200 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 29, NO. 2, JANUARY 15, 2011 Dependence of Frequency Shift of Depolarized Guided Acoustic Wave Brillouin Scattering in Photonic Crystal Fibers John E. McElhenny, Member, IEEE, OSA, Radha K. Pattnaik, Member, IEEE, OSA, and Jean Toulouse, Member, IEEE, OSA Abstract—We study through experiment, calculation and simu- lation the frequency dependence of depolarized GAWBS observed in four different photonic crystal fibers and extend the results to others through simulation. In two of the fibers studied, high fre- quency modes ( GHz) are observed in addition to the usual lower frequency torsional radial (TR) modes. The acoustic modes responsible for GAWBS are characterized through a combination of simulations and experiments. The calculations are done using the silica rod approximation, which is valid for PCFs with a low to intermediate air-fill fraction or with a very high air-filling fraction. Further simulations extend the range of photonic crystal fibers in which acoustic modes can be characterized. These are used to study the dependence of the acoustic mode frequency on key fiber param- eters such as the ratio of air to silica across the whole cross section and the lattice pitch . Index Terms—Acoustic, Brillouin, COMSOL, fibers, micro- structured fiber, photonic crystal fiber. I. INTRODUCTION I N previous papers [1]–[3], we have investigated stimulated Brillouin scattering (SMS) in which light is scattered off of a primarily longitudinal acoustic wave forward propagating along the length of the fiber. This Brillouin scattered light then propagates in the backward direction and, when the input power exceeds the threshold, the process transitions from a sponta- neous to a stimulated one. We now turn to guided acoustic wave Brillouin scattering (GAWBS) [4], also referred to as forward Brillouin scattering, specifically depolarized GAWBS in which the polarization and phase of the input or pump light is mod- ulated by torsional-radial (TR) acoustic waves. The displace- ment is radial or azimuthal unlike the waves involved in back- ward SBS in which the displacements are longitudinal, along the fiber. In optical fibers, GAWBS, much like SBS, can be either ben- eficial or detrimental, depending on the particular application. The excess noise created by GAWBS is a fundamental problem which can be a severe hindrance in a variety of applications, Manuscript received August 11, 2010; revised October 28, 2010; accepted November 01, 2010. Date of publication November 11, 2010; date of current version January 19, 2011. The authors are with the Department of Physics, Lehigh University, Beth- lehem, PA 18015 USA (e-mail: john.e.mcelhenny@us.army.mil). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2010.2091944 particularly in quantum and fiber optics. In quantum optics, the thermal excitation (and thus excess noise) hinders the generation and detection of squeezed light in optical fibers and interferes with quantum non-demolition noise measurements [5]–[10]. The search for efficient means of squeezing has been essential to the modern developments in quantum optics [11]. Optical squeezing is of interest both fundamentally, as highly nonclassical light, and for quantum communication applications such as generating entanglement and making measurements below the standard quantum noise limit. On the other hand, GAWBS can be very useful in characterizing acoustic modes in fibers. Since the resonance frequencies, , of the GAWBS modes are dependent upon the structural and environmental conditions, it can be used to measure the sound velocity, cladding diameter, temperature and tensile strain [12]. It can also be useful in realizing fiber optic temperature and strain sensors [13]. In this study, we analyze the dependence of GAWBS on the structure of the photonic crystal fiber both through experiment and simulation with the vision that a more fundamental understanding will allow for the reduction or enhancement of GAWBS, depending upon the needs of a particular implementation. GAWBS, both polarized and depolarized, has been studied extensively and is well understood in standard fibers [4], [14], [15] as well as in polarization maintaining (PM) fibers [16]–[18], and the dependence on the input polarization has been well documented by Tanaka et al. [13], [19]. In pho- tonic crystal fibers (PCFs), however, there have only been a handful of studies of GAWBS [20]–[25]. Using two different PCFs Shibata et al. [20] have shown experimentally that the acoustic velocity ratio, where and are the shear and longitudinal velocities respectively, decreases as the ratio of total air hole area to fiber cross-sectional area, , increases. As the amount of air in the cross section increases, the “effective” shear velocity (henceforth referred to as “shear velocity”) decreases and thus the frequency of the acoustic modes shifts downwards. Elser et al. [21] experimentally observed a reduction in depo- larized GAWBS (below 1 GHz) due to the mechanical isolation of the core from the outer cladding by the air-holes of the inner cladding for a specific PCF. Beugnot et al. [23] noted the same fact but for polarized GAWBS and further showed that this reduction in GAWBS in the lower frequency regime by the air holes also results in the enhancement of a fundamental longi- tudinal mode isolated in the core at higher frequencies. These 0733-8724/$26.00 © 2010 IEEE