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Journal of the Optical Society of America B

Self-interferometry by dual-wave-front generation in degenerate four-wave mixing

Naohiro Tanno, Kohichi Kawauchi, Kenichi Yokoto

Published Jan 1, 1986• 10 citations
Publisher

Abstract

A new interferometry by a novel dual-wave-front generation in degenerate four-wave mixing is described. The dual wave front created in a nonlinear medium automatically yields a self-referencing operation for a given phase of an incident probe beam. Some advantages over ordinary interferometers are shown. The basic experiments are shown to agree well with the theoretical predictions.

DOI
10.1364/josab.3.000060

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 9, 2006•0 citations
A new interferometry by a novel dual-wave-front generation in degenerate four-wave mixing is described. The dual wave front created in a nonlinear medium automatically yields a self-referencing operation for a given phase of an incident probe beam. Some advantages over ordinary interferometers are shown. The basic experiments are shown to agree well with the theoretical predictions.
This paper presents a novel aspect of dual-wave-front generation by degenerate four-wave mixing. The dual-wave-front generation referres to simultaneous generation of phase-conjugate and nonconjugate wave-front for a given probe beam, due to the third-order nonlinear polarization. The characteristics of dual-wave-front generation is theoretically studied and is experimentally confirmed using a dye-laser and Na-vapor system. It is also shown that an interesting forward phase-conjugate wave is observed by using a character-pattern in the experiment.
In this work the different schemes of propagation and interaction of the light beams in nonlinear Fabry-Perot interferometer have been studied theoretically and experimentally. Degenerate and non-degenerate four-wave mixing have been realized in the cavity of Fabry-Perot type using Rhodamine-6G dye and polymethine dye 3274U solution as saturable absorber. The diffraction efficiency of intracavity dynamic grating has been studied in dependence on intensity of interacting beams and parameters of resonator. The theoretical model of the processes of intracavity degenerate and non-degenerate four-wave mixing has been developed and applied to the analysis of the efficiency of light beams conversion by mean of Bragg diffraction from intracavity dynamic gratings. For theoretical description of typical experimental situations we used the round-trip model of nonlinear interferometer adapted for the geometry of degenerate four-wave mixing, which can be realized in the scheme of symmetrical oblique incidence of pump, signal and probe beams to the front and back mirrors of cavity.
This paper describes time evolution of an incident probe pulse in degenerate four-wave mixing with dualwave-front generation. It is shown that the incident pulse transmission results inself-conservation propagation without loss and pulse-form-change. Theoretical analysis is given by parametric propagation equations as a function of space-time. Their transient solutions reveal that interesting propagation effect which is confirmed by the experimental observation using a dye-laser and Na-vapor system.
We consider degenerate four-wave mixing in a Kerr medium with a standard noncollinear geometry and the polarization directions of all the beams parallel to one another. The two pump beams, the probe beam, and the phase-conjugate beam are denoted by the subscripts 1,2,4 and 3, respectively. The nonlinear medium is placed between z = 0 and z = 1; the values of the intensities of the beams at z = 0 and 1 are denoted by Ii0 andIi1, where i = 1,2,3,4. Beams 2 and 4 are incident at z = 1; and beam 1 is incident at z = 0. We have determined the dependence of the phase-conjugate reflectivity R = I31/I41 and the pump transmission T = I11/I10 on the following parameters: the probe ratio, q=I41/(I10 + I21); the pump ratio, r = I21/I 1 0; the absorption coefficient–path length product, al; and the coupling constant of the medium, q. In the absence of nonlinear refraction, pump depletion, and linear absorption in the medium, R = tan2q. When all of these effects are taken into account, the maximum value of R is given by Rmax = exp (-2α1)/(q(1 + r)). The minimum value that T can reach is proportional to q for q < 1. Even for small values of q, multistable solutions for R and T are obtained when q is greater than a threshold value, which we denote by qth. We have determined the dependence of qth on the parameters q and r.
Advances in the development of nonlinear interference and holographic systems based on four-wave mixing point to great potentialities of these systems for real-time processing and correction of the light fields, formation of the desired space-time structures of laser radiation, image transfer, realization of logic and mathematical operations, creation of bistable devices and adaptive optics elements. This work presents the results of theoretical and experimental studies into the processes of light field transformations upon frequency-nondegenerate four-wave mixing in nonlinear Fabry-Perot interferometer. The principal aim is to develop a theory of intracavity four-wave mixing in complex molecular media in conditions of exhibited internal (scattering from dynamic gratings) and external (resonator) feedback, to determine a mechanism of light field transformations at the dynamic holograms and by nonlinear interferometers, to work out and introduce into practice novel nonlinear-optical methods for the control over characteristics of light beams. For theoretical description of typical experimental situations we used the round-trip model of interferometer adapted for the geometry of four-wave mixing, which can be realized in the scheme of symmetrical oblique incidence of reference and signal beams to the front and back mirrors of cavity. The conditions of magnification of dynamic gratings efficiency due to contribution from multiple interference of reading light beams have been studied experimentally and by means of theoretical modeling.