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Physical Review A

Generation of odd subharmonic Raman resonances from Stokes–anti-Stokes coupling

G. S. Agarwal

Published Feb 1, 1991• 5 citations
Publisher

Abstract

The existence of odd Raman subharmonics in the nonlinear mixing of fields of frequencies ${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}$ and ${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$ is examined in a nonperturbative way. It is shown that the coupling of Stokes and anti-Stokes processes at high pump powers produces odd subharmonics in nonlinearly generated signals. It is also shown that this coupling can lead to gain at the odd subharmonics. An effective Hamiltonian is used to discuss the coupling of Stokes--anti-Stokes processes. Numerical results showing the odd subharmonics are presented. The origin of odd subharmonics in terms of transitions among dressed states is also discussed.

DOI
10.1103/physreva.43.1523

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The existence of odd Raman subharmonics in the nonlinear mixing of fields of frequencies \ensuremathωl{\mathrm{\ensuremath{\omega}}}_{\mathit{l}}\ensuremathωl​ and \ensuremathωs{\mathrm{\ensuremath{\omega}}}_{\mathit{s}}\ensuremathωs​ is examined in a nonperturbative way. It is shown that the coupling of Stokes and anti-Stokes processes at high pump powers produces odd subharmonics in nonlinearly generated signals. It is also shown that this coupling can lead to gain at the odd subharmonics. An effective Hamiltonian is used to discuss the coupling of Stokes--anti-Stokes processes. Numerical results showing the odd subharmonics are presented. The origin of odd subharmonics in terms of transitions among dressed states is also discussed.
Raman oscillation, frequency upconversion, and Raman amplification can be achieved in a second-order nonlinear medium at the phonon-polariton resonance. By beating two optical fields, a second-order nonlinear polarization is generated inside the medium. Such a polarization induces a spatially uniform nonpropagating electric field at the beat frequency, which in turn mixes with the input optical field at the lower frequency to generate or amplify the anti-Stokes optical field. Raman oscillation can be efficiently reached for the copropagating configuration. In comparison, efficient frequency upconversion and large amplifications are achievable for the counterpropagating configuration. These Raman processes can be used to effectively remove transverse-optical phonons before decaying to lower-frequency phonons, achieve laser cooling, and significantly enhance coherent anti-Stokes Raman scattering. The counterpropagating configuration offers advantages for amplifying extremely weak signals.
Molecular polarizability theory with the inclusion of the second-hyperpolarizability coefficient is used to study the transient generation of four-wave- and six-wave-mixing signals when a system interacts with laser and Stokes pulses of frequencies ${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}$ and ${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}$ lying in the region of the subharmonic Raman resonance ${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}$-${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}$\ensuremath{\approxeq}${\mathrm{\ensuremath{\omega}}}_{\mathit{R}}$/2. The dynamical equations for various fields and amplitudes of the Raman and the subharmonic mode are derived and integrated numerically to obtain the detailed characteristics, such as pulse width, pulse center, ringing, etc., of the generated signals. The effect of the chirp in the incident pump pulse is also studied.
The quantum theory of Stokes--anti-Stokes processes in a degenerate system in a cavity is developed. The Raman transition is pumped by a coherent field. Effects of many atoms, cavity losses, and thermal photons are included in the theory. An exact solution for the model is obtained. An explicit expression for the reduced density matrix of the cavity field is given. The spectrum of the cavity field is obtained and is interpreted in terms of the eigenstates of the effective Hamiltonian describing Stokes--anti-Stokes processes. The spectrum develops sidebands due to strong Raman coupling.
We consider a two-level quantum system interacting with two classical time-periodic electromagnetic fields. The frequency of one of the fields far exceeds that of the other. The effect of the high-frequency field can be averaged out of the dynamics to realize an effective transition frequency of the field-dressed two-level system. We examine the linear response, second harmonic response and Stokes and anti-Stokes Raman response of the dressed two-level system, to the weak frequency field. The vibrational resonance enhancement in each case is demonstrated for optimal strength of the high-frequency field. Our theoretical scheme is corroborated by full numerical simulation of the two-level, two-field dynamics governed by loss-free Bloch equations. We suggest that quantum optics can offer an interesting arena for the study of the vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
Analytic and numerical solutions are obtained for the equations describing the propagation of several pulses of different frequencies through a Raman medium. The transient case is treated, and the analysis includes Stokes, pump, and anti-Stokes frequency components. The effect of phase mismatch \ensuremath{\Delta}k between these waves is investigated. An analytic solution is found that describes the phenomenon of transient Stokes--anti-Stokes gain suppression in the limit \ensuremath{\Delta}k=0. For nonzero values of \ensuremath{\Delta}k, the behavior of the transient gain coefficient is found to follow a scaling rule that is the analog of a similar result known from the steady-state limit. Calculations are performed to identify conditions that enhance conversion to anti-Stokes radiation. It is found that there is an optimum strength of the Stokes seed, and that proper phase matching of the initial waves is essential.