Rishi Kant

An Analytical Solution of Vector Diffraction for Focusing Optical Systems with Seidel Aberrations: I. Spherical Aberration, Curvature of Field, and Distortion

Abstract In this paper, a method developed by the author is used to study the image formation in various aplanatic systems with Seidel (fourth-order) aberrations. We study the spherical aberration, the distortion aberration and the curvature of field aberration. Just as in the case of scalar diffraction theory, it is shown that the distortion produces a shifted intensity pattern while in contrast with the scalar theory it is shown that the curvature of the field aberration produces a different intensity distribution. We also provide expressions for the location of the diffraction foci and calculate the Strehl intensity. We find that for the case of spherical aberration, the Strehl intensity increases with the increase in the numerical aperture whereas for the case of curvature of field aberration the Strehl intensity decreases with the increase in the numerical aperture. For distortion aberration the Strehl intensity is same as the Gaussian intensity. The computations are carried out for a focusing lens. ...

An Analytical Solution of Vector Diffraction for Focusing Optical Systems

Abstract Vector diffraction theory for optical systems has been of interest for a long time. Ignatovsky and Wolf have formulated these problems in terms of diffraction integrals and Wolf has presented very interesting results. Usually, the quadrature of diffraction integrals is numerically intensive, therefore these problems have remained of interest and many authors have worked on the Ignatovsky-Wolf formulation or some variation thereof. This paper presents yet another method of solving diffraction integrals. Since a certain part of the kernel of these integrals is Riemann integrable in the interval [0, π], the Weierstrass theorem says that it can be approximated by a uniformly convergent series of orthogonal functions. Thus it is possible to expand these functions into a series of Gegenbauer polynomials of the first kind. Once these expansions are substituted in the diffraction integrals, the resulting integrals are readily evaluated, over the surface of unit sphere, in terms of the spherical Bessel fu...

Generalized Lorenz-Mie scattering theory for focused radiation and finite solids of revolution: case I: symmetrically polarized beams

Interaction of focused radiation with spherical and finite cylindrical homogeneous particles is considered. The aim of this investigation is to calculate the structure of the electromagnetic (EM) fields scattered by and propagated within the scattering objects. The incident EM fields are assumed to be focused fields in the image space of an aplanatic system with or without aberrations of category one. The radiation in the object space is assumed to be symmetrically polarized. The incident fields in the neighbourhood of the focus are calculated using the well-known theory of Richards and Wolf and a methodology developed by the author. At the interface between the homogeneous and the image space of the aplanatic system, the continuity conditions of the tangential components of the electric displacement and magnetic moment vectors are satisfied. The procedure results in dual discretized-Fredholm integral equations that are solved using orthogonal expansions. It is assumed that the scattered field, at large d...Interaction of focused radiation with spherical and finite cylindrical homogeneous particles is considered. The aim of this investigation is to calculate the structure of the electromagnetic (EM) fields scattered by and propagated within the scattering objects. The incident EM fields are assumed to be focused fields in the image space of an aplanatic system with or without aberrations of category one. The radiation in the object space is assumed to be symmetrically polarized. The incident fields in the neighbourhood of the focus are calculated using the well-known theory of Richards and Wolf and a methodology developed by the author. At the interface between the homogeneous and the image space of the aplanatic system, the continuity conditions of the tangential components of the electric displacement and magnetic moment vectors are satisfied. The procedure results in dual discretized-Fredholm integral equations that are solved using orthogonal expansions. It is assumed that the scattered field, at large distances from the focus, is a spherical wave propagating away from the focus. Scattering by objects of various materials ranging from dielectric to perfect conductor is studied. The theory and its solution developed here allow for the scattering objects to be located anywhere along the optical axis in the image space. One of the main objectives is to calculate the energy distribution at the tip of the cylindrical homogeneous particle. Numerical calculations suggest that energy density at the tip is further enhanced if the cylindrical homogeneous particle is placed away from focus.

Interaction of Focused Radiation with Magneto-optical Discs

Abstract Direct access storage devices are widely used in computers to store and manage data. In conventional magnetic recording, a magnetic head flying very close to the disc surface alters the polarization of the magnetic field at the disc surface to write and/or erase information on the disc. An optical disc is a multilayered medium consisting of a thick glass substrate on which many layers of different materials are sputtered. Only one of these layers serves as a recording medium and it is initially magnetized uniformly in one direction. To write on this disc, the initial magnetic field is altered by focusing light from a laser source with high numerical aperture (NA) lens to heat the magnetic medium beyond its Curie point, the temperature at which the magnetic medium loses its magnetization. This domain with zero magnetization is subsequently magnetized in the reversed direction by using an induction magnet. All these processes take place while the disc is rotating at a very high speed with respect t...