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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

High gain selective amplification in whispering gallery mode resonators: analysis by cavity ring down method

Patrice Féron, Alphonse Rasoloniaina, Vincent Huet, Élodie Le Cren, Stéphane Trebaol, Gualtiero Nunzi Conti, Hélène Serier‐Brault, Michel Mortier, Yannick Dumeige

Published Mar 12, 2013• 0 citations
Publisher

Abstract

We study both theoretically and experimentally the dispersive properties of single whispering gallery mode resonators. We present a simple experimental protocol which allows us to obtain in detail its coupling regime and thus their dispersive properties. We demonstrate a compact optical amplifier with a gain up to 20dB in an Erbium doped fluoride microsphere of 135μm in diameter coupled via a tapered fiber. The model is also applied to analyze the dynamic behavior of the modal coupling between two degenerate resonances of the same cavity. In particular, this can be used to describe the coupling of counterpropagating whispering gallery modes (WGM) by Rayleigh scattering. The theory is successfully compared to experiments carried out in silica microspheres

DOI
10.1117/12.2002821

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We study both theoretically and experimentally the dispersive properties of single whispering gallery mode resonators. We present a simple experimental protocol which allows us to obtain in detail its coupling regime and thus their dispersive properties. We demonstrate a compact optical amplifier with a gain up to 20dB in an Erbium doped fluoride microsphere of 135μm in diameter coupled via a tapered fiber. The model is also applied to analyze the dynamic behavior of the modal coupling between two degenerate resonances of the same cavity. In particular, this can be used to describe the coupling of counterpropagating whispering gallery modes (WGM) by Rayleigh scattering. The theory is successfully compared to experiments carried out in silica microspheres
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Summary form only given, as follows: The high Q whispering gallery modes of silica microspheres are promising for quantum optics and nonlinear optics experiments involving atoms and photons stored in very small volumes. We have developed the technology of these resonators, learning how to couple light in and out through optical fibers, how to obtain and measure record Q factors, and how to probe, by near-field optical microscopy, the electric field distribution immediately outside the sphere. Whispering gallery mode lasers have also been obtained with microspheres made of silica doped with neodymium ions. We describe these experiments and discuss projects involving the coupling of whispering gallery modes to single atoms or ions to perform cavity QED experiments in the optical domain.
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.
Silica microspheres behave as efficient optical microresonators when small-volume whispering-gallery modes (WGMs) are used. We have realized a cryogenic set-up to work with microspheres immersed in a superfluid helium bath. Quality factors up to 109 have been obtained at 2 K. In this environment, we have been able to observe a dispersive bistable behavior of the WGM resonances, due to the weak intrinsic Kerr optical nonlinearity of silica, with a threshold power of 10 (mu) W only. This result opens the way to the realization of thresholdless microlaser, based on a rare-earth doped silica microsphere and to other Cavity-QED projects with microspheres at low temperatures.
Silica microspheres have been demonstrated to provide a permanent resonator which combines small mode volumes with the highest observed quality factors (Q>2.10/sup 9/) corresponding to photon storage times of the order of one microsecond. These properties have allowed us to make a very low-threshold laser with Nd-doped silica microspheres (200 nW absorbed pump power, i.e. 10/sup 6/ excited ions/mode). These microlasers are now operated at 2 K to benefit from a smaller homogeneous linewidth. We then expect to reach the "thresholdless" regime with only a few excited ions. These experiments can also be considered as a first step toward Cavity QED experiments in the strong coupling regime with single atoms or molecules coupled to a whispering gallery mode.
The optical ring-down time in a silica microsphere resonator is measured using phase-shift cavity ring-down spectroscopy. When detecting Rayleigh backscattered light that is coupled into the input waveguide it is found that the shift of the modulation phase angle, $\ensuremath{\Delta}\ensuremath{\phi}$, is approximately linearly dependent on the amplitude modulation frequency. The microresonator therefore behaves as if it was a delay line. A model involving two different time scales for the buildup of the Rayleigh backscattered light and the decay of the whispering gallery modes is used to explain the observations.