Complex Rays with an Application to Gaussian Beams

Keller, Joseph B.; Streifer, W.

doi:10.1364/josa.61.000040

Cited by 185 publications

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“…Some methods proposed to formulate the scattering wave were presented: examples are in [1][2][3]. In this regard, some years ago, a method has been presented for solving the scattering problem as a boundary value problem [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

On Laser Radar Cross Section of Targets With Large Sizes for E-Polarization

El-Ocla¹

2006

PIER

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Abstract-In this paper a study is presented to handle the behavior of radar cross section (RCS) of partially convex targets of large sizes up to five wavelengths in free space. The nature of incident wave is an important factor in the remote sensing and radar detection applications. To investigate the effects of incident wave nature on the RCS, scattering problems of plane and beam wave incidences are considered. Targets are taking large sizes to be bigger enough than the beam width with putting into consideration a horizontal incident wave polarization (E-wave incidence). The effects of the target configuration together with the beam width on the laser RCS compared to the case with the plane wave incidence are numerically analyzed. Therefore, we will be able to have some sort of control on radar detection using beam wave incidence.

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Section: Introductionmentioning

confidence: 99%

On Laser Radar Cross Section of Targets With Large Sizes for E-Polarization

El-Ocla¹

2006

PIER

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“…The ability of ray-based CGO to describe Gaussian beam diffraction was established approximately 40 years ago [4][5][6] (see also [1,3]). Development of numerical methods allowed later describe GB propagation and diffraction in inhomogeneous media [7][8][9].…”

Section: Paraxial Complex Geometrical Optics (Cgo)mentioning

confidence: 99%

Gaussian beam diffraction in inhomogeneous and nonlinear media: analytical and numerical solutions by complex geometrical optics

Berczyński

Kravtsov²,

Zegliñski

2008

Open Physics

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Abstract:The method of paraxial complex geometrical optics (CGO) is presented, which describes Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like waveguides. By way of an example, the known analytical solution for Gaussian beam diffraction in free space is presented. Paraxial CGO reduces the problem of Gaussian beam diffraction in inhomogeneous media to the system of the first order ordinary differential equations, which can be readily solved numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. For the paraxial on-axis Gaussian beam propagation in lens-like waveguide, we compare CGO solutions with numerical results for finite differences beam propagation method (FD-BPM). The CGO method is shown to provide 50-times higher rate of calculation then FD-BPM at comparable accuracy. Besides, paraxial eikonal-based complex geometrical optics is generalized for nonlinear Kerr type medium. This paper presents CGO analytical solutions for cylindrically symmetric Gaussian beam in Kerr type nonlinear medium and effective numerical solutions for the self-focusing effect of Gaussian beam with elliptic cross section. Both analytical and numerical solutions are shown to be in a good agreement with previous results, obtained by other methods.

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“…Complex geometrical optics (CGO) has two equivalent forms: the ray−based form, which deals with complex rays [1][2][3][4][5][6], that is with trajectories in a complex space, and the eikonal−based form, which uses complex eikonal instead of complex rays [6][7][8]. A surprising feature of CGO is its ability to describe Gaussian beam (GB) diffraction in both ray−based and eikonal−based approaches.…”

Section: Introductionmentioning

confidence: 99%

Gaussian beam evolution in longitudinally and transversely inhomogeneous nonlinear fibres with absorption

Berczyński

2013

Opto-Electronics Review

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The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear Kerr type and saturable fibres. CGO reduces the problem of Gaussian beam evolution in inhomogeneous and nonlinear media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction and self-focusing effects as compared to other methods of nonlinear optics such as variational method approach, method of moments and beam propagation method. The power of CGO method is presented on the example of Gaussian beam propagation in saturable fibres with either focusing and defocusing refractive profiles. Besides, the influence of initial curvature of the wave front, phenomenon of weak absorption and effect of either transverse and longitudinal inhomogeneity on GB propagation in nonlinear fibres is discussed in this paper.

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Complex Rays with an Application to Gaussian Beams

Cited by 185 publications

References 0 publications

On Laser Radar Cross Section of Targets With Large Sizes for E-Polarization

On Laser Radar Cross Section of Targets With Large Sizes for E-Polarization

Gaussian beam diffraction in inhomogeneous and nonlinear media: analytical and numerical solutions by complex geometrical optics

Gaussian beam evolution in longitudinally and transversely inhomogeneous nonlinear fibres with absorption

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