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Journal of the Optical Society of America B

Quantum theory of multiwave mixing IV Effects of cavities on the spectrum of resonance fluorescence

David A. Holm, Stig Stenholm, M. Sargent

Published Sep 1, 1985• 30 citations
Publisher

Abstract

In the presence of a high-finesse cavity, the resonance fluorescence spectrum can be altered by stimulated emission and multiwave mixing processes. We show that under some conditions it is possible for spontaneous emission to induce conjugate fields similar to semiclassical phase conjugation, requiring the use of the multiwave quantum theory described in earlier papers in this series. The theory is applicable to laser spectroscopy and optical bistability. We present explicit spectra and suggest possible experimental tests. In particular we find a quantum limit for FM spectroscopy that shows that even if the medium under study leaves the FM phase and amplitude relationships intact according to semiclassical theory, spontaneous emission can create an AM component detectable in a square-law detector.

DOI
10.1364/josab.2.001456

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In the presence of a high-finesse cavity, the resonance fluorescence spectrum can be altered by stimulated emission and multiwave mixing processes. We show that under some conditions it is possible for spontaneous emission to induce conjugate fields similar to semiclassical phase conjugation, requiring the use of the multiwave quantum theory described in earlier papers in this series. The theory is applicable to laser spectroscopy and optical bistability. We present explicit spectra and suggest possible experimental tests. In particular we find a quantum limit for FM spectroscopy that shows that even if the medium under study leaves the FM phase and amplitude relationships intact according to semiclassical theory, spontaneous emission can create an AM component detectable in a square-law detector.
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Due to improvements in detector sensitivity, quantum noise is known to be the limiting factor of many lasers and other optical devices. In this work we present a fully quantum mechanical theory of multiwave mixing to study the effects of spontaneous emission noise on three- and four- wave mixing. The foundations of this theory have been presented in a series of papers1-3 demonstrating how such diverse topics as resonance fluorescence, saturation spectroscopy, phase conjugation, and squeezed states of light share a common origin.
Over the past three years we have developed a quantum theory of multiwave mixing designed to determine effects of quantum noise on laser and optical bistability instabilities, pump/probe saturation spectroscopy, AM and FM modulation spectroscopy, and phase conjugation. The theory treats a classical pump field and one or two quantum-mechanical sidemode fields interacting with one- or two-photon, two-level media. The theory1 produces a master equation for the reduced sidemode density operator able to describe all of the above phenomena in a uniform way closely related to the corresponding semiclassical theories. It has led to a number of significant predictions about the effects of spontaneous emission on laser spectroscopy and optical instabilities.
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We extend the quantum theory of multiwave mixing developed in previous papers in this series to include side-mode saturation. Specifically, the earlier papers calculate the absorption and resonance-fluorescence coefficients to second order in the weak-field interaction for an arbitrarily intense pump field. This paper extends those calculations to fourth order in the weak-field interaction. We find significant differences in the amplified resonance fluorescence spectra given by the second- and fourth-order treatments, particularly as the side mode approaches the laser threshold. In particular, while the second-order spectra diverge at this threshold, the fourth-order spectra remain finite. Although fourth- and higher-order theories are very desirable for applications to larger fields and optical instabilities, the present analysis reveals that their calculation is very complex. This fact poses an important limitation to the generalization of the theory to still higher-order accuracies.
We present a theory that describes how one strong classical wave and one or two weak quantum-mechanical waves interact in a nonlinear two-level medium. The analysis is applicable to several popular problems with and without cavities. In particular, the theory treats laser and optical bistability instabilities, predicting when the instabilities grow from spontaneous emission. The theory is a multimode extension of Scully-Lamb theory that derives the equations that describe population pulsations, combination tones, mode locking, resonance fluorescence, Rayleigh scattering, and phase conjugation with quantum-mechanical fields. Hence the theory both presents new results on instabilities and phase conjugation, and also unifies the treatment of a variety of phenomena in the context of Lamb theory. The present paper (first of the series) presents the basic formalism, leaving most applications to subsequent papers in this series. The following paper presents equivalent derivations based on a purely operator formalism.