9 October 1998 Equation for nonlinear optical propagation beyond the paraxial approximation
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Proceedings Volume 3418, Advances in Optical Beam Characterization and Measurements; (1998) https://doi.org/10.1117/12.326643
Event: Lasers and Materials in Industry and Opto-Contact Workshop, 1998, Quebec, Canada
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.
© (1998) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Sher Alam, Sher Alam, Cleo Bentley, Cleo Bentley, } "Equation for nonlinear optical propagation beyond the paraxial approximation", Proc. SPIE 3418, Advances in Optical Beam Characterization and Measurements, (9 October 1998); doi: 10.1117/12.326643; https://doi.org/10.1117/12.326643
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