Vector diffraction based on 3D Huygens-Fresnel principle and vector decomposition in Cartesian coordinate

Abstract

We proposed vector diffraction equations based on 3D Huygens-Fresnel principle and vector decomposition in Cartesian coordinate. Our expression should more accurate than classical Richards-Wolf diffraction, because the deduction of Richards-Wolf diffraction used a number of approximation, while our expression is based on two fundamental physical principles: vector decomposition and Huygens-Fresnel principle. Our expressions mathematical strictly satisfy conservation of energy, while Richards-Wolf’s method is based on the geometrical law of conservation of energy and RCWA(Rigorous Coupled Wave Analysis) is also an approximation. The simulated results of our vector diffraction equations with different NA (numerical aperture) are almost the same as Richards-Wolf diffraction results. Traditional Richards-Wolf vector diffraction equations, which are based on angular spectrum of plane wave, have no clear geometrical meaning, while our vector diffraction equations here have clear geometrical meaning. Our approach of vector diffraction to scalar diffraction is much simpler than Richards-Wolf’s approach. The generation of x/y/z components and their properties in the image plane can be investigated clearly by vector decomposition and synthesis. Their intensity ratios can be explained using paraxial approximation very well. The integral region of exit pupil could be reduced because of the symmetric property of the light vector decomposition and synthesis, thus our expressions have advantages on numerical simulation. Our analysis also indicate that light must ‘polarize’ in other extra dimensions and photon spin is a ‘polarize/resonate’ state in extra dimensions. Also, there is a potential convenient ability to study vector optical transfer function (OTF) analytically in Cartesian coordinate.