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Journal of the Optical Society of America B

Transient studies of nondegenerate four-wave mixing in a four-level system with saturable absorption and gain

John A. Buck, J. R. Rodriguez

Published Dec 1, 1987• 2 citations
Publisher

Abstract

We have investigated a nondegenerate transient four-wave mixing scheme that uses the coupled absorption and emission resonances in a four-level system. Strong frequency-shifted signals can be produced if high initial gain is present. In addition, the medium’s recovery time can be significantly decreased owing to the presence of stimulated emission, which occurs simultaneously with signal generation. Dyes are likely medium candidates.

DOI
10.1364/josab.4.001988

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We have investigated a nondegenerate transient four-wave mixing scheme that uses the coupled absorption and emission resonances in a four-level system. Strong frequency-shifted signals can be produced if high initial gain is present. In addition, the medium’s recovery time can be significantly decreased owing to the presence of stimulated emission, which occurs simultaneously with signal generation. Dyes are likely medium candidates.
Degenerate four-wave mixing in a separated absorption-gain system, such as that of an organic dye, is studied by using a four-level model. The effects of the nonlinearity arising from the displaced emission spectrum are found and compared with the results of the two-level model of Abrams and Lind [ Opt. Lett.2, 94 ( 1978); Opt. Lett.3, 205 ( 1978)]. A nonsymmetric saturation behavior over the width of the absorption line is shown to exist that can be detrimental to the phase-conjugate reflectivity. Otherwise, minor differences are seen from the two-level case.
This dissertation presents experimental and theoretical studies of transient degenerate four wave mixing (DFWM) in organic dyes. Chapter 1 is an introduction to DFWM. Chapter 2 describes DFWM experiments that were performed in the gain medium of a dye laser. Chapter 3 presents the theory of DFWM of short pulses in three level saturable media. Chapter 4 presents DFWM experiments of femtosecond pulses in the saturable absorber of a passively modelocked ring dye laser. Chapter 5 presents the theory of DFWM of ultrashort pulses in resonant media.
Two-frequency four-wave mixing in a dye is demonstrated, in which degenerate four-wave mixing is performed simultaneously within the absorption and emission frequency spectra, with two separate sets of beams. The coupling between the two bands gives rise to backward output waves at both frequencies, which are proportional to the phase conjugate of a single probe which can be at either of the two frequencies. Forward-propagating waves which are not conjugated are also generated at both frequencies. The frequency shifted outputs are tunable over the bandwidth of the spectrum in which they lie. A theoretical analysis is performed which is based on a four-level system model of the ground and first excited singlet states in a dye. Resulting are coupled equations, which are solved to yield the efficiencies of the various outputs. Experiments give results in good agreement with the theory.
The characteristic features of the conjugate wave's formation under transient four-wave mixing in a two-level medium are investigated. The phase modulations of the signal and conjugate waves induced in the four-wave mixing are not mutually conjugate and have the same sign. The fulfillment of the phase-conjugation for the phase modulated signal has been shown in particular to be connected with the envelope's deformation and the spectrum's change of signal pulses. The transient optical bistability connected with the nonlinear absorption's saturation in the quasi-cw four-wave mixing and with the inertia in the short pulse's regime is observed.
We model transient copolarized degenerate four-wave mixing in a saturable gain medium, using pulses of duration much shorter than the population lifetime with a finite probe beam. Initially we describe a model to include the simultaneous existence of both the reflection and transmission gratings for arbitrary field strengths. Then we develop a model to include all four possible gratings, including standing-wave gratings between counterpropagating pump beams and the probe and conjugate beams. By use of two expansion methods for the higher-order grating terms it is possible to model regimes in which either one grating is arbitrarily strong or all four gratings are strong. Comparisons are made among models including one, two, and four gratings. Good agreement is found between the theoretical four-grating case and pulsed copolarized degenerate four-wave mixing experiments in laser-pumped Ti:sapphire for a finite probe beam.