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The Journal of Chemical Physics

Implementation of a phase and amplitude modulated π pulse for coherent optical spectroscopy

C. P. Lin, J. L. Bates, J. T. Mayer, W. S. Warren

Published Mar 15, 1987• 32 citations
Publisher

Abstract

We have implemented an amplitude and phase modulated laser pulse of the form [sech(αt)]1+3i. Such a pulse shape creates uniform population inversion within a selected bandwidth, compensates for Rabi frequency inhomogeneity, and leaves transitions outside the bandwidth unaffected. The unique features of this pulse shape are verified by measuring total fluorescence in iodine vapor as a function of laser power.

DOI
10.1063/1.451976

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We have implemented an amplitude and phase modulated laser pulse of the form [sech(αt)]1+3i. Such a pulse shape creates uniform population inversion within a selected bandwidth, compensates for Rabi frequency inhomogeneity, and leaves transitions outside the bandwidth unaffected. The unique features of this pulse shape are verified by measuring total fluorescence in iodine vapor as a function of laser power.
In molecular iodine, and most other gas-phase molecules as well, generation of a π/2 or π pulse is theoretically impossible. This result can be understood by analogy with microwave spectroscopy, since the rotational contribution to the transition dipole moment is an explicit function of the projection of the total angular momentum F = J + I along the electric-field axis. The only solution is the generation of phase-modulated pulses that inherently compensate for Rabi-frequency inhomogeneity. We present theoretical and experimental evidence that crafted phase- and amplitude-modulated pulse shapes can excite a uniform, localized, and nearly complete inversion in nuclear magnetic resonance and laser spectroscopy.
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.
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.
The effects of pulse shapes with simple phase and frequency modulation (phase proportional to amplitude or intensity, frequency proportional to intensity) are explored numerically. Many such shapes can be generated by combining self-phase-modulation with modern laser pulse-shaping capabilities (which are more flexible for amplitude modulation than for frequency modulation). Even though all of these wave forms begin and end at the same frequency (and hence violate the mathematical conditions for adiabatic inversion), we show that they can generate adiabatic population inversion or suppress intramolecular energy redistribution.
Controlling stimulated emission is of importance because it competes with absorption and fluorescence under intense laser excitation. We performed resonant nonlinear optical spectroscopy measurements using femtosecond pulses shaped by π- or π/2-step phase functions and carried out calculations based on density matrix representation to elucidate the experimental results. In addition, we compared enhancements obtained when using other pulse shaping functions (chirp, third-order dispersion, and a time-delayed probe). The light transmitted through the high optical density solution was dominated by an intense stimulated emission feature that was 14 times greater for shaped pulses than for transform limited pulses. Coherent enhancement depending on the frequency, temporal, and phase characteristics of the shaped pulse is responsible for the experimental observations.