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Journal of the Optical Society of America B

Induced-grating autocorrelation of ultrashort pulses in a slowly responding medium

Alfred M. Levine, Ercüment Özïzmïr, Rick P. Trebino, Carl C. Hayden, Anthony M. Johnson, K. L. Tokuda

Published Sep 1, 1994• 19 citations
Publisher

Abstract

We consider induced-grating autocorrelation (IGA) in a slowly responding medium and study three possible geometries (two-beam coupling, three-beam induced grating, and self-diffraction) in two different limiting cases (single-pulse experiments and many-pulse accumulated-grating experiments). We find that in five of these six cases the IGA trace is given by the squared amplitude of the electric-field correlation function, thus yielding information about the spectrum of the pulse. Theoretical expressions for the IGA trace are derived for both linearly chirped and self-phase-modulated pulses. Experiments performed with self-phase-modulated pulses are in excellent agreement with the theory. In this case we show how the measured IGA trace can be used to determine both pulse duration and pulse bandwidth.

DOI
10.1364/josab.11.001609

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We consider induced-grating autocorrelation (IGA) in a slowly responding medium and study three possible geometries (two-beam coupling, three-beam induced grating, and self-diffraction) in two different limiting cases (single-pulse experiments and many-pulse accumulated-grating experiments). We find that in five of these six cases the IGA trace is given by the squared amplitude of the electric-field correlation function, thus yielding information about the spectrum of the pulse. Theoretical expressions for the IGA trace are derived for both linearly chirped and self-phase-modulated pulses. Experiments performed with self-phase-modulated pulses are in excellent agreement with the theory. In this case we show how the measured IGA trace can be used to determine both pulse duration and pulse bandwidth.
A study is made of the excitation of inhomogeneous holographic gratings by ultrashort light pulses with an arbitrary amplitude and phase modulation in a cubic nonlinear medium. The relaxation and diffusion of a pulse-induced grating is considered. The problem of diffraction of probe radiation by an inhomogeneous grating is solved using an electrodynamic theory of perturbations and also using the coupled wave approximation. It is shown that a cubic nonlinear medium may be used to store and then to retrieve uniquely a complete complex coherence function of a pulse. A simple method is proposed for the determination of the area under an exciting pulse, which makes it possible to introduce integral parameters of such a pulse (including a generalized amplitude and duration) that can serve as satisfactory estimates of the corresponding real quantities.
The excitation of nonuniform holographic gratings by ultrashort light pulses in nonlinear cubic media is considered. The relaxation and the diffusion of the pulse-induced grating are investigated. The diffraction problem of the induced grating is solved using both the perturbation theory and the coupled-wave approach. It is shown that the measurement of the angular or spectral distribution of the diffracted probe light makes it possible to determine the complex-valued coherence function completely for a single nonreproducible pulse. A simple method for the determination of the exciting pulse area is proposed; it allows us to deduce the integral amplitude and duration for the pulse, which can serve as a good approximation for their corresponding real values.
A theoretical analysis is made of the self-diffraction of short light pulses in an induced amplitude-phase grating in a thin layer of resonant medium. Expressions describing the amplitudes (intensities) of the diffracted beams are derived and analyzed. It is shown that the nature of the amplitude modulation of the light diffracted into small angles depends strongly on the amplitudes of the input pulses. It is demonstrated that transient self-diffraction of short pulses can be used in estimating the dipole moment of a saturable transition.
We analyze the phase modulation, or chirping, of coherent lossless light pulses propagating without distortion through resonant absorbers. In order to do this, we generalize the pioneering work of McCall and Hahn in two different directions. In the first place, of course, we abandon their assumption that the phase of the pulses has no temporal dependence. We prove that for slowly varying single pulses, chirping is not possible. However, we describe many multiple-pulse trains which are necessarily chirped, even under the slowly varying envelope restriction, and also describe the envelope modulations which produce large chirps. We show that certain zero-$\ensuremath{\pi}$ chirped pulse trains are contained as special cases of our general results. Our second generalization of the McCall-Hahn work concerns the background material in which the two-level resonant atoms are suspended. We allow the host medium to possess significant nonresonant nonlinearities. We find that undistorted lossless single pulses are possible in such a medium and that they are necessarily chirped.
The effect of grating dispersion on pulse evolution in a photorefractive self-pumped phase conjugator is analyzed. The broadening factors and the time-dependent phases of self-pumped phase-conjugate pulses of unchirped and chirped Gaussian pulses are obtained. When the grating dispersion and the angular dispersion cancel the material dispersion, the self-pumped phase-conjugate pulse has a minimum width, which is determined by the first-order dispersion of the grating. The self-pumped phase conjugation of an unchirped Gaussian pulse broadens and is linearly chirped whereas the self-pumped phase conjugation of a chirped Gaussian pulse is compressed when the dispersion-induced chirp cancels the initial chirp.