Analysis of Brillouin Frequency Shift and Longitudinal Acoustic Wave in a Silica Optical Fiber With a Triple-Layered Structure

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1 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 8, AUGUST Analysis of Brillouin Frequency Shift and Longitudinal Acoustic Wave in a Silica Optical Fiber With a Triple-Layered Structure Jaewang Yu, Associate Member, IEEE, Il-Bum Kwon, and Kyunghwan Oh, Member, IEEE, Member, OSA Abstract We report a thorough analysis on the Brillouin frequency shift as a function of geometrical parameters in a silica optical fiber consisting of triple-layered structure, GeO 2 -doped core, P 2 O 5, and F co-doped inner cladding, and pure silica outer cladding. General characteristic equations for the Brillouin frequency shift were analytically derived and analyzed for various fiber parameters. In experiments, three-layered optical fibers were fabricated and their Brillouin frequency shifts were measured in the wavelength region of 1.55 m by a pump-probe technique. The longitudinal acoustic velocity in each layer was found significantly affected by the thermal stress as well as the dopant concentrations. We confirmed both in theory and experiment that the inner cladding of a three-layered optical fiber does provide a new degree of freedom in precise control of the Brillouin frequency shift. Index Terms Brillouin frequency shift, inner cladding, longitudinal acoustic waves, silica optical fiber, stimulated Brillouin scattering (SBS), thermal expansion coefficient, thermal stress, thermoelasticity. I. INTRODUCTION THE STIMULATED Brillouin scattering (SBS) process in optical fiber is being extensively investigated both in optical communication and sensor systems. Recent applications include hybrid erbium/brillouin amplifiers [1], lasers [2], Brillouin/Raman multiwavelength comb generation [3], distributed measurement of strain and temperature [4] [6], and fiber-based optical parametric amplifiers [7], [8], to name a few. SBS is induced by a parametric acoustooptic interaction among the pump photon, the Stokes photon, and acoustic waves guided in optical fibers [9]. In a cylindrical optical fiber, there exist three types of acoustic modes, such as longitudinal, torsional, and flexural modes [10], [11]. Among them, the lowest longitudinal acoustic mode, the mode, mainly interacts with the input pump photon and gives rise to backscattered Stokes-shifted photon whose frequency is downshifted by the characteristic acoustic frequency, the Brillouin frequency shift [9]. The impacts of optical fiber material on SBS have been previously Manuscript received September 6, 2002; revised May 14, This work was supported in part by the KOSEF through the Ultra-Fast-Fiber-Optic Networks Research Center, the Korean Ministry of Education through the BK21 Program, and the ITRC-CHOAN program. J. Yu and K. Oh are with the Department of Information and Communications, Kwangju Institute of Science and Technology, Gwangju , Korea ( koh@kjist.ac.kr). I.-B. Kwon is with the Nondestructive Measurement Group, Korea Research Institute of Standard and Science, Daejon , Korea ( ibkwon@kriss.re.kr). Digital Object Identifier /JLT reported and GeO -doped silica was found to be an optimal glass host for the core considering the figure of merit, which is the ratio of SBS gain to optical loss per unit fiber length [12]. Various methods to control Brillouin frequency shift change have been demonstrated experimentally by changing a waveguide in a dual-shape core profile [13], by changing the dopant concentration [14], and by externally induced periodical residual strain [15]. Among these techniques, changing geometrical parameters of an optical fiber was found to be the most reproducible and flexible method to control the Brillouin frequency shift. The core structure of an optical fiber [17] has been one of the primary interests because it will simultaneously affect photon guiding properties and the Brillouin responses. For a double-layered optical fiber structure composed of GeO -doped silica core and pure silica cladding, the acoustic modes have been theoretically analyzed solving the scalar wave equation along with the continuity condition at the core cladding boundary [16]. In the analysis, an important prediction has been made such that the Brillouin frequency shift monotonically decreases as the core radius increases. Based upon this prediction, suppression of SBS has been attempted in various types of double-layered specialty optical fibers introducing nonuniform axial distributions of radius and refractive index of the core [17] [19]. The SBS process in optical fibers can be further characterized by SBS threshold. Recently experimental measurements of SBS thresholds have been reported using a versatile Brillouin optical time domain reflectometer (BOTDR) technology [20]. These reports on the SBS thresholds, however, are mainly based on experimental measurements, and a thorough analysis on the impacts of detailed geometrical optical fiber structures over the Brillouin characteristics has not been reported yet. The fundamental ability to control the Brillouin frequency shift would generate a variety of novel features in current SBS applications, especially in dense-wavelength-division-multiplexing (DWDM) devices where the precise spectral locations of the SBS outputs are emphasized in accordance with International Telecommunication Union (ITU) standard grids [3]. Another contribution would be to enable high pump launching for efficient conversion of the pump to nonlinear optical throughput and optical gain [21] [23], by distributing the Brillouin frequency shift in an appropriate manner, which will in effect increase the SBS threshold. Inner cladding layers are generally deposited between the core and the silica outer cladding in order not only to control /03$ IEEE

2 1780 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 8, AUGUST 2003 Fig. 1. Schematic profiles of refractive index (solid line) and acoustic velocity (dashed line) of optical fibers with matched inner cladding. a is core radius, b is the radius of inner cladding, and c is the radius of outer cladding. waveguide properties such as chromatic dispersion [24], [25] but also to reduce additional optical loss induced at the interface between the core and the silica cladding [26], [27]. Due to differences in thermoelastic properties of each layer in the triple-layered structure, a residual stress distribution is formed across the three layers and a detailed analysis on thermal stress profiles has been reported elsewhere by the authors [28]. The stress profile induces nontrivial density distribution to result in an acoustic velocity distribution as schematically shown in Fig. 1. For the guided acoustic waves, therefore, the continuity conditions and subsequent characteristic equations at the two boundaries, the core inner cladding and the inner outer cladding interfaces, could endow a new ability to control the Brillouin frequency shift that has not been achieved in the prior double-layered structures where only one boundary was defined [17]. In this report, we introduce a new technique to precisely control the Brillouin frequency shift in a silica optical fiber by utilizing thermoelastic effects of the inner cladding layer in a triple-layered structure, for the first time to the best knowledge of the authors. We analyzed the influences of the inner cladding layer on acoustic waves and Brillouin frequency shift systematically in the following steps. First, thermoelastic analysis [28] is applied to the three-layered fiber structure to find the acoustic velocity in each layer. For the given distribution of the acoustic velocity, boundary value problems for the lowest longitudinal acoustic mode are then solved to derive a general characteristic equation for the Brillouin frequency shift. Detailed analysis is followed regarding the impacts of the inner cladding geometry. Finally, theoretical predictions are compared with the Brillouin frequency shifts experimentally measured with a pump-probe method for fibers of various core radii. The newly formulated analytic solutions, which are in a good accordance with experimental results, will provide a new systematic method to design novel fiber SBS devices. II. ACOUSTIC WAVES IN OPTICAL FIBERS The refractive index profile and corresponding acoustic velocity profile in the proposed triple-layered structure optical fiber are schematically shown in Fig. 1. The core is doped with GeO to increase the refractive index and the inner cladding is co-doped with P O and F to lower the processing temperature as well as to adjust the refractive index relative to that of the pure silica cladding. The thermal expansion coefficient of a binary silica glass shows a linear response in a low-dopant-concentration range [29] and the overall thermal properties of multiple dopants, such as P O and F in the inner cladding, could be well approximated as a linear superposition of contributions from individual dopants. These assumptions are valid for the dopant concentration range, less than a few-mole percent, used in conventional single-mode fiber (SMF) fabrication processes and will be applied in the following discussions. When a preform with multiple glass layers are drawn to fiber with a negligible tension, the density of doped silica glass fiber is mainly affected by thermal stress, which are developed by the differences in thermal expansion coefficients of constituent layers. In contrast, the mechanical stress will play a major role for the fiber with a large viscosity difference [28] drawn at a high tension and high speed. In this analysis, a low speed and low tension in the fiber drawing process will be assumed such that the density of each layer in an optical fiber is determined mainly by the thermal stress distribution. As the optical fiber exits the furnace, it rapidly cools below the glass transition temperatures of individual layers, and the glass layers change from the liquid state into the solid state, developing a unique thermal stress profile across the fiber. The thermal stress in the cylindrical coordinate [30] is expressed as (detailed procedures to calculate the thermal stress in a triplelayered optical fiber have been described in [28]) where is Young s modulus,, and is Poisson s ratio. is the thermal expansion coefficient, which depends on the radial position. Using the boundary conditions for the radial stress,, where is the radius of silica outer cladding, unknown constant of (1) (3) can bewritten as When of the inner cladding is lower than those of the outer cladding and the core, compressive stress is built up in the inner cladding, as shown in Fig. 2. Here, we assumed that the dopant concentrations in each layer were 3.36 mol% GeO for the core, 2.12 mol% P O, and 1 mol% F for the inner cladding. (1) (2) (3) (4)

3 YU et al.: BRILLOUIN FREQUENCY SHIFT AND LONGITUDINAL ACOUSTIC WAVE IN A SILICA OPTICAL FIBER 1781 Fig. 2. Calculated thermal stress profile of matched inner cladding fiber. In this calculation, the elastic modulus E = 68: Pa, the Poisson ratio = 0.17, T = C, the core radius a = 3 m, the outer radius of inner cladding b = 6.32 m, the outer radius of outer cladding c = 62.5 m, the thermal expansion coefficients = = C, = 4: = C, =5210 = C [28], [32]. The strain can be expressed by three orthogonal stress components [30] The density of the glass fiber in the presence of thermal volumetric stress can be written as where is the density in the absence of volumetric stress. The compressive stress in the inner cladding, therefore, will develop the density distribution as shown in Fig. 3. Given the density, we can estimate the longitudinal acoustic wave velocity in the individual layers [30], as follows: As summarized in (1) (7), the acoustic velocity in each layer can be modified by the thermal stress, which are in turn determined by the dopant concentration and the relative geometry of the constituent layers. By the sequential effects of thermal stress, volumetric strain, and density, we can obtain a new degree of freedom to change the acoustic velocity of each layer independent of the refractive index profile. Safaai-Jazi et al. have previously analyzed the acoustic modes in optical fibers with a double-layer structure, GeO -doped silica core and pure silica cladding [16]. In his report, assumptions are made such that,, and, where,, and are the longitudinal velocities, the shear velocities, and densities, respectively. Superscripts and indicate the core and the cladding, (5) (6) (7) Fig. 3. Corresponding density profile resulted from the thermal stress of Fig. 2. In this calculation, the density in the absence of volumetric stress = kg/m [32]. respectively. In those assumptions, the Brillouin frequency shift was found to monotonically decrease as a function of the core radius [17]. For the case of triple-layered structure, as in this paper, however, the acoustic wave analysis has to be modified to fully understand the inner cladding contributions [16] as follows: if if (8) if where is the zero-order solution of acoustic scalar wave equation, is an integer, and and denote the radii of core and inner cladding, respectively. Here, we assumed infinite silica cladding as was in the previous analysis [16].,, and are expressed as (9) (10) (11) where,, and are the longitudinal velocities of core, inner cladding, and outer cladding, respectively. is the phase velocity of the longitudinal acoustic mode and is expressed as [31] (12) where is the refractive index of core, is the Brillouin frequency shift or acoustic frequency, and is the optical wavelength. III. ANALYSIS OF BRILLOUIN FREQUENCY SHIFT Among guided acoustic modes, the lowest longitudinal acoustic mode, the mode, mainly interacts with the input pump photon in the SBS process. Brillouin frequency shift is,

4 1782 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 8, AUGUST 2003 Fig. 4. Acoustic velocity distributions for two cases. (a) The acoustic velocity of the inner cladding is assumed to be slower than that of the core. (b) The acoustic velocity of the inner cladding is faster than that of the core. Fig. 5. Brillouin frequency shift versus the core radius for various inner cladding radii b. In the calculation, acoustic velocities at the core, the inner cladding, the outer cladding were V =5 691 m/s, V = m/s, and V = m/s, respectively. Note that we assume V > V, where the compressive stress develops at the inner cladding. thus, obtained by solving the characteristic equation of the mode [17]. For acoustic modes, the relations between the frequency and the phase velocity can be obtained from the continuity of and at the boundaries of the fiber [16]. The triple-layered structure defines two boundaries, for the core-inner cladding and for the inner cladding outer cladding interfaces. The boundary conditions result in a general characteristic equation for a triple-layer optical fiber, as follows: (13) Therefore, the Brillouin frequency shift is to be obtained by solving (9) (13) for a given geometry and compositions in a triple-layered optical fiber. Numerical analysis on the impact of inner cladding was performed in two perspectives, which are shown schematically in Fig. 4. First, the acoustic velocity of the inner cladding is assumed to be lower than that of the core, shown Fig. 4(a), as a result of compressive stress. The second case is that the acoustic velocity of the inner cladding is higher than that of the core, which assumes a tensile stress in the inner cladding, manifested in conventional fiber drawing process with a high speed and a high tension. For the case of compressive stress in the inner cladding, the Brillouin frequency shift was calculated as a function of the core radius in Figs. 5 7 for independent parameters such as the inner cladding radius, the core acoustic velocity, the inner cladding acoustic velocity. Fig. 5 shows the plot of the Brillouin frequency shift versus the core radius for different inner cladding radii. The acoustic velocities of the core, the inner cladding, and Fig. 6. Brillouin frequency shift versus the core radius for various acoustic velocities at the core V. In the calculation, the inner cladding radius was b = 6.32 m. The acoustic velocities at the inner cladding and the outer cladding were V = m/s and V = m/s, respectively. Note that we assume V >V, where the compressive stress develops at the inner cladding. the outer cladding were set as 5 691, 5 677, and m/s, respectively. The acoustic velocity of the outer cladding was calculated from (7) using elastic properties of pure silica such as Poisson s ratio 0.17, density kg m, and Young s modulus 68.5 GPa [32]. The acoustic velocities at the core and inner cladding were numerically obtained assuming the compressive stress in the inner cladding as shown in Fig. 2 and the consequent density distribution in Fig. 3. As in Fig. 5, it is found that the Brillouin frequency shift does increase by over 5 MHz as the core radius increases from m, which is directly opposite to the previous reports in the two-layer optical fibers composed of the core and the silica cladding [17]. Moreover, it is found that the Brillouin frequency shift was very sensitive to the inner cladding dimension such that Brillouin frequency varied by as much as MHz for the inner cladding radius change by 0.4 m. A larger inner cladding radius resulted

5 YU et al.: BRILLOUIN FREQUENCY SHIFT AND LONGITUDINAL ACOUSTIC WAVE IN A SILICA OPTICAL FIBER 1783 Fig. 7. Brillouin frequency shift versus the core radius for various acoustic velocities at the inner cladding V. In the calculation, the inner cladding radius was b = 6.32 m. The acoustic velocities at the core, and the outer cladding were V = m/s and V = m/s. Note that we assume V >V, where the compressive stress develops at the inner cladding. in a lower Brillouin frequency shift. The Brillouin frequency shift was, therefore, found to be as sensitive to the inner cladding structure as to the core radius. The Brillouin frequency shift was plotted as a function of the core radius for various core acoustic velocities in Fig. 6 assuming a compressive stress at the inner cladding where. The inner cladding radius was assumed to 6.32 m, and the acoustic velocities at the inner cladding and the outer cladding were and m/s, respectively. Similar to Fig. 5, the Brillouin frequency shift increases as the radius and the acoustic velocity of the core increase. It is found that the larger difference in the acoustic velocity resulted in a larger variation in the Brillouin frequency. Especially for the case of m/s, the magnitude of variation in the Brillouin frequency was more than 12 MHz for the core radius range of 3.0 to 6.0 m. The effect of the acoustic velocity at the inner cladding on the Brillouin frequency was analyzed in Fig. 7, where the inner cladding radius was 6.32 m, and the acoustic velocities at the core and the outer cladding were and m/s, respectively. Similar to Figs. 5 and 6, the Brillouin frequency shift increases as a function of the core radius and it also increases as increases. We confirmed that the Brillouin frequency shift becomes more sensitive to the core radius variation as the difference in the acoustic velocities between the core and the inner cladding gets larger. The compressive stress at the inner cladding and subsequent distribution of the acoustic velocity in a triple-layered optical fiber, therefore, resulted in a consistent dispersion relation between the Brillouin frequency shift and the core radius as in Figs. 5 7 such that the Brillouin frequency shift increases with the core radius contrast to the previous results for the two-layered optical fibers. It was also found that the plot of the Brillouin frequency versus the core radius could be divided into three regions (e.g., see the graph at the top of Fig. 6), such as a plateau region for 3 m 4 m, a linear slope region for 4 m 5 m, and another plateau Fig. 8. Brillouin frequency shift versus the core radius for various inner cladding radii b. In the calculation, acoustic velocities at the core, the inner cladding, the outer cladding were V = m/s, V = m/s, and V = m/s, respectively. Note that we assume V < V, where the tensile stress develops at the inner cladding. region for 5 m 6 m. The Brillouin frequency shift is, therefore, more sensitive to the variation of the core radius change in the linear slope region than in the plateau regions. Now, for the second case where the acoustic velocity at the inner cladding is assumed higher than that at the core, the behaviors of the Brillouin frequency shift are analyzed in Figs In this case, we assume a tensile stress in the inner cladding, which is a result of conventional fiber drawing at a high speed and a high tension [28]. Fig. 8 shows the plot of the Brillouin frequency shift versus the core radius for various inner cladding radii. In the calculation, acoustic velocities at the core, the inner cladding, the outer cladding were m s, m s, and m s, respectively. The acoustic velocity of inner cladding could be higher than that of core because the density of inner cladding does decrease for a tensile stress. In this case where, the Brillouin frequency shift decreases as a function of core radius. A larger inner cladding radius resulted in a lower Brillouin frequency shift similar as in Fig. 5. The Brillouin frequency shift was plotted as a function of the core radius for various core acoustic velocities in Fig. 9. The inner cladding radius was assumed to 6.32 m, and the acoustic velocities at the inner cladding and the outer cladding were m/s and m/s, respectively. Similar to Fig. 8, the Brillouin frequency shift does decrease as the core radius increases. A higher inner cladding acoustic velocity, on the while, resulted in a higher Brillouin frequency shift. At a relatively lower of and m/s in Fig. 9, a steep change of the Brillouin frequency shift of about 20 MHz was found for the change of the core radius from 4.5 to 5.5 m, which is attributed to the multimode characteristics of acoustic wave resulting from a large difference between acoustic velocities of core and inner cladding. The effect of the acoustic velocity at the inner cladding on the Brillouin frequency was analyzed in Fig. 10, where the inner cladding radius was 6.32 m, and the acoustic velocities at the core and the outer cladding were m/s and m/s, respectively. Consistent with Fig. 8 and Fig. 9, the Brillouin frequency shift decreases as a function of the core radius while it

6 1784 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 8, AUGUST 2003 Fig. 11. Experimental setup for the measurement of SBS gain spectra and the Brillouin frequency shift. Fig. 9. Brillouin frequency shift versus the core radius for various acoustic velocities at the core V. In the calculation, the inner cladding radius was b = 6.32 m. The acoustic velocities at the inner cladding and the outer cladding were V = m/s and V = m/s, respectively. Note that we assume V <V, where the tensile stress develops at the inner cladding. Fig. 10. Brillouin frequency shift versus the core radius for various acoustic velocities at the inner cladding V. In the calculation, the inner cladding radius was b = 6.32 m. The acoustic velocities at the core and the outer cladding were V = m/s and V = m/s. Note that we assume V < V, where the tensile stress develops at the inner cladding. increases as increases. At a relatively higher of and m/s in Fig. 10, a steep change of the Brillouin frequency shift of about 20 MHz was found for the change of the core radius from 5.0 to 5.5 m. The steep change was also attributed to multimode characteristics of multimode resulting from the difference between acoustic velocities of core and inner over 16 m/s. As discussed in Figs. 8 10, the Brillouin frequency shift was found to decrease with the core radius consistent with the prior reports when the acoustic velocity of inner cladding is faster than that of core. It is, therefore, observed through numerical analysis that the relative magnitude between the acoustic velocity at the core and the inner cladding or will determine the overall response of Brillouin frequency shift to the core radius. IV. EXPERIMENT AND RESULTS In order to experimentally confirm the numerical analysis discussed in the previous section, three types of optical fibers with the triple-layered structure were fabricated. The core was doped with GeO, and the inner cladding was co-doped with P O and F. The refractive index of the inner cladding was matched to that of the silica outer cladding. All the parameters of optical fibers were kept same except for the core radius. The inner cladding radius was 6.35 m, and the relative refractive index difference between the core and the cladding was of 0.35% similar to that of conventional SMFs. The core radii of fabricated fibers were 4, 4.7, and 5.2 m. The outer diameter of the fibers were kept at 125 m with a variation less than 0.1 m. The fiber was drawn at a tension less than 1 g to insure that the thermal stress would play a major role across the fiber cross section, with suppressed mechanical stress impacts. The fibers were coated with commercially available ultraviolet (UV) curable acrylate polymer and the cured diameter was 270 m. The drawing conditions were carefully kept identical for each preforms such that we could make quantitative comparisons among three types of fibers. After the initial drawing, the fibers were re-winded on a spool and special care was given monitoring tension gauge to keep the winding strain identical. In order to measure the Brillouin frequency shift, a conventional pump and probe technique was used [12]. Fig. 11 is the experimental setup for the measurement of Brillouin gain spectra of test single-mode optical fibers. The output of a tunable laser diode (LD) was equally divided by a 3-dB fiber coupler, whose outputs were used as the pump and the probe light, respectively. The pump light with frequency was amplified by an erbium-doped fiber amplifier (EDFA) to achieve an optical power over SBS threshold and then launched into the one end of test fiber through an optical circulator. The probe signal was frequency-modulated using a LiNbO intensity modulator to and, where is the optical frequency of the tunable LD and is the modulation frequency. The unmodulated probe signal that would resulted in Rayleigh scattering was eliminated by appropriate dc bias voltage to the intensity modulator. Note that the probe signals and pump photon were propagating in the opposite direction, and the SBS process will amplify the probe signal transferring the power from the counterpropagating pump. By the phase matching condition for the SBS process, the power transfer from the pump to probe signal

7 YU et al.: BRILLOUIN FREQUENCY SHIFT AND LONGITUDINAL ACOUSTIC WAVE IN A SILICA OPTICAL FIBER 1785 Fig. 12. Brillouin frequency shifts measured for three fibers with different core radii. The curve represents the theoretical fitting where fiber parameters were assumed as b = 6.35 m, V = 5694 m=s, V = 5676 m=s, and V = 5759 m=s. Here b is the inner cladding radius, and V, V, and V are the acoustic velocities at the core, the inner cladding, and the outer cladding, respectively. across the fiber layers was found to be significantly affected by thermal stress and subsequent volumetric density distribution. Especially the relative magnitude between the core and the inner cladding acoustic velocity was found to play a pivotal role to determine the overall behavior of the Brillouin frequency shift. In the case of compressive thermal stress where the acoustic velocity at the inner cladding is lower than that of the core (i.e., ), the Brillouin frequency shift was found both theoretically and experimentally to increase with the core radius, which is opposite of the prior results for the case of double-layer optical fibers (i.e., ). The proposed triple-layer structure, along with a modification of inner cladding parameters, could provide a new method to precisely control the Brillouin frequency shift and novel design of SBS devices. ACKNOWLEDGMENT The authors would like to thank Dr. Y. Park of ETRI for his continuous advices. will be observed as the modulation frequency is swept in the region of the Brillouin frequency shift of test fibers. The peak position in the measured SBS gain spectrum was then assigned as the Brillouin frequency shift for the fibers. It is known that the strain of results in the Brillouin frequency shift changof as much as 5 MHz [33]. Furthermore, a temperature change of 1 C induces a Brillouin frequency shift change of about 1.2 MHz in a 270- m acrylate microjacketed fiber [33], [34]. In order to remove uneven temperature distribution and mechanical disturbances along the fiber, the test fibers were kept in a thermally insulated condition on a vibration-isolated optical table during the measurement. The measurement resolution for the Brillouin frequency was 100 khz. Note that the identical re-winding conditions for the fiber spool could further eliminate undesirable effects due to fiber strains. The measured Brillouin frequency shifts were , , and GHz for the core radius of 4, 4.7, and 5.18 m, respectively, as shown in Fig. 12. The experimental results were then theoretically fitted assuming a m inner cladding radius and acoustic velocities of 5 694, 5 676, and m/s, corresponding to the core, the inner cladding, and the outer cladding, respectively. Fig. 12 shows that the experimental results have a good agreement with the theoretical fitting. The error in the fitting is attributed to contribution from other acoustic modes such as torsional or flexural modes to the Brillouin frequency shift, which has been neglected in the numerical analysis. Note that the Brillouin frequency shift did increase with the core radius as predicted in Figs. 5 7 due to a compressive stress in the inner cladding and subsequent acoustic velocity distribution that satisfies in the triple-layered fiber structure. V. CONCLUSION In summary, we have developed a new analytic formulation for the Brillouin frequency shift in a triple-layered optical fiber structure. The longitudinal acoustic velocity distribution REFERENCES [1] S. J. Strutz and K. J. Williams, Low-noise hybrid erbium/brillouin amplifier, Electron. Lett., vol. 36, pp , Aug [2] G. J. Cowle, D. Y. Stepanov, and Y. T. Chieng, Brillouin/Erbium fiber lasers, J. 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Krebber, Distributed beat length measurement in single-mode optical fibers using stimulated Brillouin-scattering and frequency-domain analysis, J. Lightwave Technol., vol. 18, pp , Mar [34] J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution, J. Lightwave Technol., vol. 19, pp , Nov Jaewang Yu (S 99 A 01) received the B. S. and M.S. degrees in electrical engineering from Jeonbuk National University, Jeonbuk, South Korea, in 1996 and 1998, respectively. He is currently working toward the Ph.D. degree in the area of optical fiber devices for optical communications with the Department of Information and Communications, Kwangju Institute of Science and Technology, Gwangju, Korea. Il-Bum Kwon, photograph and biography not available at the time of publication. Kyunghwan Oh (M 90) received the B.S. and M.S. degrees in physics from Seoul National University, Seoul, Korea, in 1986 and 1988, respectively, and the M. S. degree in engineering and Ph.D. degree in physics from Brown University, Providence, RI, in 1991 and 1994, respectively. He was subsequently appointed as a Postdoctoral Research Associate in the Laboratory for Lightwave Technology, Brown University. Returning to Korea, he was involved in specialty fiber development as a Senior Researcher in the fiber optics and telecommunication laboratory in LG Cable in From 1996 to 2000, he was an Assistant Professor in the Department of Information and Communications, Kwangju Institute of Science Technology (K-JIST), Gwangju, South Korea, where he became an Associate Professor in In the summer of 1998, he was appointed as a Visiting Professor of research with the Division of Engineering at Brown University. From September 2000 to February 2002, he was a Visiting Scientist with Bell Laboratories, Lucent Technologies, Murray Hill, NJ. In summer 2002, he was a Visiting Scientist with the fiber-optic material research center at Rutgers University, Piscataway, NJ. His research interests are in the areas of specialty fiber design and fabrication for active and passive fiber devices in optical communications. Dr. Oh is a Member of the IEEE Lasers and Electro-Optics Society (LEOS) and the Optical Society of America (OSA).