Nonlinear optics in spheres: from second harmonic scattering to quasi‐phase matched generation in whispering gallery modes

Abstract

Over the last fifteen years, a series of theoretical and experimental investigations have demonstrated the usefulness of circular geometries to tailor second-order nonlinear optical effects. However, until recently, such effects have remained rather weak, calling for their enhancement. In parallel, developments in the field of high quality factor spherical or ring resonators have shown that many different types of light-matter interactions can be dramatically amplified when light is coupled in the whispering gallery modes of such resonators. In high-quality spherical micro-resonators, close to one million interactions can occur between a nonlinear molecule and a circulating light pulse. Recent research on nonlinear optics in spherical geometry is reviewed, from micrometer-size spheres to whispering gallery mode resonators.

Optical Frequency Conversion in Silica-Whispering-Gallery-Mode Microspherical Resonators

“…The pump mode is the first order mode at 1567 nm (n p ¼ 1, l p ¼ 159, m p ¼ 150), and the THG mode is the first order mode at 522 nm (n THG ¼ 1, l THG ¼ 497, m THG ¼ 450). This case satisfies the quantum rules for angular momentum composition [2] and represents a perfect phase match, since the coherence length of a WGM resonance for THG is infinite for m THG ¼ 3m p ðl coh ¼ πR=jm THG − 3m p jÞ, and it has the largest angular overlap (l THG ∼ 3l p ) [17].…”

“…We analyze, experimentally and theoretically, a variety of χ ð3Þ nonlinear interactions in silica microspheres, consisting of third harmonic generation and Raman assisted third order sum-frequency generation in the visible. A tunable, room temperature, cw multicolor emission in silica microspherical whispering-gallery-mode microresonators has been achieved by controlling the cavity mode dispersion and exciting nonequatorial modes for efficient frequency conversion.Whispering-gallery-mode resonators (WGMR) play an extremely important role in modern optics, being fundamental not only in many laser devices, but also as tools for very accurate frequency measurements and for nonlinear optics experiments as frequency conversion [1,2]. The extraordinary high quality factors, up to 10 11 , and the small volume modes make them an ideal device for shaping and enhancing light-matter interactions [3,4].…”

“…Whispering-gallery-mode resonators (WGMR) play an extremely important role in modern optics, being fundamental not only in many laser devices, but also as tools for very accurate frequency measurements and for nonlinear optics experiments as frequency conversion [1,2]. The extraordinary high quality factors, up to 10 11 , and the small volume modes make them an ideal device for shaping and enhancing light-matter interactions [3,4].…”

Three‐wave mixing in whispering gallery resonators

“…Comparing Eqs. (18), (25), (29), and (36), we see that the maximum conversion efficiency of three-wave mixing processes is…”

Nonlinear and Quantum Optics with Whispering Gallery Resonators

“…Analysis of nonlinear optical processes dynamics in phasematched WGM resonators has been reported for the SHG [107,213,256,317,335] and OPO [213,[253][254][255][256]336], as well as for the sum-frequency generation (SFG) [320,321,337,338] and difference-frequency generation (DFG) [339]. Usually this analysis is carried out in terms of coupled ODEs such as given by equation (25).…”