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Physical Review

Stimulated Emission into Optical Whispering Modes of Spheres

C. G. B. Garrett, W. Kaiser, Walter L. Bond

Published Dec 15, 1961• 317 citations
Publisher

Abstract

Stimulated emission into optical whispering modes of a spherical sample of Ca${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{++}$ has been observed. Light produced by the stimulated emission is radiated tangentially form each point on the surface of the sphere. The experimental results have been interpreted in terms of the electromagnetic analog of the Rayleigh theory of the whispering gallery.

DOI
10.1103/physrev.124.1807

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Stimulated emission into optical whispering modes of a spherical sample of CaF2{\mathrm{F}}_{2}F2​: Sm++{\mathrm{Sm}}^{++}Sm++ has been observed. Light produced by the stimulated emission is radiated tangentially form each point on the surface of the sphere. The experimental results have been interpreted in terms of the electromagnetic analog of the Rayleigh theory of the whispering gallery.
Optical behavior analogous to electromagnetically induced transparency and absorption is observed in experiments using coupled fused-silica microspheres. This behavior results from interference between coresonant whispering-gallery modes of the two spheres. Coupled-resonator-induced transparency and absorption are observed. Which effect is seen depends on the strength of coupling of incident light from a tapered fiber into the first sphere and on the strength of coupling between the two spheres. The observed effects can enhance microresonator performance in various applications.
Is it possible to form an image using light produced by stimulated emission? Here we study light scatter off an assembly of excited chromophores. Due to the Optical Theorem, stimulated emission is necessarily accompanied by excited state Rayleigh scattering. Both processes can be used to form images, though they have different dependencies on scattering direction, wavelength and chromophore configuration. Our results suggest several new approaches to optical imaging using fluorophore excited states.
Remarkable demonstrations of a cavity-induced giant reduction of the Raman lasing threshold in silica microspheres have been reported in Spillane et al. [Nature (London) 415, 621 (2002)], yet a complete quantum electrodynamics (QED) treatment of this process including the rigorous expressions for the electromagnetic modes of the sphere is lacking. In this paper, we employ a cavity QED approach to describe Raman lasing in microscopic spherical dielectric resonators with third-order nonlinearity to derive explicit expressions for the Raman gain and lasing threshold in terms of mode-overlapping coefficients determined from full analytic expressions of the electromagnetic eigenmodes of a dielectric sphere. We present dependencies of the Raman lasing threshold on the the order nnn of overlapping whispering gallery modes for microspheres with diameter in the range 20--35 $\ensuremath{\mu}$m, demonstrating ultralow thresholds of between 70 and 90 $\ensuremath{\mu}$W, consistent with recent experimental results. We explain the reduction of the lasing threshold as due to an increase in the overlapping coefficients as the mode order is increased toward the regime where the modal energy is mostly confined to the surface region of the resonator. The presented theory can be easily generalized to any microcavity of regular morphology and for any combination of interacting whispering gallery modes.
A third-order optical nonlinear effect in a spherical glass resonator doped with Sm(3+) ions has been observed on stimulated emission lines of the (4)G(5/2)-(6)H(7/2) transition, in which the excitation beam of an Ar(+) laser in a 488-nm single line is coupled with the glass resonator through a prism. A spherical form is produced during a free fall of fractional glasses in a longitudinal electric furnace configured vertically. The prism-coupled glass microsphere exhibits sufficient performance to confine photon energy as a resonance of light inside the sphere and offers the prospect of new applications to functional photonic circuits.