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Nonlinear Dynamics in Optical Systems

Degenerate Optical Parametric Oscillator with a Saturable Absorber

Ruo-Ding Li, Paul Mandel

Published Jan 1, 1990• 0 citations
Publisher

Abstract

We consider a degenerate optical parametric oscillator (DOPO). A coherent signal is injected with real amplitude ϵ and phase 2iω0t. The cavity has two resonant modes at frequencies ν1 ≃ ω0 and ν2 ≃ 2ω0. A nonlinear crystal converts photons of frequency ν2 into pairs of photons of frequency ν1 = v2/2. A saturable absorber is inserted in the cavity and can absorb photons at the frequency ν1. The absober is described by a collection of N homogeneously broadened two-level atoms with atomic frequency ω ≃ ω0.

DOI
10.1364/nldos.1990.ob263

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We consider a degenerate optical parametric oscillator (DOPO). A coherent signal is injected with real amplitude ϵ and phase 2iω0t. The cavity has two resonant modes at frequencies ν1 ≃ ω0 and ν2 ≃ 2ω0. A nonlinear crystal converts photons of frequency ν2 into pairs of photons of frequency ν1 = v2/2. A saturable absorber is inserted in the cavity and can absorb photons at the frequency ν1. The absober is described by a collection of N homogeneously broadened two-level atoms with atomic frequency ω ≃ ω0.
We consider a composite system consisting of a degenerate optical parametric oscillator (DOPO) and a set of N homogeneously broadened two-level atoms. When the atoms are on or near resonance with the subharmonic-frequency field generated through the frequency down-conversion process, bistability appears in the intracavity field near the DOPO threshold. The bistability region will decrease as the detuning between the atomic transition frequency and the frequency of the subharmonic field increases. When the detuning becomes large enough, the atoms decouple from the cavity field and the system behaves like a normal DOPO. There are several features distinguishing this bistable behavior from the usual atomic optical bistability occurring with atoms in an optical cavity driven by an external field.
Although an ideal degenerate optical parametric oscillator (DOPO) can generate perfect squeezing at the output of a one-sided optical cavity when operating just below threshold, its intracavity squeezing is limited to less than one-half (50%) of its perfect value. However, when two-level atoms are introduced into the DOPO cavity, the amount of intracavity squeezing can be enhanced, from its maximum value of 50%, to a maximum value of 75% in the good-cavity limit due to the strong interaction between the two-level atoms and the subharmonic field mode. This extra intracavity squeezing is significant in studying spectroscopy of atoms interacting with a squeezed field mode inside an optical cavity.
We study transmitted optical spectra from a realistic system which consists of a degenerate optical parametric oscillator (DOPO) and N two-level atoms. Optical bistability appears when parameters are suitable. Below the modified threshold of the DOPO (lower turning point of the bistable curve), the coherent intensity is always zero at the lower branch, which allows us to describe this system with a set of linear differential equations. By transforming the field and atomic variables into corresponding quadratures, we find that, for the resonance case, one atomic quadrature will only couple to one field quadrature. By separating these two quadratures, we are able to study the effects due to squeezed and unsqueezed quadratures on the atoms. The optical and atomic spectra of this system are obtained, analytically, for arbitrary coupling strength and cavity linewidth.
In the first section we discuss the stationary solutions for a laser with an injected signal, the active counterpart of the optical bistability analyzed in Chapter 11. Next, in Section 13.2 we consider another very interesting system, namely a laser with a saturable absorber, a free-running laser in which the optical cavity contains a passive medium in addition to the active medium. The single-mode model for this system can be constructed by combining the single-mode models for the free-running laser and for optical bistability. The discussion is then focussed on its stationary states. In Section 13.3 we return to the single-mode model for optical bistability and, by introducing an appropriate “cubic limit” on the parameters in play, we derive a cubic model for dispersive optical bistability with two-level atoms. The stationary equation for such a model formally coincides with that derived and discussed for a Kerr medium in Section 11.2. In the last section we start from the equations for a quadratic nonlinear medium in the degenerate configuration derived in Chapter 6 and combine them with the appropriate boundary conditions for the two field envelopes in play, assuming that the quadratic medium is contained in a ring cavity as happens in an optical parametric oscillator or in second-harmonic generation in a cavity. Next, by introducing the low-transmission limit and the single-mode limit we derive a two-mode model that describes the dynamics of a degenerate optical parametric oscillator or of second-harmonic generation in a cavity. Finally, for the case of a parametric oscillator we illustrate extensively the stationary solutions of the equations. A laser with an injected signal From a technical point of view, this system is interesting because of the possibility of stabilizing the frequency and the phase of separate lasers by taking advantage of the known affinity of nonlinear oscillators to lock onto a periodic forcing element. In 1972 Spencer and Lamb [125] predicted the possibility of bistable behavior in a laser with an injected signal before the surge of interest in optical bistability in the passive configuration.
We study the classical and quantum properties of a degenerate optical parametric oscillator (DOPO) tuned to the first family of transverse modes at the down-converted frequency, under the injection of a resonant TEM10{}_{10}10​ mode. Unlike the usual single-mode DOPO with injected signal, large levels of squeezing are predicted even for relatively large injections. We interpret these results in connection with the spontaneous symmetry breaking predicted for this system in the absence of injection and with the existence of a bifurcation giving rise to the switching on of the (noninjected) TEM01{}_{01}01​ mode.
In this talk I will review our recent results in the field of optical parametric oscillation. In particular, the demonstration of Degenerate Optical Parametric Oscillation (DOPO) using a phase-coherent dual-tone pump scheme will be discussed. This work highlights the potential of photonic molecules as a platform for achieving high-quality DOPO, which could have important applications in areas such as quantum communication, quantum cryptography, and quantum computing. The phase-matching conditions are carefully controlled to achieve maximum DOPO efficiency, and the results show that the DOPO signal can be efficiently generated and optimized. This work opens new avenues for further investigation in the field of DOPO and its applications.