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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Nonlinear coherence transformation for pulsed multimode laser radiation

Mikalai U. Karelin, Alexander M. Lazaruk

Published May 9, 2001• 1 citation
Publisher

Abstract

Nonlinear self-action of light fields in a layer of cubic nonlinear medium can serve as a convenient tool for controllable coherence manipulation. In the present work this scheme is considered for partially coherent input light. Due to experimental requirements, we consider the model of multimode laser. For the purely phase statistics of the input beam (when the average intensity can be represented in factorized form I(r,t) equals I(r)I(t)), it is possible to find out rather simply the dependence of the effective number of (coherent) modes in output radiation on the input number of modes and the nonlinearity parameter.

DOI
10.1117/12.426697

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Nonlinear self-action of light fields in a layer of cubic nonlinear medium can serve as a convenient tool for controllable coherence manipulation. In the present work this scheme is considered for partially coherent input light. Due to experimental requirements, we consider the model of multimode laser. For the purely phase statistics of the input beam (when the average intensity can be represented in factorized form I(r,t) equals I(r)I(t)), it is possible to find out rather simply the dependence of the effective number of (coherent) modes in output radiation on the input number of modes and the nonlinearity parameter.
Nonlinear interaction of light with matter is described from the quantum-statistical point of view. The cases of two-photon absorption, Raman transition, sum-frequency generation, parametric amplification, and incoherent scattering are discussed. It is shown that the nonlinear optical effects depend strongly on the statistical properties of the light fields. The rate of nonlinear absorption, generation, and amplification is higher for chaotic than for coherent, and also higher for multimode than for single-mode pump fields. Measurements of the statistics of the output fields may yield information about the statistics of the input fields and the properties of the medium.
Ideally, strong nonlinearities could be used to implement quantum gates for photonic qubits by well-controlled two-photon interactions. However, the dependence of the nonlinear interaction on frequency and time makes it difficult to preserve a coherent pulse shape that could justify a single-mode model for the time-frequency degree of freedom of the photons. In this paper, we analyze the problem of temporal multimode effects by considering the pulse shape of the average output field obtained from a coherent input pulse. It is shown that a significant part of the two-photon state transformation can be derived from this semiclassical description of the optical nonlinearity. The effect of a nonlinear system on a two-photon state can then be determined from the density-matrix dynamics of the coherently driven system using input-output theory. As an example, the resonant nonlinearity of a single two-level atom is characterized. The results indicate that the most efficient nonlinear effect may not be the widely studied single-mode phase shift, but the transfer of one of the photons to an orthogonal mode distinguished by its temporal and spectral properties.
The interaction of intense laser fields with matter is accompanied by a multitude of phenomena, ranging from the generation of coherent radiation across various spectral ranges (from terahertz to soft X-rays) to the creation of beams of accelerated charged particles and micromodification of the volume and surface of various samples.To describe this diversity of phenomena, several theoretical approaches have been developed to date.These approaches utilize different approximations to address this complex nonlinear problem, allowing for the explanation of specific aspects of such interactions.The developed theoretical frameworks consider the interaction at both microscopic and macroscopic levels; at the microscopic level, they investigate the characteristics of single atoms interacting with laser fields, while at the macroscopic level, they analyze nonlinear susceptibilities that describe the nonlinear polarization of the medium during the propagation of laser radiation through it.This work presents an overview of methods describing some of the most commonly employed theoretical approaches to model the response of a medium at a microscopic (quantum-mechanical) level, as well as various methods for controlling the properties of generated coherent radiation.A model for the gas medium is described that accounts for both the response characteristics of individual atoms and allows for consideration of phase and quasiphase matching effects during radiation generation.The influence of medium parameters on the efficiency of generation and polarization properties of generated radiation is analyzed under both phase and quasi-phase matching conditions.A detailed description of an analytical method for calculating the nonlinear susceptibility of a gas medium is provided.The obtained values of nonlinear susceptibility for arbitrary orders may be useful in numerical calculations concerning the propagation of laser radiation in matter.Various channels for radiation generation are analyzed as parameters of the laser field are varied.
A consistent quantum theory of self-action and cross-interaction of coherent light pulses in a cubically nonlinear medium is developed by using the momentum operator of the field, which takes into account the inertial nonlinearity. Specific features of generation of the quadrature-squeezed states of light pulses are considered. The spectrum of fluctuations of a quadrature below the shot-noise level is analyzed as a function of the relaxation time of nonlinearity and the magnitude of nonlinear phase additions, related to the self-action and cross-interaction.
A study is made of the excitation of inhomogeneous holographic gratings by ultrashort light pulses with an arbitrary amplitude and phase modulation in a cubic nonlinear medium. The relaxation and diffusion of a pulse-induced grating is considered. The problem of diffraction of probe radiation by an inhomogeneous grating is solved using an electrodynamic theory of perturbations and also using the coupled wave approximation. It is shown that a cubic nonlinear medium may be used to store and then to retrieve uniquely a complete complex coherence function of a pulse. A simple method is proposed for the determination of the area under an exciting pulse, which makes it possible to introduce integral parameters of such a pulse (including a generalized amplitude and duration) that can serve as satisfactory estimates of the corresponding real quantities.
We calculate the spectrum of third-harmonic generation (THG) for multimode fundamental input fields. We consider input fields from (1) a laser with gain on several cavity modes, (2) pulses with short temporal duration, and (3) frequency-modulated input fields. The effects of phase modulation in the nonlinear medium on the spectrum of the THG field are considered. Using the estimates by Miles and Harris [IEEE J. Quantum Electron. QE-9, 470 (1973)] for the nonlinear susceptibilities ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega}) and ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-\ensuremath{\omega};\ensuremath{\omega},-\ensuremath{\omega},\ensuremath{\omega}) in alkali-metal vapors, we find that phase modulation can profoundly affect the efficiency and the spectrum of the THG. Generally, the self-phase modulation of the fundamental will tend to reduce the phase matching of an intense fundamental field and the third harmonic and thereby lower the conversion efficiency. New frequencies not contained in the set of frequencies ${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{j}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{k}}$, where {${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$} are frequencies in the fundamental laser spectrum, are created even at relatively low conversion due to phase modulation. Effects of cross phase modulation are also studied.