A novel approach to the nonlinear propagation of wide light beams

2008

his article addresses several types of optical beams, and their propagation along different media. Initially, the proprieties and the evolution of the Gaussian beam propagating through a homogeneous linear media are studied using the paraxial approximation. The results allow the understanding of more complex beams, e.g., rectangular and hyperbolic secant profiles, which are analyzed using a numerical method based on the Fast Fourier Transform (FFT). Taking into account the properties of the simpler beams, the Hermite – Gaussian high order beams are subsequently studied, using the time independent Schrödinger equation and the solutions of the quantum harmonic oscillator. After this, a brief analysis of the propagation of the Hermite – Gaussian beams through an anisotropic media is done. In the presence of nonlinear media the Gaussian, the Hermite – Gaussian and the existence of spatial solitons are studied, the lately bearing in mind their behavior under the influence of self – focus...

Journal of Plasma Physics, 1980

An analytic investigation is made of the nonlinear propagation characteristics of laser beams with elliptically shaped Gaussian intensity cross-sections. Explicit analytic criteria, in terms of inital conditions, are given, which determine the dynamical behaviour of the transverse dimensions of the beam, i.e. its self- focusing and defocusing properties. Approximate analytic solutions are also given, which display the characteristic features of the general variation of beam width with distance of propagation.

Optik - International Journal for Light and Electron Optics, 2004

Using a direct variational technique involving elliptic Gaussian laser beam trial function, the combined effect of nonlinearity and diffraction on wave propagation of optical beam in a homogeneous higher order nonlinear medium is presented. Particular emphasis is put to understand the variation of beam width and longitudinal phase delay with the distance of propagation in case of lossless and lossy medium. It is also observed that stationary self-trapping is possible in lossless medium at higher laser intensity where fifth order nonlinearity becomes comparable to third order nonlinearity. The phase is also seen to be always negative.

An investigation to identify the role of quintic nonlinearity on induced focusing of two laser beams and on the conversion of a Gaussian laser beam into an elliptic Gaussian beam has been presented. We have evaluated threshold for induced focusing and the role played by quintic nonlinearity in determining this threshold. It has been found that less power is required for induced focusing in comparison to self focusing of single beam. We have shown that influence of quintic nonlinearity is maximum when wavelengths of both beams are same. For elliptic Gaussian beams, we have shown that when power of both beams is above certain threshold, t he effective radius of both beams collapses and collapse distance depends on power. We have shown that using induced focusing a circular Gaussian laser beam can be converted into elliptic Gaussian beam. Roles played by quintic nonlinearity on this conversion are highlighted.

In this work propagation of different types of optical beam were studied. Beam propagation is generally affected by diffraction and nonlinearity of the medium. Keeping these two factors under consideration propagation of beam was observed and stability was tested. Both one-dimensional and twodimensional beam were used in this study.

Journal of the Optical Society of America B, 2000

We show that the increase in critical power for elliptic input beams is only 40% of what had been previously estimated based on the aberrationless approximation. We also find a theoretical upper bound for the critical power, above which elliptic beams always collapse. If the power of an elliptic beam is above critical, the beam self-focuses and undergoes partial beam blowup, during which the collapsing part of the beam approaches a circular Townesian profile. As a result, during further propagation additional small mechanisms, which are neglected in the derivation of the nonlinear Schrödinger equation (NLS) from Maxwell's equations, can have large effects, which are the same as in the case of circular beams. Our simulations show that most predictions for elliptic beams based on the aberrationless approximation are either quantitatively inaccurate or simply wrong. This failure of the aberrationless approximation is related to its inability to capture neither the partial beam collapse nor the subsequent delicate balance between the Kerr nonlinearity and diffraction. We present an alternative two-stage approach and use it to analyze the effect of nonlinear saturation, nonparaxiality, and time dispersion on the propagation of elliptic beams. The results of the two-stage approach are found to be in good agreement with NLS simulations.

Journal of the Optical Society of America B, 2005

The steady-state focusing-defocusing of a laser beam in a medium characterized by built-in radial inhomogeneity and nonlinearity of a saturating nature has been investigated in the paraxial approximation. By use of the parabolic equation for wave propagation and a complex eikonal, coupled differential equations for the beam-width parameter, absorption parameter, and nonlinearity parameter have been obtained. The numerical solution of these equations for a typical set of parameters yields the dependence of the beam width and axial irradiance on distance of propagation. A discussion of the results follows. The situations for which the analysis may be applicable are indicated in the introduction.

Journal of Optics A: Pure and Applied Optics, 2005

An investigation to identify the role of quintic nonlinearity in induced focusing of two laser beams and in the conversion of a circular laser beam into an elliptic Gaussian beam is presented. To derive relevant beam width equations, a set of two coupled nonlinear Schrödinger equations has been solved using variational formalism. The threshold for induced focusing has been evaluated and the role played by quintic nonlinearity in determining this threshold has been identified. It has been found that less power is required for induced focusing in comparison to self-focusing of a single beam. For elliptic Gaussian beams, it has been shown that when the power of both beams is above a certain threshold the effective radius of both beams collapses, and the collapse distance depends on power. It has been further predicted that using induced focusing a circular laser beam can be converted into an elliptic Gaussian beam. The role played by quintic nonlinearity in this conversion is highlighted.

Starting from the Huygens-Fresnel diffraction integral, the propagation of an Elegant Hermite-cosh- Gauss field (EHChG) through a first-order paraxial optical ABCD system has been studied in the perturbed case. The propagation equations in free space and focusing of the elegant-Hermite-cosh-Gauss beam have been derived in closed forms. It is shown that the propagation properties depend on the beam parameters such as: the Fresnel number and the aperture width. Results corresponding to the unapertured EHChG beam are obtained as a limiting case when the truncation parameter tends to infinity. Furthermore, this study provides a general characteristics because cosh-Gaussian, elegant Hermite- Gaussian and fundamental Gaussian beams can be considered as the particular cases of EHChG beams.

Applied Optics, 1993

The evolution of non-Gaussian and nonspherical high-power laser beams in cubic nonlinear media is described by means of their mean or gross parameters: width, mean curvature radius, and quality factor. The influence of the beam over its own propagation is contained in a new mean parameter that measures the ability of a beam to build its own waveguide. Beam quality and threshold power for self-focusing are connected. The ABCD and invariance laws for modified complex beam parameter and quality factor allow one to transform in one step the mean beam parameters through a sequence of nonlinear propagations, lenses, mirrors, and nonlinear quadratic graded index.