Dual nanoweb fibre for optomechanics

Tight confinement of photons and phonons in nano-scale optical waveguides or cavities has revealed a rich landscape of optoacoustic phenomena. We have continued to study the "dual-nanoweb" fibre, first proposed at MPL [Butsch (2012)]. It consists of two closely-spaced ultra-thin nanowebs, suspended in a capillary, that act as optically coupled planar waveguides, supporting eigenmodes with symmetric and anti-symmetric transverse field distributions. Optical gradient forces deflect the mechanically compliant nanowebs and cause an increase in modal refractive index with launched optical power [Butsch (2012a)]. This optomechanical nonlinearity is strongly enhanced when the fundamental flexural resonance of the nanowebs is driven. Simulations show that the frequencies of upper and lower nanoweb are slightly different due to structural asymmetry.

(a) Scanning electron micrograph of dual-nanoweb waveguide region. The ~22 µm-wide nanowebs are ~440 nm thick and spaced by ~550 nm. (b) Normalised transverse field distribution of TE-polarised fundamental optical mode, simulated for a wavelength of 1.55 µm. (c)-(d) Simulated normalised deflection profiles of fundamental flexural resonance in (c) upper and (d) lower nanoweb.

Self-oscillation at mW powers

An evacuated dual-nanoweb fibre was to observed self-oscillate when the launched power of single-frequency light at 1.55 µm exceeded several mW. Simultaneously a frequency comb spaced by 5.611 MHz, the self-oscillation frequency, appeared in the transmitted optical spectrum. The underlying mechanism turns out to be stimulated Raman-like scattering (SRLS) by the flexural resonance in one nanoweb, initiated by thermal phonons and providing unprecedentedly high gain (of the order ~105 W‑1m‑1). The nanoweb vibration mediating SRLS is almost entirely transverse, so that, close to flexural cut-off, the phonon wavevector can be freely chosen while keeping the frequency fixed. We studied this effect using a novel interferometric scanning technique to probe nanoweb vibrations at high spatial resolution from the side of the fibre, perpendicularly to its axis. After these highly detailed experimental measurements, an extensive theory showed that self-oscillation is the result of stimulated intermodal scattering (SIMS) unbalancing SRLS gain suppression [Koehler (2016)]. This novel mechanism allows the design of single-pass optomechanical resonators requiring only a few mW pump power, without electronics or any optical resonator. The design could also be implemented in silicon or any other suitable material.

(a) Optical frequency comb with 5.611 MHz line spacing (red line), centred at pump, generated by self-oscillation for 22 mW launched power (insets: optical field distributions, blue dots/green squares: calculated modal component powers). (b) Phase-modulation and peak deflection for self-oscillating nanowebs probed from the side along the fibre (red/blue lines: calculated contributions of SRLS/forward SIMS). (c) Spatial and spectral map of flexural vibrations close to the SRLS frequency for 18 mW launched dual-frequency power (below threshold). (d)-(e) Dispersion scheme of combined SIMS and SRLS for zero frequency detuning. (d) Frustration of SRLS gain suppression by SIMS, (e) cascaded SRLS and self-oscillation by interplay with SIMS.

Squeezed-film damping in dual-nanoweb fibre

We have explored the frequency response of the optomechanical nonlinearity for different gas pressures, finding that the gas, trapped in the gap between the oscillating nanowebs, contributes "squeezed-film" damping involving both viscous damping and a significant increase in mechanical stiffness [Koehler (2013)]. As a consequence of the unusually narrow slot between the nanowebs (22 µm by 550 nm), the gas-spring effect causes a pressure-dependent frequency shift that is some 15 times larger than typically measured in micro-electro-mechanical devices. In vacuum the quality factor of the mechanical nanoweb resonance (at ~6 MHz) reaches values of several thousand. When the structure was driven using an intensity-modulated laser beam, the optomechanical nonlinearity at resonance exceeded the Kerr-related nonlinearity by a factor of ~60,000. Moreover, we obtained very good quantitative agreement between experimental data and a free-molecular “energy transfer model”. 

(a) SEM of the dual-nanoweb fibre cross-section. (b) Fundamental optical and (c) mechanical eigenmodes of the structure. (d) Measured frequency (red dots) and Q-factor (black squares) of the flexural resonance as function of pressure inside the fibre, fitted to the theoretical predictions of the gas-spring model (red curve) and the energy transfer model (black curve).