Research On The Non-paraxial Scalar Diffraction Theory And Its Application

The light density has been directly defined as the square of an absolute value and it is used to describe the propagation and transformation of laser beam in the traditional scalar diffraction theory. In fact, the traditional definition of the light intensity is only suitable to the paraxial-scalar diffraction light field, not to the non-paraxial scalar diffraction light field and vector 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. It is expressed as the time average of the amount of energy which crosses in a unit time and a unit area, so it can be applied to measure quantity of the light intensity at any curved surface. Especially as an important consequence, the light intensity on the transverse plane perpendicular to the propagation axis has been given.In these thesis, the theory of the angular spectrum representation has been applied and the diffraction field of the plane aperture has been calculated and is expressed as the homogeneous waves and evanescent waves; based on the accurate formula of the light intensity of the scalar light field, the energy propagation law of paraxial and non-paraxial beam has been studied systematically; for the Gaussian beam diffraction field of the small plane aperture, the light intensity and the energy flux of the light spots and the total energy flux on the transverse plane perpendicular to the propagation axis have been calculated; by taking the vectorial property of time average energy flow density and the accurate formula of the light intensity into account, the propagation law of the light second intensity moments is obtained for axially symmetric non-paraxial scalar beam. Based on it, the beam waist radius, the far-field divergence angle and the beam quality factor M2 are given, and the calculation results have been compared with the corresponding results of traditional ones; the value of the beam quality factor M2 of the paraxial and non-paraxial beam are discussed, we get some new results; the non-paraxial Gaussian beam quality factor of the small plane aperture and the non-paraxial cosh-Gaussian beam quality factor and the non-paraxial sinh-Gaussian beam quality factor are calculated, comparing with the results of traditional light intensity, we get some new results. The theory of the angular spectrum and the uncertainty relation in quantum theory are applied to discuss the ultra-highresolution beyond Rayleigh diffraction limit.