Vector electromagneticXwaves

Springer Series in Optical Sciences, 2009

In the previous chapters, we have considered electromagnetic beams whose longitudinal field component (along the propagation direction) is negligible. In other words, the electric field vector was assumed to be transverse to the z-axis and, consequently, it was represented by means of two components. This paraxial approach and the subsequent quasi-transversality assumption have provided in the above chapters a considerable simplification in both, the calculations and the characterization of this kind of beams. However, in high-resolution microscopy, particle trapping, high-density recording and tomography, to mention only some recent applications, the light beam is strongly-focused and raises waist sizes smaller than the wavelength. In such cases, the paraxial approximation is no longer valid, and a non-paraxial treatment is required. This is a topic of considerable current interest, which has been extensively investigated in the last decade (see, for example,

Optics Communications, 2002

We present a formalism describing optical propagation in a homogeneous medium of a fully vectorial highly nonparaxial field, characterized by a waist smaller than the wavelength. The method allows us to derive an analytical expression for a field possessing an initial Gaussian transverse distribution of width w, in the extreme nonparaxial regime w < k, valid for propagation distances z J d, where d ¼ w 2 =k is the diffraction length. Ó

Physical Review A, 1980

The propagation of a vector electromagnetic beam in a linear homogeneous dielectric half-space is considered using the Whittaker potentials for the electromagnetic fields. A relation between the~ittaker potentials and the vector and scalar potentials of the electromagnetic theory is obtained. The polarization properties of the beam are discussed in the paraxial approximation and beyond.

Journal of the Optical Society of America B, 2012

The angular spectrum of a vectorial laser beam is expressed in terms of an intrinsic coordinate system instead of the usual Cartesian laboratory coordinates. This switch leads to simple, elegant, and new expressions, such as for the angular spectrum of the Hertz vectors corresponding to the electromagnetic fields. As an application of this approach, we consider axially symmetric vector beams, showing nondiffracting properties of these beams, without invoking the paraxial approximation.

A relatively simple method for calculating the properties of a paraxial beam of electromagnetic radiation propagating in vacuum is presented. The central idea of the paper is that the vector potential field is assumed to be plane-polarized. The nonvanishing component of the vector potential obeys a scalar wave equation. A formal solution employing an expansion in powers of mal is obtained, where mo is the beam waist and l the diffraction length. This gives the same result for the lowest-order components of the transverse and longitudinal electric field of a Gaussian beam that was derived by Lax, Louisell, and McKnight using a more complicated approach. We derive explicit expressions for the second-order transverse electric field and the third-order longitudinal field corrections.

Localized Waves, 2008

A time-domain approach is proposed for the propagation of ultrashort electromagnetic wave packets beyond the paraxial and the slowly-varying-envelope approximations. An analytical method based on perturbation theory is used to solve the wave equation in free space without resorting to Fourier transforms. An exact solution is obtained in terms of successive temporal and spatial derivatives of a monochromatic paraxial beam. The special case of a radially polarized transverse magnetic wave packet is discussed.

Journal of the Optical Society of America A, 1987

We present exact, nonsingular solutions of the scalar-wave equation for beams that are nondiffracting. This means that the intensity pattern in a transverse plane is unaltered by propagating in free space. These beams can have extremely narrow intensity profiles with effective widths as small as several wavelengths and yet possess an infinite depth of field. We further show (by using numerical simulations based on scalar diffraction theory) that physically realizable finite-aperture approximations to the exact solutions can also possess an extremely large depth of field.

High Power Laser Science and Engineering, 2015

We deduce a complete wave propagation equation that includes inhomogeneity of the dielectric constant and present this propagation equation in compact vector form. Although similar equations are known in narrow fields such as radio wave propagation in the ionosphere and electromagnetic and acoustic wave propagation in stratified media, we develop here a novel approach of using such equations in the modeling of laser beam propagation in nonlinear media. Our approach satisfies the correspondence principle since in the limit of zero-length wavelength it reduces from physical to geometrical optics.

In this work, which essentially deals with exact solutions to the wave equations, we begin by introducing the topic of Non-Diffracting Waves (NDW), including some brief historical remarks, and by a simple definition of NDWs: Afterwards we present some recollections -besides of ordinary waves (gaussian beams, gaussian pulses)-of the simplest nondiffracting waves (Bessel beams, X-shaped pulses,...). More details can be found in the first two (introductory) chapters of the volume on Localized Waves published[1] by J.Wiley (Hoboken, NJ, USA) in 2008. In Section 2 we go on to show how to eliminate any backward-traveling components (also known as non-causal components), first in the case of ideal NDW pulses, and then, in Section 3, for realistic, finite-energy NDW pulses. In