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Journal of the Optical Society of America B

Dynamic spatiotemporal pulse shaping in two-photon active biomolecular media

Edeltraud Gehrig, Ortwin G. Hess

Published Feb 15, 2007• 4 citations
Publisher

Abstract

The propagation of ultrashort light pulses in two-photon media is investigated on the basis of a density-matrix formalism for the molecular levels and a wave equation for the dynamics of the light fields. The simulation shows that the dynamic light-matter coupling and level dynamics lead to saturation effects and space-dependent pulse shaping that determine the dynamic response of the molecular medium.

DOI
10.1364/josab.24.000522

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The propagation of ultrashort light pulses in two-photon media is investigated on the basis of a density-matrix formalism for the molecular levels and a wave equation for the dynamics of the light fields. The simulation shows that the dynamic light-matter coupling and level dynamics lead to saturation effects and space-dependent pulse shaping that determine the dynamic response of the molecular medium.
We model the response of a molecular medium to an intense pulse of light. We begin by reducing the Maxwell-Bloch equations for a multilevel molecular model system to a set of simplified propagation equations. We thereby obtain expressions for the frequency, temperature, and field intensity dependence of the ground and excited electronic state absorption cross sections, and the emission cross section, as well as the temperature dependence of the decay rate of the excited state. The phenomena of saturation, excited-state absorption, optically induced dichroism and birefringence, vibronic energy transfer, induced molecular alignment, decay of the matter-field interaction energy, and rotational diffusion are considered within the general formalism for describing the propagation of an intense pulse of light in the molecular medium. We find that the cross section for absorption (emission) of a photon is not identical to the cross section for molecular excitation (deexcitation) via the matter-field interaction. This is explained in terms of an energy balance between the matter, radiation, the matter-radiation interaction, and the bath responsible for the broadening of the molecular transitions. The inequality of these cross sections determines whether the system supplies or draws energy from the thermal bath. The rise in the vibrational temperature of molecules subjected to an intense short pulse is shown to significantly affect propagation of the pulse. The alignment of the molecular system resulting from saturation of the ground-state transition by a polarized laser pulse and the effects of the orientational dependence of the matter-field interaction including effects of rotational diffusion are determined. As an example of the formalism we consider pulse propagation in a Rhodamine 6G solution. We fit the parameters of the model to determine the frequency dependence of the ground- and excited-state absorption cross sections and the emission cross section and compare with experimentally determined cross sections. We describe the propagation of a pulse whose temporal width is comparable to the rotational diffusion time of the molecules in the dye solution and calculate polarization pulse probe signals.
The Maxwell–Schrödinger equations describing the ultrashort laser pulse propagation in multilevel molecular media are shown to be analytically solvable and to reduce to nonlinear multisine-Gordon equations for certain models of the field–molecule system. Special cases of level schemes are shown to lead to soliton propagation. A numerical study is presented in order to examine the effect of nonresonant (virtual) transitions on pulse propagation and amplification in a three-level molecular system as a function of intensity and detuning.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi.  In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).
We establish a first-principle model for the simulation of spatiotemporal light pulse dynamics based on the combination of the time-dependent Schrödinger equation and the unidirectional propagation equation. The proposed numerical scheme enables computationally efficient simulation while being stable and accurate. We use the new model to examine self-focusing of a short pulse in atomic hydrogen and show that an accurate description of the excited-levels dynamics can only be achieved by a propagation model with an ab-initio description of the light-matter interaction, which accounts for the laser-dressed multilevel structure of the system, including bound and free states, and its sub-cycle response.
Propagation of strong femtosecond hyper-Gaussian pulses in an organic molecular medium is studied by solving numerically the Maxwell-Bloch equations using an iterative predictor-corrector finite-difference time-domain technique. The carrier-wave frequency of the field is tuned in two-photon resonance with the molecular system simplified by a cascade three-level model. Strong two-photon absorption induced optical power limiting behavior is observed for the hyper-Gaussian pulses of different orders. For the ultrashort hyper-Gaussian pulses, it is found that the ”two-photon area” is no further the deciding quantity of the two-photon induced dynamics, and pulses with different temporal profiles will induce different two-photon absorption dynamics and optical limiting processes. With the same pulse duration and field amplitude, pulses of a lower order is found to have a larger input ”two-photon area” but a smaller output area, and therefore show a better optical limiting behavior. The population distribution and the generation of new fields during pulse propagation also depend on the shape of the incident field.
The spatiotemporal evolutions of ultrashort pulses in two dimensions are investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly varying envelope approximation and rotating-wave approximation. For an on-axis $2n\ensuremath{\pi}$ sech pulse, local delay makes the temporal split $2\ensuremath{\pi}$ sech pulses crescent-shaped in the transverse distribution. Due to the transverse effect, the temporal split $2\ensuremath{\pi}$ sech pulses become unstable and experience reshaping during the propagation process. Then, interference occurs between the successive crescent-shaped pulses and multiple self-focusing can form.