Description of light propagation through a circular aperture using nonparaxial vector diffraction theory

Abstract

Using nonparaxial vector diffraction theory derived using the Hertz vector formalism, integral expressions for the electric and magnetic field components of light within and beyond an apertured plane are obtained for an incident plane wave. For linearly polarized light incident on a circular aperture, the integrals for the field components and for the Poynting vector are numerically evaluated. By further two-dimensional integration of a Poynting vector component, the total transmission of a circular aperture is determined as a function of the aperture radius to wavelength ratio. The validity of using Kirchhoff boundary conditions in the aperture plane is also examined in detail.

Vector diffraction theory of light propagation through nanostructures

“…Oscillations in the radial direction perpendicular to the incident polarization were also reported in Ref. [4] for a circular aperture. When contrasting diffraction patterns observed for diffraction of light by a circular aperture with the diffraction of light by an elliptical aperture, there are a few of noticeable differences between intensity beam profiles.…”

“…Evaluation of the two-dimensional profiles of the fields as well as that of the Poynting vector in the plane of the circular aperture and for points near the aperture show strong anisotropy and interesting maxima and minima of light distributions. Strong radial asymmetries in the calculated electromagnetic fields in the aperture plane [4] agree with previously measured experimental results [6].…”

“…Recently vector diffraction theory has been used in a wide variety of scientific and engineering fields including focusing of light by micro-lenses [1], lithography [2], tight laser beam focusing [3], etc. For a plane wave incident upon an aperture of arbitrary shape, the Hertz vector method provides a convenient way to describe the distribution of all the components of the electromagnetic field beyond the aperture [4,5]. The fields can be expressed in terms of single integrals both in the geometrical "illuminated" region beyond the aperture as well as in the geometrical "shadow" region.…”

“…In the boundary region between the illuminated and the shadow region it is computationally more efficient to use the two-dimensional integral expressions for the fields. In reference [4], the detailed expressions for these integrals have been presented for the case of a circular aperture in an opaque screen. Evaluation of the two-dimensional profiles of the fields as well as that of the Poynting vector in the plane of the circular aperture and for points near the aperture show strong anisotropy and interesting maxima and minima of light distributions.…”

“…Using the formalism of Ref. [4] the ellipticity of the aperture is incorporated into the integration over the aperture plane. The effects of the polarization orientation of the incident light is then incorporated as the superposition of two incident orthogonal waves of appropriate amplitudes that are parallel to the ellipse's natural axes.…”