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.
Highlights
Even though the diffraction of light by an aperture is a fundamental phenomenon in optics and has been studied for a long time [1,2,3], it continues to be of modern interest [4,5,6,7,8]
The finite difference time domain (FDTD) method provides an accurate description of light distributions in the vicinity of the aperture without Kirchhoff or paraxial approximations, but can become computationally time-intensive at larger distances of propagation
In this paper we show that using modern desktop computers, detailed solutions for all the electric and magnetic field components for all points in space in the aperture plane and beyond are obtainable for a/λ ≥ 0.1, within a reasonable period of time using vector diffraction theory but without invoking any approximations
Summary
Even though the diffraction of light by an aperture is a fundamental phenomenon in optics and has been studied for a long time [1,2,3], it continues to be of modern interest [4,5,6,7,8]. In this paper we show that using modern desktop computers, detailed solutions for all the electric and magnetic field components (as well as the Poynting vector) for all points in space in the aperture plane and beyond are obtainable for a/λ ≥ 0.1, within a reasonable period of time (minutes) using vector diffraction theory but without invoking any approximations. The electric (E) and magnetic (H) fields of an electromagnetic wave of wavelength λ and traveling in vacuum can be determined from the polarization potential [15], or Hertz vector (Π), through the relations. For the case of a plane wave which is linearly polarized (say along the x-direction) and propagating in the +z direction, all of the E and H field components can be calculated from Πx, the x-component of the Hertz vector [12], and have the following forms: Ex k2Πx. I, j, kdenote the unit vectors in the x, y and z directions
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