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Physical Review A

Single-cycle coherent terahertz-pulse propagation in rigid-rotor molecular media

Robert Marskar, Ulf L. Österberg

Published Aug 24, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.92.023843

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Recent progress in ultrafast technology has led to the generation of optical pulses as short as 8 fs. The propagation of such short pulses in nonlinear optical media requires new computational techniques in which the standard approximations such as the slowly-varying envelope approximation (SVEA) and rotating-wave approximation (RWA) are not made while using the Maxwell-Bloch equations [1]. Previous calculations, which used the finite-difference time-domain (FDTD) method, found that for a a Kerr-like instantaneous nonlinearity [2] significant differences can occur when the full vector Maxwell equations are used instead of the nonlinear Schrodinger equation. Recently, the FDTD method has been extended to the case of a homogeneously broadened two-level atomic system [3].
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.
We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly varying-envelope approximations. The method of solution is based on the Maxwell-Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pulses of large enough area. Moreover, deviations from the area theorem appear to be strongly dependent on the pulse shape that cannot be observed for longer few-cycle pulses.
We focus on the propagation properties of a single-cycle laser pulse through a two-level medium by numerically solving the full-wave Maxwell–Bloch equations. The counter-rotating terms in the spontaneous emission damping are included such that the equations of motion are slightly different from the conventional Bloch equations. The counter-rotating terms can considerably suppress the broadening of the pulse envelope and the decrease of the group velocity rooted from dispersion. Furthermore, for incident single-cycle pulses with envelope area 4 π , the time delay of the generated soliton pulse from the main pulse depends crucially on the carrier-envelope phase of the incident pulse. This can be utilized to determine the carrier-envelope phase of the single-cycle laser pulse.