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Progress of Theoretical Physics Supplement

On the Theories of Nonlienar Spectroscopy

Mario Yokota

Published Jan 1, 1984• 0 citations
Publisher

Abstract

The interrelation between the theories of transition probability and susceptibility χ on nonlinear spectroscopy becomes clear through a new formula with which we can evaluate the emission rate of observed photon energy. Necessary assumptions, on which the emission rate of the fourth wave in a four-wave light mixing processes is proportional to |χ|2, are investigated.

DOI
10.1143/ptps.80.189

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The interrelation between the theories of transition probability and susceptibility χ on nonlinear spectroscopy becomes clear through a new formula with which we can evaluate the emission rate of observed photon energy. Necessary assumptions, on which the emission rate of the fourth wave in a four-wave light mixing processes is proportional to |χ|2, are investigated.
Abstract Nonlinear optics processes lie at the heart of photonics and quantum optics for their indispensable role in light sources and information processing. During the past decades, the three- and four-wave mixing (χ(2) and χ(3)) effects have been extensively studied, especially in the micro-/nano-structures by which the photon-photon interaction strength is greatly enhanced. So far, the high-order nonlinearity beyond the χ(3) has rarely been studied in dielectric materials due to their weak intrinsic nonlinear susceptibility, even in high-quality microcavities. Here, an effective five-wave mixing process (χ(4)) is synthesized by incorporating χ(2) and χ(3) processes in a single microcavity. The coherence of the synthetic χ(4) is verified by generating time-energy entangled visible-telecom photon pairs, which requires only one drive laser at the telecom waveband. The photon-pair generation rate from the synthetic process shows an estimated enhancement factor over 500 times upon intrinsic five-wave mixing. Our work demonstrates a universal approach of nonlinear synthesis via photonic structure engineering at the mesoscopic scale rather than material engineering, and thus opens a new avenue for realizing high-order optical nonlinearities and exploring functional photonic devices.
The dispersion characteristics of the nonlinear susceptibility χ ( n ) ( n =3, 5, 7) describing a new type of optical mixing have been calculated for their application to the study of ultra-fast relaxation dynamics in resonant media. The process is that two incident light waves at frequencies ω 1 and ω 2 produce new light waves at ω 1 - m ε and ω 1 + n ε ( ε =ω 2 -ω 1 ; m , n =1, 2, 3, …) under the conditions of two-photon resonance (2ω 1 , 2ω 2 ≃optical transition frequency) and Rayleigh-type resonance (|ω 1 -ω 2 |≃relaxation rate). Results of analysis based on an inhomogeneously broadened three-level model revealed that Rayleigh-type dispersions involving the longitudinal and transverse relaxation rates appear in χ ( n ) ( n ≧5) and χ ( n ) ( n ≧7), respectively. Their analogy with two-photon resonant photon echo and various precautions in applying them to actual situations are also discussed.
We present a microscopic theory of the nonlinear susceptibility χ(3) of a crystal composed of interacting two-level absorbers. The relationship between the signals in a steady-state four-wave mixing experiment and in a time-resolved transient grating experiment is established. In general, the steady-state signal is not simply the Fourier transform of the time-resolved signal, although such a relationship does hold under certain experimental conditions. We evaluate χ(3) for the Haken–Strobl model. χ(3) displays a dephasing-induced extra resonance, whose intensity and line shape are sensitive to the degree of exciton coherence. We also calculate χ(3) for a crystal of interacting three-level absorbers, under the assumption that population in the higher excited state relaxes rapidly to the lower excited state. We propose steady-state four-wave mixing as an alternative to the transient grating experiment in investigating the nature of exciton motion.