Formal selection rules for Brillouin scattering in integrated waveguides and structured fibers

Impacts of spatial symmetries on stimulated Brillouin scatterings in nanoscale silicon waveguides: a theoretical and numerical study considering material anisotropies

Fully considering the mechanical and photoelastic anisotropies of monocrystalline silicon, the impacts of spatial symmetries on the stimulated Brillouin scatterings (SBSs) in nanoscale suspended silicon waveguides are studied theoretically and numerically based on group theory. First, starting from an assumption that the principal material coordinate system can be arbitrarily orientated in a waveguide with fixed geometry, the silicon waveguides are systematically classified into a number of point groups according to their spatial symmetry features. Thereafter, the symmetry characteristics of physical fields and SBS opto-mechanical coupling characteristics in the silicon waveguides belonging to different point groups are further examined, and the major new findings can be summarized as follows: The SBS opto-mechanical couplings in several kinds of silicon waveguides with certain nontrivial symmetry features exhibit relatively predictable behaviors in that the opto-mechanical coupling coefficients can be deterministically vanishing or nonvanishing under very few constraints, which can thus serve as general symmetry selection rules for SBSs in suspended silicon waveguides. The results obtained in the present study could be a useful theoretical reference for the design of novel SBS-active silicon photonic devices.

Enhanced stimulated Brillouin scattering in the unsuspended silicon waveguide assisted with genetic algorithms

Stimulated Brillouin scattering (SBS), originating from the coupling between optical and acoustic waves, has been widely applied in many fields. Silicon is the most used and important material in micro-electromechanical systems (MEMS) and integrated photonic circuits. However, strong acoustic-optic interaction in silicon requires mechanical release of the silicon core waveguide to avoid acoustic energy leakage into the substrate. This will not only reduce the mechanical stability and thermal conduction, but also increase the difficulties for fabrication and large-area device integration. In this paper, we propose a silicon-aluminium nitride(AlN)-sapphire platform for realizing large SBS gain without suspending the waveguide. AlN is used as a buffer layer to reduce the phonon leakage. This platform can be fabricated via the wafer bonding between silicon and commercial AlN-sapphire wafer. We adopt a full-vectorial model to simulate the SBS gain. Both the material loss and the anchor loss of the silicon are considered. We also apply the genetic algorithm to optimize the waveguide structure. By limiting the maximum etching step number to two, we obtain a simple structure to achieve the SBS gain of 2462 W^-1m^-1 for forward SBS, which is 8 times larger than the recently reported result in unsuspended silicon waveguide. Our platform can enable Brillouin-related phenomena in centimetre-scale waveguides. Our findings could pave the way toward large-area unreleased opto-mechanics on silicon.

Tailorable stimulated Brillouin scattering in a partially suspended aluminium nitride waveguide in the visible range

Stimulated Brillouin scattering (SBS) has been widely applied in narrow line-width laser, microwave filters, optical gyroscopes, and other fields. However, most research is limited within near-infrared to mid-infrared range. This is due to the limited transparent window in most materials, such as silicon and germanium. Aluminium nitride (AlN) is a novel III-V material with a wide transparent window from 200 nm and an appropriate refractive index to confine the light. In this paper, we first validate the full-vectorial formalism to calculate SBS gain based on the measured results from a silicon platform. Compared to previous research, our model achieves higher accuracy in terms of frequency, Q factor, as well as Brillouin gain coefficient without modifying the waveguide width. It also reveals the importance of matching rotation matrix and crystalline coordinate system. Then, we investigate the SBS in a partially suspended AlN waveguide at 450 nm based on the validated method. It shows a wide tunability in frequency from 16 GHz to 32 GHz for forward SBS and a range from 42 GHz to 49 GHz for backward SBS. We numerically obtain the value of Brillouin gain of 1311 W^-1m^-1 when Q factor is dominated by anchor loss for forward SBS of transverse electric mode. We also find out that in the case for forward SBS of transverse-magnetic mode, anchor loss could be greatly suppressed when the node point of the selected acoustic mode matches with the position of pillar anchor. Our findings, to the best of our knowledge, pave a new way to obtain Brillouin-related applications in integrated photonic circuit within the visible range.

Suspended mid-infrared waveguides for Stimulated Brillouin Scattering

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, 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 structures, and find forward intramodal-SBS gains up to 1750 m^-1W^-1, which compares favorably with the proposed MIR SBS designs based on buried germanium waveguides. This large gain is achieved thanks to the nearly complete suppression of acoustic radiative losses.

Mode symmetry in microstructured fibres revisited

Motivated by the recent development of hollow-core, microstructured optical fibres without a translationally-periodic cladding structure, an analysis of the symmetry-induced properties of the modes of a uniform fibre with CM_v point group symmetry is presented. Modes are classified according to the irreducible representations of the longitudinal components of the electric and magnetic fields; the radial component of the electric field and azimuthal component of the magnetic field share the symmetry of the longitudinal component of the electric field, while the radial component of the magnetic field and the azimuthal component of the electric field have the same symmetry as the longitudinal magnetic field. The symmetry class of the lowest order modes in fibres with point group CM_v with M from 1 to 10 is given. The work is closely related to previous analyses, but clarifies the symmetry relationship between the two orthogonal modes in a degenerate pair and how the different symmetries of the longitudinal electric and magnetic field components emerge from the governing equations.

Brillouin Dynamic Gratings-A Practical Form of Brillouin Enhanced Four Wave Mixing in Waveguides: The First Decade and Beyond

Brillouin-Enhanced Four-Wave-Mixing techniques, which couple four optical beams through Brillouin nonlinearity, have gained popularity in the 1980's largely owing to their phase conjugation properties. Experiments were mainly conducted in liquid cells. The interest in Brillouin-Enhanced Four-Wave-Mixing has reawakened in the 2000's, following the quest for dynamically reconfigurable gratings in optical fibers. Termed Brillouin Dynamic Grating this time around, it is, in fact, an acoustic wave, optically generated by stimulated Brillouin scattering process between two pump waves. The acoustic wave either carries the coherent information encoded by the pump beams, or in the case of sensing applications, its properties are determined by the environmental parameters. This information, in turn, is imparted to the third phase-matched optical probe wave through the elasto-optic effect. Over the last decade, this mechanism allowed for the realization of many all-optical signal processing functions and has proven instrumental in distributed sensing applications. This paper describes the basics, as well as the state of the art, of BDG-based applications in optical fibers. It also surveys the efforts being done to carry over these concepts to the photonic chip level.

Optomechanical time-domain reflectometry

Optical fibres constitute an exceptional sensing platform. However, standard fibres present an inherent sensing challenge: they confine light to an inner core. Consequently, distributed fibre sensors are restricted to the measurement of conditions that prevail within the core. This work presents distributed analysis of media outside unmodified, standard fibre. Measurements are based on stimulated scattering by guided acoustic modes, which allow us to listen where we cannot look. The protocol overcomes a major difficulty: guided acoustic waves induce forward scattering, which cannot be mapped using time-of-flight. The solution relies on mapping the Rayleigh backscatter contributions of two optical tones, which are coupled by the acoustic wave. Analysis is demonstrated over 3 km of fibre with 100 m resolution. Measurements distinguish between air, ethanol and water outside the cladding, and between air and water outside polyimide-coated fibres. The results establish a new sensor configuration: optomechanical time-domain reflectometry, with several potential applications.

Stimulated Brillouin scattering in silicon/chalcogenide slot waveguides

We study slot waveguide geometries, comprising a combination of soft glasses and high-index guiding structures, for enhancing stimulated Brillouin scattering (SBS). We show that strong optical and acoustic mode confinement in these waveguides can lead to a substantial increase in SBS gain, comparable to or greater than recently proposed suspended silicon nanowire structures. We compute the optimal parameters of the structure and examine the physics of optical and acoustic confinement within slot waveguides. Finally, we compute the effects of linear and nonlinear loss mechanisms on optimum pump/Stokes powers and waveguide lengths.

Multimode Brillouin spectrum in a long tapered birefringent photonic crystal fiber

We investigate the stimulated Brillouin scattering (SBS) in a long tapered birefringent solid-core photonic crystal fiber (PCF) and compare our results with a similar but untapered PCF. It is shown that the taper generates a broadband and multipeaked Brillouin spectrum, while significantly increasing the threshold power. Furthermore, we observe that the strong fiber birefringence gives rise to a frequency shift of the Brillouin spectrum which increases along the fiber. Numerical simulations are also presented to account for the taper effect and the birefringence. Our findings open a new means to control or inhibit the SBS by tapering photonic crystal fibers.