter to a smaller diameter, said generator (660) coupled to said fiber at a location thereon at which the cladding diameter is sufficiently large to prevent coupling light out of said fiber at said location. The apparatus as defined in any one of Claims 1 to 25, characterized in that said optical fiber has a core of elliptical cross section. The apparatus as defined in Claim 26, characterized in that one of said modes includes two orthogonal lobe orientations, the degree of ellipticity of said core selected to cause said orthogonal lobe orientations to be non-degenerate. The apparatus as defined in any one of Claims 1 to 27, further characterized by a mode selector (640) comprising a second dissimilar optical fiber (652) positioned in the evanescent field of said optical fiber (602) so that optical energy propagating in said optical fiber (602) in said second propagation mode is exclusively coupled to said second dissimilar optical fiber (652) in a selected propagation mode of said second dissimilar optical fiber to thereby separate said optical energy at said second optical frequency from said optical energy at said first optical frequency. The apparatus as defined in any one of Claims 1 to 28, further characterized by: an acoustic horn (756), acoustically coupled to said optical fiber (700), and an acoustic transducer for generating surface acoustic waves on a surface of said horn, said horn adiabatically transforming said surface waves into longitudinal waves for exciting said traveling flexural wave in said fiber (700) to cause coupling of light between said modes. The apparatus defined in Claim 29, further characterized by a device (758) for suppressing propagation of bulk acoustic waves in said horn (756). A method of coupling the optical energy of an optical signal traveling in a first spatial propagation mode in a multimode fibre at a first frequency and at a first phase propagation velocity to a second spatial propagation mode at a second frequency and at a second phase propagation velocity, comprising the step of injecting the optical signal to be shifted in frequency into a first end of said multimode optical fiber (300, 500, 602, 662a, 662b, 700); in such a manner that said signal propagates in said first mode and providing acoustic vibration to said optical fiber to produce microbends which form a travelling flexural wave which propagates in said fiber, the wave length and propagation velocity of said flexural wave being selected to provide a microbend propagation constant which is substantially equal to the difference in the propagation constants of the two propagation modes for the optical signals travelling within the fiber whereby. said propagating microbends cause a portion of the optical energy in said first propagation mode to be coupled to said second propagation mode and shifted in frequency by a frequency magnitude equal to said frequency of said flexural wave.

Inventors: BLAKE JAMES N, ENGAN HELGE E, KIM BYOUNG Y, SHAW HERBERT J, BLAKE, JAMES N., ENGAN, HELGE E, KIM, BYOUNG Y., SHAW, HERBERT J.
Applicants: UNIV LELAND STANFORD JUNIOR, THE BOARD OF TRUSTEES OF THE LELAND STANFORD JUNIOR UNIVERSITY
Application year: 1987
Main classification: G02B6
IPC codes: G02B6, G02F1, G02F2, G02B26