Low-Threshold Optical Parametric Oscillations in a Whispering Gallery Mode Resonator

In whispering gallery mode (WGM) resonator light is guided by continuous total internal reflection along a curved surface. Fabricating such resonators from an optically nonlinear material one takes advantage of their exceptionally high quality factors and small mode volumes to achieve extremely efficient optical frequency conversion. Our analysis of the phase-matching conditions for optical parametric down-conversion (PDC) in a spherical WGM resonator shows their direct relation to the sum rules for photons’ angular momenta and predicts a very low parametric oscillation threshold. We realized such an optical parametric oscillator (OPO) based on naturally phase-matched PDC in lithium niobate. We demonstrated a single-mode, strongly nondegenerate OPO with a threshold of $6.7\mu \mathrm{W}$ and linewidth under 10 MHz. This work demonstrates the remarkable capabilities of WGM-based OPOs.

Figure 1

(a) The radial overlap factor for the pump WGM nearest to the surface ($q_p=1$) and various signal and idler WGMs. (b) The intensity distribution inside a WGM resonator for various mode numbers $\ell ,m,q$. (c) The normalized angular overlap factor for an equatorial pump WGM and various signal and idler WGMs.

Figure 2

Experimental setup for PDC.

Figure 3

WGM resonances at 532 and 1064 nm wavelengths.

Figure 4

PDC and pump output versus pump frequency detuning.

Figure 5

The measurement and theoretical fit for the resonant OPO output versus in-coupled pump for a critically (inset) and weakly coupled resonator.

Figure 6

Optical spectrum of the parametric light: two different mode pairs ($A$ and $B$) are excited under different conditions. Inset: A zoom on one spectral component proves single-mode operation (solid and dashed lines represent different conditions).