Propagation properties of vectorial Hermite–cosine–Gaussian beams beyond the paraxial approximation

Abstract

Starting from the vectorial Rayleigh–Sommerfeld diffraction integrals, the analytical propagation expressions of vectorial nonparaxial Hermite–cosine–Gaussian (HCosG) beams in free space are derived. The on-axis intensity, far-field equation and, in particular, paraxial expressions are given and treated as special cases of our result. It is shown that for vectorial nonparaxial HCosG beams, the parameter f = 1/kw ₀, with k being the wave number and w ₀ being the waist width, determines their nonparaxiality. What is more, the decentered parameter also affects their intensity distribution and nonparaxial behavior. The calculation results indicate that the position of maximum on-axis intensity changes with the mode indices.

Keywords:

• propagation optics
• vectorial nonparaxial
• Hermite–cosine–Gaussian beam
• vectorial
• Rayleigh–Sommerfeld intergrals
• f parameter
• decentered parameter

Acknowledgements

This work was supported by Scientific Research Fund of Jiangsu Provincial Education Department under Grant 08KJD140007 and the Scientific Fund of Jiangsu Polytechnic University under Grant ZMF08020014. The authors are indebted to the reviewer for valuable comments.