It is well known that a simple transformation of the electric dipole interaction provides a convenient means for ascertaining the effects of permanent dipoles on the optical behaviour of systems with a response dominated by two energy levels. By establishing the general validity of the procedure for parametric processes such as harmonic generation, it is shown how the detailed structure of the optical susceptibilities associated with arbitrary forms of optical nonlinearity can be ascertained by an algorithmic method, based on a novel interpretation of the relevant quantum electrodynamical Feynman diagrams. Application of the algorithm to second and third harmonic generation illustrates its usefulness and simplicity, whilst also providing new results and revealing features, related to the role of permanent dipoles, which have not hitherto been apparent.

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An algorithm for the nonlinear optical susceptibilities of dipolar molecules, and an application to third harmonic generation

On the competition between permanent dipole and virtual state two-photon excitation mechanisms, and two-photon optical excitation pathways, in molecular excitation

Nonlinear two-component electromagnetic pulse propagation through a resonant axially symmetric anisotropic medium having a permanent dipole moment is analyzed under conditions of strong coupling between the ordinary (short-wavelength) and extraordinary (long-wavelength) pulse components It is shown that a pulse can propagate through the medium in regimes different from self-induced transparency if its ordinary component is detuned off resonance In particular, a pulse propagating in the regime of self-induced super-transparency substantially changes quantum-level populations, but its group velocity remains almost equal to the linear velocity If a pulse propagates in the extraordinary transparency regime and the carrier-frequency detuning from resonance is small, then its group velocity is substantially lower, while the level populations remain virtually invariant Regimes of propagation through weakly excited media under quasi-resonance conditions are also identified

Resonant transparency regimes under conditions of long/short-wave coupling

In this paper we present a derivation of the rotational line strengths involved in fully resonant degenerate four wave mixing processes (DFWM). General expressions are given for diatomic molecules with different Hund's coupling cases. More precisely, we tabulated the rotational line strengths for the electronic transition 2Σ+ -2Π of OH and NO. For the ground state, Hund's cases (b), (a) and the intermediate case (a-b) are considered. We also stress the dependence of the line strengths with respect to the geometry and to the polarization of the incident beams. So, we consider the optical phase conjugation (OPC) geometry and the forward (FDFWM) one. We also give expressions for the line strengths in different polarization arrangements, i.e. parallel or crossed polarized beams. A comparison is made between these cases. Finally, theoretical simulations, using our line strengths calculations, are compared with experimental spectra of OH obtained in a methane-air flame using OPC and FDFWM.

Rotational line strengths in degenerate four wave mixing

Generation of attosecond pulses in a system with permanent dipole moment

The main goal of this paper is to analyze a two-photon degenerate four-wave-mixing process that occurs in an isotropic media modeled by homogeneously broadened two-level systems having unequal permanent dipole moments and subject to rotational diffusion. Our theoretical treatment is based upon a third-order perturbative solution of the density-matrix equations and does not require the rotating-wave approximation. The medium being excited by three stationary fields, we give an analytical expression of the macroscopic polarization up to the third order, including permanent dipole moments, orientational diffusion, and field polarizations. We apply these general results to the description of a degenerate four-wave-mixing process by selecting, in the expressions, the contributions in the direction ${\mathbf{k}}_{\mathrm{\ensuremath{\alpha}}}$-${\mathbf{k}}_{\mathrm{\ensuremath{\beta}}}$+${\mathbf{k}}_{\ensuremath{\gamma}}$, ${\mathbf{k}}_{\mathrm{\ensuremath{\alpha}}}$, ${\mathbf{k}}_{\mathrm{\ensuremath{\beta}}}$, and ${\mathbf{k}}_{\ensuremath{\gamma}}$ being, respectively, the wave vectors of the exciting fields. We show that the two-photon degenerate four-wave mixing is dependent on the permanent dipole moments and is not present if these dipole moments are equal or zero. We analyze the influence of rotational diffusion. Different cases of field polarizations are also considered, and we discuss a comparison of the well-known one-photon degenerate four-wave-mixing process and this two-photon process. This process is also discussed in the particular case of phase conjugation.

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Effects of permanent dipole moments in degenerate four-wave-mixing processes

Degenerate four-wave-mixing phase conjugation is analyzed in the case of two-photon transitions between levels having unequal dipole moments. The theoretical treatment is based upon a nonperturbative solution of the density matrix and does not require the rotating-wave approximation. We give an analytical expression for the polarization component oscillating at the field frequency for a medium excited by stationary waves. In the weak-probe-beam limit, the contributions in the direction of the probe and conjugated beams are evaluated. For instance, by using this two-photon process, instead of the usual single-photon one which is independent of the permanent dipole moments even in the strong-field limit, it is shown that lower intensities are sufficient to reach higher reflectivities. The influences of the permanent dipole moments, relaxation rates, and field frequency are also discussed.

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Theoretical description of two-photon phase conjugation in polar molecules

Microscopic dynamics of materials can be studied by time delayed four-wave mixing spectroscopy. Dephasing constants can be measured by such experiments. Experimental results are easily analyzed when the correlation time τc of the exciting field is much shorter than the dephasing time, T2. However, when these quantities are on the same time scale, numerical fits are necessary. In the present work, we analyzed theoretically a time delayed four-wave mixing experiment. The material is described by an ensemble of two-level systems. Using the third order term of the density matrix, we establish a relation between T2 τc and τm the time delay for which the maximum of the diffracted light intensity is observed. The condition to obtain an estimate of T2 from the measurement of τm are discussed.

Jean-Pascal Lavoine

Papers

Effects of permanent dipole moments in degenerate four-wave-mixing processes

Theoretical description of two-photon phase conjugation in polar molecules

Theoretical study of ultrafast dephasing by four-wave mixing