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We theoretically and numerically study the evolution of soliton-like waves supported by stimulated Brillouin scattering. First, the emergence and unusual behaviour of resonant solitary waves are investigated for both backward and forward three wave interactions. We find that these waves can be characterized by the ratio between the optical and acoustic damping coefficients. We also examine a second class of non-resonant anti-symmetric soliton-like waves, which have a more complicated pulse shape than traditional solitons. These waves are superluminal, with pulse velocities that can be tuned by the input Stokes and pump fields. We discuss the excitation of these types of waves and the physical conditions required for their observation., Comment: 9 pages, 7 figures

Few known material systems can simultaneously guide optical and elastic fields through total internal reflection. This natural limit has restricted the realization of strong optoacoustic effects to highly-specialised and purpose-built platforms which employ either exotic materials, or complex waveguide designs. Here we apply the concept of Anti-Resonant Reflecting Acoustic Waveguides (ARRAWs) as a potential solution to this issue. ARRAWs confine the elastic field to a high-elastic-velocity core via the anti-resonances of a cladding layer of lower elastic velocity. We numerically study the appearance and dispersion of ARRAW-guided modes in a conventional silicon-on-insulator rib waveguide geometry. Applying the technique to the problem of efficient backwards Stimulated Brillouin Scattering (SBS), we predict that ARRAW guidance, in conjunction with conventional optical confinement, can produce Brillouin gains comparable to those of more exotic geometries., Comment: 9 pages, 7 figures

Signal processing based on stimulated Brillouin scattering (SBS) is limited by the narrow linewidth of the optoacoustic response, which confines many Brillouin applications to continuous wave signals or optical pulses longer than several nanoseconds. In this work, we experimentally demonstrate Brillouin interactions at the 150 ps time scale and a delay for a record 15 ns which corresponds to a delay of 100 pulse widths. This breakthrough experimental result was enabled by the high local gain of the chalcogenide waveguides as the optoacoustic interaction length reduces with pulse width. We successfully transfer 150ps-long pulses to traveling acoustic waves within a Brillouin-based memory setup. The information encoded in the optical pulses is stored for 15 ns in the acoustic field. We show the retrieval of eight amplitude levels, multiple consecutive pulses and low distortion in pulse shape. The extension of Brillouin-based storage to the ultra-short pulse regime is an important step for the realisation of practical Brillouin-based delay lines and other optical processing applications., Comment: 6 pages, 6 figures

Cavity optomechanics aims to establish optical control over vibrations of mechanical systems, to heat, cool or to drive them toward coherent, or nonclassical states. This field was recently extended to include molecular optomechanics, which describes the dynamics of THz molecular vibrations coupled to the optical fields of lossy cavities via Raman transitions, and was developed to understand the anomalous amplification of optical phonons in Surface-Enhanced Raman Scattering experiments. But the molecular platform should prove suitable for demonstrating more sophisticated optomechanical effects, including engineering of nonclassical mechanical states, or inducing coherent molecular vibrations. In this work, we propose two pathways towards implementing these effects, enabled or revealed by the strong intrinsic anharmonicities of molecular vibrations. First, to prepare a nonclassical mechanical state, we propose an incoherent analogue of the mechanical blockade, in which the molecular aharmonicity and optical response of hybrid cavities isolate the two lowest-energy vibrational states. Secondly, we show that for a strongly driven optomechanical system, the anharmonicity can effectively suppress the mechanical amplification, shifting and reshaping the onset of coherent mechanical oscillations. Our estimates indicate that both effects should be within reach of the existing implementations of the Surface Enhanced Raman Scattering, opening the pathway towards the coherent and nonclassical effects in molecular optomechanics.

Non-reciprocal optical components such as isolators and circulators are crucial for preventing catastrophic back-reflection and controlling optical crosstalk in photonic systems. While non-reciprocal devices based on Brillouin intermodal transitions have been experimentally demonstrated in chip-scale platforms, harnessing such interactions has required a suspended waveguide structure, which is challenging to fabricate and is potentially less robust than a non-suspended structure, thereby limiting the design flexibility. In this paper, we numerically investigate the performance of a Brillouin-based isolation scheme in which a dual-pump-driven optoacoustic interaction is used to excite confined acoustic waves in a traditional ridge waveguide. We find that acoustic confinement, and therefore the amount of Brillouin-driven mode conversion, can be enhanced by selecting an appropriate optical mode pair and waveguide geometry of two arsenic based chalcogenide platforms. Further, we optimize the isolator design in its entirety, including the input couplers, mode filters, the Brillouin-active waveguide as well as the device fabrication tolerances. We predict such a device can achieve 30 dB isolation over a 38 nm bandwidth when 500 mW pump power is used; in the presence of a +/- 10 nm fabrication-induced width error, such isolation can be maintained over a 5-10 nm bandwidth.

We use a recently derived gauge-invariant formulation of the problem of a two-level system coupled to an optical cavity, to explore the transition between the weak, and the ultra-strong coupling regimes of light-matter interaction. We explore this transition using the intensity correlations $g^{(2)}(\tau)$ of the emitted light, and find strong, unbounded bunching of the emission from systems governed by the Rabi Hamiltonian. Surprisingly, this effect is observed not only in the ultra-strong coupling regime, but also for weakly coupled systems, where the Jaynes-Cummings Hamiltonian would predict the opposite, antibunched emission. This suggests that the higher-order correlations are a particularly sensitive probe of the divergence between the Jaynes-Cummings and Rabi Hamiltonians, and can serve as an indicator of the breakdown of the rotating wave approximation. Our findings indicate also that the boundary between the weakly, strongly, and ultra-strongly coupled dynamics, is much richer than currently accepted.

We theoretically and numerically study the efficiency of Brillouin-based opto-acoustic data storage in a photonic waveguide in the presence of thermal noise and laser phase noise. We compare the physics of the noise processes and how they affect different storage techniques, examining both amplitude and phase storage schemes. We investigate the effects of storage time and pulse properties on the quality of the retrieved signal, and find that phase storage is less sensitive to thermal noise than amplitude storage., Comment: 12 pages, 9 figures

We present a numerical method for modelling noise in Stimulated Brillouin Scattering (SBS). The model applies to dynamic cases such as optical pulses, and accounts for both thermal noise and phase noise from the input lasers. Using this model, we compute the statistical properties of the optical and acoustic power in the pulsed spontaneous and stimulated Brillouin cases, and investigate the effects of gain and pulse width on noise levels. We find that thermal noise plays an important role in the statistical properties of the fields, and that laser phase noise impacts the SBS interaction when the laser coherence time is close to the time-scale of the optical pulses. This algorithm is applicable to arbitrary waveguide geometries and material properties, and thus presents a versatile way of performing noise-based SBS numerical simulations, which are important in signal processing, sensing, microwave photonics and opto-acoustic memory storage., Comment: 10 pages, 12 figures

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 the formulation and find potentially measurable consequences in the dynamics of Brillouin experiments involving ultra-short pulses., Comment: 5 pages, 3 figures

Quantum acoustodynamics (QAD) is a rapidly developing field of research, offering possibilities to realize and study macroscopic quantum-mechanical systems in a new range of frequencies, and implement transducers and new types of memories for hybrid quantum devices. Here we propose a novel design for a versatile diamond QAD cavity operating at GHz frequencies, exhibiting effective mode volumes of about $10^{-4}\lambda^3$. Our phononic crystal waveguide cavity implements a non-resonant analogue of the optical lightning-rod effect to localize the energy of an acoustic mode into a deeply-subwavelength volume. We demonstrate that this confinement can readily enhance the orbit-strain interaction with embedded nitrogen-vacancy (NV) centres towards the high-cooperativity regime, and enable efficient resonant cooling of the acoustic vibrations towards the ground state using a single NV. This architecture can be readily translated towards setup with multiple cavities in one- or two-dimensional phononic crystals, and the underlying non-resonant localization mechanism will pave the way to further enhance optoacoustic coupling in phoxonic crystal cavities.

Development of acoustic and optoacoustic on-chip technologies calls for new solutions to guiding, storing and interfacing acoustic and optical waves in integrated silicon-on-insulator (SOI) systems. One of the biggest challenges in this field is to suppress the radiative dissipation of the propagating acoustic waves, while co-localizing the optical and acoustic fields in the same region of an integrated waveguide. Here we address this problem by introducing Anti-Resonant Reflecting Acoustic Waveguides (ARRAWs) -- mechanical analogues of the Anti-Resonant Reflecting Optical Waveguides (ARROWs). We discuss the principles of anti-resonant guidance and establish guidelines for designing efficient ARRAWs. Finally, we demonstrate examples of the simplest silicon/silica ARRAW platforms that can simultaneously serve as near-IR optical waveguides, and support strong backward Brillouin scattering.

We describe NumBAT, an open-source software tool for modelling stimulated Brillouin scattering in waveguides of arbitrary cross-section. It provides rapid calculation of optical and elastic dispersion relations, field profiles and gain with an easy-to-use Python front end. Additionally, we provide an open and extensible set of standard problems and reference materials to facilitate the bench-marking of NumBAT against subsequent tools. Such a resource is needed to help settle discrepancies between existing formulations and implementations, and to facilitate comparison between results in the literature. The resulting standardised testing framework will allow the community to gain confidence in new algorithms and will provide a common tool for the comparison of experimental designs of opto-acoustic waveguides., Comment: 17 pages, 18 figures

Inelastic scattering processes such as Brillouin scattering can often function in cascaded regimes and this is likely to occur in certain integrated opto-acoustic devices. We develop a Hamiltonian formalism for cascaded Brillouin scattering valid for both quantum and classical regimes. By regarding Brillouin scattering as the interaction of a single acoustic envelope and a single optical envelope that covers all Stokes and anti-Stokes orders, we obtain a compact model that is well suited for numerical implementation, extension to include other optical nonlinearities or short pulses, and application in the quantum-optics domain. We then theoretically analyze intra-mode forward Brillouin scattering (FBS) for arbitrary waveguides with and without optical dispersion. In the absence of optical dispersion, we find an exact analytical solution. With a perturbative approach, we furthermore solve the case of weak optical dispersion. Our work leads to several key results on intra-mode FBS. For negligible dispersion, we show that cascaded intra-mode FBS results in a pure phase modulation and discuss how this necessitates specific experimental methods for the observation of fibre-based and integrated FBS. Further, we discuss how the descriptions that have been established in these two classes of waveguides connect to each other and to the broader context of cavity opto-mechanics and Raman scattering. Finally, we draw an unexpected striking similarity between FBS and discrete diffraction phenomena in waveguide arrays, which makes FBS an interesting candidate for future research in quantum-optics., Comment: 18 pages, 8 figures

We study the impact of structural variations (that is slowly varying geometry aberrations and internal strain fields) on the width and shape of the stimulated Brillouin scattering (SBS) resonance in nanoscale waveguides. We find that they lead to an homogeneous resonance broadening through two distinct mechanisms: firstly, the acoustic frequency is directly influenced via mechanical nonlinearities; secondly, the optical wave numbers are influenced via the opto-mechanical nonlinearity leading to an additional acoustic frequency shift via the phase-matching condition. We find that this second mechanism is proportional to the opto-mechanical coupling and, hence, related to the SBS-gain itself. It is absent in intra-mode forward SBS, while it plays a significant role in backward scattering. In backward SBS increasing the opto-acoustic overlap beyond a threshold defined by the fabrication tolerances will therefore no longer yield the expected quadratic increase in overall Stokes amplification. Finally, we illustrate in a numerical example that in backward SBS and inter-mode forward SBS the existence of two broadening mechanisms with opposite sign also opens the possibility to compensate the effect of geometry-induced broadening. Our results can be transferred to other micro- and nano-structured waveguide geometries such as photonic crystal fibres., Comment: 18 pages, 6 figures

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 and maximal realisable Stokes amplification of any given waveguide structure are determined by a dimensionless parameter $\mathcal{F}$ involving the SBS-gain and all loss parameters. We provide simple expressions for optimal pump power, waveguide length and realisable amplification and demonstrate their utility in two example systems. Notably, we find that 2PA-induced FCA is a serious limitation to SBS in silicon and germanium for wavelengths shorter than 2200nm and 3600nm, respectively. In contrast, three-photon absorption is of no practical significance.

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 materials and waveguide designs in the presence of fifth-order losses. From this, we determine the optimal waveguide length for the case of 2PA alone and upper bounds for the total Stokes amplification for the case of 2PA as well as fifth-order losses. The analysis is performed analytically using a small-signal approximation and is compared to numerical solutions of the full nonlinear modal equations.

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 radiation pressure is included separately from the scattering action that the acoustic field exerts on the optical field. In contrast to this, we show here that the effects of radiation pressure and motion of the waveguide boundaries are inextricably linked. Central to this insight is a new formulation of the SBS interaction that unifies the treatment of light and sound, incorporating all relevant interaction mechanisms --- radiation pressure, waveguide boundary motion, electrostriction and photoelasticity --- from a rigorous thermodynamic perspective. Our approach also clarifies important points of ambiguity in the literature, such as the nature of edge-effects with regard to electrostriction, and of body-forces with respect to radiation pressure. This new perspective on Brillouin processes leads to physical insight with implications for the design and fabrication of SBS-based nanoscale devices.

Colour centres in diamond are promising candidates as a platform for quantum technologies and biomedical imaging based on spins and/or photons. Controlling the emission properties of colour centres in diamond is a key requirement for developing efficient single photon sources with high collection efficiency. A number of groups have produced enhancement in the emission rate over narrow wavelength ranges by coupling single emitters in nanodiamond crystals to resonant electromagnetic structures. Here we characterise in detail the spontaneous emission rates of nitrogen-vacancy centres positioned in various locations on a structured substrate. We show an average factor of 1.5 enhancement of the total emission rate when nanodiamonds are on an opal photonic crystal surface, and observe changes in the lifetime distribution. We present a model to explain these observations and associate the lifetime properties with dipole orientation and polarization effects., Comment: 16 pages, 10 figures