Non-paraxial Propagation Of Light Beams And A Study Of Light Intensity At Transverse Plane

It is well known that the paraxial approximation is no longer valid for the beams with large divergence angle or small spot size comparable with the wavelength. Thus, a rigorous non-paraxial treatment becomes necessary. As yet, power-series expansion has been well discussed. In Lax's study, he found that the paraxial result is the zeroth-order solution of Maxwell's equations when the fields are expanded in the powers of an expansion parameter f, which is the ration of the beam waist and the so-called diffraction length. He also obtained equations for high-order field in a consistent manner.In these theses, based on the scalar diffraction theory of the angular spectrum representation, the non-paraxial corrections to the paraxial solution are derived;If certain conditions are satisfied and further approximations are performed, series expansion solution is obtained from the non-paraxial solution;non-paraxial solution and series expansion solution are both obtained for the circular aperture diffraction and detailed numerical calculation for them is performed and compared;their validities are studied thoroughly;It is pointed out that the higher-order non-paraxial corrections are necessary in the near field or in the non-paraxial area;It is shown that the applicable range of the series expansion approach depends on the waist width, propagation distance and order of the series expansion;It is found that for hard-edged aperture diffractions, the contribution due to the high-frequency components cannot be neglected, so its applicable range is very limited;Generally speaking, the series expansion approach should be applied to dealing with free-space optical propagation.The traditional definition of the light intensity is expressed as the square of an absolute value, which is only suitable to the paraxial-scalar diffraction light field. Considering the vectorial property of the time -average energy flow density, a new extensive definition of the light intensity has been proposed. The energy flux density vector is introduced as the accurate formula of the light intensity for nonparaxial scalar beams. In the vectorial diffraction theory, the time-averageenergy flow density which crosses in a unit time and a unit area can be applied to measuring quantity of the light intensity at any curved surface.In these theses, based on the vectorial diffraction theory of the angular spectrum representation and taken the circular aperture diffraction as an example, the formulae for three different kinds of light intensity are obtained. Detailed numerical calculation is performed and illustrated. The different results are compared. It is pointed out that vectorial property of the light field must be taken into account in order to analyze the diffracting behavior in near-field region or for small apertures. The result can be applied to the research on second intensity moments and optical beam quality of the vectorial light beams.