# Scalar and Vector computations using an optical Interferometer

Verma, Gaurav (2023) Scalar and Vector computations using an optical Interferometer. Masters thesis, Indian Institute of Science Education and Research Kolkata.

 Text (MS dissertation of Gaurav Verma (18MS009)) Thesis_18MS009.pdf - Submitted Version Restricted to Repository staff only Download (38MB)
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## Abstract

The superposition of different polarizations of Hermite-Gauss (HG) and Laguerre- Gauss (LG) modes generate a complex polarization state of the vector beam. Higher-order spatial modes of HG and LG are the scalar solutions of the paraxial wave equation in Cartesian and cylindrical coordinates, respectively. These modes are polarization-independent but vector beams are formed with spatial modes having some particular polarization. These beams exhibit both polarization (or intensity) and phase singularities. The spin and orbital angular momentum of light work as a bridge between the classical and quantum mechanical interpretation of light waves. The spin-orbit interaction from the structure plate (q-plate) has allowed the generation of some exotic polarization structures, i.e. vector vortex beams that carry both spin and orbital angular momentum of light, Poincaré beams and 3D polarization structures. In this thesis, we discuss a novel interferometer which can confine the light in N order of a polygonal loop called a polygonal loop interferometer. Here, for simplicity, we use N=4 i.e. rectangular (or square) loop interferometer (RLI). First, we use the polygonal loop interferometer to calculate the sum of any converging geometric series. Since we are using light, it will perform calculations at the speed of light with the limiting aspect being the readout time of detectors. We will get different series by using different kinds of beam splitters at the vertices of the polygon. We calculated the sum of many series and found an average accuracy of 90%-95% by considering the losses of intensity from the mirrors and beam splitters. The extra error of 5%- 10% might be due to paraxial beam approximation and losses in the air. Second, till now there are many ways to generate OAM, one is by using q-Plate, which are half-wave retarders where the principal axis rotates with an azimuth angle. These q-plates are fabricated with fixed q-value having special liquid crystal patterns. We can add and subtract or change the sign of the charge, only by combining q-plates with half-wave plate plates (HWP). Generally, a q-plate with topological charge q can generate 2qћ angular momentum (AM) per photon. However, here we show that we can increase the value of AM just by using a single q-plate. Theoretically, we use the Jones matrix formalism to generate an infinite orthogonal basis set of OAM of light as the beams rotate in the RLI but experimentally we are able to measure l = -2 to 2 order after that beams are slightly misaligned in the interferometer. For that, we use a q-plate with topological charge q=1/2 and put it with HWP in one arm of a rectangular loop interferometer. For an input circularly polarized (RCP/LCP) Gaussian beam passes through a q-plate. It generates both spin angular momentum (SAM) and orbital angular momentum (OAM), since the beam will rotate inside the RLI, It will increase the value of OAM on every complete rotation of the beam. To check the result, we take the Gaussian Beam as a reference and interfere it with outgoing beams from the interferometer. The interference of the beams shows the fork patterns, which ensure that the beams are carrying OAM. On each rotation of the beam into the interferometer the value of OAM and intensity keep increasing and decreasing respectively. Third, using this RLI we can generate a complex polarization state of the vector beam by the superposition of monopole, dipole, hexapole, octupole the polarization of light, i.e. multipole expansion of the polarization (or electric field). On each rotation of the beams into the interferometer the size of the singularity point increases but also the polarization changes. We measure the polarization of the beam by calculating the Jones vector and compared with simulation. In addition, experimentally we also measure the polarization of the beams by using Stokes vector analysis. We can generate multipole polarization-encoded structured light by trapping the light in a polygonal loop interferometer. Structured light has three degrees of freedom- amplitude, phase and polarization distribution, by manipulating these parameters we can construct a highly customized vector and vortex structured beam. However, vector vortex beams are spatially varying polarization having spiral phase structure. Indeed, the superposition of vortex fields with different OAM modes can generate vector beams. For the last two decades, LG beams have been used as a tool in application-based research and in studying fundamental problems due to their orbital angular momentum (OAM) nature.

Item Type: Thesis (Masters) Supervisor: Prof. Ayan Banerjee Geometric Series; HWP; Interferometer; Multipole Polarization; Optical Interferometer; Orbital Angular Momentum; Poynting Vector; QWP; Q-Plate; Spin Angular Momentum; Vortex Beam Q Science > QC Physics Department of Physical Sciences IISER Kolkata Librarian 15 Nov 2023 10:35 15 Nov 2023 10:35 http://eprints.iiserkol.ac.in/id/eprint/1469