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Soviet Journal of Quantum Electronics

Possibility of effective amplification of optical signals in four-wave resonant parametric processes

Valery S. Butylkin, Gennady M. Krochik, Yu. G. Khronopulo

Published Mar 31, 1978• 0 citations
Publisher

Abstract

A theoretical analysis is made of the possibility of the amplification of optical signals in four-wave parametric processes involving two-photon (second-order) resonances. An expression is obtained for the gain in the case of spatial phase matching between the pump, signal, and idler waves. Conditions for achieving a high gain (of the order of 103–105) are determined.

DOI
10.1070/qe1978v008n03abeh010044

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InTech eBooks•Jul 25, 2018•1 citation
A theoretical analysis is made of the possibility of the amplification of optical signals in four-wave parametric processes involving two-photon (second-order) resonances. An expression is obtained for the gain in the case of spatial phase matching between the pump, signal, and idler waves. Conditions for achieving a high gain (of the order of 103–105) are determined.
Optical parametric amplifiers rely on second-order susceptibility (three-wave mixing) or third-order susceptibility (four-wave mixing) in a nonlinear process where the energy of incoming photons is not changed (elastic scattering). In the latter case, two pump photons are converted to a signal and to an idler photon. Under certain conditions, related to the phase evolution of the waves involved, this conversion can be very efficient, resulting in large amplification of an input signal. As the nonlinear process can be very fast, all-optical applications aside from pure amplification are also possible. If the amplifier is implemented in an optical input-phase-sensitive manner, it is possible to amplify a signal wave without excess noise, i.e., with a noise figure of 0 dB. In this paper, we will provide the fundamental concepts and theory of such amplifiers, with a focus on their implementation in highly nonlinear optical fibers relying on four-wave mixing. We will discuss the distinctions between phase-insensitive and phase-sensitive operation and include several experimental results to illustrate their capability. Different applications of parametric amplifiers are also discussed, including their use in optical communication links.
A parametric amplification of input signal wave in the field of broadband incoherent light is analyzed at group-velocity matching of pump and idler waves. It is shown that such group-velocity matching is possible both in Type-I and Type-II phase-matching nonlinear crystals. The appropriate conditions at which an evolution of the signal wave in the field of the incoherent pump coincides with an evolution in the field of the monochromatic pump wave are demonstrated. The large parametric gain of the signal wave which is not sensitive to pump fluctuations is feasible in Type-II phase-matching nonlinear crystals.
Abstract We present results of a theoretical analysis of an optical parametric amplification (OPA) in a collinear nearly degenerate four-wave mixing configuration close to the resonance of a two-level transition in χ ′ ′ ′ media. It is performed both for homogeneously and for inhomogeneously broadened spectral line using a standard set of Bloch equations in the semiclassical approximation. Unlike the traditional approach of a coupled propagation of the signal/idler waves, we treat OPA as a coupled propagation of the amplitude and phase modulations of the pump wave with the signal/idler waves as the modulation sidebands. We show that for low frequency off-sets between the pump and the signal/idler waves, OPA process is basically manifested in a unidirectional transformation of the input amplitude modulation of the pump wave into the output phase modulation. The frequency band of the OPA is determined by detuning the pump wave from the resonance transition. The obtained results are applied to evaluate the expected OPA gain for the acetylene-filled micro-structured fiber with the resonance vibration-rotational transitions in the 1500–1550 nm spectral range.
Abstract The processes of parametric amplification and oscillation in a medium with cubic polarization is investigated in parametric approximation. For the case of amplification the threshold power of the pump wave is calculated. The influence of a finite phase mismatching and of the initial phases on the amplification process is discussed. For larger values of mismatching a periodical change between amplification and depletion may appear. For the cases of a single resonant oscillator (for the signal wave only), a double resonant oscillator (for both signal and idler wave) and a double resonant oscillator with the pump wave reflected at the second mirror the threshold power of the pump wave and the rise time are calculated. Characteristic differences between four‐photon and three‐photon parametric oscillators are discussed. A numerical estimation of the threshold power for some media with nonlinear susceptibilities known from literature leads to the conclusion that the realization of a four‐photon parametric oscillator should be possible. In the appendix we discuss the influence of diffraction, focussing, birefrigence, nonstationarity and depletion of the pump wave on the studied process as well as the conditions under which these effects can be neglected.
Abstract The processes of parametric amplification and oscillation in a medium with cubic polarization are investigated theoretically taking into consideration the depletion of the pump wave. We suppose that phase‐matching is realized exactly (a possible nonlinear detuning of the exact phase‐matching should be compensated by a suitable subsequent adjustment of the frequencies). A consequence of linear losses is the appearance of a threshold for the parametric amplification. There exist a maximum length, a minimum length and an optimum length of the nonlinear medium for the process of parametric amplification. The threshold intensity, the optimum length of the nonlinear medium and the optimum reflection coefficient for outcoupling are determined for two arrangements of the double resonant parametric four‐photon oscillator (ring resonator, FABRY‐PEROT resonator). It is shown that for the above mentioned arrangements of the single resonant and the double resonant four‐photon oscillator the efficiency is a monotonous function of the threshold excess. On the contrary in case of the three‐photon oscillator there exists an optimum value of the threshold excess.
Optical parametric amplifiers (PAs) utilize highly efficient nonlinear effects in an optical fiber and they have the ability to operate in phase-sensitive mode. The inclusion of PAs in optical systems can give an ultimate limit for lumped amplified links in terms of achievable signal to noise ratio. The drawback is the complexity stemming from the requirement of phase matching a number of waves at each amplifier, phase lock, and the extra spectrum consumed by idler waves. In this chapter, the theories of a parametric amplifier, including the quantum-optical equations, are given. The properties of the gain saturation and the noise figure are presented. Practical amplifier systems and their applications in phase-sensitive amplification, all-optical signal regeneration, and squeeze state generation are outlined.