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Physical Review A

Theory of stimulated emission processes in spherical microparticles

Gershon Kurizki, Abraham Nitzan

Published Jul 1, 1988• 19 citations
Publisher

Abstract

A semiclassical theory of stimulated processes in dielectric spherical particles is formulated. The theory applies to the small-signal regime and to isotropic (but radially nonuniform) pumping. Iterative treatment of the pumped-medium susceptibility by scattering theory demonstrates the basic features observed experimentally by Chang and co-workers [H. M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 499 (1984); S. X. Qian and R. K. Chang, Phys. Rev. Lett. 56, 926 (1986)], namely, the drastic reduction of the threshold for lasing and multiorder stimulated Raman processes, and the frequency pulling from Mie resonances of the inactive medium.

DOI
10.1103/physreva.38.267

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Stimulated resonance Raman scattering (review)

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An analysis is made of some features of spontaneous resonance Raman scattering representing a noise signal which is amplified by a strong field in a nonlinear medium. A detailed review is made of the experimental results obtained in investigations of the spectra of stimulated preresonance and resonance Raman scattering in nonlasing and lasing systems. It is shown that, depending on the experimental conditions, these spectra may be due to transitions between vibrational levels of molecules which are in the ground or first excited electronic states. The example of several compounds is used to demonstrate the information which can be derived from such spectra. Possible practical applications of studies of such spectra are indicated. The physical basis of the theory of stimulated resonance Raman scattering is discussed and conclusions are drawn on the nature and mechanism of this Raman effect.

Soviet Journal of Quantum Electronics•Mar 31, 1977•6 citations
A semiclassical theory of stimulated processes in dielectric spherical particles is formulated. The theory applies to the small-signal regime and to isotropic (but radially nonuniform) pumping. Iterative treatment of the pumped-medium susceptibility by scattering theory demonstrates the basic features observed experimentally by Chang and co-workers [H. M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 499 (1984); S. X. Qian and R. K. Chang, Phys. Rev. Lett. 56, 926 (1986)], namely, the drastic reduction of the threshold for lasing and multiorder stimulated Raman processes, and the frequency pulling from Mie resonances of the inactive medium.
Nonlinear optical processes in spherical microdroplets whose studies have been pioneered by Chang and co-workers are intriguing from the point of view of applications because of the extremely low thresholds they exhibit for the generation of stimulated output, but also from the theoretical point of view, because they require a synthesis between the methods of nonlinear optics and Mie scattering theory. The basis for such a synthesis has been given in the semiclassical theory of Kurizki and Nitzan, which implies that the nonlinearly amplified component of the scattered field is spatially orthogonal ('out of phase') with the linearly scattered field component (the ordinary Mie solution). This approach allows the calculation of amplification coefficients in various nonlinear processes, as a function of the Mie resonant denominators and spatial overlap of the input and output spherical waves. Recently, this approach has been extended to quantized solutions for parametric amplification and oscillation via four-wave mixing in microdroplets. The very low thresholds for oscillation at Mie resonances are predicted to correspond to strong squeezing, i.e., suppression of the photocurrent noise associated with the detection of the output waves below the noise level associated with an ideal laser. Even well below threshold, the spatially orthogonal output waves allow for strong squeezing at periodically recurring distances from the droplet.
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.
The nonlinear theory of stimulated Raman scattering of high-energy long laser pulses in two-level media is constructed and provides a unified global interpretation of the experiments of Dr\"uhl, Wenzel, and Carlsten [Phys. Rev. Lett. 51, 1171 (1983)]. It is proved that the model, resulting from the slowly varying envelope approximation and including phase mismatch and detuning from Raman resonance, is integrable by the spectral transform method for arbitrary boundary values. The essential variable in the theory is the phase of the Stokes pulse relative to the pump. For long duration input pump pulses and when pump and Stokes pulses experience a rapid \ensuremath{\pi} phase shift, an anomalous spike of pump radiation is created in the pump depletion zone. It is shown in particular that the decay of Raman spikes is related to the velocity of this \ensuremath{\pi} phase shift. For fast flips, the possibility of observing spike overflow is established and, with multiple phase flips, a multiple-spike phenomenon is produced, suggesting new experiments. Lastly, the number of optical phonons participating to the interaction is explicitly calculated.
In the first part of this thesis, a detailed analysis of lasing in random multiple-light-scattering media with gain is presented. Random laser emission is analyzed using a time-dependent diffusion model for light propagating in the medium containing active atoms. We demonstrate the effects of scatterers to narrow the emission spectral linewidth and to shorten the emitted pulse duration at a specific threshold pump intensity. This threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results. The coherence properties of the random laser are studied using a generalized master equation. The random laser medium is treated as a collection of low quality-factor cavities, coupled by random photon diffusion. Laser-like coherence, on average, is demonstrated above a specific pumping threshold. We demonstrate that with stronger scattering, the pumping threshold for the transition from chaotic to isotropic coherent light emission decreases and enhanced optical coherence for the emitted light is achieved above threshold. The second part of this thesis presents a study of lasing in photonic crystals (PCs). The emission from an incoherently pumped atomic system in interaction with the electro-magnetic reservoir of a PC is analyzed using a set of generalized semiclassical Maxwell-Bloch equations. We demonstrate that the photonic band edge facilitates the enhancement of stimulated emission and the reduction of internal losses, leading to an important lowering of the laser threshold. In addition, an increase of the laser output at a photonic band edge is demonstrated. We next develop a detailed quantum theory of a coherently pumped two-level atom in a photonic band gap material, coupled to both a multi-mode wave-guide channel and a high-quality micro-cavity embedded within the PC. The cavity field characteristics are highly distinct from that of a corresponding high-Q cavity in ordinary vacuum. We demonstrate enhanced, inversionless, and nearly coherent light generation when the photon density of states (DOS) jump between the Mollow spectral components of atomic resonance fluorescence is large. In the case of a vanishing photon DOS on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian and the cavity field exhibits quadrature coherence.
An analysis is made of some features of spontaneous resonance Raman scattering representing a noise signal which is amplified by a strong field in a nonlinear medium. A detailed review is made of the experimental results obtained in investigations of the spectra of stimulated preresonance and resonance Raman scattering in nonlasing and lasing systems. It is shown that, depending on the experimental conditions, these spectra may be due to transitions between vibrational levels of molecules which are in the ground or first excited electronic states. The example of several compounds is used to demonstrate the information which can be derived from such spectra. Possible practical applications of studies of such spectra are indicated. The physical basis of the theory of stimulated resonance Raman scattering is discussed and conclusions are drawn on the nature and mechanism of this Raman effect.