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Optics Letters

Quantum theory of laser and optical-bistability instabilities

M. Sargent, F. De Martini, Muhammad Suhail Zubairy

Published Feb 1, 1983• 21 citations
Publisher

Abstract

We present the first reported fully quantum-mechanical theory of laser/optical-bistability instabilities that shows how cavity side modes grow from spontaneous emission. Because of three-wave mixing, a two-peaked spontaneous-emission spectrum is obtained in contrast to the three-peaked spectrum of resonance fluorescence. The theory is a multimode extension of Scully-Lamb theory that shows how population pulsations, combination tones, mode locking, and phase conjugation occur with quantum-mechanical fields.

DOI
10.1364/ol.8.000076

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This dissertation formulates and applies a theory describing how one or two strong classical waves and one or two weak quantum mechanical waves interact in a two-level medium. The theory unifies many topics in quantum optics, such as resonance fluorescence, saturation spectroscopy, modulation spectroscopy, the build up of laser and optical bistability instabilities, and phase conjugation. The theory is based on a quantum population pulsation approach that resembles the semiclassical theories, but is substantially more detailed. Calculations are performed to include the effects of inhomogeneous broadening, spatial hole burning, and Gaussian transverse variations. The resonance fluorescence spectrum in a high finesse optical cavity is analyzed in detail, demonstrating how stimulated emission and multiwave processes alter the spectrum from the usual three peaks. The effects of quantum noise during the propagation of weak signal and conjugate fields in phase conjugation and modulation spectroscopy are studied. Our analysis demonstrates that quantum noise affects not only the intensities of the signal and conjugate, but also their relative phase, and in particular we determine a quantum limit to the semiclassical theory of FM modulation spectroscopy. Finally, we derive the corresponding theory for the two-photon, two-level medium. This yields the first calculation of the two-photon resonance fluorescence spectrum. Because of the greater number of possible interactions in the two-photon two-level model, the theoretical formalism is considerably more complex, and many effects arise that are absent in the one-photon problem. We discuss the role of the Stark shifts on the emission spectrum and show how the Rayleigh scattering is markedly different.

•Jan 1, 1985•0 citations
We present the first reported fully quantum-mechanical theory of laser/optical-bistability instabilities that shows how cavity side modes grow from spontaneous emission. Because of three-wave mixing, a two-peaked spontaneous-emission spectrum is obtained in contrast to the three-peaked spectrum of resonance fluorescence. The theory is a multimode extension of Scully-Lamb theory that shows how population pulsations, combination tones, mode locking, and phase conjugation occur with quantum-mechanical fields.
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.
In a recent paper1, a quantum theory of multiwave interactions with a two-level medium is presented. In this paper we apply this theory to sidemode instabilities pertinent to cavity con figurations in optical bistability and ring lasers. We assume the cavity to oscillate on a single mode, and we evaluate the gain and spontaneous emission at other frequencies. Because of the saturating presence of the strong, laser mode, two symmetrically situated sidemodes can grow together, inducing populations pulsations that influence the other sidemode. The instability must therefore be treated as a double sidemode problem.
Given one oscillating mode in a laser or an optical bistability cavity, can other modes build up, that is, is single-mode operation unstable? The answer depends on an interplay of spontaneous emission, saturated gain, and four-wave mixing processes that permit one or more sidemodes both to be resonant with cavity modes and to have more gain than loss. We discuss this problem for cavities containing one- or two-photon two-level media subjected to a classical wave of arbitrary intensity and one or two weak quantized sidemodes. While a single sidemode may have gain, two sidemodes symmetrically placed about a strong pump mode can have greater gain due to four-wave mixing contributions sometimes called combination tones. The theory is valid for the buildup of sidemodes from quantum noise until the sidemodes begin to saturate. Subsequent dynamics including chaos must be handled by a theory that allows all modes to saturate. The same physical mechanisms are important in saturation spectroscopy and control the generation of squeezed states in a cavity. However while the instabilities depend on sidemode gain and spontaneous emission, the generation of squeezed states of the vacuum avoids these phenomena, depending solely on quantum combination tones.
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.
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.
This dissertation formulates and applies a theory describing how one or two strong classical waves and one or two weak quantum mechanical waves interact in a two-level medium. The theory unifies many topics in quantum optics, such as resonance fluorescence, saturation spectroscopy, modulation spectroscopy, the build up of laser and optical bistability instabilities, and phase conjugation. The theory is based on a quantum population pulsation approach that resembles the semiclassical theories, but is substantially more detailed. Calculations are performed to include the effects of inhomogeneous broadening, spatial hole burning, and Gaussian transverse variations. The resonance fluorescence spectrum in a high finesse optical cavity is analyzed in detail, demonstrating how stimulated emission and multiwave processes alter the spectrum from the usual three peaks. The effects of quantum noise during the propagation of weak signal and conjugate fields in phase conjugation and modulation spectroscopy are studied. Our analysis demonstrates that quantum noise affects not only the intensities of the signal and conjugate, but also their relative phase, and in particular we determine a quantum limit to the semiclassical theory of FM modulation spectroscopy. Finally, we derive the corresponding theory for the two-photon, two-level medium. This yields the first calculation of the two-photon resonance fluorescence spectrum. Because of the greater number of possible interactions in the two-photon two-level model, the theoretical formalism is considerably more complex, and many effects arise that are absent in the one-photon problem. We discuss the role of the Stark shifts on the emission spectrum and show how the Rayleigh scattering is markedly different.