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Quantum Electronics and Laser Science Conference

Morphology-dependent resonance at small size parameter

Robert Pastel, Allan Alexander Struthers, R. Ringle, Michael J. Renn

Published Jan 20, 2003• 0 citations
Publisher

Abstract

Summary form only given. Morphology-dependent resonances (MDR) have previously been observed in dye-doped microdroplets above size parameter 30. We report a novel laser trapping technique which allows manipulation of droplets as small as 50 nm radius, and observations of cavity quantum enhanced MDR between size parameter 10 to 30. Below size parameter 15, we observe an increase in MDR linewidth and corresponding decrease in peak intensity with decreasing size parameter.

DOI
10.1109/qels.1999.807518

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Summary form only given. Morphology-dependent resonances (MDR) have previously been observed in dye-doped microdroplets above size parameter 30. We report a novel laser trapping technique which allows manipulation of droplets as small as 50 nm radius, and observations of cavity quantum enhanced MDR between size parameter 10 to 30. Below size parameter 15, we observe an increase in MDR linewidth and corresponding decrease in peak intensity with decreasing size parameter.
Micrometer-sized transparent droplets act as natural high-Q cavities to visible light, and this paper shows them to exhibit strongly enhanced dye emission owing to cavity quantum-electrodynamic effects. A vibrating-orifice aerosol generator1 was used to produce a linear stream of virtually identical (less than 2 parts in 105 diameter variation) falling droplets 14 μm diameter, 10-5 M solution of Rhodamine 6G in ethanol; the droplets were excited by a cw argon-ion laser. Droplet emission was examined with a double 1 m Spex spectrograph and a photomultiplier. Recent development of elastic-scattering-size spectroscopy1,2 allowed identification of the various cavity modes contributing to the emission. This was necessary because of the different Q values and spatial properties of the resonant modes. Q values were calculated from Lorenz-Mie theory and were found to be consistent with observed fluorescence linewidths for the experimentally resolvable fourth-order modes. It was experimentally determined that Q's of only 103 were sufficient to observe sizable enhancements in the A coefficient. Lasing was observed to occur at reduced thresholds, e.g., 400 W/cm2 for fourth order modes having Q's of 2 × 103. This corresponds to a cavity induced enhancement in the B coefficient of 103.
Stimulated Brillouin scattering in a micrometer-sized liquid droplet is treated theoretically using recently developed techniques, with emphasis on the doubly resonant case, in which the frequencies of both the laser field and the scattered Brillouin field fall within a morphology-dependent resonance, leading to input and output enhancement. An important difference from a bulk medium is the replacement of the selection rules based on momentum conservation by those based on angular momentum conservation, with the latter most conveniently expressed through the spherical wave modes. Special attention is paid to the eigenvalue equation defining the gains and Brillouin shifts, in particular to the difference between small and large droplets. For large droplets, and for given angular momenta of the laser field and the scattered field, there is only one allowed shift with a positive gain. Numerical results for gain and threshold are shown for a droplet of size parameter about 30, and a simple approximate analytic formula for the gain is presented.
A significant limitation in the detection and spectroscopy of individual dye molecules in liquid room temperature samples is the loss of fluorescence signal through chromophore photobleaching. Although often considered a fundamental restriction on sensitivity, it has been shown that the probability per excitation cycle of photobleaching may be reduced by enhancing the spontaneous emission rate of the chromophore located inside a microdroplet, which acts as a optical cavity. Studies of glycerol microdroplets containing R6G dye molecules, and levitated in a three-dimensional electrodynamic trap, have demonstrated a significant enhancement of both the fluorescence decay rate [1] and the total fluorescence yield [2] of the chromophore. Modification of the emission rate is greatest for molecules located near the surface of small (< 10 μm) microdroplets, where the influence of the droplet cavity modes of the droplet is most significant. To exploit this surface sensitivity, surfactant forms of rhodamine dyes were recently studied [3]. Fluorescence emission of the dye molecules, constrained to the droplet surface and with fixed transition moments perpendicular to the surface normal, were shown to be significantly enhanced at small droplet sizes. Additionally, at larger droplet sizes corresponding to higher droplet Q’s, preferential emission into the cavity modes was observed, however the detection of fluorescence photons was delayed by the storage time of the cavity, which may be on the same order as the fluorescence lifetime. These measurements, performed on relatively concentrated dye solutions, suggest that microcavity effects may be exploited to greatly enhance single molecule detection sensitivity in glycerol microdroplets. Furthermore, the large cavity storage time of the high-Q droplets opens the possibility for re-excitation of the molecule following emission into the droplet resonance, and subsequent stimulated emission, that is, single-molecule lasing.
Measurements of the integrated fluorescence yield per molecule of Rhodamine 6G (R6G) in 4–16-μm-diameter levitated microdroplets show a size dependence that is attributed to a net increase in the fluorescence decay rate for the smaller (4–5-μm) droplets. The average fluorescence yield in 4-μm droplets (for which we have previously observed emission-rate enhancement) is approximately a factor of 2 larger than the yield measured for larger droplets for which emission-rate enhancement does not occur. These results suggest that there is little emission-rate inhibition in this system, even though the fluorescence emission spectrum overlaps several cavity resonances. A mechanism based on spectral diffusion is postulated for the apparent absence of cavity-inhibited emission and is illustrated by Monte Carlo calculations using time-dependent line-shape functions.