Optomechanical Coupling in a Two-Dimensional Photonic Crystal Defect Cavity

Periodically structured materials can sustain both optical and mechanical modes. Here we investigate and observe experimentally the optomechanical properties of a conventional two-dimensional suspended photonic crystal defect cavity with a mode volume of $\sim 3(\lambda /n{)}^3$. Two families of mechanical modes are observed: flexural modes, associated to the motion of the whole suspended membrane, and localized modes with frequencies in the GHz regime corresponding to localized phonons in the optical defect cavity of diffraction-limited size. We demonstrate direct measurements of the optomechanical vacuum coupling rate using a frequency calibration technique. The highest measured values exceed 80 kHz, demonstrating high coupling of optical and mechanical modes in such structures.

Figure 1

(a) Scanning electron microscope side view of the cavity. (b) Microphotoluminescence spectrum of the photonic crystal slab cavity obtained under nonresonant continuous optical excitation at normal incidence with an excitation power of $100\mu \mathrm{W}$ at 532 nm (c) Micrograph (false colors) of a defect cavity-fiber taper system used to read out mechanical motion of the cavity. (d) Experimental setup (ECDL: External-cavity diode laser, OI: optical isolator, EOM: electro-optical modulator, FPC: fiber polarization controller, PhC: photonic crystal defect cavity, PD: photodiode).

Figure 2

(a) Detected frequency noise spectrum in the 1 MHz–200 MHz range presenting a series of peaks corresponding to the different mechanical modes labeled by numbers (Black curve). The red curve represents a spectrum acquired with the laser being detuned out of resonance. Inset: Calibrated frequency noise spectrum of the fundamental mode (#1) with a Lorentzian fit (red line). (b) Spatial displacement patterns of exemplary six mechanical modes, as obtained from finite element modeling.

Figure 3

(a) Detected frequency noise spectrum in the 200 MHz–1.2 GHz range presenting a series of peaks corresponding to the different mechanical modes with the localized modes labeled by numbers (Black curve). The mode on the left of the first order localized mode could not be identified through simulations. The red curve represents a spectrum acquired with the laser being detuned out of resonance. CP denotes the calibration peak resulting from the frequency modulation measurement. Inset: Measured versus simulated frequency for mechanical modes which could be accurately identified (#1–19). (b) Spatial displacement pattern for the first four orders of localized mechanical modes, as obtained from finite element modeling. (c) Simulated (blue) and experimentally determined (red) progression of the resonance frequency of the localized modes versus mode number (mode #19 was determined in a separate measurement).

Figure 4

(a) Simulated distribution of the electromagnetic field (left), scanning electron microscope image of the defect (middle) and simulated third order localized mechanical mode (right). (b) Calibrated frequency noise spectrum of the third order localized mechanical mode #18 (blue points) with a Lorentzian fit (red line). A vacuum optomechanical rate of $g_0/2\pi =84\mathrm{kHz}$ is determined.