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Journal of the Optical Society of America B

Measurement of the phase of a frequency-swept ultrashort optical pulse

Joshua E. Rothenberg, D. Grischkowsky

Published Apr 1, 1985• 36 citations
Publisher

Abstract

We show theoretically and confirm experimentally that, by propagating a frequency-swept ultrashort pulse through an ensemble of two-level systems, it is possible to measure the time-dependent relative phase of the pulse with respect to that of the impact-excited oscillating resonant polarization. The phase is obtained from the intensity modulation of the pulse as measured by a cross-correlation technique.

DOI
10.1364/josab.2.000626

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We show theoretically and confirm experimentally that, by propagating a frequency-swept ultrashort pulse through an ensemble of two-level systems, it is possible to measure the time-dependent relative phase of the pulse with respect to that of the impact-excited oscillating resonant polarization. The phase is obtained from the intensity modulation of the pulse as measured by a cross-correlation technique.
We treat the problem of four-wave resonant mixing of ultrashort laser pulses in gaseous media. We show that for some transitions, for example, quadrupole transitions, the polarization effects can be strongly manifested. For four-wave two-photon resonant mixing we find that the signal-wave plane rotation depends on the parameters of the resonant medium and the pulses mixed. We show that for long pump pulses and short signal pulses in the ultrashort-pulse time domain the angle of rotation of the plane of polarization of the signal plane can reach several dozen degrees. We show that the effect of altering the state of polarization of the short signal pulse can be used for measuring its shape and duration. Since the polarization measurements are precise and the proposed regimes of four-wave mixing do not depend on phase and amplitude fluctuations of the measuring pulse, the polarization four-wave mixing technique can be more accurate than the technique widely used for such purposes, measurement of the second-order intensity correlation function. We also discuss new nonlinear spectroscopy for measuring fast resonant susceptibilities (in particular, second-order polarizabilities) of the medium, based on the rotation of the polarization plane or the polarization ellipse of the signal pulse.
The main regularities of induced change of light polarization in the field of powerful ultrashort pulses in the resonant gaseous medium are investigated. Frequency- tunable ultrashort pulses allows to observe the polarization plane rotation at large values of detuning, in the different schemes of single-photon and two-photon interaction. On the other hand, the high intensity of these pulses allows to investigate the nonresonant interaction in the crystalline and solid transparent media. Our experiments carried out permit to propose the polarization technique for forming the given parameters pulses or train of pulses. In the observing medium placed between crossed polarizers, at counter propagation, powerful pump and linearly polarized probe pulses interact, because of which the probe pulse polarization changes. The polarization rotation angle as a time function is determined by the intensity of ultrashort pulse, the parameters of medium and frequencies of interacting waves. At the definite choice of the experimental conditions, requiring a probe wave after a crossed polarizer we can obtain the pulse which duration is determined by the length of medium, where interaction occurs. Using a nonresonant transparent media we have the possibility of forming the pulses of given duration tunable in a wide spectral region.
The effects of coherent excitation of a two-level system with a linearly chirped pulse are studied theoretically and experimentally [in Rb (5s-5p)] in the low field regime. The coherent transients are measured directly on the excited state population on an ultrashort time scale. A sharp step corresponds to the passage through resonance. It is followed by oscillations resulting from interferences between off-resonant and resonant contributions. We finally show the equivalence between this experiment and Fresnel diffraction by a sharp edge.
An analytic solution is obtained for the self-consistent equations describing propagation of an ultrashort pulse in a resonant two-level medium. The first approximation in respect of the dispersion is used to allow for phase modulation and for the dependence of the group velocity on the intensity and on the running value of the frequency. The conditions for the formation of a shock wave are established. It is shown that asymmetric broadening of the spectrum of a pulse results in coherent absorption, as a result of which the propagation of this pulse in such a medium leaves behind a polarization at the atomic transition frequency responsible for the radiation represented by the pulse.