Optically tunable acoustic wave band-pass filter

The acoustic properties of a hybrid composite that exhibits both photonic and phononic behavior are investigated numerically with finite-element and finite-difference time-domain simulations. The structure is constituted of a periodic array of photonic resonant cavities embedded in a background superlattice. The resonant cavities contain a photo-elastic chalcogenide glass that undergoes atomic-scale structural reorganization when irradiated with light having energy close to its band-gap. Photo-excitation of the chalcogenide glass changes its elastic properties and, consequently, augments the acoustic transmission spectrum of the composite. By modulating the intensity of light irradiating the hybrid photonic/phononic structure, the position and spectral width of phonon passing-bands can be controlled. This demonstration offers the technological platform for optically-tunable acoustic wave band-pass filters.


I. INTRODUCTION
A phononic crystal (PC) is a composite structure comprised of a spatially periodic array of inclusions of one material embedded in a different background matrix material.PCs come in one-, twoand three-dimensional forms and, depending on their application, have length scales that vary from meters to several hundreds of nanometers.Phonon dispersion in PCs can be controlled by (1) varying the shape and/or filling fraction of the dispersed inclusions or (2) selecting alternative constituent materials with different elastic properties.][24] Similar functionalities have been demonstrated for semi-infinite systems. 25and PC plates. 26,27n spite of more than 20 years of research, PCs have found limited success in transitioning from the laboratory to industry.The primary reason resides in the fact that the advantage of using current PC technology in modern devices does not outweigh the detriment of replacing outright the technologies used presently in industry with comparable functions.The current state of knowledge and technical development in the field of phononics indicates a strong need for PCs with more diverse functionalities.Toward achieving this goal, some investigators have considered the efficacy of coupling linear waves to anharmonic modes in phononic systems employing nonlinear materials.This strategy, for instance, enabled theoretical 28 and experimental 29 demonstrations of acoustic rectification.Other investigators have considered controlling phonons in PCs with external stimuli such as an applied magnetic field. 30,31In these works, exploitation of magnetoacoustic coupling led to PCs with tunable acoustic properties 30 and facilitated the development of reconfigurable phononic waveguides. 31ndeed these functionalities are unattainable in ordinary materials which gives tunable phononic systems a distinct advantage over other technologies for future industrial applications.With this as motivation, we aim to explore the scientific and technological merit of incorporating chalcogenide glasses into phononic crystal designs.Chalcogenide glasses are a distinct class of amorphous semiconductors that exhibit a wide range of intriguing, light-induced phenomena such as photo-darkening, 32 photo-expansion, 33 photo-anisotropy 34 and photo-fluidity. 35Moreover, some chalcogenide glasses exhibit photo-elasticity, 36 a phenomenon where the elastic properties of the glass change when irradiated with light having energy close to its band-gap.Utilizing a photo-elastic chalcogenide glass as a constituent material in a phononic structure is a pathway toward achieving novel acoustic functionalities as phonon dispersion depends on the electromagnetic radiation impinging upon the system.
In this work, we exploit the phenomenon of photo-elasticity in chalcogenide glasses to offer a tunable phononic material with acoustic properties dependent on the intensity of light irradiating the structure.A hybrid composite exhibiting both photonic and phononic properties is considered.The structure is constituted of a periodic array of photonic resonant cavities embedded in a background superlattice.The photonic resonant cavities contain a photo-elastic chalcogenide glass.When irradiated with light of a particular wavelength, a photonic eigenmode is activated inside the cavities which induces photo-elastic softening of the longitudinal elastic constant (C 11 ) of the chalcogenide glass.This strongly augments phonon dispersion and, consequently, the acoustic transmission spectrum of the superlattice.Due to the reversible nature of photo-elasticity in chalcogenide glasses, 36 when the light source is removed the acoustic properties of the superlattice are restored back to that of the non-irradiated system.This technology offers a platform on which optically-tunable acoustic wave band-pass filters can be developed.This paper is organized as follows.First, in Section II: Background, the phenomenon of photo-elasticity in chalcogenide glasses is briefly reviewed.Second, in Section III: Models and Methods, we describe the numerical models, namely finite-element (FE) and finite-difference time-domain (FDTD) simulations, used to characterize wave propagation in the hybrid photonic/phononic superlattice.Subsequently, in Section IV: Results and Discussion, phonon dispersion curves and transmission spectra are presented for the superlattice under different photon irradiation conditions.Finally, in Section V: Conclusions, we comment on the efficacy of the demonstrated technology for radio frequency signal processing applications.The work presented in this paper represents a strong push to broaden the range of functionalities associated with phononic systems.

II. BACKGROUND
Chalcogenide glasses are comprised of chains of divalent atoms (S, Se and Te) cross-linked with elements of higher covalent coordination such as Ge, As and Sb.The atomic constituents of these materials have similar electronegativity and consequently the glass structure is described as a network of covalent bonds. 37Chalcogenide glasses are amorphous semiconductors with band gap energies around 1-2 eV. 38A distinct property of chalcogenide glasses is their ability to undergo structural reorganization during photo-excitation with light having energy close to its band-gap.The excitation of localized electrons from the top of the band-gap creates electron-hole pairs that facilitate the creation of metastable defect configurations within the covalent network.This phenomenon leads to such effects as photo-darkening, 32 photo-expansion, 33 photo-anisotropy, 34 photo-fluidity 35 and photo-elasticity. 36Gump et al. demonstrated experimentally that the Ge-Se family of chalcogenide glasses undergo reversible changes in their elastic properties when irradiated with focused light having energy close to the material's band-gap. 36Specifically, when irradiated with a laser at 2mW power, C 11 of a glass with composition GeSe 4 was reduced by approximately 5% with respect to C 11 for the non-irradiated system.In ramping-up the power of the laser to a maximum of 6mW, C 11 of GeSe 4 was shown to decrease by as much as 50%.The stiffness of the glass was fully recovered upon ramping-down the laser from 6mW to 2mW, indicating that photo-elasticity in Ge-Se systems is a reversible phenomenon.
In this manuscript, GeSe 4 is utilized as a functional component in a hybrid phononic/photonic superlattice.The distinctive response of this material to photon irradiation enables the function of tunable phonon passing-bands.Similar functionality was recently demonstrated experimentally for a solid/fluid PC constituted of an array of steel cylinders in a background polymer hydrogel matrix. 39In that work, with application of a thermal stimulus (infrared light), changes in the effective elastic properties of the hydrogel as well as the lattice constant of the PC could be induced, thereby augmenting the phonon band structure of the system.The steel/hydrogel PC was suggested as a tunable filter for ultrasonic waves.In contrast to this work, the present study considers a system that is entirely solid and suitable for radio frequency signal processing applications.Specific details are highlighted in the next section.

III. MODEL AND METHODS
In this work, we utilize both FE and FDTD methodologies to characterize the acoustic properties of our system of interest.Though either method could have been used exclusively, we employed both techniques for computational convenience.FE simulations are facilitated by the commercial software package COMSOL Multiphysics whereas the algorithms for FDTD simulations were developed in-house.FE simulations are used to calculate dispersion diagrams for the photonic and phononic components of the proposed hybrid photonic/phononic structure.FDTD simulations are utilized to simulate the propagation of broad-band acoustic wave packets through the hybrid composite to ascertain data pertaining to acoustic wave transmission.As is shown in subsequent data plots, the agreement between both methods is excellent.
The primitive unit cell (supercell) of the hybrid photonic/phononic structure considered in this manuscript is picture in Figure 1(a).
It has periodicity (a 2 ) and is constituted of a slab of GeSe 4 (the photonic resonance cavity) sandwiched in between two quarter-wave Bragg reflectors.Each Bragg reflector is a photonic superlattice of periodicity (a 1 ) and consists of alternating layers of GeSe 4 and epoxy.The thickness of the GeSe 4 and epoxy layers is λ/4 where λ is the wavelength of light required to initiate photo-elastic softening of GeSe 4 .FE simulations are employed to generate the photonic band structure of the Bragg reflectors with n = 2.46 and n = 1.315 for GeSe 4 and epoxy resin, respectively, where n is refractive index.These calculations indicate that the Bragg reflectors each possess a photonic band gap at λ = 800 nm (see Figure 1(b)).This, in combination with the fact that the photonic resonance cavity is λ thick, allows a photonic resonance mode to be established in the GeSe 4 cavity at the irradiation wavelength λ = 800 nm.Additional FE simulations are employed to characterize the normal modes supported in the GeSe 4 resonance cavity.Figures 1(c) and 1(d) show normalized electric field and photon intensity, respectively, along the x-axis of the superlattice for the cavity eigenmode at λ = 800 nm.Photon energy is strongly localized on the GeSe 4 region of the structure which induces large changes in the elastic properties of the material via the mechanism of photo-elasticity.The intensity associated with this eigenmode is not entirely confined within the bounds of the defect cavity.Accordingly, neighboring regions of GeSe 4 to the defect cavity will undergo photo-elastic softening as well.This detail is accounted for in subsequent FE and FDTD calculations involving the supercell.
In FE and FDTD simulations, GeSe 4 is modelled as an isotropic material with variable elastic properties that depend on light intensity.Two specific photon irradiation conditions are considered: laser OFF and laser ON.For the OFF condition, the structure is not irradiated with light.In this circumstance, the elastic properties of GeSe 4 are ρ = 4361 kg/m 3 , C L = 2052 m/s, C T = 1114 m/s, where ρ is density, C L is longitudinal speed of sound and C T is transverse speed of sound. 40For the ON condition, electromagnetic radiation impinges upon the hybrid photonic/phononic structure at power level equal to 6mW and excites photonic resonance modes compatible with the irradiation wavelength.This excitation coincides with significant photo-elastic softening of C 11 of the chalcogenide glass.Accordingly, the elastic properties of GeSe 4 are modified under the assumption of 50% reduction in C 11 , 36 and 6.4% volume expansion to yield the following elastic properties: ρ = 4099 kg/m 3 , C L = 1486 m/s, C T = 578 m/s.For epoxy resin, in both conditions, we use ρ = 1180 kg/m 3 , C L = 2535 m/s, C T = 1157 m/s.The time-scale for photo-induced structural transition in Ge-Se chalcogenide glasses can be estimated from knowledge of the frequency interval over which Raman-active, vibrational modes reside.With typical values between 100 cm −1 -500 cm −1 , 37,38 the time-scale for transition between a stable covalent network of atoms to a metastable defect configuration via covalent bond switching is approximated to be on the order of several thousand atomic oscillations, or equivalently, a few hundred nanoseconds.This conservative estimate suggests that Ge-Se glasses can indeed be used as a platform for GHz-frequency filters capable of rapid-switching.
A finite system, comprised of 10 repetitions of the supercell pictured in Figure 1(a), is utilized for later FDTD simulations to compute phonon transmission spectra for the superlattice in the laser OFF and laser ON conditions.This configuration, sandwiched in between an inlet and outlet region of homogeneous GeSe 4 , is illustrated in Figure 2. FIG. 2. Finite hybrid phononic/photonic superlattice comprised of 10 repetitions of the supercell pictured in Figure 1(a).This configuration is used for subsequent FDTD simulations to compute phonon transmission spectra for the superlattice in the laser OFF and laser ON conditions.Positioned above each supercell (resonance cavity) is a laser of wavelength λ.The structure is irradiated from the top at a grazing angle to maximize the longitudinal component of the light k-vector and ensure optimal coupling into the photonic resonance cavities.In FDTD simulations, a broad-band pressure wave packet is launched from the inlet domain at normal incidence to the superlattice.The signal propagates through the finite hybrid phononic/ photonic superlattice and exits the simulation at the end (right hand side) of the outlet domain.A probe in the outlet domain detects displacement over time, the Fourier transform of which provides insight on the spectral properties of the phononic system (e.g.acoustic band gaps and phonon passing-bands).In practice, Mur 1 st order absorbing boundary conditions 41 are utilized to avoid reflections at the left and right ends of the simulation domain.In the following section we present results for the phononic properties of the superlattice under the irradiation conditions of laser OFF and laser ON.

IV. RESULTS AND DISCUSSION
In Figure 3 we show one plot (top) with two superposed phonon band structures and three plots (bottom) each with two superposed phonon transmission spectra for the hybrid superlattice when the lasers are OFF (blue lines) and ON (red lines).
The three phonon transmission plots zoom-in on specific regions of the phonon band structure to illuminate the change in position and spectral width of phonon passing-bands.When the structure is irradiated with monochromatic light (laser ON), phonon branches are down-shifted in frequency leading to substantial changes in the acoustic transmission properties of the overall structure.Specifically, the passing-bands identified in Figure 3 with markers Branch 1, Branch 2 and Branch 3 increase in width by 21.4%, 17.7% and 31.0%,respectively, when the lasers are turned on.Furthermore, the frequency values on which these bands are centered are modulated (down-shifted) by 1.2%, 2.3% and 3.1%, respectively.This example shows that an external light source can be used to actively switch the acoustic transmission properties of the hybrid superlattice in a reversible fashion.Moreover, the position and spectral-width of the passing-bands in Figure 3 can be precisely tuned by modulating the power of the laser irradiating the structure.This functionality, which is fully enabled by the unique behavior of photo-elastic chalcogenide glass, indeed can serve purpose in radio frequency signal processing applications such as high-precision filtering.

V. CONCLUSIONS
We have theoretically demonstrated active control over the acoustic properties of a hybrid phononic/photonic superlattice via an application of an external monochromatic light source.The validated technology offers a platform on which more complex radio frequency signal processing functionalities can be constructed.Over the past two decades, the number of wireless technologies utilizing radio frequencies has increased tremendously.This influx has severely crowded the radio spectrum and, as a consequence, stimulated the need for innovative technologies to facilitate equal-sharing and enhanced access to radio frequency communication.The functions offered by this technology may assist in developing solutions to some of the emerging challenges in radio frequency communications.

FIG. 1 .
FIG. 1.(a) Illustration of supercell for the hybrid phononic/photonic superlattice.The supercell consists of a GeSe 4 slab (photonic resonance cavity) sandwiched in between two quarter-wave Bragg reflectors (photonic crystals) each comprised of alternating thin-films of GeSe 4 and epoxy resin.The characteristic length-scales of the quarter-wave Bragg stack and supercell are a 1 and a 2 , respectively.Additionally, a 2 is the phononic lattice parameter.(b) Photonic band structure of an infinite quarter-wave Bragg reflector showing complete photonic band gap at irradiation wavelength (λ = 800 nm).(c) Horizontal cut along x-axis of the supercell showing normalized electric field for the cavity eigenmode at the irradiation wavelength (λ = 800 nm).Notice the strong localization on the GeSe 4 region of the structure.(d) same as (c) except for photon intensity.

FIG. 3 .
FIG. 3. (top) two superposed phonon dispersion curves for conditions of laser OFF (blue lines) and laser ON (red lines).Phonon band structures were computed with FE simulations (COMSOL Multiphysics).(bottom) three plots for phonon transmission corresponding to different phonon branches, laser OFF (blue lines) and laser ON (red lines).Photo-induced changes in the elastic properties of GeSe 4 facilitate active control over position and spectral width of phonon passing-bands.