A silicon Brillouin laser

TL;DR

This paper demonstrates a silicon-based Brillouin laser using hybrid photonic-phononic waveguides, enabling strong nonlinear interactions and phonon linewidth narrowing, paving the way for integrated photonic applications.

Contribution

The work introduces the first silicon Brillouin laser leveraging hybrid waveguides, showcasing novel nonlinear dynamics and linewidth narrowing in silicon photonics.

Findings

Successful demonstration of silicon Brillouin lasing.

Observation of phonon linewidth narrowing.

Potential for integrated photonic applications.

Abstract

Brillouin laser oscillators offer powerful and flexible dynamics as the basis for mode-locked lasers, microwave oscillators, and optical gyroscopes in a variety of optical systems. However, Brillouin interactions are exceedingly weak in conventional silicon photonic waveguides, stifling progress towards silicon-based Brillouin lasers. The recent advent of hybrid photonic-phononic waveguides has revealed Brillouin interactions to be one of the strongest and most tailorable nonlinearities in silicon. Here, we harness these engineered nonlinearities to demonstrate Brillouin lasing in silicon. Moreover, we show that this silicon-based Brillouin laser enters an intriguing regime of dynamics, in which optical self-oscillation produces phonon linewidth narrowing. Our results provide a platform to develop a range of applications for monolithic integration within silicon photonic circuits.

Figures

C). In addition to low-loss optical modes (Figs. 1Eiii-iv), this structure also supports guidance of a 6 GHz acoustic wave (Fig. 1Eii), which mediates efficient Brillouin coupling between symmetric and antisymmetric optical modes. By contrast, the fixed waveguide bends do not permit acoustic guidance. The Brillouin-active waveguide structure is identical in design to that described in Ref. Kittlaus et al. ([2017](#bib.bib19)), which yields a peak inter-modal Brillouin gain coefficient of $G_{\textup{b}}\cong 470\ {\rm W}^{-1}{\rm m}^{-1}$ at a Brillouin frequency ($\Omega_{\textup{b}}$) of 6.0

C). In addition to low-loss optical modes (Figs. 1Eiii-iv), this structure also supports guidance of a 6 GHz acoustic wave (Fig. 1Eii), which mediates efficient Brillouin coupling between symmetric and antisymmetric optical modes. By contrast, the fixed waveguide bends do not permit acoustic guidance. The Brillouin-active waveguide structure is identical in design to that described in Ref. Kittlaus et al. ([2017](#bib.bib19)), which yields a peak inter-modal Brillouin gain coefficient of $G_{\textup{b}}\cong 470\ {\rm W}^{-1}{\rm m}^{-1}$ at a Brillouin frequency ($\Omega_{\textup{b}}$) of 6.0

C). In addition to low-loss optical modes (Figs. 1Eiii-iv), this structure also supports guidance of a 6 GHz acoustic wave (Fig. 1Eii), which mediates efficient Brillouin coupling between symmetric and antisymmetric optical modes. By contrast, the fixed waveguide bends do not permit acoustic guidance. The Brillouin-active waveguide structure is identical in design to that described in Ref. Kittlaus et al. ([2017](#bib.bib19)), which yields a peak inter-modal Brillouin gain coefficient of $G_{\textup{b}}\cong 470\ {\rm W}^{-1}{\rm m}^{-1}$ at a Brillouin frequency ($\Omega_{\textup{b}}$) of 6.0

A) Materials and methods are available as supplementary materials ([2018](#bib.bib23)). The threshold and slope efficiency of this laser were quantified by measuring the total emitted Stokes power as a function of pump power (Fig. 2B). These data reveal a threshold on-chip pump power of 10.6 mW, corresponding to an intracavity power of 19 mW. This laser threshold agrees well with the condition for net amplification in Brillouin waveguides of this design Kittlaus et al. ([2017](#bib.bib19)). Further analysis of these data reveal an on-chip slope efficiency of 3% (supplementary materials 1.3.2 a

A and red points of Fig. 3C). A complementary sub-coherence self-heterodyne technique characterizes the laser coherence at higher powers (see Fig. 3B-C and supplementary materials 2) Materials and methods are available as supplementary materials ([2018](#bib.bib23)). Above threshold, the Stokes wave becomes exceptionally coherent with the incident pump field, with an excess phase noise linewidth ($\Delta\nu_{\textup{b}}$) of less than 800 Hz (corresponding to a compression factor of $10^{4}$). Due to the three-wave dynamics in this system, this phase noise corresponds directly to the phonon li

Equations

$$\Delta {\nu }_{\text{b}}=\frac{\Gamma }{4\pi {\beta }^2}(n_{\text{b}}^{\text{th}}+n_{\mathrm{s}}^{\text{th}}+1).$$

Full text

I Introduction

With the ability to control the optical and electronic properties of silicon, the field of silicon photonics has produced a variety of chip-scale optical devices Reed et al. (2010); Liang and Bowers (2010); Leuthold et al. (2010) for applications ranging from high-bandwidth communications Alduino and Paniccia (2007) to biosensing on a chip Vos et al. (2007). The rapid proliferation of these technologies has spurred interest in strategies to reshape the spectral and coherence properties of light for a wide array of on-chip functionalities. One promising approach to customize on-chip light involves using the nonlinear optical properties of silicon to create optical laser oscillators Leuthold et al. (2010). For example, Raman nonlinearities have been harnessed to create all-silicon Raman lasers Boyraz and Jalali (2004); Rong et al. (2005). Brillouin interactions, produced by the coupling between light and sound, could offer a complementary set of behaviors and capabilities for laser technologies in silicon. By exploiting these nonlinearities in a variety of physical systems, Brillouin lasers have been designed to yield everything from frequency-tunable laser emission Takuma and Jennings (1964) and mode-locked pulsed lasers Lecoeuche et al. (1998) to low-noise oscillators and optical gyroscopes Smith et al. (1991); Loh et al. (2015); Kabakova et al. (2013); Li et al. (2017).

Within an optical cavity, Brillouin lasing occurs when optical gain from stimulated Brillouin scattering (SBS) overcomes round-trip loss. This nonlinear light-sound coupling is typically strong, overtaking Kerr and Raman interactions in most transparent media. However, the same integrated silicon waveguides that enhance Raman and Kerr nonlinearities tend to produce minuscule Brillouin couplings due to substrate-induced acoustic dissipation Rakich et al. (2012). The recent advent of a class of suspended waveguides—which tightly confine both light and sound—has enabled appreciable nonlinearities through forward stimulated Brillouin scattering Rakich et al. (2012); Shin et al. (2013); Van Laer et al. (2015); Kittlaus et al. (2016). While these suspended structures have produced large optical Brillouin gain Shin et al. (2013); Van Laer et al. (2015) and net amplification Laer et al. (2015); Kittlaus et al. (2016), innovative strategies are needed to translate Brillouin interactions into silicon laser oscillators Kittlaus et al. (2017); Espinel et al. (2017).

We demonstrate a Brillouin laser in silicon by leveraging a form of guided-wave forward Brillouin scattering, termed stimulated inter-modal Brillouin scattering (SIMS), which couples light fields guided in distinct optical spatial modes Kittlaus et al. (2017); Kang et al. (2010); Bahl et al. (2011). Our silicon Brillouin laser system is fabricated from a single-crystal silicon-on-insulator (SOI) wafer (supplementary materials 6.2) Materials and methods are available as supplementary materials (2018). The laser is composed of a 4.6-cm long racetrack resonator cavity with two extended Brillouin-active gain regions (Fig. 1A). Throughout the device, light is guided by total internal reflection using a ridge waveguide (Fig. 1. Ei). This multimode waveguide provides low-loss guidance of both symmetric (red) and antisymmetric (blue) TE-like spatial modes (with respective propagation constants $k_{1}(\omega)$ and $k_{2}(\omega)$), yielding two distinct sets of high quality-factor ($Q$) cavity modes with slightly different free spectral ranges (FSR) ($Q_{1}\cong 2.4\times 10^{6},\rm FSR_{1}\cong 1.614$ GHz and $Q_{2}\cong 4\times 10^{5},\rm FSR_{2}\cong 1.570$ GHz, respectively; see supplementary materials 3.7) Materials and methods are available as supplementary materials (2018). Simulated electric field profiles for these two optical spatial modes are shown in Fig. 1. Eiii-iv. To access the cavity modes, we use a directional coupler that couples strongly to the antisymmetric and weakly to the symmetric mode, yielding a characteristic multimode transmission spectrum (Fig. 1B).

Optical gain is supplied by forward inter-modal Brillouin scattering within the Brillouin-active segments (dark gray). These regions are created by removing the oxide undercladding to yield a continuously-suspended waveguide that produces large inter-modal Brillouin gain (Fig. 1C). In addition to low-loss optical modes (Figs. 1Eiii-iv), this structure also supports guidance of a 6 GHz acoustic wave (Fig. 1. Eii), which mediates efficient Brillouin coupling between symmetric and antisymmetric optical modes. By contrast, the fixed waveguide bends do not permit acoustic guidance. The Brillouin-active waveguide structure is identical in design to that described in Ref. Kittlaus et al. (2017), which yields a peak inter-modal Brillouin gain coefficient of $G_{\textup{b}}\cong 470\ {\rm W}^{-1}{\rm m}^{-1}$ at a Brillouin frequency ($\Omega_{\textup{b}}$) of 6.03 GHz with a resonance bandwidth of 13 MHz (full width at half maximum, FWHM). For efficient nonlinear coupling, this scattering process requires that both energy conservation ($\omega_{\textup{p}}=\omega_{\textup{s}}+\Omega_{\textup{b}}$) and phase-matching ($k_{\textup{2}}(\omega_{\textup{p}})=k_{\textup{1}}(\omega_{\textup{s}})+q(\Omega_{\textup{b}})$) conditions be satisfied. Here, $\omega_{\textup{p}}$ and $\omega_{\textup{s}}$ are the respective pump and Stokes frequencies, and $q(\Omega)$ is the wavevector of the acoustic wave. In inter-modal Brillouin scattering, these conditions produce a form of phase-matched symmetry breaking that decouples the Stokes from the anti-Stokes process, permitting single-sideband amplification Kittlaus et al. (2017).

Laser oscillation of the symmetric cavity mode occurs when Brillouin gain matches the round-trip loss, producing coherent laser emission at the Stokes frequency ($\omega_{\rm s}$). These lasing requirements are met by injecting pump light (of power $P_{\rm p}$) into an antisymmetric cavity mode that is separated in frequency from a symmetric cavity mode by the Brillouin frequency (Fig. 1B). Because the FSRs of the two sets of cavity modes differ by 3.1%, this resonance frequency condition is satisfied by symmetric and antisymmetric cavity mode pairs that occur frequently (every 0.40 nm) across the C-band (from 1530-1565 nm). When this dual-resonance condition is satisfied and the pump power exceeds the threshold power ($P_{\rm p}>P_{\rm th}$), the Stokes field builds from thermal noise (produced by spontaneous Brillouin scattering) to yield appreciable line-narrowing and coherent Stokes emission at frequency $\omega_{\rm s}=\omega_{\rm p}-\Omega_{\textup{b}}$.

Many properties of this system could prove advantageous for scalable and robust integration of Brillouin lasers in complex silicon photonic circuits. Because this laser uses a forward scattering process, it alleviates the need for on-chip isolator and circulator technologies that would otherwise be necessary to integrate traditional Brillouin lasers (which use backward SBS). In addition, as this Brillouin nonlinearity is created through structural control, it is possible to independently engineer a range of characteristics, including Brillouin frequency, acoustic dissipation rate, and Brillouin gain, providing a flexible and robust laser design space. Moreover, the multimode properties of this system eliminate size constraints that are present in backward Brillouin lasers (i.e., FSRs that must correspond to Brillouin frequencies) and provide exceptional control over cascading dynamics (supplementary materials 5.4).

Brillouin lasing was investigated by injecting continuous-wave (cw) pump light into an antisymmetric cavity mode while analyzing the emission of Stokes light from a symmetric cavity mode. The power and coherence properties of the emitted laser light were characterized through high-resolution heterodyne spectral analysis (Fig. 2A) Materials and methods are available as supplementary materials (2018). The threshold and slope efficiency of this laser were quantified by measuring the total emitted Stokes power as a function of pump power (Fig. 2B). These data reveal a threshold on-chip pump power of 10.6 mW, corresponding to an intracavity power of 19 mW. This laser threshold agrees well with the condition for net amplification in Brillouin waveguides of this design Kittlaus et al. (2017). Further analysis of these data reveal an on-chip slope efficiency of 3% (supplementary materials 1.3.2 and 4.1) Materials and methods are available as supplementary materials (2018).

As the pump power increases, the emitted Stokes light exhibits spectral compression characteristic of laser oscillation. When the emitted Stokes spectrum is broader than the linewidth of optical local oscillator ($\sim 13$ kHz, derived from the same source as the pump wave), the heterodyne microwave spectrum provides an excellent representation of the emitted Stokes linewidth. Fig. 2C compares the Stokes spectrum emitted by the laser (red) with the spontaneous Stokes spectrum emitted from an identical Brillouin-active waveguide segment (gray) in the absence of optical feedback. We see that optical feedback produces spectral compression by a factor of $\sim 10^{3}$; the relatively broad spontaneous Stokes spectrum (FWHM $\cong 13.1$ MHz) is compressed to a resolution-limited value of 20 kHz.

Heterodyne spectral analysis was used to measure the emitted Stokes linewidth below threshold at various Stokes powers (see Fig. 3A and red points of Fig. 3C). A complementary sub-coherence self-heterodyne technique characterizes the laser coherence at higher powers (see Fig. 3B-C and supplementary materials 2) Materials and methods are available as supplementary materials (2018). Above threshold, the Stokes wave becomes exceptionally coherent with the incident pump field, with an excess phase noise linewidth ($\Delta\nu_{\textup{b}}$) of less than 800 Hz (corresponding to a compression factor of $10^{4}$). Due to the three-wave dynamics in this system, this phase noise corresponds directly to the phonon linewidth, revealing phonon linewidth narrowing far below that of the incident pump field. This behavior represents a marked departure from the linewidth narrowing dynamics conventionally exhibited by Brillouin lasers.

To understand our experimental observations, we derive simple analytical and numerical models that describe the basic spatial and temporal behavior of laser oscillation in this system (see supplementary materials 2) Materials and methods are available as supplementary materials (2018). Steady-state analysis of the coupled envelope equations reveal that this silicon laser exhibits spatial dynamics (i.e., field evolution along the direction of propagation) that are characteristic of Brillouin lasers. Specifically, because the phonon field is spatially heavily damped and the only feedback mechanism is optical, this laser produces optical self-oscillation of the Stokes wave (see supplementary materials 1.1) Materials and methods are available as supplementary materials (2018). Building on established treatments of Brillouin laser physicsLi et al. (2012); Debut et al. (2000), a simplified mean-field model was developed to explore the salient features of the temporal dynamics. This model incorporates parameters that are consistent with the measured resonator and nonlinear waveguide characteristics (see supplementary materials 3.5,3.8) Materials and methods are available as supplementary materials (2018).

Well above threshold, this model predicts Stokes emission that is highly coherent with the incident pump field, with an excess phase noise linewidth given by

[TABLE]

Here, $\Gamma$ is the intrinsic acoustic dissipation rate, $\beta^{2}$ is the coherently-driven phonon occupation number, $n^{\textup{th}}_{\textup{b}}$ is the thermal occupation number of the phonon field, $n^{\textup{th}}_{\rm s}$ is average thermal occupation number of the symmetric mode of the optical resonator ($n^{\textup{th}}_{\rm b}\approx 10^{3}$ and $n^{\textup{th}}_{\rm s}\approx 0$), and the $+1$ is due to vacuum fluctuations. As a result of the three-wave dynamics of this system, the pump-Stokes coherence provides a direct window into the spectrum of the distributed acoustic wave (see supplementary materials 1.3) Materials and methods are available as supplementary materials (2018), revealing that this regime of Brillouin lasing produces Schawlow-Townes linewidth narrowing of the coherent acoustic field. While closed-form analytical expressions for phase noise are tractable well below and above threshold, stochastic numerical simulations are necessary to model the noise characteristics in the vicinity of laser threshold (see Fig. 3C), revealing good qualitative agreement with our measurements.

These linewidth narrowing dynamics are distinct from those typically produced in glass-based Brillouin lasers Smith et al. (1991); Li et al. (2012), which yield Schawlow-Townes optical linewidth narrowing (see supplementary materials 1.6-7) Materials and methods are available as supplementary materials (2018). In this silicon system, phonon linewidth narrowing arises from an inverted dissipation hierarchy in which the phonon temporal dissipation rate is much smaller than the optical dissipation rates for the pump and Stokes cavity modes (i.e., $\gamma_{\textup{p}},\gamma_{\textup{s}}\gg\Gamma$), in contrast to the temporal dissipation hierarchy conventionally realized in Brillouin lasers ($\gamma_{\textup{p}},\gamma_{\textup{s}}\ll\Gamma$) Debut et al. (2000). As a result, this silicon Brillouin laser simultaneously operates where the spatial acoustic decay length (63 $\rm\mu m$) is far smaller than the optical decay length ($\sim$0.1-1 m), while the intrinsic phonon lifetime (77 ns) exceeds that of the optical fields ($\sim$ 2-12 ns). This combination of spatial and temporal dynamics is made possible by the unusually large Brillouin coupling in this system ($\sim 10^{3}\times$ that of silica fibers) and the disparate velocities of the interacting light and sound waves.

The observed phonon coherence is reminiscent of that produced in optomechanical self-oscillation Grudinin et al. (2010); Jiang et al. (2012); Bahl et al. (2011) (phonon lasing). However, in contrast to phonon lasers, this Brillouin laser does not possess a phonon cavity that permits acoustic feedback necessary for phonon self-oscillation (see supplementary materials 1.7.3-4) Materials and methods are available as supplementary materials (2018). Here we show that, despite large acoustic spatial damping and lack of phonon feedback (i.e., more than 1000 dB round-trip acoustic propagation loss), optical self-oscillation of the Stokes wave produces linewidth narrowing of the acoustic field, as long as the temporal acoustic dissipation rate is lower than that of the optical fields. In this way, this system is analogous to an extreme limit of singly-resonant optical parametric oscillator physics, with a slow, ballistic, and long-lived idler wave (see supplementary materials 1.7) Materials and methods are available as supplementary materials (2018). Interestingly, other Brillouin laser systems may have operated near or in this temporal dissipation hierarchy Hill et al. (1976); Abedin (2006); Morrison et al. (2017). However, these dynamics were not identified. It is due to the stability of this monolithic silicon system that we are able to study this unusual combination of spatial and temporal dynamics.

I.1 Acknowledgements

We thank A. D. Stone for discussions regarding the laser dynamics and M. Rooks for assistance with the fabrication. Funding: This work was supported through a seedling grant under the direction of D. Green at DARPA MTO and by the Packard Fellowship for Science and Engineering. N.T.O. acknowledges support from the National Science Foundation Graduate Research Fellowship under grant No. DGE1122492. Z.W. acknowledges support from the National Science Foundation under grant No. 1641069. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of DARPA or the National Science Foundation. Author contributions: P.T.R., N.T.O., and E.A.K. developed device concept and design. N.T.O. and E.A.K. fabricated the devices and performed the experiments. R.O.B. and N.T.O. developed theory with assistance from P.T.R. and Z.W. All authors contributed to the preparation of the manuscript. Competing interests: None declared. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper or the supplementary materials.