JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 8, AUGUST 2003 1779 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 -doped core, P O , 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, longitu- dinal acoustic waves, silica optical fiber, stimulated Brillouin scat- tering (SBS), thermal expansion coefficient, thermal stress, ther- moelasticity. I. INTRODUCTION T HE 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], Bril- louin/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, 2003. This work was supported in part by the KOSEF through the Ultra-Fast-Fiber-Optic Net- works 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 Communica- tions, Kwangju Institute of Science and Technology, Gwangju 500-712, Korea (e-mail: koh@kjist.ac.kr). I.-B. Kwon is with the Nondestructive Measurement Group, Korea Re- search Institute of Standard and Science, Daejon 305-600, Korea (e-mail: ibkwon@kriss.re.kr). Digital Object Identifier 10.1109/JLT.2003.815500 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 period- ical 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-multi- plexing (DWDM) devices where the precise spectral locations of the SBS outputs are emphasized in accordance with In- ternational 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 0733-8724/03$17.00 © 2003 IEEE