Guided-Acoustic Stimulated Brillouin Scattering in Silicon Nitride Photonic Circuits
Roel Botter, Kaixuan Ye, Yvan Klaver, Radius Suryadharma, Okky Daulay, Gaojian Liu, Jasper van den Hoogen, Lou Kanger, Peter van der Slot, Edwin Klein, Marcel H… 展开作者
Roel Botter, Kaixuan Ye, Yvan Klaver, Radius Suryadharma, Okky Daulay, Gaojian Liu, Jasper van den Hoogen, Lou Kanger, Peter van der Slot, Edwin Klein, Marcel Hoekman, Chris Roeloffzen, Yang Liu, David Marpaung
Coherent optomechanical interaction between acoustic and optical waves known as stimulated Brillouin scattering (SBS) can enable ultra-high resolution signal processing and narrow linewidth lasers important for next generation wireless communications, precision sensing, and quantum information processing. While SBS has recently been studied extensively in integrated waveguides, many implementations rely on complicated fabrication schemes, using suspended waveguides, or non-standard materials such as As$_2$S$_3$. The absence of SBS in standard and mature fabrication platforms prevents large-scale circuit integration and severely limits the potential of this technology. Notably, SBS in standard silicon nitride integration platform is currently rendered out of reach due to the lack of acoustic guiding and the infinitesimal photo-elastic response of the material. In this paper, we experimentally demonstrate advanced control of backward SBS in multilayer silicon nitride waveguides. By optimizing the separation between two silicon nitride layers, we unlock gigahertz acoustic waveguiding in this platform for the first time, leading up to 15 $\times$ higher SBS gain coefficient than previously possible in silicon nitride waveguides. Using the same principle, we experimentally demonstrate on-demand inhibition of SBS by preventing acoustic guiding in the waveguide platform. We utilize the enhanced SBS gain to demonstrate a microwave photonic notch filter with high rejection (30 dB). We accomplish this in a low-loss, standard, and versatile silicon nitride integration platform without the need of suspending the SBS-active waveguide or hybrid integration with other materials.
Silicon nitride (Si3N4) has emerged as a promising material for integrated nonlinear photonics and has been used for broadband soliton microcombs and low-pulse-energy supercontinuum generation. Therefore understanding all nonlinear optical properties of Si3N4 is important. So far, only stimulated Brillouin scattering (SBS) has not been reported. Here we observe, for the first time, backward SBS in fully cladded Si3N4 waveguides. The Brillouin gain spectrum exhibits an unusual multi-peak structure resulting from hybridization with with high-overtone bulk acoustic resonances (HBARs) of the silic…
We propose a method for generating cascaded forward Brillouin scattering (CFBS), based on a counter-propagated pump-probe technique, utilizing backward stimulated Brillouin scattering as its seed. The CFBS, induced by forward stimulated Brillouin scattering (FSBS), is generated via the energy transfer from the probe light to other acoustic resonance frequencies. Experimental results for the CFBS generated in a 390-m-long highly nonlinear fiber indicate that it has a high signal-to-noise ratio (SNR) and that the center frequencies of its acoustic resonance peaks agree with theoretical values. T…
We report the first observation of stimulated Brillouin scattering (SBS) with Brillouin lasing, and Brillouin-coupled four-wave-mixing (FWM) in an ultra-high-Q silica microbottle resonator. The Brillouin lasing was observed at the frequency of $Ω_B=2π\times10.4$ GHz with a threshold power of $0.45$ mW. Coupling between Brillouin and FWM was observed in both backward and forward scattering directions with separations of $2Ω_B$. At a pump power of $10$ mW, FWM spacing reached to 7th and 9th order anti-Stokes and Stokes, respectively.
We theoretically investigate a new class of silicon waveguides for achieving Stimulated Brillouin Scattering (SBS) in the mid-infrared (MIR). The waveguide consists of a rectangular core supporting a low-loss optical mode, suspended in air by a series of transverse ribs. The ribs are patterned to form a finite quasi-one-dimensional phononic crystal, with the complete stopband suppressing the transverse leakage of acoustic waves, and confining them to the core of the waveguide. We derive a theoretical formalism that can be used to compute the opto-acoustic interaction in such periodic structure…
Optical non-reciprocity, which breaks the symmetry between forward and backward propagating optical waves, has become vital in photonic systems and enables many key devices, such as optical isolators, circulators and optical routers. Most conventional optical isolators involve magneto-optic materials, but devices based on optical nonlinearities, optomechanically induced transparency and stimulated Brillouin scattering (SBS) have also been demonstrated. So far, however, they have only been implemented for linearly or randomly polarized LP01-like fundamental modes. Here we report a light-driven …
We present an experimental and theoretical study of cascaded high order Stimulated Brillouin Scatterings (SBS) in single mode fibers. It is shown that because of the back-scattering nature of the process, feedback in the input port is needed for obtaining a significant cascaded effect in nonresonant systems. We also discuss similarities to nonlinear photorefractive processes.
While nanoscale modal confinement radically enhances a variety of nonlinear light-matter interactions within silicon waveguides, traveling-wave stimulated Brillouin scattering nonlinearities have never been observed in silicon nanophotonics. Through a new class of hybrid photonic-phononic waveguides, we demonstrate tailorable traveling-wave forward stimulated Brillouin scattering in nanophotonic silicon waveguides for the first time, yielding 3000 times stronger forward SBS responses than any previous waveguide system. Simulations reveal that a coherent combination of electrostrictive forces a…
We demonstrate the first functional signal processing device based on stimulated Brillouin scattering in a silicon nanowire. We use only 1 dB of on-chip SBS gain to create an RF photonic notch filter with 48 dB of suppression, 98 MHz linewidth, and 6 GHz frequency tuning. This device has potential applications in on-chip microwave signal processing and establishes the foundation for the first CMOS-compatible high performance RF photonic filter.
Stimulated Brillouin scattering (SBS) has been demonstrated in silicon waveguides in recent years. However, due to the weak interaction between photons and acoustic phonons in these waveguides, long interaction length is typically necessary. Here, we experimentally show that forward stimulated Brillouin scattering in a short interaction length of a 20 um radius silicon microring resonator could give 1.2 dB peak gain at only 10mW coupled pump power. The experimental results demonstrate that both optical and acoustic modes can have efficient interaction in a short interaction length. The observe…
We predict and experimentally observe a nonlinear variant of stimulated Brillouin scattering in a single-mode fiber that arises from consideration of higher-order processes for phonon generation. The effect manifests itself at high laser excitation as the appearance of Stokes gain for a detuning equal to half of the conventional Brillouin frequency in the fiber, with no accompanying anti-Stokes absorption at the opposite detuning, and requires counter-propagating pump beams for phase-matching. We believe that this could be a new nonlinear optical effect that has not been observed before.
Brillouin scattering in optical fibres is a fundamental interaction between light and sound with important implications ranging from optical sensors to slow and fast light. In usual optical fibres, light both excites and feels shear and longitudinal bulk elastic waves, giving rise to forward guided acoustic wave Brillouin scattering and backward stimulated Brillouin scattering. In a subwavelength-diameter optical fibre, the situation changes dramatically, as we here report with the first experimental observation of stimulated Brillouin scattering from surface acoustic waves. These Rayleigh-typ…
We develop a novel approach to enable the full-wave simulation of stimulated Brillouin scattering and related phenomena in a frequency-domain, finite-element environment. The method uses transformation optics techniques to implement a time-harmonic coordinate transform that reconciles the different frames of reference used by electromagnetic and mechanical finite-element solvers. We show how this strategy can be successfully applied to bulk and guided systems, comparing the results with the predictions of established theory.
Stimulated Brillouin scattering in optical waveguides is a fundamental interaction between light and acoustic waves mediated by electrostriction and photoelasticity. In this paper, we revisit the usual theory of this inelastic scattering process to get a joint system in which the acoustic wave is strongly coupled to the interference pattern between the optical waves. We show in particular that, when the optoacoustic coupling rate is comparable to the phonon damping rate, the system enters in the strong coupling regime, giving rise to avoided crossing of the dispersion curve and Rabi-like split…
Recent experiments demonstrating storage of optical pulses in acoustic phonons based on stimulated Brillouin scattering raise a number of questions about the spectral and temporal capacities of such protocols and the limitations of the theoretical frameworks routinely used to describe them. In this work, we consider the dynamics of photon-phonon scattering induced by optical pulses with temporal widths comparable to the period of acoustic oscillations. We revisit the widely adopted classical formalism of coupled modes and demonstrate its breakdown. We propose a simple extension to generalise t…
Stimulated emission of sensitized Erbium atoms is reported in silicon-rich silicon nitride waveguides. Visible pump and infrared probe measurements are carried out in waveguides fabricated from erbium-doped silicon rich silicon nitride. A decrease in the photoinduced absorption of the probe in the wavelength range of the erbium emission is observed and is attributed to stimulated emission from erbium atoms excited indirectly via the silicon excess in an SiNx matrix. A near 50% decrease in absorption is measured, corresponding to an 8% fraction of inverted erbium atoms. This fraction is an orde…
A framework for simulating the elastic-wave modes in waveguides, taking into account the full tensorial nature of the stiffness tensor, is presented and implemented in the open-source finite element solver, FEniCS. Various approximations of the elastic wave equation used in the stimulated Brillouin scattering literature are implemented and their validity and applicability are discussed. The elastic mode-solver is also coupled with an electromagnetic counterpart to study the influence of elastic anisotropies on Brillouin gain.
Impact of Stimulated Brillouin Scattering on Modulation Instability in Fiber Fabry-Perot Resonators
Laboratoire Physique des Lasers, Atomes et Molécules, UMR No. 8523, CNRS, University of Lille（里尔大学）；Service OPERA-Photonique, Université libre de Bruxelles (ULB)（布鲁塞尔自由大学）
Phase and/or intensity modulation techniques to broaden the Linewidth of an optical source are well known methods to suppress stimulated Brillouin scattering (SBS) in optical fibers. A common technique used to achieve significant bandwidth enhancement in a simple fashion is to phase modulate with a filtered noise source. We will demonstrate here that, in this case the stochastic nature of noise requires an inclusion of length dependent corrections to the SBS threshold enhancement. This effect becomes particularly significant for short fiber lengths common to most high power fiber amplifiers.
Silicon is an ideal material for on-chip applications, however its poor acoustic properties limit its performance for important optoacoustic applications, particularly for Stimulated Brillouin Scattering (SBS). We theoretically show that silicon inverse opals exhibit a strongly improved acoustic performance that enhances the bulk SBS gain coefficient by more than two orders of magnitude. We also design a waveguide that incorporates silicon inverse opals and which has SBS gain values that are comparable with chalcogenide glass waveguides. This research opens new directions for opto-acoustic app…
A passive white light cavity (WLC) based on a fiber resonator can be used for high-bandwidth optical data buffering. Here, we report on experimental studies of such a WLC, employing stimulated Brillouin scattering (SBS)for producing the negative dispersion, using two different configurations. In one configuration, an absorption peak produced by a Brillouin pump is used. In the other configuration, two gain peaks produced by two separate Brillouin pumps are employed. In each case, we see evidence of the WLC effect. However, the range of parameters accessible experimentally limits the degree of …
Cascaded stimulated Brillouin scattering (SBS) is a complex nonlinear optical process that results in the generation of several optical waves that are frequency shifted by an acoustic resonance frequency. Four-wave mixing (FWM) between these Brillouin shifted optical waves can create an equally spaced optical frequency comb with a stable spectral phase, i.e. a Brillouin frequency comb (BFC). Here, we investigate phase-locking of the spectral components of BFCs, considering FWM interactions arising from the Kerr-nonlinearity as well as from coupling by the acoustic field. Deriving for the first…
Stimulated Brillouin scattering has attracted renewed interest with the promise of highly tailorable integration into the silicon photonics platform. However, significant Brillouin amplification in silicon waveguides has yet to be shown. In an effort to engineer a structure with large photon-phonon coupling, we analyzed both forward and backward Brillouin scattering in high-index-contrast silicon slot waveguides. The calculations predict that gradient forces enhance the Brillouin gain in narrow slots. We estimate a currently feasible gain of about $10^{5} \, \text{W}^{-1}\text{m}^{-1}$, which …
We present a novel approach to cascaded stimulated Brillouin scattering and frequency comb generation in which the multitude of interacting pump, Stokes, and anti-Stokes optical fields are described by a single forward wave and a single backward wave at a single carrier frequency. The envelopes of these two waves are modulated through coupling to a single acoustic oscillation and through four-wave mixing. Starting from a single pump field, we observe the emergence of a comb of frequencies as the intensity is increased. The set of three differential equations derived here are sufficient to desc…
We study the role of stimulated Brillouin scattering in a fiber cavity by numerical simulations and a simple theoretical model and find good agreement between experiment, simulation and theory. We also investigate an optomechanical system based on a fiber cavity in the presence on the nonlinear Brillouin scattering. Using simulation and theory, we show that this hybrid optomechanical system increases optomechanical damping for low mechanical resonance frequencies in the unresolved sideband regime. Furthermore, optimal damping occurs for blue detuning in stark contrast to standard optomechanics…
We theoretically and numerically study the effects of thermal noise on pulses in backwards Stimulated Brillouin Scattering (SBS). Using a combination of stochastic calculus and numerical methods, we derive a theoretical model that can be used to quantitatively predict noise measurements. We study how the optical pulse configuration, including the input powers of the pump and Stokes fields, pulse durations and interaction time, affects the noise in the output Stokes field. We investigate the effects on the noise of the optical loss and waveguide length, and we find that the signal-to-noise rati…
In this paper, we prove theoretically that both the stimulated Stokes scattering and its reverse process can occur simultaneously for the light and acoustic waves at different points of the medium, resulting in transient and alternate energy flow between the pump and Stokes waves in the stimulated Brillouin scattering. Furthermore, it is found that stimulated Stokes scattering and its reverse process will dominate alternately on the whole during the three-wave coupling, but the eventual net energy flow must be from the pump wave to the Stokes wave as a result of the finite lifetime of acoustic…
We develop a general method of calculating Stimulated Brillouin Scattering (SBS) gain coefficient in axially periodic waveguides. Applying this method to a silicon periodic waveguide suspended in air, we demonstrate that SBS nonlinearity can be dramatically enhanced at the brillouin zone boundary where the decreased group velocity of light magnifies photon-phonon interaction. In addition, we show that the symmetry plane perpendicular to the propagation axis plays an important role in both forward and backward SBS processes. In forward SBS, only elastic modes which are even about this plane are…
Stimulated Brillouin scattering (SBS) has many applications, for example, in sensing, microwave photonics and signal processing. Here we report the first experimental study of SBS in chiral photonic crystal fiber (PCF), which displays optical activity and robustly maintains circular polarization states against external perturbations. As a result, circularly polarized pump light is cleanly back-scattered into a Stokes signal with the orthogonal circular polarization state, as is required by angular momentum conservation. By comparison, untwisted PCF generates a Stokes signal with an unpredictab…
We report the superluminal phenomenon of both Stokes and pump light in stimulated Brillouin scattering (SBS) via an optical-fiber ring lasing resonator. In our experiment, the superluminal generation of Stokes light firstly delayed with 33.79 ns and then propagated with the advancement of 93.34 ns within an 8-m single mode fiber (SMF), when the pump power increased from the SBS threshold to a higher power. This proves the first evidence that the optical interaction is determined by the group velocity even at the negative group velocity superluminal propagation. It is important that, this impli…
We report a theoretical study of Stimulated Brillouin Scattering (SBS) in general anisotropic media, incorporating the effects of both acoustic strain and local rotation in all calculations. We apply our general theoretical framework to compute the SBS gain for layered media with periodic length scales smaller than all optical and acoustic wavelengths, where such composites behave like homogeneous anisotropic media. We theoretically predict that a layered medium comprising nanometre-thin layers of silicon and As$_2$S$_3$ glass possesses a bulk SBS gain of $1.28 \times 10^{-9} \, \mathrm{W}^{-1…
Realizing highly sensitive interferometry is essential to accurate observation of quantum properties. Here we study two kinds of Ramsey interference fringes in a whispering-gallery resonator, where the coherent phonons for free evolution can be achieved by stimulated Brillouin scattering. These two different fringes appear, respectively, in the regimes of rotating wave approximation (RWA) and anti-RWA. Our work shows particularly that the anti-RWA Ramsey interference takes some quantum properties of squeezing, which enhances the strength and visibility of the fringes and shows robustness again…
Noncontact Brillouin spectroscopy is a purely optical and label-free method to retrieve fundamental material viscoelastic properties. Recently, the extension to a three-dimensional imaging modality has paved the way to novel exciting opportunities in the biomedical field, yet the detection of the Brillouin spectrum remains challenging as a consequence of the dominant elastic background light that typically overwhelms the inelastic Brillouin peaks. In this Letter, we demonstrate a fully integrated and ultra-compact Brillouin notch filter based on an optical ring resonator fabricated on a silico…
Strong acousto-optic interaction in silicon-based waveguides generally requires releasing of the silicon core to avoid mechanical leakage into the underlying silica substrate. This complicates fabrication, limits thermalization, reduces the mechanical robustness and hinders large area optomechanical devices on a single chip. Here, we overcome this limitation by employing vertical photonic-phononic engineering. Specifically, the insertion of a thick silicon nitride layer between the silicon guiding core and the silica substrate contributes to reduce GHz-frequencies phonon leakage enabling large…
We develop a general framework of evaluating the gain coefficient of Stimulated Brillouin Scattering (SBS) in optical waveguides via the overlap integral between optical and elastic eigen-modes. We show that spatial symmetry of the optical force dictates the selection rules of the excitable elastic modes. By applying this method to a rectangular silicon waveguide, we demonstrate the spatial distributions of optical force and elastic eigen-modes jointly determine the magnitude and scaling of SBS gain coefficient in both forward and backward SBS processes. We further apply this method to inter-m…
A generalized Wigner-Moyal statistical theory of radiation is used to obtain a general dispersion relation for Stimulated Brillouin Scattering (SBS) driven by a broadband radiation field with arbitrary statistics. The monochromatic limit is recovered from our general result, reproducing the classic monochromatic dispersion relation. The behavior of the growth rate of the instability as a simultaneous function of the bandwidth of the pump wave, the intensity of the incident field and the wave number of the scattered wave is further explored by numerically solving the dispersion relation. Our re…
Noncontact label-free biomechanical imaging is a crucial tool for unraveling the mechanical properties of biological systems, which play critical roles in the fields of engineering, physics, biology and medicine; yet, it represents a significant challenge in microscopy. Spontaneous Brillouin microscopy meets this challenge, but often requires long acquisition times or lacks high specificity for detecting biomechanical constituents with highly overlapping Brillouin bands. We developed stimulated Brillouin scattering (SBS) microscopy that provides intrinsic noncontact biomechanical contrast and …
We demonstrate a 5-GHz-broadband tunable slow-light device based on stimulated Brillouin scattering in a standard highly-nonlinear optical fiber pumped by a noise-current-modulated laser beam. The noise modulation waveform uses an optimized pseudo-random distribution of the laser drive voltage to obtain an optimal flat-topped gain profile, which minimizes the pulse distortion and maximizes pulse delay for a given pump power. Eye-diagram and signal-to-noise ratio (SNR) analysis show that this new broadband slow-light technique significantly increases the fidelity of a delayed data sequence, whi…
We study the impact of two-photon absorption (2PA) and fifth-order nonlinear loss such as 2PA-induced free-carrier absorption in semiconductors on the performance of Stimulated Brillouin Scattering devices. We formulate the equations of motion including effective loss coefficients, whose explicit expressions are provided for numerical evaluation in any waveguide geometry. We find that 2PA results in a monotonic, algebraic relationship between amplification, waveguide length and pump power, whereas fifth-order losses lead to a non-monotonic relationship. We define a figure of merit for material…
Pulse compression processing based on stimulated Brillouin scattering (SBS) in an optical fiber is theoretically and experimentally demonstrated. Broadband microwave signal is electro-optically modulated onto the pump lightwave that is launched into one end of the fiber. Acoustic wave in the fiber inherits the amplitude and phase information of the pump lightwave and thus the coupling between the acoustic wave and pump lightwave leads to the auto-correlated process of the pump lightwave as well as the modulated microwave signal. Derivation of the SBS coupling equations shows that the short-pul…
We compute the SBS gain for a metamaterial comprising a cubic lattice of dielectric spheres suspended in a background dielectric material. Theoretical methods are presented to calculate the optical, acoustic, and opto-acoustic parameters that describe the SBS properties of the material at long wavelengths. Using the electromagnetic and strain energy densities we accurately characterise the optical and acoustic properties of the metamaterial. From a combination of energy density methods and perturbation theory, we recover the appropriate terms of the photoelastic tensor for the metamaterial. We…
A theoretical study on the stimulated Brillouin scattering (SBS) in a sub-wavelength anisotropic waveguide is conducted. The optical, photoelastic and mechanical anisotropies of the waveguide materials are all taken into account. First, the integral formulae for calculating the acousto-optical coupling coefficients (AOCCs) due to the photoelastic and moving interface effects in SBS are extended to an optically anisotropic waveguide. Then, with the extended formulae, the SBSs in an elliptical nanowire with strong transverse anisotropies are simulated. In the simulations, the elastic fields are …
We derive a set of design guidelines and a figure of merit to aid the engineering process of on-chip waveguides for strong Stimulated Brillouin Scattering (SBS). To this end, we examine the impact of several types of loss on the total amplification of the Stokes wave that can be achieved via SBS. We account for linear loss and nonlinear loss of third order (two-photon absorption, 2PA) and fifth order, most notably 2PA-induced free carrier absorption (FCA). From this, we derive an upper bound for the output power of continuous-wave Brillouin-lasers and show that the optimal operating conditions…
