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Days on Diffraction

Propagation of laser pulse with a few cycle duration in multi-level media

Vyacheslav A. Trofimov, Dmitry Yu. Zagursky, Irina G. Zakharova

Published May 1, 2015• 2 citations
Publisher

Abstract

1D propagation of a THz Gaussian pulse, containing a few cycles, in multi-level media is studied using computer simulation. Electromagnetic field evolution is governed by Maxwell's equations whereas a medium response is described in the frame-work of the density matrix formalism. For the pulse with a sufficiently broad spectrum we demonstrate the appearance of a cascade mechanism for molecule energy level excitation. As a result, the spectrum of the THz pulse, transmitted through a medium layer, is broadened essentially in comparison with the incident pulse spectrum. We also take into account the incident pulse absolute phase influence on the pulse spectrum broadening.

DOI
10.1109/dd.2015.7354889

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Physical Review A•Aug 24, 2015•2 citations
1D propagation of a THz Gaussian pulse, containing a few cycles, in multi-level media is studied using computer simulation. Electromagnetic field evolution is governed by Maxwell's equations whereas a medium response is described in the frame-work of the density matrix formalism. For the pulse with a sufficiently broad spectrum we demonstrate the appearance of a cascade mechanism for molecule energy level excitation. As a result, the spectrum of the THz pulse, transmitted through a medium layer, is broadened essentially in comparison with the incident pulse spectrum. We also take into account the incident pulse absolute phase influence on the pulse spectrum broadening.
Recent experimental realizations of single-cycle pulses in the terahertz, infrared, and optical regions provide promising light sources for applications in telecommunication, medical imaging, spectroscopy, and coherent control. In the resonant regime, the short duration of such pulses imply that they may escape certain effects that are detrimental to coherence; spontaneous emission is one such example. In combination with an octave-spanning spectral bandwidth, an adequate theoretical approach necessitates a semiclassical coherence model outside the conventional few-level, rotating wave, and slowly varying envelope approximations. The evolution equations that govern the underlying dynamics of such systems are inherently nonlinear and possess solutions only in certain idealized, limiting cases. In this thesis we investigate the viability of obtaining general-purpose numerical solutions to such problems.\n\nA computational approach based on Maxwell’s equations coupled with a multi-level quantum mechanical model for homogeneously and inhomogeneously broadened media is reported. The formulation leads to a numerical algorithm applicable to bi-directional propagation of pulses of arbitrary duration along all three spatial coordinates. For sufficiently dense inhomogeneously broadened materials we show, numerically, that when the forward propagation approximation of Maxwell’s wave equation is not valid, certain types of optical solitons may lose a significant amount of energy with increasing propagation distance through the co-excitation of a backward mode.\n\nA second set of computational routines is based on neglection of optical backpropagation in Maxwell’s wave equation. The resulting propagation equation generalizes the paraxial wave equation to the single-cycle pulse regime and is shown to be susceptible to numerical integration in conjunction with quantum theory. Our computer code is applied to femtosecond conical emission in atomic sodium. We find that cone emission occurs together with spatiotemporal pulse breakup analogous to the soliton-type splitting observed in self-induced transparency. We furthermore support these results by presenting complementary numerical calculations of the same phenomenon in the picosecond pulse regime. The angular structure of the conical emission observed numerically agrees with expermental measurements performed by others. Our computational results resolve some of the underlying questions surrounding conical emission in alkali metal vapors.\n\nConsideration of optical selection rules in rigid-rotor molecules is shown to greatly simplify the numerical evaluation of single-cycle pulse propagation in multi-level molecular systems. Numerical application of linearly polarized single-cycle terahertz pulses in rigid rotor molecular media, incorporating a full rotational manifold, shows that coherent bleaching effects ultimately lead to self-steepening of the driving pulse. A possible practical consequence of these results is that coherent, nonlinear saturation effects may partially cancel dispersion-induced temporal broadening of single-cycle pulses, opening up the possibility of increased energy transmission of terahertz pulses through molecular media.
The spectrum evolution of a few-cycle optical pulse in a resonant two-level atom medium is studied theoretically by using the full Maxwell-Bloch equations. On the propagating pulse, significantly much faster oscillation components separated with the main pulse appear due to strong self-phase modulation and pulse reshaping. In this case, ideal self-induced transparency cannot occur for a 2π pulse. The spectrum of the 4π pulse shows an evident oscillatory feature because of the continuum interference of the separate pulses. For larger pulse areas, continuum generation from near ultraviolet to infrared occurs.
The spectrum evolution of a few-cycle optical pulse in a resonant two-level atom medium is studied theoretically by using the full Maxwell-Bloch equations. On the propagating pulse, significantly much faster oscillation components separated with the main pulse appear due to strong self-phase modulation and pulse reshaping. In this case, ideal self-induced transparency cannot occur for a 2 pi pulse. The spectrum of the 4 pi pulse shows an evident oscillatory feature because of the continuum interference of the separate pulses. For larger pulse areas, continuum generation from near ultraviolet to infrared occurs.
We theoretically analyze linear and nonlinear coherent propagation of linearly polarized, plane-wave, resonant single-cycle terahertz pulses through spatially extended rigid-rotor molecular media. Our model incorporates mixed state medium preparation, nonperturbative nonlinearities, saturation, coherence, memory effects, and propagation, but ignores the effects of damping. Explicit solutions are reported in the linear propagation regime. These solutions are the multilevel superposition of linear, single-cycle $0\ensuremath{\pi}$ pulses, and appear as temporal beats in the time domain. For media initially in thermal equilibrium, the pulse and molecular beats are dispersive and broaden temporally with increased propagation distance. In the simplified limit of equal rotational line strength (an idealized situation), the emitted impulses are exact temporal copies of the input pulse. An efficient, scalable computational method for solving the reduced multilevel Maxwell-Bloch equations for molecular media is reported. This method is based on a standard differential method for the propagation equation together with an operator splitting method for the Bloch equations. It invokes neither the slowly varying envelope (SVEA) or rotating wave approximations (RWA), and incorporates a large number of possible energy eigenstates (we solve for 7744 levels). Case studies of nonlinear single-cycle pulse propagation are then provided by means of computer solutions. In the nonlinear regime, we observe strong molecular orientations and suppression of the pulse and orientational revivals predicted by linear theory. For sufficiently strong pulses, coherent bleaching effects lead to increased transmission of the driving pulse, which also bears signs of self-modulation and carrier-shock formation.