Systematic Control of Nonlinear Optical Processes Using Optimally Shaped Femtosecond Pulses

Abstract

This article reviews experimental efforts to control multiphoton transitions using shaped femtosecond laser pulses, and it lays out the systematic study being followed by us for elucidating the effect of phase on nonlinear optical laser-molecule interactions. Starting with a brief review of nonlinear optics and how nonlinear optical processes depend on the electric field inducing them, a number of conclusions can be drawn directly from analytical solutions of the equations. From a Taylor expansion of the phase in the frequency domain, we learn that nonlinear optical processes are affected only by the second- and higher-order terms. This simple result has significant implications on how pulse-shaping experiments are to be designed. If the phase is allowed to vary arbitrarily as a continuous function, then an infinite redundancy that arises from the addition of a linear phase function across the spectrum with arbitrary offset and slope could prevent us from carrying out a closed-loop optimization experiment. The early results illustrate how the outcome of a nonlinear optical transition depends on the cooperative action of all frequencies in the bandwidth of a laser pulse. Maximum constructive or destructive interference can be achieved by programming the phase using only two phase values, 0 and pi. This assertion has been confirmed experimentally, where binary phase shaping (BPS) was shown to outperform other alternative functions, sometimes by at least on order of magnitude, in controlling multiphoton processes. Here we discuss the solution of a number of nonlinear problems that range from narrowing the second harmonic spectrum of a laser pulse to optimizing the competition between two- and three-photon transitions. This Review explores some present and future applications of pulse shaping and coherent control.

Two-photon excited fluorescence enhancement with broadband versus tunable femtosecond laser pulse excitation

“…For ultrashort pulses, TPEF enhancement can be accomplished via broad SH power spectrum and high spectral density which results from both degenerate (v 1 ¼ v 2 ) and nondegenerate (v 1 ≠ v 2 ) mixing of pulse spectral components. These SH properties also suggest TPEF enhancements in selective excitation schemes by coherent quantum control of broadband fs-pulse [23][24][25] relative to narrowband fs-pulse tuning. However, these advantages of broadband fs-pulse excitation may be mitigated in cases where the dye TPE maximum is detuned such that the fs-pulse SH power spectrum overlaps with low absorptive wing (e.g., fluorescent protein variants Venus and DsRed 26 ).…”

Tailoring a coherent control solution landscape by linear transforms of spectral phase basis

“…The fitness maps or "landscapes" associated with these functions have discrete coordinates, representing symbolic binary codes of different phase profiles [26]. There can be dramatic differences between the phase profiles (and hence fitness values) of consecutive binary codes, contrary to the landscapes addressed in our study.…”

Coherent control of two photon fluorescence with a high-resolution spectral phase shaper

“…Optical pulse shaping has a range of interesting possibilities from coherent control of gas-phase diatomic molecules to the selective excitation of large (pathogenic) proteins [1] The presented work demonstrates that the phase of the second harmonic spectrum is of importance for two photon fluorescence.…”