Coupling of light into and out of whispering- gallery-mode (WGM) optical resonators can be enhanced by designing and fabricating the resonators to have certain non- axisymmetric shapes (see figure). Such WGM resonators also exhibit the same ultrahigh values of the resonance quality factor (Q) as do prior WGM resonators. These WGM resonators are potentially useful as tunable narrow-band optical filters having throughput levels near unity, high-speed optical switches, and low-threshold laser resonators. These WGM resonators could also be used in experiments to investigate coupling between high-Q and chaotic modes within the resonators.
For a WGM resonator made of an optically nonlinear material (e.g., lithium niobate) or another material having a high index of refraction, a prism made of a material having a higher index of refraction (e.g., diamond) must be used as part of the coupling optics. For coupling of a beam of light into (or out of) the high-Q resonator modes, the beam must be made to approach (or recede from) the resonator at a critical angle determined by the indices of refraction of the resonator and prism materials. In the case of a lithium niobate/diamond interface, this angle is approximately 22°.
For a beam of laser light traveling through the prism and having a typical axisymmetric cross-sectional power density that varies as a Gaussian function of radius from its cylindrical axis, the cross section of the phase front changes from circular to elliptical at the interface. In the case of the lithium niobate/diamond interface, the ratio between the lengths of the semimajor and semiminor axes of the ellipse is about 2.7. In order to optimize the coupling of the beam into the high-Q modes of the resonator, the ratio between the horizontal and vertical curvatures of the resonator must be made to equal the aforesaid material-dependent ratio between the lengths of the axes of the ellipse. (Here, "vertical" and "horizontal" refer to planes onto which are projected the narrowest and widest views, respectively, of the resonator, as in the figure.) It is difficult to fabricate a WGM resonator surface to such an exacting specification at a specific point on its surface, but the task can be simplified as described next if one does not insist on a specific location.
If the WGM resonator is shaped to have a constant radius of curvature at its periphery as seen in a vertical plane but is asymmetrical (or at least non-axisymmetric) in a horizontal plane (for example, if its shape in a horizontal plane is elliptical), then its horizontal radius of curvature and the ratio between the two curvatures varies continuously with position along the periphery. Consequently, by suitable choice of the shape, it is possible to make the ratio between these curvatures equal the desired material-dependent ratio at some location along the periphery.
Several working prototype WGM resonators have been designed and fabricated according to this concept. In tests, these resonators exhibited Q values of about 108 and coupling efficiencies >0.7.
This work was done by Makan Mohageg and Lute Maleki of Caltech for NASA's Jet Propulsion Laboratory.
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