Contribution to the Theory of Total Reflection

摘要

The problem of total reflection is approached on the basis of equations published earlier by the author, which take into account the finite aperture of the incident beam and the resulting diffraction effects, first for a cylindrical wave as the incident wave. While the conventional treatment of total reflection contains a contradiction in the result, the present paper shows that this contradiction disappears. The appearance of an energy flow in the second medium is due to the fact that there are points on the planes of separation of the two media at which energy continuously (averaged in time) passes from the first medium into the second at a very low angle of inclination to each plane. At other points of the planes of separation all of this energy returns to the first medium. The energy oscillation back and forth across the planes of separation is on the order of magnitude of the incident energy. The same situation is discussed for a plane wave, and the same energy transfer is observed again. Formulas are derived in the mathematical treatment that can be considered as a generalization of the Fresnel integral. A generalization of Cornu's spiral is advantageous for the discussion of energy characteristics using these integrals. Equations are given for calculating those generalized integrals and the generalized spirals. (ERA citation 07:045237)