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Quantum Electronics and Laser Science Conference

Altering excitation dynamics in optically dense media using shaped ultrafast laser pulses

J. C. Davis, Matthew R. Fetterman, Debabrata Goswami, Wei Guo Yang, Dorine Keusters, W. S. Warren

Published Jan 20, 2003• 1 citation

Abstract

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.

DOI: 10.1109/qels.1999.807372

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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.

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.

We show that pulses of electromagnetic radiation with a hyperbolic-secant envelope and a hyperbolic-tangent frequency sweep are capable of exciting an inversion line shape in a collection of two-level absorbers that is highly insensitive to optical density. This is not true of the hyperbolic-secant \ensuremath{\pi} pulse (with no frequency modulation) which undergoes significant reshaping as it propagates. The analysis is based on numerical solutions of the coupled Maxwell-Bloch equations in both the plane-wave and paraxial approximations. We also show an additional insensitivity of the inversion profile to finite relaxation times (

{T}_{2}

) that approach the pulse width.

Using the numerical solution of the Maxwell–Bloch equations, we study the interaction of short light pulses with resonant amplifying media. We consider pulses of various shapes – with Gaussian, rectangular, and exponential envelopes, the latter of which has recently attracted increased attention due to its potential for implementing new effects such as virtual absorption. We show that by choosing the shape and duration of the incident pulses, we can control the intensity and time of the amplified radiation generation, as well as the population dynamics of the medium levels.

We discuss experimental applications of specific phase and amplitude modulated laser pulse shapes. Electronic transitions in real molecules generally do not have a well-defined Rabi frequency because of the distribution of the orientation of the transition dipole, and because the density of states for all but the very simplest molecules causes many Doppler broadened transitions (including hyperfine components) to overlap. Crafted pulse shapes generate complete population inversions regardless of Rabi frequency, as well as provide a uniform inversion over the pulse bandwidth.1 These experiments directly observe population transfer between frequency ranges by giving two different frequency π pulses at different times—the use of crafted pulses increases signal to noise by now inverting the entire Rabi distribution. Experimental modifications which select a single velocity range in an arbitrarily complex molecule while retaining the other advantages of pulse shaping are presented, and the velocity dependence of fluorescence and coherence lifetimes in molecular gases is analyzed.2 Applications to monitoring velocity-changing collisional dynamics and generating large vibrational population inversions in l2 are presented, as will experimental methods to extend these sequences to more complex molecules, where velocity selection and frequency resolution are not equivalent.

Analytical solutions for the slowly varying phase as well as the field amplitude are obtained for invariant pulse propagation in resonant absorbing media consisting of interacting two-level atoms. Such media, having many atoms within a cubic wavelength, have been shown to exhibit large frequency chirps in pulse propagation owing to near-dipole–dipole interactions. Departures from hyperbolic-secant pulse envelopes and pulse areas other than 2π have been shown to occur in invariant pulse propagation. We show that self-phase modulation results from the near-dipole–dipole interactions and can cause strong modification of pulse shapes, including temporal narrowing and multipulse behavior.