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Physical Review Letters

Propagation of Complex Laser Pulses in Optically Dense Media

Matthew R. Fetterman, J. C. Davis, Debabrata Goswami, Weiguo Yang, W. S. Warren

Published May 17, 1999• 20 citations
Publisher

Abstract

Ultrafast laser pulses with complex envelopes (amplitude and frequency modulated) are used to excite an optically dense column of rubidium vapor. Pulse reshaping, stimulated emission dynamics, and residual electronic excitation in the Rb vapor are all shown to depend strongly on the laser pulse shape. Pulses that produce adiabatic passage in the optically thin limit exhibit more complex behavior in optically thick samples, including an unexpected dependence on the sign of the frequency sweep. Numerical solutions of the Maxwell-Bloch equations are shown to account for our results.

DOI
10.1103/physrevlett.82.3984

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Ultrafast laser pulses with complex envelopes (amplitude and frequency modulated) are used to excite an optically dense column of rubidium vapor. Pulse reshaping, stimulated emission dynamics, and residual electronic excitation in the Rb vapor are all shown to depend strongly on the laser pulse shape. Pulses that produce adiabatic passage in the optically thin limit exhibit more complex behavior in optically thick samples, including an unexpected dependence on the sign of the frequency sweep. Numerical solutions of the Maxwell-Bloch equations are shown to account for our results.
We examine the propagation of shaped (amplitude- and frequency-modulated) ultrafast laser pulses through optically dense rubidium vapor. Pulse reshaping, stimulated emission dynamics, and residual electronic excitation all strongly depend on the laser pulse shape. For example, frequency swept pulses, which produce adiabatic passage in the optically thin limit (independent of the sign of the frequency sweep), behave unexpectedly in optically dense samples. Paraxial Maxwell optical Bloch equations can model our ultrafast pulse propagation results well and provide insight.
Summary form only given. We study the interaction between intense (50 MW peak power), shaped ultrafast laser pulses and optically dense samples of Rb vapor. In particular, we concentrate our attention on laser pulses with a the complex hyperbolic secant envelope, or equivalently, a sech electric field envelope with a tanh frequency sweep. In order to produce and characterize the shaped laser pulses used in our experiments, we exploited several new technologies: amplified, shaped laser pulses were generated using an acousto-optic modulator-based system combined with a chirped-pulse regenerative amplifier. The amplitude and phase of these pulses were then characterized by the STRUT (spectrally and temporally resolved upconversion technique). The STRUT was used to measure the laser pulses both before and after propagating through Rb vapor. Examples of such experimental STRUT images are presented. The complex sech pulse was selected because, in optically thin media, only it and rectangular pulses give complete analytical solutions to the Bloch equations. This shape has been found to generate complete population inversion over a well-defined and amplitude-insensitive bandwidth. In optically dense samples the excited state dynamics are not so straightforward. We have found, both in experiments and theoretically, that the extent and character of the population inversion is related to the frequency sweep of the laser pulses as does the amount of residual excited population after the pulse and any subsequent stimulated emission.
We investigate ultrashort pulse propagation in a dense medium of two-level atoms. We numerically solve the coupled nonlinear Maxwell-Bloch equations by assuming that the fields are slowly varying in time only. We find that while intrinsic optical switching of the atomic inversion persists in extended media, self-phase-modulation effects, coherent energy transfer, and reflections can be large even for films that are only a small fraction of a wavelength thick. If the propagation distance is sufficiently large, a physical boundary that separates fully excited atoms from atoms in the ground state can be created within the medium. In turn, this leads to a rapid spatial modulation of the nonlinear polarization, and a deterioration of the intrinsic optical switching mechanism. We then show that, although the slowly varying envelope approximation in space may be preempted by the fast longitudinal variation of the field and atomic variables, the mean-field approximation remains valid in the regime of ultrafast optical switching, provided the film thickness is sufficiently small such that the medium is nearly uniformly excited. These results are generated by utilization of our calculational method that fully accounts for the longitudinal dynamics of the fields, including reflections.
Optical precursor is the sharp optical pulse front that does not show delay in absorptive media. In this thesis, optical precursor behavior in rubidium (Rb) vapor was investigated in the picoseconds regime. An amplified femtosecond laser was shaped to a 7-ps square pulse with sharp rising and trailing edges. This pulse was then sent into a hot rubidium vapor, and the center frequency of the laser pulse was absorbed. The output pulses were measured by a fast streak camera with 2-picosecond resolution. By varying the temperature of the Rb vapor, the measured pulse shapes showed the progression of formation of optical precursors. The measured pulses shapes showed good agreement with theory.\n \nOn the other hand, a connection between optical precursors and femtosecond laser pumped 3-photon superradiance was investigated in this thesis. Maxwell-Bloch equations were numerically solved in two steps with commercial software Mathematica 8. A good agreement was found between simulation and experiment. It was confirmed that, at low excitation regime, superradiance generated from hot rubidium vapor, which were pumped by a femtosecond laser, can be understood as the formation of optical precursors.
Motivated by the production of strong optical forces on atoms, we have done numerical studies of adiabatic rapid passage in light that is both frequency and amplitude modulated in the form of chirped pulses, and we found unanticipated regularities. We have quantified these regularities in terms of a periodic Hamiltonian, and obtained a result similar to the Bloch theorem, but in the time domain. This led to further numerical studies and a quantitative description of the behavior of an atom under multiply repetitive sweeps.