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Proceedings Paper

Equation for nonlinear optical propagation beyond the paraxial approximation
Author(s): Sher Alam; Cleo Bentley
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Paper Abstract

The beam propagation in optics is not only a fundamental but a practical problem. The commonly used approach is the paraxial approximation. It is natural in some situations such as the catastrophic beam collapse in self-focusing media to go beyond the paraxial approximation. Indeed since the late eighties and now more recently the problem of going beyond the paraxial approximation has been revisited numerically and analytically by several groups. In most of these approaches the refractive index variation associated with Kerr nonlinearity is incorporated but they do not take into account the vectorial effects and consequently fail to satisfy the divergence equation. More recently there have been attempts to incorporate the vectorial nature by considering the interaction between propagation and polarization. In particular the interaction between propagation and polarization was considered in a guiding structure for the description of intrafiber geometric rotation of polarization. Recently Crosignani et al. have proposed a different approach based on the coupled mode theory to deal with the problem of nonparaxial propagation. The purpose and motivation of this work is to examine the general equation for linear and nonlinear optical propagation beyond the paraxial approximation in the context of the coupled mode approach. The complete set of equations incorporating the backward propagating modes are written out. The relation between self-focusing and nonparaxiality is discussed. It is well-known that the model equation for propagation of a laser beam in a nonlinear Kerr media is the nonlinear Schrodinger equation (NLS). The singularities of NLS equation near the self-focusing region are looked at from the point of view of the general equation for propagation. In particular we attempt to examine the region of validity of NLS and compare the self-focusing region in NLS and the general propagation equation. It is interesting to look at the power in the paraxial and non-paraxial parts.

Paper Details

Date Published: 9 October 1998
PDF: 11 pages
Proc. SPIE 3418, Advances in Optical Beam Characterization and Measurements, (9 October 1998); doi: 10.1117/12.326643
Show Author Affiliations
Sher Alam, KEK-High Energy Accelerator Research Organization (Japan) and Univ. of Peshawar (Pakistan) (Japan)
Cleo Bentley, Prairie View A&M Univ. (United States)

Published in SPIE Proceedings Vol. 3418:
Advances in Optical Beam Characterization and Measurements
Michel Piche, Editor(s)

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