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A silicon Brillouin laser

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Science  08 Jun 2018:
Vol. 360, Issue 6393, pp. 1113-1116
DOI: 10.1126/science.aar6113

Making silicon shine bright

Silicon is the workhorse of the semiconductor electronics industry, but its lack of optical functionality is a barrier to developing a truly integrated silicon-based optoelectronics platform. Although there are several ways of exploiting nonlinear light-matter interactions to coax silicon into optical functionality, the effects tend to be weak. Otterstrom et al. used a suspended silicon waveguide racetrack structure to stimulate the stronger nonlinear effect of Brillouin scattering and achieve lasing from silicon. The ability to engineer the nonlinearity and tune the optical response through the design of the suspended cavity provides a powerful and flexible route for developing silicon-based optoelectronic circuits and devices.

Science, this issue p. 1113

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 markedly weak in conventional silicon photonic waveguides, stifling progress toward 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. In this study, we have harnessed these engineered nonlinearities to demonstrate Brillouin lasing in silicon. Moreover, we show that this silicon-based Brillouin laser enters a 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.

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 (13) for applications ranging from high-bandwidth communications (4) to biosensing on a chip (5). 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 (3). For example, Raman nonlinearities have been harnessed to create all-silicon Raman lasers (6, 7). 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 (8) and mode-locked pulsed lasers (9) to low-noise oscillators and optical gyroscopes (1013).

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 because of substrate-induced acoustic dissipation (14). The recent advent of a class of suspended waveguides—which tightly confine both light and sound—has enabled appreciable nonlinearities through forward SBS (1417). Though these suspended structures have produced large optical Brillouin gain (15, 16) and net amplification (17, 18), innovative strategies are needed to translate Brillouin interactions into silicon laser oscillators (19, 20).

We demonstrate a Brillouin laser in silicon by leveraging a form of guided-wave forward Brillouin scattering, termed stimulated intermodal Brillouin scattering, which couples light fields guided in distinct optical spatial modes (19, 21, 22). Our silicon Brillouin laser system is fabricated from a single-crystal silicon-on-insulator wafer (supplementary materials section 6.2) (23). 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 with a ridge waveguide (Fig. 1E, i). This multimode waveguide provides low-loss guidance of both symmetric (red) and antisymmetric (blue) transverse electric (TE)–like spatial modes [with respective propagation constants k1(ω) and k2(ω), where ω is frequency], yielding two distinct sets of high–quality factor (Q) cavity modes with slightly different free spectral ranges (FSRs) (Q1 ≅ 2.4 × 106, FSR1 ≅ 1.614 GHz, and Q2 ≅ 4 × 105, FSR2 ≅ 1.570 GHz, respectively) (supplementary materials 3.7) (23). Simulated electric field profiles for these two optical spatial modes are shown in Fig. 1E, iii and iv. To access the cavity modes, we used a directional coupler that couples strongly to the antisymmetric mode and weakly to the symmetric mode, yielding a characteristic multimode transmission spectrum (Fig. 1B).

Fig. 1 Schematic of laser cavity and basic operation.

(A) The Brillouin laser consists of a multimode racetrack cavity with two Brillouin-active regions (dark gray). Pump light (blue) is coupled into the antisymmetric spatial mode of the racetrack resonator. Intermodal Brillouin scattering mediates energy transfer from the pump wave (antisymmetric) to the Stokes wave (symmetric; red). L, length. (B) The idealized transmission spectrum for the racetrack cavity. Narrower and broader resonant features correspond to the symmetric and antisymmetric resonances, respectively. Brillouin lasing occurs when the resonance conditions for the pump (antisymmetric) and Stokes (symmetric) waves are simultaneously satisfied. (C and D) Cross sections of the suspended Brillouin-active region and the racetrack bend, respectively. (E) (i) Dimensions of the Brillouin-active waveguide. (ii) Strain profile εxx(x, y) of the 6-GHz Lamb-like acoustic mode that mediates intermodal scattering. (iii and iv) x-directed electric field profiles (Ex) of the TE-like symmetric and antisymmetric optical modes, respectively. Red and blue represent the respective positive and negative values of the electric field and strain profiles.

Optical gain is supplied by forward intermodal 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 intermodal Brillouin gain (Fig. 1C). In addition to low-loss optical modes (Fig. 1E, iii and iv), this structure also supports guidance of a 6-GHz elastic wave (Fig. 1E, ii), which mediates efficient Brillouin coupling between symmetric and antisymmetric optical modes. By contrast, the fixed waveguide bends do not permit phononic guidance. The Brillouin-active waveguide structure is identical in design to that described in (19), which yields a peak intermodal Brillouin gain coefficient of Gb ≅ 470 W−1 m−1 at a Brillouin frequency (Ωb) 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 (ωp = ωs + Ωb) and phase-matching [k2p) = k1s) + qb)] conditions be satisfied. Here, ωp and ωs are the respective pump and Stokes frequencies, and q(Ω) is the wave vector of the acoustic wave. In intermodal Brillouin scattering, these conditions produce a form of phase-matched symmetry breaking that decouples the Stokes process from the anti-Stokes process, permitting single-sideband amplification (19).

Laser oscillation of the symmetric cavity mode occurs when Brillouin gain matches the round-trip loss, producing coherent laser emission at the Stokes frequency ωs. These lasing requirements are met by injecting pump light (of power Pp) 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 to 1565 nm). When this dual-resonance condition is satisfied and the pump power exceeds the threshold power (Pp > Pth), the Stokes field builds from thermal noise (produced by spontaneous Brillouin scattering) to yield appreciable line narrowing and coherent Stokes emission at frequency ωs = ωp − Ωb.

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 (FSRs that must correspond to Brillouin frequencies) and provide exceptional control over cascading dynamics (supplementary materials 5.4).

We investigated Brillouin lasing by injecting continuous-wave pump light into an antisymmetric cavity mode while analyzing the emission of Stokes light from a symmetric cavity mode. We characterized the power and coherence properties of the emitted laser light through high-resolution heterodyne spectral analysis (Fig. 2A) (23). 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 (19). Further analysis of these data reveal an on-chip slope efficiency of 3% (supplementary materials 1.3.2 and 4.1) (23).

Fig. 2 Experimental apparatus and laser threshold behavior.

(A) Apparatus used for heterodyne spectroscopy. Continuous-wave pump light (Agilent 81600B, linewidth = 13 kHz) used to initiate Brillouin lasing is amplified by an erbium-doped fiber amplifier (EDFA) and coupled on-chip by grating couplers. Laser light is frequency shifted (+44 MHz) by an acousto-optic modulator (AOM) in a reference arm and combined with the output Stokes light for heterodyne detection. RF, radio frequency. (B) Theory and experiment for the output laser power versus the input pump power. Intracavity pump powers are estimated by using the transmitted pump power and the detuning from resonance, and intracavity Stokes power is determined from the measured bus Stokes power and comparison with the theoretical model (supplementary materials 4.1) (23). (C) Heterodyne spectra of spontaneously scattered Stokes light from a linear waveguide (multiplied by 107) and the linewidth-narrowed intracavity laser spectrum above the laser threshold.

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 the optical local oscillator (~13 kHz, derived from the same source as the pump wave), the heterodyne microwave spectrum provides an excellent representation of the emitted Stokes linewidth. Figure 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 ~103; the relatively broad spontaneous Stokes spectrum (FWHM ≅ 13.1 MHz) is compressed to a resolution-limited value of 20 kHz.

We used heterodyne spectral analysis to measure the emitted Stokes linewidth below the laser threshold at various Stokes powers (Fig. 3A and red points in Fig. 3C). A complementary subcoherence self-heterodyne technique characterizes the laser coherence at higher powers (Fig. 3, B and C, and supplementary materials 2) (23). Above the threshold, the Stokes wave becomes exceptionally coherent with the incident pump field, with an excess phase noise linewidth (Δνb) of less than 800 Hz (corresponding to a compression factor of 104). Because of 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.

Fig. 3 Linewidth measurements.

(A) Standard heterodyne spectroscopy apparatus to measure the pump-Stokes excess phase noise (or phonon) linewidth (Embedded Image), given by the FWHM of the heterodyne spectrum. (B) Subcoherence self-heterodyne apparatus used to probe the phonon dynamics at higher-output Stokes powers (supplementary materials 2) (23). The phonon linewidth is determined by measuring the fringe contrast or coherence between output Stokes and pump waves (C). τd, delay line transit time. (C) Experimental and theoretical comparison of phonon linewidths (Embedded Image) as a function of peak spectral density. Below the threshold, we use standard heterodyne spectroscopy (A) (red data points). At higher powers, this measurement becomes resolution bandwidth limited (supplementary materials 4.2) (23). For this reason, we use the subcoherence self-heterodyne technique (B), yielding the blue data points (error bars represent the 95% confidence interval of fits to data) (supplementary materials 4.2) (23).

To understand our experimental observations, we derived simple analytical and numerical models that describe the basic spatial and temporal behavior of laser oscillation in this system (supplementary materials 2) (23). Steady-state analysis of the coupled envelope equations reveals that this silicon laser exhibits spatial dynamics (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 (supplementary materials 1.1) (23). Building on established treatments of Brillouin laser physics (24, 25), we developed a simplified mean-field model to explore the salient features of the temporal dynamics (supplementary materials 1.2 to 1.5). This model incorporates parameters that are consistent with the measured resonator and nonlinear waveguide characteristics (supplementary materials 3.5 and 3.8) (23).

Well above the laser threshold, this model predicts Stokes emission that is highly coherent with the incident pump field, with an excess phase noise linewidth given byEmbedded Image(1)Here, Γ is the intrinsic acoustic dissipation rate, β2 is the coherently driven phonon occupation number, Embedded Image is the thermal occupation number of the phonon field, Embedded Image is the average thermal occupation number of the symmetric mode of the optical resonator (Embedded Image and Embedded Image), 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 field (supplementary materials 1.3) (23), revealing that this regime of Brillouin lasing produces Schawlow-Townes linewidth narrowing of the coherent acoustic field. Although closed-form analytical expressions for phase noise are tractable well below and above the threshold, stochastic numerical simulations are necessary to model the noise characteristics in the vicinity of the laser threshold (Fig. 3C), revealing good qualitative agreement with our measurements.

These linewidth-narrowing dynamics are distinct from those typically produced in glass-based Brillouin lasers (10, 24), which yield Schawlow-Townes optical linewidth narrowing (supplementary materials 1.6 and 1.7) (23). In this silicon system, phonon linewidth narrowing arises from an inverted dissipation hierarchy in which the phonon temporal dissipation rate is much lower than the optical dissipation rates for the pump and Stokes cavity modes Embedded Image, in contrast to the temporal dissipation hierarchy conventionally realized in Brillouin lasers Embedded Image (25). As a result, this silicon Brillouin laser simultaneously operates where the spatial acoustic decay length (63 μm) is far smaller than the optical decay length (~0.1 to 1 m), whereas the intrinsic phonon lifetime (77 ns) exceeds that of the optical fields (~2 to 12 ns). This combination of spatial and temporal dynamics is made possible by the unusually large Brillouin coupling provided by this silicon system (~103 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 (22, 26, 27) (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 (supplementary materials 1.7.3 and 1.7.4) (23). Here we show that, despite a high degree of acoustic spatial damping and lack of phonon feedback (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 (supplementary materials 1.7) (23). Other Brillouin laser systems may have operated near or in this temporal dissipation hierarchy (2830); however, these dynamics were not identified. It is because of the stability of this monolithic silicon system that we are able to study this unusual combination of spatial and temporal dynamics.

Supplementary Materials

www.sciencemag.org/content/360/6393/1113/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S14

Tables S1 to S3

References (3142)

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: 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 NSF graduate research fellowship under grant DGE1122492. Z.W. acknowledges support from the NSF under grant 1641069. Any opinions, 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 NSF. Author contributions: P.T.R., N.T.O., and E.A.K. developed the 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.
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