Ultralow Raman lasing threshold and enhanced gain of whispering gallery modes in silica microspheres

摘要

Remarkable demonstrations of a cavity-induced giant reduction of the Raman lasing threshold in silicanmicrospheres have been reported in Spillane et al. [Nature (London) 415, 621 (2002)], yet a complete quantumnelectrodynamics (QED) treatment of this process including the rigorous expressions for the electromagneticnmodes of the sphere is lacking. In this paper, we employ a cavity QED approach to describe Raman lasingnin microscopic spherical dielectric resonators with third-order nonlinearity to derive explicit expressions fornthe Raman gain and lasing threshold in terms of mode-overlapping coefficients determined from full analyticnexpressions of the electromagnetic eigenmodes of a dielectric sphere. We present dependencies of the Ramannlasing threshold on the the order n of overlapping whispering gallery modes for microspheres with diameternin the range 20–35 μm, demonstrating ultralow thresholds of between 70 and 90 μW, consistent with recentnexperimental results. We explain the reduction of the lasing threshold as due to an increase in the overlappingncoefficients as the mode order is increased toward the regime where the modal energy is mostly confined to thensurface region of the resonator. The presented theory can be easily generalized to any microcavity of regularnmorphology and for any combination of interacting whispering gallery modes.