# Spatiotemporal Complex Geometrical Optics (CGO) of N 3D Interacting Asymmetric Gaussian Wave Packets in Nonlinear Medium - CGO as the Simplest and Efficient Method for Spatiotemporal Evolution

### Pawel Berczynski, Slawomir Marczynski

#### Abstract

The complex geometrical optics (CGO) was applied for the spatiotemporal evolution of arbitrary number of 3D mutually incoherent (with different carrier frequencies) Gaussian wave packets (GWPs) interacting and propagating in a nonlinear medium of Kerr type. The CGO reduced description of the propagation of the beam, the pulse and the wave packet to complex ordinary differential equations (ODE) This leads to exceptionally fast numerical algorithms. We observed high efficiency of the CGO method to compute interactions of arbitrary number of 3D Gaussian wave packets propagating in a nonlinear (anomalous) dispersive medium of the Kerr type. The derived CGO equations were compared with equations obtained by the variational method. CGO described the Gaussian beam propagation in free space as well as the Gaussian pulse spreading in the linear anomalous dispersive medium more illustratively than both the Fourier transform method and the Fresnel diffraction integral method. The spatiotemporal CGO has been proven to be a method more practical than the spectral analysis, the variational method, the method of moments and the method of the generalized eikonal approximation. Complementary to the presented results, an on-line CGO solver, implemented in Javascript, is freely available at the authorsâ€™ website: http://slawek.ps.pl/odelia.html.

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#### Paper Citation

#### in Harvard Style

Berczynski P. and Marczynski S. (2015). **Spatiotemporal Complex Geometrical Optics (CGO) of N 3D Interacting Asymmetric Gaussian Wave Packets in Nonlinear Medium - CGO as the Simplest and Efficient Method for Spatiotemporal Evolution** . In *Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,* ISBN 978-989-758-092-5, pages 53-60. DOI: 10.5220/0005291600530060

#### in Bibtex Style

@conference{photoptics15,

author={Pawel Berczynski and Slawomir Marczynski},

title={Spatiotemporal Complex Geometrical Optics (CGO) of N 3D Interacting Asymmetric Gaussian Wave Packets in Nonlinear Medium - CGO as the Simplest and Efficient Method for Spatiotemporal Evolution},

booktitle={Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,},

year={2015},

pages={53-60},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005291600530060},

isbn={978-989-758-092-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,

TI - Spatiotemporal Complex Geometrical Optics (CGO) of N 3D Interacting Asymmetric Gaussian Wave Packets in Nonlinear Medium - CGO as the Simplest and Efficient Method for Spatiotemporal Evolution

SN - 978-989-758-092-5

AU - Berczynski P.

AU - Marczynski S.

PY - 2015

SP - 53

EP - 60

DO - 10.5220/0005291600530060