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 ratio can be significantly improved, or reduced, for specific combinations of waveguide properties and pulse parameters.
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 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…
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…
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…
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…
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…
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…
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.
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…
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）
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…
Examining the physical properties of materials - particularly of toxic liquids - under a wide range of thermodynamic states is a challenging problem due to the extreme conditions the material has to be exposed to. Such temperature and pressure regimes, which result in a change of refractive index and sound velocity can be accessed by optoacoustic interactions such as Brillouin-Mandelstam scattering. Here we experimentally demonstrate Brillouin-Mandelstam measurements of nanoliter volumes of liquids in extreme thermodynamic regimes. We use a fully-sealed liquid-core optical fiber containing car…
Phase conjugation with stimulated Brillouin scattering can be used to correct wavefront aberrations in high-power laser systems. Here, we consider such process with cylindrical vector lasers beams. By using a vectorial approach and a modal decomposition, we obtain a differential matrix equation that enables the calculation of the structure of Stokes vector eigenmodes and their Brillouin gain. The emphasis is put on the mode with the largest gain, which contributes the most to the Stokes beam. We show that the phase conjugation of orbital angular momentum in cylindrical vector beams is prevente…
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 report on strong backward stimulated emission at 337 nm in Nitrogen gas pumped by circularly polarized femtosecond laser pulses at 800 nm. A distinct dependence of the backward UV spectrum on pump laser polarization and intensity is observed, pointing to the occurrence of backward amplified spontaneous emission inside filaments. We attribute the population inversion to inelastic collision between the free electrons produced by the pump laser and neutral N2 molecules. The addition of Oxygen molecules is detrimental for the gain, reducing it to near threshold at atmospheric concentration.
We address the problem of the interaction of powerful laser radiation with a transparent substance containing a low concentration of strongly absorbing nanoparticles under the condition of Stimulated Brillouin scattering (SBS) whose behavior in such media was unexplored. SBS energies in N-methyl-2-pyrrolidone (NMP) and water are measured at the wavelength of 532 nm. An experimental value $g_B = 18.6 \pm 1.8$ cm/GW for a previously unknown Brillouin gain factor of NMP is reported. A strong SBS quenching in the liquids by graphene nanoflakes is found. SBS threshold linear dependences on graphene…
Light with transverse polarization structure, such as radial and azimuthal polarization, enables and revives lots of applications based on light-matter interaction due to their unique focal properties. To date, studies referring to this topic mainly concentrate in weak-light domain, yet it should have gained more attention in strong-light domain. A main factor contributing to the current situation is that the generation devices cannot afford high power. Here, in this proof-of-principle work, we demonstrate the generation of strong single-longitudinal-mode (SLM) cylindrical vector (CV) short pu…
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…
The notion that Stimulated Brillouin Scattering (SBS) is primarily defined by bulk material properties has been overturned by recent work on nanoscale waveguides. It is now understood that boundary forces of radiation pressure and electrostriction appearing in such highly confined waveguides can make a significant contribution to the Brillouin gain. Here, this concept is extended to show that gain enhancement does not require nanoscale or subwavelength features, but generally appears where optical and acoustic fields are simultaneously confined near a free surface or material interface. This s…
We examine the effect of acoustic mode confinement on Stimulated Brillouin Scattering in optical waveguides that consist of a guiding core embedded in a solid substrate. We find that SBS can arise due to coupling to acoustic modes in three different regimes. First, the acoustic modes may be guided by total internal reflection; in this case the SBS gain depends directly on the degree of confinement of the acoustic mode in the core, which is in turn determined by the acoustic V-parameter. Second, the acoustic modes may be leaky, but may nevertheless have a sufficiently long lifetime to have a la…
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…
Recent theoretical studies of Stimulated Brillouin Scattering (SBS) in nanoscale devices have led to an intense research effort dedicated to the demonstration and application of this nonlinearity in on-chip systems. The key feature of SBS in integrated photonic waveguides is that small, high-contrast waveguides are predicted to experience powerful optical forces on the waveguide boundaries, which are predicted to further boost the SBS gain that is already expected to grow dramatically in such structures because of the higher mode confinement alone. In all recent treatments, the effect of radia…
We use theoretical analysis and numerical simulation to investigate the operation of a laser oscillating from gain supplied by stimulated Brillouin scattering (SBS) in a microresonator. The interaction of the forward, backward, and density waves within the microresonator results in a set of coupled-mode equations describing both the laser's phase and amplitude evolution over time. Using this coupled-mode formalism, we investigate the performance of the SBS laser under noise perturbation and identify the fundamental parameters and their optimization to enable low-noise SBS operation. The intrin…
Highly selective and reconfigurable microwave filters are of great importance in radio-frequency signal processing. Microwave photonic (MWP) filters are of particular interest, as they offer flexible reconfiguration and an order of magnitude higher frequency tuning range than electronic filters. However, all MWP filters to date have been limited by trade-offs between key parameters such as tuning range, resolution, and suppression. This problem is exacerbated in the case of integrated MWP filters, blocking the path to compact, high performance filters. Here we show the first chip-based MWP ban…
Using full opto-acoustic numerical simulations, we demonstrate enhancement and suppression of the SBS gain in a metamaterial comprising a subwavelength cubic array of dielectric spheres suspended in a dielectric background material. We develop a general theoretical framework and present several numerical examples using technologically important materials. For As$_2$S$_3$ spheres in silicon, we achieve a gain enhancement of more than an order of magnitude compared to pure silicon, and for GaAs spheres in silicon, full suppression is obtained. The gain for As$_2$S$_3$ glass can also be strongly …
State Key Laboratory of Extreme Photonics and Instrumentation, College of Optical Science and Engineering, Zhejiang University（浙江大学光学工程學院极端光子与仪器国家重点实验室）；ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University（浙江大学紫金港全球科创中心）；Laboratory of Infrared Material and Devices, Advanced Technology Research Institute, Ningbo University（宁波大学先进技术研究研究院红外材料与器件实验室）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
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…
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…
