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Optics Letters

Saturated absorption and degenerate four-wave mixing in Nd^3+ beta″ alumina

Robert W. Boyd, Bruce Dunn, Dongliang Yang, Mark T. Gruneisen, Paul Narum, David J. Simkin

Published Mar 1, 1986• 25 citations
Publisher

Abstract

Nd3+ beta″ alumina is one of a family of potentially useful nonlinear-optical materials based on rare-earth ions substituted into a beta″ alumina host. The saturation intensity of Nd3+ beta″ alumina has been measured to be in the range 16 to 35 kW cm−2. Phase conjugation by degenerate four-wave mixing has been demonstrated, and the phase-conjugate reflectivity has been measured as a function of both laser wavelength and intensity.

DOI
10.1364/ol.11.000162

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IEEE Journal of Quantum Electronics•Jul 1, 1986•19 citations
Nd3+ beta″ alumina is one of a family of potentially useful nonlinear-optical materials based on rare-earth ions substituted into a beta″ alumina host. The saturation intensity of Nd3+ beta″ alumina has been measured to be in the range 16 to 35 kW cm−2. Phase conjugation by degenerate four-wave mixing has been demonstrated, and the phase-conjugate reflectivity has been measured as a function of both laser wavelength and intensity.
We report the first observation of the nearly degenerate four-wave--mixing spectrum of Nd3+{\mathrm{Nd}}^{3+}Nd3+-doped \ensuremath{\beta}''-Na-alumina. In a new application of continuous-wave high-resolution nearly degenerate four-wave mixing, a linewidth analysis of \ensuremath{\sim}1-kHz-wide optical resonances in heavily doped samples has been used to explain concentration-dependent, nonradiative decay of Nd ions which is obscured in conventional fluorescence-decay studies. Quantitative four-wave--mixing saturation studies also reveal a transition between a ``closed'' and an ``open'' quantum system due to pair interactions at a Nd density of \ensuremath{\sim}6\ifmmode\times\else\texttimes\fi{}1020{10}^{20}1020 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.
Phase distortion correction of an optical wave propagating in laser media is a crucial problem to be taken into account in most of laser systems. For this purpose, phase conjugation through stimulated Brillouin scattering using the master oscillator-power amplification configuration has shown a very good potential to obtain high beam quality in solid-state lasers that operate at variable repetition rates. Another attractive alternative to generate the phase-conjugate wavefronts is to use a four-wave mixing (DFWM) process in the laser amplifier. In this medium, the interference between the interacting beams leads to a spatial modulation of the complex susceptibility of the medium by gain saturation (amplitude gain grating). This all-solid-state solution presents the advantage of suppressing the external nonlinear medium and would realize the required functions in the laser medium itself. Moreover, due to the amplification experienced by all the interacting beams, associated to the resonant nonlinearity of the gain saturation, high reflectivities already have been achieved in Nd:YAG amplifiers using a multipass geometry.1,2
The phase-conjugate reflectivity attainable by degenerate four-wave mixing in an idealized saturable absorbing medium is calculated for arbitrary values of the laser intensity, laser frequency, and absorption path-length of the nonlinear medium. The influence of pump-wave absorption, including saturation and standing-wave effects, is included in the theory. The treatment is based on an analytic expression for the intensity distribution of the counterpropagating waves. The theoretical predictions differ substantially from those based on theories that ignore pump absorption effects. The results of the present calculation are used to predict the minimum laser intensity, absorption path-length, and detuning required to obtain unit reflectivity and self-oscillation.