Nonparaxial propagation of a vectorial apertured off-axis Lorentz beam

Based on the vectorial Rayleigh--Sommerfeld integral formula and thecomplex Gaussian expansion of the hard-edge aperture function, ananalytical propagation expression for a nonparaxial vectorialoff-axis Lorentz beam passing through a rectangular aperture isderived. The unapertured case, the far field expression and thescalar paraxial result are also presented as special cases of thegeneral formulae, respectively. Some numerical examples are alsogiven to show the propagation characteristics of a nonparaxialvectorial off-axis Lorentz beam through a rectangular aperture. Itis indicated that the f parameter, the off-axis displacement andthe truncation parameter all play an important role in determiningnonparaxial propagation behaviour.