Propagation of vectorial laser beams

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 vector corresponding to the electromagnetic fields. As an application of this approach, we consider axially symmetric vector beams, showing non-diffracting properties of these beams, without invoking the paraxial approximation. Further, we indicate the relevance of the method for analyzing nonparaxial resonators, such as microresonators

The angular spectrum representation as method to solve the electric vector Helmholtz equation in 3D is well known, in particular for beam propagation studies, where the field is predominantly directed along the optical axis. The inversion formulas then transform the electric field into its angular spectrum ( and vice versa). By using an intrinsic coordinate system instead of the usual 3D Cartesian system, we arrive at compact 2D inversion formulas as solutions. Furthermore, next to the 2D intrinsic version, a 2D Cartesian version of the 3D field vectors is derived, by considering the fields in the 2D sections transverse to the optical axis. It is shown that this polarization representation is rigorously correct and simultaneously describes 3D fields without paraxial approximation . The ability to switch between the field and its spectrum shows that studying polarization in the Fourier domain can be advantageous to studying it in the more familiar spatial domain.

2003

Optics Letters, 2020

We consider a new type of vector beam, the vector Lissajous beams (VLB), which is of double order (p,q) and a generalization of cylindrical vector beams characterized by single-order p. The transverse components of VLBs have an angular relationship corresponding to Lissajous curves. A theoretical and numerical analysis of VLBs was performed, showing that the ratio and parity of orders (p,q) affect the properties of different components of the electromagnetic field (EF) (whether they be real, imaginary, or complex). In addition, this allows one to engineer the imaginary part of the longitudinal component of the electromagnetic field and control the local spin angular momentum density, which is useful for optical tweezers and future spintronics applications.

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 Optics A: Pure and Applied Optics, 2006

A new kind of tridimensional scalar optical beams is introduced. These beams are called Lorentz beams because the form of their transverse pattern in the source plane is the product of two independent Lorentz functions. Closed-form expression of free-space propagation under paraxial limit is derived and pseudo non-diffracting features pointed out. Moreover, as the slowly varying part of these fields fulfils the scalar paraxial wave equation, it follows that there exist also Lorentz-Gauss beams, i.e. beams obtained by multipying the original Lorentz beam to a Gaussian apodization function. Although the existence of Lorentz-Gauss beams can be shown by using two different and independent ways obtained recently from Kiselev [Opt. Spectr. 96, 4 (2004)] and Gutierrez-Vega et al. [JOSA A 22, 289-298, (2005)], here we have followed a third different approach, which makes use of Lie's group theory, and which possesses the merit to put into evidence the symmetries present in paraxial Optics.

Optics Express, 2006

We introduce the generalized vector Helmholtz-Gauss (gVHzG) beams that constitute a general family of localized beam solutions of the Maxwell equations in the paraxial domain. The propagation of the electromagnetic components through axisymmetric ABCD optical systems is expressed elegantly in a coordinate-free and closed-form expression that is fully characterized by the transformation of two independent complex beam parameters. The transverse mathematical structure of the gVHzG beams is form-invariant under paraxial transformations. Any paraxial beam with the same waist size and transverse spatial frequency can be expressed as a superposition of gVHzG beams with the appropriate weight factors. This formalism can be straightforwardly applied to propagate vector Bessel-Gauss, Mathieu-Gauss, and Parabolic-Gauss beams, among others.

The vector Helmholtz–Gauss (vHzG) beam is known as a general family of localized vector beam solutions of the Maxwell equations in the paraxial limit and the vector Mathieu–Gauss beam constitutes its version in elliptic cylindrical coordinates system. In this work, starting from the expansion of the scalar Mathieu–Gauss beam in term of Bessel–Gauss beams, we give a general expression of vector Mathieu–Gauss beams in cylindrical coordinates. Within the frame work of the Collins diffraction integral formula we derive the analytical expressions of transverse vector Mathieu–Gauss beams through an axisymmetric ABCD optical system. Some numerical calculations are performed to illustrate the propagation of the vector Mathieu–Gauss beam in free space and through a simple lens system. The results are analyzed and discussed.

Based on the expansion of the scalar Mathieu-Gauss beam in terms of Bessel-Gauss beams we give a general expression of vector Mathieu-Gauss (vMG) beams in cylindrical coordinates. Furthermore, the analytical expression of transverse vector Mathieu-Gauss beams through any axisymmetric optical ABCD system is derived by using the Collins diffraction formula. Particularly, the propagation of the vector Mathieu-Gauss beam in free space and through a simple lens system are illustrated numerically and discussed.

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