Regularization of complex beams

Mahillo-Isla, R.; González-Morales, M. J.; Dehesa-Martínez, C.

doi:10.1109/mmet.2008.4580954

Cited by 4 publications

(6 citation statements)

References 1 publication

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“…From the physical point of view, the complex displacement of the source location, ib, has important interpretations which require the study of the delta function of complex argument, [8,14], but this fact is out of the purposes of this paper. From the mathematical point of view, a displacement ib of the source is equivalent to a displacement −ib of the observation points as it was established in Section 2.…”

Section: Complex-point-source Radiation Problemsmentioning

confidence: 99%

Complex Polar Coordinates in Electromagnetics

González-Morales¹,

Mahillo-Isla²,

Gago-Ribas³

et al. 2011

Journal of Electromagnetic Waves and Applications

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The definition of a complex polar coordinate system that unifies complex distances and complex angles together with their relations with the real observation space is presented in this paper. Its utility is shown through some applications to electromagnetic problems: (i) new solutions are obtained from well-known solutions in real polar coordinates, (ii) the parameterization of the real space in terms of the complex polar coordinates helps to understand the physical behaviour of those solutions, and (iii) the results provide a better physical insight of the complex distances and angles.

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Section: Complex-point-source Radiation Problemsmentioning

confidence: 99%

Complex Polar Coordinates in Electromagnetics

González-Morales¹,

Mahillo-Isla²,

Gago-Ribas³

et al. 2011

Journal of Electromagnetic Waves and Applications

Self Cite

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“…This solution has been proposed in order to extend the validity of the GB beyond the paraxial zone and exhibits the required cylindrical symmetry. Using the Green's function of the inhomogeneous Helmholtz equation for a point source located in complex space at coordinates x = ix R and y = 0, one obtains the CSB solution [68] ϕ i (r) = H…”

Section: Beam-shape Coefficients For a Plane Wavementioning

confidence: 99%

“…The waist plane is thus located in the branch cut. It should be noted that to obtain a regular solution in that plane, one can combine linearly independent CSB solutions as described in [68]. The CSB solution reduces, up to a multiplicative constant, to a canonical Gaussian beam in the paraxial zone x y.…”

Section: Beam-shape Coefficients For a Plane Wavementioning

confidence: 99%

Lorenz–Mie theory for 2D scattering and resonance calculations

Gagnon¹,

Dubé²

2015

J. Opt.

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This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell's equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell-Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers. CONTENTS

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“…The CSB is continuous everywhere in the real plane except across the branch cut connecting the two singularities at (x, y) = (0, x R ) and (x, y) = (0, −x R ). For the purposes of this paper, we shall restrict our attention to scatterers located in the positive x plane, referring the reader to [26] for regularization strategies in the waist plane. Since the H (1) 0 function converges rapidly to a complex exponential, one can readily show that, for x > 0,…”

Section: Scattering Of Complex-source Beams By Phcsmentioning

confidence: 99%

Beam shaping using genetically optimized two-dimensional photonic crystals

2012

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We propose the use of two-dimensional (2D) photonic crystals (PhCs) with engineered defects for the generation of an arbitrary-profile beam from a focused input beam. The cylindrical harmonics expansion of complex-source beams is derived and used to compute the scattered wave function of a 2D PhC via the multiple scattering method. The beam shaping problem is then solved using a genetic algorithm. We illustrate our procedure by generating different orders of Hermite-Gauss profiles, while maintaining reasonable losses and tolerance to variations in the input beam and the slab refractive index.

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Regularization of complex beams

Abstract: The well known 2D complex-point-source beam presents undesired field characteristics. This paper proposes some combinations of simple complex beams which allow the construction of well behaved fields.

Cited by 4 publications

References 1 publication

Complex Polar Coordinates in Electromagnetics

Complex Polar Coordinates in Electromagnetics

Lorenz–Mie theory for 2D scattering and resonance calculations

Beam shaping using genetically optimized two-dimensional photonic crystals

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