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Optics Letters

Intensity dependence of two-wave mixing absorption in a resonant medium

Gang He, J. W. Mirick, R. S. F. Chang, Nicholas Djeu

Published Aug 1, 1987• 0 citations
Publisher

Abstract

Two-wave mixing absorption in a supersonic beam containing I2 has been studied. The results are in agreement with theory for probe intensities comparable with the pump intensity. However, at very low probe-beam intensities, the absorption deviates substantially from the predicted value and becomes the same as that for the pump beam alone. We believe that this behavior is caused by density variations in the molecular beam and suggest that this effect can be developed into a tool for probing optical inhomogeneities on a microscopic scale.

DOI
10.1364/ol.12.000582

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Abstract : This program investigated the feasibility of producing degenerate two wave mixing gain in a noninverted resonant medium with local response. According to theory, two wave mixing gain should be possible if the resulting index grating is shifted in space with respect to the intensity grating produced by the two crossed beams. A pulsed molecular beam valve operated at 100 C was used to produce the supersonically cooled I2 jet. To achieve the moving grating effect, the pump and probe beams were to be crossed in a plane containing the flow axis, with each beam nearly perpendicular to that axis. The pulsed beam valve produced a broad forward peaked distribution of molecules. The velocity distribution at any given point, however, was mainly along the direction of the line joining that point to the nozzle orifice. This was the evidenced by the fluorescence pattern along the laser beam path, which consisted of sharp filaments across the laser beam corresponding to various hyperfine components of a single rotational transition Doppler tuned into resonance with the laser beam at various angles of inclination. Gain in the planned experiment would be observable only within a narrow range of detuning (obtained by crossing the pump and probe beams), and therefore only a small solid angle of the I2 jet is useful. Various nozzles were tried with the pulsed valve device. Under the best circumstances, an integrated absorption of only about 10% was measured. With the required angular selection, the expected gain would be on the order of .01%. Since the stability of the laser was such that even after signal averaging a noise of the order of 0.1% remained, it precluded our attempt to demonstrate gain, self pumped, supersonic flow. Keywords: Iodine.

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Theory of pump-wave propagation and its effect on degenerate four-wave mixing

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We have derived an analytic expression for the intensity distribution of two counterpropagating waves of arbitrary input intensity in a saturable absorber. We use this distribution to extend the theory of degenerate four-wave mixing to include the effects of pump wave absorption. In particular, the spatial variation of the nonlinear absorption and coupling constants that appear in the coupled-amplitude equations for the probe and the signal (i.e., conjugate) waves are determined. These coupled-amplitude equations are solved numerically in a noniterative manner, leading to a prediction for the phase-conjugate reflectivity. The nature of the predictions differs qualitatively from those1,2 derived from theories that ignore pumpwave absorption, especially for the case of off-line-center excitation. At large values of the input pump intensities, the phase conjugate reflectivity can be larger than that predicted by theories that ignore pump-wave absorption.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations
Two-wave mixing absorption in a supersonic beam containing I2 has been studied. The results are in agreement with theory for probe intensities comparable with the pump intensity. However, at very low probe-beam intensities, the absorption deviates substantially from the predicted value and becomes the same as that for the pump beam alone. We believe that this behavior is caused by density variations in the molecular beam and suggest that this effect can be developed into a tool for probing optical inhomogeneities on a microscopic scale.
The effect of an intense pump field and the chemical concentration of the solution on the forward four-wave mixing signal of molecular systems with an inhomogeneous distribution of resonance frequencies, has been studied. A perturbative treatment to all orders in the pump and to first order in the probe and signal beams, including the propagation of the fields as the variable to be studied, was used. The present results are compared to local regimes of propagation and to the case of a homogeneously distributed spectral line. The behaviour of the non-linear signal, characterized by tridimensional intensity surfaces, is explained in terms of saturation and/or absorption processes taking place under the present study conditions.
The solution of the nondegenerate two-wave-mixing problem in an absorptive Kerr medium including the contribution from nonlinear absorption is obtained for the first time to our knowledge. This solution enables us to analyze the influence of nonlinear absorption on the two-wave-mixing gain and account for previously unexplained results reported for ruby and Cr3+:YAlO3. The effect of nonlinear absorption of a pump beam on the gain of a probe beam is shown to be minimized when incident intensities of the interacting beams are equal. The intensity dependence of the two-wave-mixing gain for dispersive (ruby and Cr3+:YAlO3) media and the gain measurements for absorptive (fluorescein-doped glass) media are also in agreement with the new theory.
The influence of the high-pump-field intensity saturation and dynamic Stark effects on the resonant nearly degenerate four-wave-mixing signal (${\mathrm{\ensuremath{\omega}}}_{3}$=2${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$) is studied in a frequency space defined by the pump- and probe-field frequencies, ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, respectively. Variable inhomogeneous widths have been considered ranging from extremely narrow (homogeneous distribution) to extremely wide. Remarkable differences between nearly homogeneously broadened systems and extreme inhomogeneous ones are exhibited. It is shown, for the situation of homogeneous broadening, that the spectra carried on with fixed probe and fixed pump frequency values have substantial differences in shape. These differences disappear in the situation of extreme inhomogeneous broadening. Fixed-pump-frequency resonant and fixed-probe-frequency nonresonant spectra are proposed as very convenient tools to yield useful evidence about the width of the inhomogeneous molecular distribution.
The influence of molecular collisions on the production of the degenerate four-wave mixing signal in I(2) is presented. Measurements were performed on gaseous molecular iodine, I(2), contained in a glass cell in which pressure, temperature, and species concentration are easily and independently varied. Frequencydoubled outputs from a seeded Nd:YAG laser and an excimer-pumped dye laser were used as excitation sources. We have studied the dependence of signal strength versus buffer gas pressure, with pump intensity as a third parameter. It is evident from our results that, for pump intensities of less than 1 MW/cm(2), the pressure dependence of the signal follows that given by a simple two-level model in the homogeneously broadened regime. In this regime collisional deexcitation becomes significant, leading to changes in saturation intensity. This is evidenced by a reduction in the signal with an increase in buffer gas pressure. This behavior is similar to that seen in laser-induced fluorescence. At higher pump intensities, the signal is seen to increase with pressure; this behavior cannot be described by the simple two-level model.
Abstract : This program investigated the feasibility of producing degenerate two wave mixing gain in a noninverted resonant medium with local response. According to theory, two wave mixing gain should be possible if the resulting index grating is shifted in space with respect to the intensity grating produced by the two crossed beams. A pulsed molecular beam valve operated at 100 C was used to produce the supersonically cooled I2 jet. To achieve the moving grating effect, the pump and probe beams were to be crossed in a plane containing the flow axis, with each beam nearly perpendicular to that axis. The pulsed beam valve produced a broad forward peaked distribution of molecules. The velocity distribution at any given point, however, was mainly along the direction of the line joining that point to the nozzle orifice. This was the evidenced by the fluorescence pattern along the laser beam path, which consisted of sharp filaments across the laser beam corresponding to various hyperfine components of a single rotational transition Doppler tuned into resonance with the laser beam at various angles of inclination. Gain in the planned experiment would be observable only within a narrow range of detuning (obtained by crossing the pump and probe beams), and therefore only a small solid angle of the I2 jet is useful. Various nozzles were tried with the pulsed valve device. Under the best circumstances, an integrated absorption of only about 10% was measured. With the required angular selection, the expected gain would be on the order of .01%. Since the stability of the laser was such that even after signal averaging a noise of the order of 0.1% remained, it precluded our attempt to demonstrate gain, self pumped, supersonic flow. Keywords: Iodine.
We have derived an analytic expression for the intensity distribution of two counterpropagating waves of arbitrary input intensity in a saturable absorber. We use this distribution to extend the theory of degenerate four-wave mixing to include the effects of pump wave absorption. In particular, the spatial variation of the nonlinear absorption and coupling constants that appear in the coupled-amplitude equations for the probe and the signal (i.e., conjugate) waves are determined. These coupled-amplitude equations are solved numerically in a noniterative manner, leading to a prediction for the phase-conjugate reflectivity. The nature of the predictions differs qualitatively from those1,2 derived from theories that ignore pumpwave absorption, especially for the case of off-line-center excitation. At large values of the input pump intensities, the phase conjugate reflectivity can be larger than that predicted by theories that ignore pump-wave absorption.