Coherent control of ultrafast optical four-wave mixing with two-colorω−3ωlaser pulses

Abstract

A theoretical investigation on the quantum control of optical coherent four-wave mixing interactions in two-level systems driven by two intense synchronized femtosecond laser pulses of central angular frequencies ω and 3ω is reported. By numerically solving the full Maxwell-Bloch equations beyond the slowly-varying envelope and rotating-wave approximations in the time domain, the nonlinear coupling to the optical field at frequency 5ω is found to depend critically on the initial relative phase φ of the two propagating pulses; the coupling is enhanced when the pulses interfere constructively in the center (φ = 0), while it is nearly suppressed when they are out of phase (φ = π). The tuning of the initial absolute phase of the different frequency components of synchronously propapagating ω-3ω femtosecond pulses can serve as a means to control coherent anti-Stokes Raman (CARS) processes.In recent years, encouraged by the developments in the engineering of intense ultrashort laser fields with a well defined absolute phase [1], studies on the phase control of the interaction of two-color strong ultrashort laser pulses in nonlinear materials have received a great interest [2,3,4,5,6,7]. Phenomena arising from such ultrashort pulse interaction can be of extreme importance in fields as diverse as optoelectronics and materials research, in biological applications such as spectroscopy and microscopy, in high harmonic generation, and in photoionization or molecular dissociation, among others.It is known that when the pulses duration approach the duration of only several optical cycles, theories based on the slowly-varying envelope approximation (SVEA) and the rotating-wave approximation (RWA) are not appropriate, since phenomena such as electric field timederivatives leading to carrier-wave reshaping [8], or the generation of high spectral components [9], can not be described by such theories. In these situations, accurate numerical modeling based on the finite-difference timedomain (FDTD) method [10] is being increasingly used to investigate the full set of optical Maxwell-Bloch equations [7,8,9,11].In this Letter, we investigate the possibility of phase control of transient four-wave mixing interactions in twolevel systems driven by two mutually coherent intense ultrashort pulses of central angular frequencies ω and 3ω. We employ a standard predictor-corrector FDTD numerical approach which incorporates all propagation effects -such as nonlinearity, dispersion, absorption, dissipation, saturation, and other resonance effects- [8], to study the sensitivity on the relative phase φ of the nonlinear coupling of the ω-3ω pulses to the field at frequency 5ω, which results from the interaction of the waves through the third order susceptibility of the medium (χ (3) ) [12].By describing the evolution of the field spectrum as the two-color pulses propagate through the medium, our simulations demonstrate that the generation of the 5ω-component is enhanced when the two pulses are in phase (φ = 0), while it is nearly suppressed when ...

Control of harmonic generation in a quantum well with two-colour few-cycle pulses

“…In the present work, we apply two-colour few-cycle ultrashort pulses, a fundamental laser field (ω 0 ) and its third harmonic field (3ω 0 ) to investigate the phase control of the spectra in a semiconductor QW with consideration of quantum size effects. Usually, in the ω 0 −3ω 0 scenario, the symmetry of the multi-photon pathway is always preserved, thus even-order harmonic generations are rarely found in inversion symmetric medium [24,33]. Here, our results demonstrate that, for fewcycle pulses, the spectral peak at 4ω 0 can be achieved even for ω 0 − 3ω 0 combinations.…”

“…The excited-state lifetime τ 1 and the dephasing time τ 2 are 100 ps and 1 ps, respectively [34]. The equations of the system are solved by employing an iterative predictor-corrector finitedifference time-domain technique without invoking any of the standard approximations such as the slowly varyingenvelope approximation and the rotating-wave approximation [24][25][26][27][37][38][39][40][41][42][43][44][45].…”

“…Usually, coherent control is the ability to control the dynamics through adjusting laser parameters such as phase and intensity [20][21][22][23]. Some novel phenomena have been found when using two-colour few-cycle pulses [24][25][26][27]. By controlling the relative phase of the two-colour few-cycle pulses, the anti-Stokes Raman component and ultrafast fourwave mixing have obvious changes [24][25][26].…”

“…Some novel phenomena have been found when using two-colour few-cycle pulses [24][25][26][27]. By controlling the relative phase of the two-colour few-cycle pulses, the anti-Stokes Raman component and ultrafast fourwave mixing have obvious changes [24][25][26]. The higher spectral components depend crucially on the relative phase of the two-colour few-cycle pulses: continuum and distinct peaks can be achieved by controlling the relative phase [26].…”

Propagation and nonlinear scattering of ultrashort pulses : examples of modeling and applications

“…As a tool to find and validate routes to obtain CARS spectroscopy images with a sub-diffraction limited resolution, we model the CARS process using the density matrix approach (see also, e.g., the work by Serrat et al [72]). From the polarizations described by the off-diagonal elements of the density matrix, the field as radiated by the molecule can be determined as will be shown in more detain in section 4.2.2, while the diagonal elements display any population changes that may occur during CARS emission.…”