A new mechanism for generating on-chip optical frequency combs: the mechanical Kerr nonlinearity

01 January 2013 → 31 December 2016
Regional and community funding: IWT/VLAIO
Research disciplines
  • Engineering and technology
    • Computer hardware
    • Computer theory
    • Scientific computing
    • Other computer engineering, information technology and mathematical engineering
Kerr nonlinearity fotonica phonons
Project description

THE SCIENCE of light seeks to manipulate photons. It has done so with great success in the past decades: photons are ideal messengers given their low propagation loss and high bandwidth [1–3]. Thus they are already the dominant long-haul information carriers, transmitting data at everincreasing rates under the oceans. Photonics has now begun taking over chipto-chip communication too [4], solving major issues –such as heat generation and signal distortion [1, 2] –associated with electronic interconnects. Hence there was a great push for photonic circuitry at the nanoscale, following the shrinking electronics on the path of Moore’ law [5]. Modern optical waveguides trap light to cross-sections below 0.1 mm2 and can be made from the ubiquitous material silicon, in line with mass-fabrication capabilities of existing semiconductor fabs. This begs the question whether optics could perform certain computations too [6, 7], which requires some photons to control the flow of others [8]. The grand challenge lies in enhancing the weak interactions between photons. As photon-photon interactions are negligible in vacuum [9, 10], harnessing intermediate material excitations is the only viable route to do so. Thus there has been tremendous effort on improving light-matter coupling, from exploiting Kerr [11–14], Raman [15–17], free-carrier [18, 19] and thermal [20, 21] effects to cavity QED [22, 23]. Although they already filter radio-frequency signals in every smartphone and laptop [24, 25], mechanical systems did not arrive on the photonics scene until about a decade ago. Initially, mostly megahertz-range vibrations were excited and probed optically in e.g. microtoroids [26], silicon beams [27–29] and nitride disks [30]. These low-frequency oscillators generate nonlinearities orders of magnitude stronger than intrinsic material effects [31, 32]. It is desirable, however, to scale up the mechanical frequencies into the gigahertz range. This lets them enter the world of microwave photonics [33, 34] and handle higher data rates. In this work, we realize an efficient and highly tailorable optical nonlinearity interfaced by gigahertz phonons. The nonlinearity is often called stimulated Brillouin scattering (SBS). In addition, we focus on waveguides that confine both light and sound, so that their interaction can build up over many diffraction lengths. These waveguides are optically broadband in the sense that the driving laser’ frequency is free within a range of about 10 THz. However, we are confronted with the difficulty of stiff gigahertz mechanics yielding displacements below a picometer. In addition, we lose on the powerefficiency associated with optical cavities [35]. To begin with, we theoretically explore the physics of photon-phonon interactions in both waveguides and cavities (fig.1). Conventional assumptions turn out to no longer be warranted in existing systems. For instance, photons traditionally travel farther than phonons and their interaction strength is normally swamped by the propagation losses. This case results in amplification of an optical seed slightly red-detuned from a strong optical pump; the classical Brillouin gain [36, 37]. If the interaction on the contrary exceeds the propagation losses, photons can be converted into phonons, back into photons, back into phonons, etc. as they fly along the waveguide. We call this spatial strong coupling, bringing Brillouin scattering in line with major themes in other areas of physics such as cavity QED. Further, a mean-field transition generates the dynamics of highfinesse cavities from that of waveguides. It proves a link between two wellknown figures of merit: the Brillouin gain coefficient [36, 37] and the vacuum optomechanical coupling rate [35]. The link elucidates the connections between effects such as Brillouin gain, ground-state cooling [38], induced transparency [39], the optical spring effect [40] and sound-induced slow light [41]. Simultaneously, it places a diverse set of systems –such as Brillouin fiber lasers [55], microtoroids [56], plasmonic Raman cavities [51] and silicon waveguides –in a broader theory of photon-phonon coupling. These ideas, inspired by symmetry, may result in optical control over the flow of sound and heat [42]. Next, we move on to experiments on nanoscale silicon-on-insulator waveguides. These high-index-contrast waveguides strongly confine 193 THz light by total internal reflection. However, sound moves faster in the silicon-dioxide substrate than in the silicon core, forbidding acoustic confinement by internal reflection. Therefore, we instead trap phonons by removing the oxide substrate as much as possible. We thus exploit the huge mismatch in acoustic impedance between the silicon core and the surrounding air. In addition, we reconcile the phononic confinement with centimeter-scale interaction lengths by still leaving a small oxide pillar (fig.2). This compromise between acoustic confinement and interaction length leads to the first observation of Brillouin scattering in silicon nanowires. In a series of experiments (fig.3), we show that the Brillouin effect is now the strongest third-order nonlinearity of these waveguides. Indeed, compressing both light and sound to the 0.1 mm2 core results in an exquisitely efficient process. In particular, we observe a Fabry-Pérot-like acoustic mode at 9.2GHz that has a good overlap with the fundamental quasi-TE optical mode at 193 THz. Notably, the wavelengths of both light and sound are about 1 mm at these frequencies –which is related to the good overlap (fig.2d). The gain experiment (fig.3a-b) shows up to 175% on/off Brillouin gain in a 4 cmlong spiral, improving on a previous result [43] in silicon/nitride waveguides by a factor 19. The shorter wires are essentially transparent in a 35 MHz-wide band. The four-wave mixing experiment finds the Brillouin nonlinearity to be 2.5 times stronger than the Kerr effect (fig.3c-d), in agreement with the gain experiment. These devices enable acoustic quality factors and gain coefficients up to 306 and 3218W 1m 1. To eliminate the acoustic leakage, we next study a cascade of fully suspended silicon nanowires (fig.4). This enhances the quality factors and gain coefficients up to 1010 and 104W 1m 1, the highest so far among gigahertzclass devices. The Brillouin gain now exceeds the propagation loss in the shorter wires (fig.5). The net gain remains limited to 0.5 dB by (1) the available pump power (no free-carrier effects were seen), (2) the higher propagation losses after suspension and (3) inhomogeneous broadening of the acoustic resonance. In particular, we observe line broadening from about 9.2MHz for 6 suspensions to more than 20MHz for 66 suspensions. The broadening is likely caused by static fluctuations in the waveguide’ width, which modulate the acoustic resonance frequency. Better fabrication aside, we suggest to tackle this effect via the indirect sensitivity of the mechanics to the optical dispersion. Finally, we simulate narrow-gap silicon slot waveguides (fig.6) in an effort to engineer yet stronger light-sound interactions. A horizontal-slot geometry is attractive as it enables (1) the fabrication of arbitrarily small gaps and (2) the fundamental flexural mode to be excited efficiently. We simulate gain coefficients beyond 105W 1m 1 for 5 nm-gap slots, an order of magnitude above those observed in stand-alone silicon nanowires. We actually fabricated such slots but it remains to be seen how the device fares in terms of optical absorption. This field is wide open. In only a few years, it witnessed order-of-magnitude performance improvements and a noteworthy explosion of approaches. Besides their clear applications in microwave processing, these waveguides may help solve other pressing issues. Indeed, the pursuit of Moore’ law in its original sense may soon be abandoned [5]. The limits on computation [44] are driving investigations into exceedingly diverse technologies, from millivolt switches [45, 46] to reversible [47, 48] and quantum [49, 50] computing. Phonons may not be ideal messengers, but they certainly have interesting properties as interfaces beween photons, plasmons [51], magnons [52], excitons [53] and others [54].