Rotating elliptical gaussian beams in nonlinear media

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.

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.

Journal of The Optical Society of America B-optical Physics, 1994

We present an analysis for self-focusing of an elliptic Gaussian laser beam in a saturable nonlinear medium. It is shown that stationary self-trapped propagation is forbidden in a saturable medium. Though self-trapped propagation does not occur, a virtual threshold power for self-focusing can be defined. Above this threshold power value, but not far from it, the beam focuses. Below this threshold the beam defocuses. It is also shown that the effective beam radius never reaches zero, which is a property of a Gaussian laser beam.

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.

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.

Pramana, 2005

We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam, which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed to convert a circular Gaussian beam into an elliptic Gaussian beam.

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.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2003

We present a systematic study of propagation of circularly polarized beams in a Kerr medium. In contrast to previous studies, vectorial effects (i.e., coupling to the axial component of the electric field and the grad-div term) and nonparaxiality are not neglected in the derivation. This leads to a system of equations that takes into account nonparaxiality, vectorial effects, and coupling to the opposite circular component (i.e., the one rotating in the opposite direction). Using this system we show that the standard model in the literature for self-focusing of circularly polarized beams can lead to completely wrong results, that circular polarization is stable during self-focusing, and that nonparaxiality and vectorial effects arrest collapse, leading instead to focusing-defocusing oscillations. We also show that circularly polarized beams are much less likely to undergo multiple filamentation than linearly polarized beams.

Plasma Physics, 1979

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 selffocusing 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.

Journal of Modern Optics, 1997

We study the three-dimensional field distribution of a focused axially symmetric flattened Gaussian beam. In particular, exact closed-form expressions for the intensity along the optical axis and at the focal plane are provided, together with a comparison between our results and those pertinent to the case of a converging spherical wave diffracted by a hard-edge circular aperture. Some hints for future investigations are also given.