Phase matching is necessary for exploitation of nonlinear optical phenomena.
Phase matching of diverse electromagnetic modes (specifically, coexisting optical and microwave modes) in a whispering-gallery-mode (WGM) resonator has been predicted theoretically and verified experimentally. Such phase matching is necessary for storage of microwave/terahertz and optical electromagnetic energy in the same resonator, as needed for exploitation of nonlinear optical phenomena.
WGM resonators are used in research on nonlinear optical phenomena at low optical intensities and as a basis for design and fabrication of novel optical devices. Examples of nonlinear optical phenomena recently demonstrated in WGM resonators include low-threshold Raman lasing, optomechanical oscillations, frequency doubling, and hyperparametric oscillations.
The present findings regarding phase matching were made in research on low-threshold, strongly nondegenerate parametric oscillations in lithium niobate WGM resonators. The principle of operation of such an oscillator is rooted in two previously observed phenomena: (1) stimulated Raman scattering by polaritons in lithium niobate and (2) phase matching of nonlinear optical processes via geometrical confinement of light. The oscillator is partly similar to terahertz oscillators based on lithium niobate crystals, the key difference being that a novel geometrical configuration of this oscillator supports oscillation in the continuouswave regime. The high resonance quality factors (Q values) typical of WGM resonators make it possible to achieve oscillation at a threshold signal level much lower than that in a non-WGM-resonator lithium niobate crystal.
The applicable theory states that the parametric interaction takes place in a WGM resonator if the photon-energy-conservation law and the phase-matching condition are satisfied. The photon-energy-conservation law can be stated simply as ωp = ωs + ωi, where ω is proportional to the frequency or energy of the photon denoted by its subscript and p, s, and i denote the pump, signal, and idler frequencies, respectively. The phase-matching condition is satisfied if the volume integral of the product of the complex amplitudes of the pump, signal, and idler electromagnetic fields differs from zero.
In the general case, phase matching of an optical field with a microwave field cannot be achieved in a WGM resonator because the indices of refraction of the bulk resonator material are different in the optical and microwave frequency ranges. However, the theory also shows that it is possible to tailor the spatial structures of the WGM modes, so as to obtain phase matching of fields at resonance frequencies that satisfy the photon-energy-conservation law, through appropriate tailoring of the size and shape of the WGM resonator. This is equivalent to matching of effective indices of refraction for the pump, signal, and idler fields.
Evidence that phase matching can be achieved through suitable choice of size and shape was obtained in experiments on an apparatus depicted schematically in the figure. In each experiment, laser light centered at a wavelength of ≈1,319 nm or ≈1,559 nm was sent through a polarization controller, a grating-index-of-refraction (GRIN) lens, and a diamond prism into a lithium niobate WGM resonator, and light was coupled out of the WGM resonator through the diamond prism, another GRIN lens, and optical fibers to a photodiode and an optical spectral analyzer. In one experiment, the spectrum of light coming out of the WGM resonator was found to include side-bands associated with strongly nondegenerate parametric oscillations that had been predicted theoretically. In other experiments, oscillations with, variously, confined or unconfined idler fields were observed.
This work was done by Anatoliy Savchenkov, Dmitry Strekalov, Nan Yu, Andrey Matsko, Makan Mohageg, and Lute Maleki of Caltech for NASA’s Jet Propulsion Laboratory.
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