Microstructured non-diffracting beams in electromagnetic scattering: a study of continuous and vector Frozen Waves in the generalized Lorenz-Mie theory

• Grant number: 17/16413-3
• Support type: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): December 01, 2017
• Effective date (End): November 30, 2018
• Field of knowledge: Engineering - Electrical Engineering
• Principal researcher: Leonardo Andre Ambrosio
• Grantee: Vinicius Soares de Angelis
• Home Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This proposal aims to provide a natural and challenging extension for the student in relation to the concepts developed in his first FAPESP scientific research. To do so, it presents a theoretical study about a specific class of non-diffracting beams which is highly promising in optical trapping: the so-called continuous and vector frozen waves (CVFWs). It is an extension of the concepts already seen by the student that, so far, have involved Bessel beams, discrete and scalar frozen waves (DSFWs) and optical forces produced by light beams on particles much smaller than (Rayleigh regime) or much greater than the wavelength (ray optics regime), in electromagnetic scattering and light-matter interaction. The schedule, which is divided into trimesters, is composed of a first stage related to advanced studies concerning non-diffracting beams and CVFWs. Then, the student will advance into the Generalized Lorenz-Mie Theory (GLMT) in order to have a full comprehension about concepts in electromagnetic theory and electromagnetic scattering such as scattering cross-section and Mie's coefficients and also to deal with special functions which do not belong to the current undergraduate courses' syllabus at the Department of Electrical Engineering. Finally, the relation between CVFWs and GLMT will be established by using the so-called Beam Shape Coefficients (BSCs) for incident fields, and simple numerical computations will be performed (in Python language or through Mathematica or Matlab software) to determine optical forces produced by those beams on spherical and dielectric micro-sized particles. (AU)