# Paulo A. BrandãoUniversidade Federal de Alagoas · Institute of Physics (IF)

Paulo A. Brandão

Doctor of Physics

## About

42

Publications

3,752

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

137

Citations

Introduction

Additional affiliations

July 2016 - present

**Institute of Physics - UFAL**

Position

- Professor

Description

- https://sites.google.com/fis.ufal.br/brandao

May 2012 - April 2016

January 2006 - December 2012

## Publications

Publications (42)

Perturbation theory is applied to one-dimensional scattering systems consisting of a general class of inhomogeneous and isotropic slabs having size $L$ described by the relative permittivity $\varepsilon(z) = 1 + \alpha \chi(z)$, where $\chi(z)$ is the electric susceptibility and $\alpha$ the perturbation parameter. The transmitted and reflected am...

Band theory for partially coherent light is introduced by using the formalism of second-order classical coherence theory under paraxial approximation. It is demonstrated that the cross-spectral density function, describing correlations between pairs of points in the field, can have bands and gaps and form a correlation band structure. The propagati...

Inspired by the concept of coherent frozen waves, this paper introduces one possible theoretical framework of its partially coherent version, a frozen spatial coherence, in which a desired two-point correlation structure of an optical field is created on the propagation axis by superposing partially coherent zero-order Bessel beams. It is shown tha...

Inspired by the concept of coherent frozen waves, this paper introduces one possible theoretical framework of its partially coherent version, a frozen spatial coherence, in which a desired two-point correlation structure of an optical field is created on the propagation axis by superposing partially coherent zero-order Bessel beams. It is shown tha...

The scattering of light by localized three-dimensional dielectrics having gain and loss defies the usual Born approximation, since the material can increase the amplitude of the incident field within the scatterer, making the weak-scattering assumption invalid. The convergence of the Born series is rarely discussed in analytical treatments, as the...

A broad class of planar, electromagnetic, stationary optical sources obeying the PT symmetry conditions is introduced. On deriving a set of Fourier reciprocity relations obeyed by such sources and far fields they radiate we discover that the latter can only have linear polarization states.

We investigated the statistical properties of partially coherent optical vortex beams scattered by a $\mathcal {PT}$ dipole, consisting of a pair of point particles having balanced gain and loss. The formalism of second-order classical coherence theory is adopted, together with the first Born approximation, to obtain the cross-spectral density of t...

A potential scattering theory from parity-time (PT) collections of particles with gain and loss is introduced, and the forms of their structure and pair-structure factors are elucidated. An example relating to light scattering from a random distribution of a pair of particles with gain and loss is considered.

We derive simple formulas for the transmittance T and reflectance R of Gaussian-Schell beams incident upon any stratified dielectric structure by using second-order classical coherence theory in the space-frequency picture. The formalism is applied to a particular structure consisting of a double layer, with balanced gain and loss, satisfying parit...

A theoretical framework is developed for scattering of scalar radiation from stationary, three-dimensional media with correlation functions of scattering potentials obeying PT symmetry. It is illustrated that, unlike in scattering from deterministic PT-symmetric media, its stationary generalization involves two mechanisms leading to symmetry breaki...

A potential scattering theory from deterministic and random PT collections of particles with gain and loss is introduced and the forms of their structure and pair-structure factors are elucidated. An example relating to light scattering from a random distribution of a pair of particles with gain and loss is considered.

It was recently proposed (P A Brandão and S B Cavalcanti 2019 Phys. Rev. A 100 043822) that two small (Dirac) scatterers, one having gain and the other having loss, drastically modifies the spectral density of the scattered radiation field. Here, we extend this previous work by studying the scattering of stochastic radiation by two finite spheres h...

We derive simple formulae for the transmittance T and reflectance R of Gaussian-Schell beams incident upon any stratified dielectric structure by using second-order classical coherence theory in the space-frequency picture. The formalism is applied to a particular structure consisting of a double-layer, with balanced gain and loss, satisfying the p...

A theoretical framework is developed for scattering of scalar radiation from stationary, three-dimensional media with correlation functions of scattering potentials obeying PT-symmetry. It is illustrated that unlike in scattering from deterministic PT-symmetric media, its stationary generalization involves two mechanisms leading to symmetry breakin...

A theoretical model is proposed to study the propagation of monochromatic electromagnetic plane waves through very thin slabs having gain or loss. The analysis is based on solving the differential equations directly and applying the appropriate boundary conditions. The optical response of the slabs is considered in the linear and nonlinear regimes...

It was recently proposed [P. A. Brandão and S. B. Cavalcanti, Phys. Rev. A 100, 043822 (2019)] that two small (Dirac) scatterers, one having gain and the other having loss, drastically modifies the spectral density of the scattered radiation field. Here we extend this previous work by studying the scattering of stochastic radiation by two finite sp...

The scattering of partially coherent radiation by a localized continuous material having parity-time (PT) symmetry is considered under the formalism of classical coherence theory and the assumption that the Born approximation is valid. Our results suggest that the correlation-induced spectral changes are strongly dependent upon the gain and loss pr...

A theoretical model is proposed to study the propagation of monochromatic electromagnetic plane waves through very thin slabs having gain or loss. The analysis is based on solving the differential equations directly and applying the appropriate boundary conditions. The optical response of the slabs is considered in the linear and nonlinear regimes...

The scattering of partially coherent radiation by a localized continuous material having Parity-Time (PT) symmetry is considered under the formalism of classical coherence theory and the assumption that the Born approximation is valid. Our results suggest that the correlation-induced spectral changes are strongly dependent upon the gain/loss proper...

This is a tutorial hands-on approach whose main objective is the numerical implementation scheme based on the split-step Fourier method applied to Schrödinger-like propagation equations, such as the paraxial wave equation of optics. I have included one specific example to demonstrate the validity of the algorithm by comparing the simulation results...

A theoretical model based on two-point scatterers is suggested to investigate scattering of partially coherent radiation by a non-Hermitian localized structure, invariant under the simultaneous symmetry operations of parity inversion and time reversal. Within the first-order Born approximation, and the formalism of classical coherence theory, the s...

The physical aspects of partially coherent radiation interacting with deterministic non-Hermitian periodic materials remain largely unexplored in the statistical optics literature. Here, we consider the scattering of partially coherent radiation by a deterministic periodic medium, symmetric under the simultaneous transformations of parity inversion...

A theoretical model based on two point scatterers is suggested to investigate for the first time scattering of partially coherent radiation by a non-Hermitian localized structure, invariant under the simultaneous symmetry operations of parity inversion and time reversal. Within the first-order Born approximation, and the formalism of classical cohe...

The physical aspects of partially coherent radiation interacting with deterministic non-Hermitian periodic materials remain largely unexplored in the statistical optics literature. Here, we consider the scattering of partially coherent radiation by a deterministic periodic medium, symmetric under the simultaneous transformations of parity inversion...

I have applied multiple-scale perturbation theory to a generalized complex PT-symmetric Mathieu equation in order to find the stability boundaries between bounded and unbounded solutions. The analysis suggests that the non-Hermitian parameter present in the equation can be used to control the shape and curvature of these boundaries. Although this w...

The evolution of a pair of resonant Bragg modes situated at the edges of the Brillouin zone of a periodic photonic lattice, characterized by a complex one-dimensional PT-symmetric permittivity, is thoroughly investigated. Analytic solutions of Maxwell's equations are derived beyond the paraxial approximation to study Bragg oscillations, understood...

I've applied multiple-scale perturbation theory to a generalized complex PT-symmetric Mathieu equation in order to find the stability boundaries between bounded and unbounded solutions. The analysis suggests that the non-Hermitian parameter present in the equation can be used to control the shape and curvature of these boundaries. Although this was...

We study optical Rabi-like oscillations between a pair of resonant Bragg modes in a linear P J symmetric periodic photonic structure by analytically solving the paraxial wave equation.

When a monochromatic beam of light propagates through a periodic structure with the incident angle satisfying the Bragg condition, its Fourier spatial spectra oscillates between the resonant modes situated on the edges of the Brillouin zones of the lattice with a nontrivial dynamics. We wish to study here these Bragg-induced oscillations in a speci...

We propose a simple singularity-free coordinate transformation that could be implemented in Maxwell's equations in order to simulate one aspect of a Kerr black hole. Kerr black holes are known to force light to rotate in a predetermined direction inside the ergoregion. By making use of cosmological analogies and the theoretical framework of transfo...

We study Bragg-induced power oscillations in Fourier space between a pair of optical resonant transverse modes propagating through a periodic PT symmetric lattice, represented by a refractive index that includes gain and loss in a balanced way. Our results imply that the PT symmetric system shows exceptionally rich phenomena absent in its Hermitian...

http://www.sciencedirect.com/science/article/pii/S0003491617301409
Propagation of optical pulses in adiabatic conditions in two-level systems was reported to induce Rabi oscillations if the initial state has atomic coherence. This is a surprising result since in ordinary conditions the population dynamics follows the temporal field profile. In thi...

[http://www.sciencedirect.com/science/article/pii/S0030401817303772]
Propagation of wide optical beams in transverse periodic lattices have been reported to induce power oscillations between Fourier modes related by the Bragg resonance condition, resulting from the coupling between the beam and the periodic structure. These oscillations have been...

Simple full vectorial analytical exact results are obtained for the propagation of Bessel beams through an interface separating different media characterized by material parameters and . A real space description is used and all the results are written in terms of the transverse wavevector of the incident beam, taken as an input parameter. It is sho...

By using a triangular shaped aperture it was shown recently that the topological charge of a coherent optical beam could be measured. As the diffraction pattern generated by any setup depends exclusively on the coherence properties of the optical field, we have extended this method by including partially coherent light into the system.

We have performed a theoretical study of various arrangements of one-dimensional heterostructures composed by bilayers made of nondispersive (A)/dispersive linear (B) materials and illuminated by an obliquely incident electromagnetic wave, which are shown to exhibit a robust bulk-like plasmon-polariton gap for frequencies below the plasma frequency...

Within the framework of the Huygens-Fresnel approach, we evaluate the coherent superposition of surface plasmon (SP) modes excited by an incident circularly polarized light propagating through an array of subwavelength holes. Numerical results of the plasmonic distribution exhibit a rich structure that reveals the creation and annihilation of vorte...

A new formalism is developed for diffraction-free vector beams in free space. The solutions of Maxwell's equations are separated into two polarization modes, TE and TM. We discuss the validity of the method by applying it to a particular solution, the vectorial Bessel beam of order m.

The interaction of optical vortices (or phase singularities, screw
dislocations) with ordinary matter is treated with simple approach. Using total
internal reflection phenomenon and superposition of four plane waves incident
on a material with refractive index lower than the original propagating medium,
we are able to show birth and annihilation of...

## Projects

Projects (2)