[Paper Review] Cavity optomechanical bistability with an ultrahigh reflectivity photonic crystal membrane

Feng Zhou, Yiliang Bao+2 more|arXiv (Cornell University)|Nov 18, 2022

Mechanical and Optical Resonators4 citations

TL;DR

This paper demonstrates a photonic crystal membrane with ultrahigh reflectivity (R = 0.999835) used as a mirror in a Fabry-Perot cavity, achieving a record finesse of F = 35,000(500). The system exhibits robust optomechanical bistability with hysteresis in cavity transmission at sub-milliwatt input powers, and strong dynamical backaction induces mechanical oscillations exceeding 1 MHz despite air damping, enabled by a high mechanical quality factor (Q = 1.1 × 10⁶) and low mass.

ABSTRACT

Photonic crystal (PhC) membranes patterned with sub-wavelength periods offer a unique combination of high reflectivity, low mass, and high mechanical quality factor. We demonstrate a PhC membrane that we use as one mirror of a Fabry-Perot cavity with finesse as high as $F=35,000(500)$, corresponding to a record high PhC reflectivity of $R=0.999835(6)$. The fundamental mechanical frequency is 426 kHz, more than twice the optical linewidth, placing it firmly in the resolved-sideband regime. The mechanical quality factor in vacuum is $Q=1.1(1) imes 10^6$, allowing us to achieve values of the single-photon cooperativity as high as ${\cal C}_0=6.6 imes10^{-3}$. We easily see optomechanical bistability as hysteresis in the cavity transmission. As the input power is raised well beyond the bistability threshold, dynamical backaction induces strong mechanical oscillation above 1~MHz, even in the presence of air damping. This platform will facilitate advances in optomechanics, precision sensing, and applications of optomechanically-induced bistability.

Motivation & Objective

• To develop a photonic crystal membrane with ultrahigh reflectivity for use in high-finesse optomechanical cavities.
• To achieve a record-high cavity finesse by optimizing the PhC geometry for 1550 nm operation.
• To demonstrate optomechanical bistability in a system with high mechanical quality factor and low mass.
• To explore the interplay between static bistability and dynamical backaction in a resolved-sideband regime.
• To enable future applications in quantum optomechanics, precision sensing, and all-optical nonlinear devices.

Proposed method

• Fabricated a 220 nm thick silicon nitride membrane with a hexagonal lattice of circular holes using electron-beam lithography and reactive ion etching.
• Optimized the PhC geometry using S⁴ software and Rigorous Coupled Wave Analysis (RCWA) to maximize reflectivity at 1550 nm.
• Integrated the PhC membrane as one mirror in a Fabry-Perot cavity, measuring finesse via transmission spectrum fitting and Lorentzian line shape analysis.
• Performed detuning sweeps of the input laser to observe hysteresis in cavity transmission, identifying the bistable regime.
• Measured mechanical response under varying input power, observing strong mechanical oscillations due to dynamical backaction.
• Calculated single-photon cooperativity (C₀ = 6.6 × 10⁻³) and mechanical quality factor (Q = 1.1 × 10⁶) in vacuum to assess quantum optomechanical potential.

Experimental results

Research questions

• RQ1 Can a photonic crystal membrane with a hexagonal hole lattice achieve reflectivity and finesse comparable to or exceeding state-of-the-art 1D high-contrast gratings in a 2D photonic crystal structure?
• RQ2 What is the maximum achievable finesse in a Fabry-Perot cavity using a mechanically compliant PhC membrane as a mirror?
• RQ3 How does the system exhibit optomechanical bistability at low optical input powers, and what role does radiation pressure play in inducing hysteresis?
• RQ4 To what extent does dynamical backaction induce mechanical oscillations above 1 MHz, even in air, and how does this affect the observation of static bistability?
• RQ5 What is the single-photon cooperativity of the system, and how does it compare to existing optomechanical platforms?

Key findings

• The photonic crystal membrane achieved a record-high reflectivity of R = 0.999835(6), corresponding to a cavity finesse of F = 35,000(500).
• The cavity finesse exhibited a Lorentzian dependence on wavelength, consistent with a global transmission spectrum shaped by the PhC's filtering and loss characteristics.
• The fundamental mechanical mode has a frequency of 426 kHz, exceeding the optical linewidth and placing the system firmly in the resolved-sideband regime.
• Optomechanical bistability was clearly observed as hysteresis in cavity transmission with input powers below 500 μW.
• Despite air damping, dynamical backaction induced strong mechanical oscillations with an optically-sprung frequency exceeding 1 MHz at input powers of 4 mW.
• The single-photon cooperativity was measured at C₀ = 6.6 × 10⁻³, significantly higher than typical values in similar systems (e.g., 10⁻⁷ to 10⁻⁴), indicating strong light-matter coupling.