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Soviet Journal of Quantum Electronics

Nonlinear optical resonators (excited by external radiation) (review)

V. N. Lugovoǐ

Published Oct 31, 1979• 14 citations
Publisher

Abstract

A review is given of theoretical and experimental investigations of optical resonators excited by an external light beam and filled with a nonlinear medium. An analysis is made of various types of nonlinearities (Kerr, Raman, Brillouin, and quadratic nonlinearities, saturation in a medium of two-level particles) and equations which describe the dynamics of optical oscillations in a resonator, are derived. Descriptions are given of the main properties such as limitation of the transmitted beam intensity, bistability and hysteresis, intensity pulsations, and amplification of amplitude-frequency deviations in the optical beam. Transient processes are also discussed. In the description of the experimental results, not only the resonator parameters and the observed properties are indicated but attention is also paid to identification of the type of nonlinearity. An analysis is also made of hybrid systems in which the nonlinearity is simulated (and deliberately increased) by radioelectronics.

DOI
10.1070/qe1979v009n10abeh009501

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A review is given of theoretical and experimental investigations of optical resonators excited by an external light beam and filled with a nonlinear medium. An analysis is made of various types of nonlinearities (Kerr, Raman, Brillouin, and quadratic nonlinearities, saturation in a medium of two-level particles) and equations which describe the dynamics of optical oscillations in a resonator, are derived. Descriptions are given of the main properties such as limitation of the transmitted beam intensity, bistability and hysteresis, intensity pulsations, and amplification of amplitude-frequency deviations in the optical beam. Transient processes are also discussed. In the description of the experimental results, not only the resonator parameters and the observed properties are indicated but attention is also paid to identification of the type of nonlinearity. An analysis is also made of hybrid systems in which the nonlinearity is simulated (and deliberately increased) by radioelectronics.
A review is given of theoretical and experimental investigations of optical resonators excited by an external light beam and filled with a nonlinear medium. An analysis is made of various types of nonlinearities (Kerr, Raman, Brillouin, and quadratic nonlinearities, saturation in a medium of two-level particles) and equations which describe the dynamics of optical oscillations in a resonator, are derived. Descriptions are given of the main properties such as limitation of the transmitted beam intensity, bistability and hysteresis, intensity pulsations, and amplification of amplitude-frequency deviations in the optical beam. Transient processes are also discussed. In the description of the experimental results, not only the resonator parameters and the observed properties are indicated but attention is also paid to identification of the type of nonlinearity. An analysis is also made of hybrid systems in which the nonlinearity is simulated (and deliberately increased) by radioelectronics.
The properties are considered of an optical resonator excited by an external light beam and filled with a non-linear (Raman or Mandel'stam-Brillouin active) medium for single-mode (exciting and the first Stokes) radiation components in the resonator. The form of the hysteresis of light intensity inside the resonator and of the intensity of the beam transmitted through the resonator for both the radiation components on the variation of the external beam intensity are investigated. Also, periodic pulsations of the radiation component intensities are discussed and the phase modulation of the components at the regimes in question is predicted, the conditions for these pulsations being derived. Conditions are also found under which the resonator amplifies the amplitude (phase) modulation of the external light beam and the properties of the regimes of the amplification are also discussed. The use of the resonator in question as the element of optical memory, a switching device, the generator of optical pulses and optical ‘transistor’ is proposed.
A multiple interferometer is proposed and stimulated Raman radiation, stimulated Mandel’stam–Brillouin radiation, and Cerenkov-type optical parametric oscillation are considered in this interferometer, which is excited by an external light beam. An extremely low threshold intensity of the exciting beam is noted. Optical bistability and hysteresis, self-pulsing of the radiation intensities, amplification of amplitude-phase deviations in the incident pumping beam, limitation of the intensity of the beam transmitted by the interferometer, and nonlinear reflection of the beam from the multiple interferometer are predicted and discussed. It is also noted that the threshold for generation of the second Stokes component of stimulated Raman radiation and stimulated Mandel’stam–Brillouin radiation under the conditions discussed is usually not achieved, even for high excess of the exciting beam intensity over the threshold for generation of the first Stokes component.
An analysis is made of nonlinear nonstationary equations describing dynamics of the stimulated Raman scattering in optical resonators excited by external nonmonochromatic radiation. The threshold of the excitation of the stimulated scattering by nonmonochromatic radiation is found and its dependence on the dispersion of the active medium is deduced. Solutions are obtained for steady-state oscillations in a resonator and their characteristics are investigated as a function of the spectrum of the exciting radiation and of the dispersion of the active medium.
A comprehensive analysis of the interaction of pulsed light beams with nonlinear planar resonators is presented, covering both arbitrary types of nonlinearity and arbitrary states of polarization of the incident field. The characteristic of the optical response is discussed in its dependence on the crucial parameters of the resonator system as well as of the input pulse. Numerical results are given for the transmission response of a multiple-film configuration under oblique incidence, which is endowed with a dynamic, saturable nonlinearity. In particular, conditions for optical bistability to occur are derived.
In the last chapter, we examined the effect of cubic nonlinearity on selfrefraction of an optical beam. We have also seen that the presence of a quadratic nonlinearity can also contribute to change in the profile of a Gaussian beam in a crystal. In this chapter we will see how the effect of nonlinearity, alongwith the proper feedback, can give rise to optical bistability and hysteresis. This is not unexpected as hysteresis and bistability are also observed in nonlinear electronic circuits with feedback, such as in the Schmitt trigger, as well as in hybrid optical devices, such as an acoustooptic device with feedback (Banerjee and Poon, 1991). In what follows, we will examine two different types of optically bistable devices based on optical nonlinearities. The first is a nonlinear ring resonator comprising a two-level gain medium as the nonlinear element. We will treat both absorptive and dispersive bistability. Absorptive bistability is the case when the incident optical frequency is close to or equal to the transition frequency of the atoms from one level to another. In this case, the absorption coefficient becomes a nonlinear function of the incident intensity. On the other hand, if the frequencies are far apart, the medium behaves like a Kerr-type material and the system exhibits what is called dispersive bistability. In this case the material can be modeled by an effective n2 or v (3), meaning that the refractive index becomes a nonlinear function of the optical intensity. The second configurationwewill examine is a linear-nonlinear interface. In this case, the interface provides the feedback due to refractive index mismatch. In fact, the reflection coefficient (as well as the transmission coefficient) is modified due to the nonlinearity, which, as we shall see later, is responsible for demonstrating optical switching and bistability.