Boundary Wave Diffraction Theory

In1663, the Italian scholar Francesco Maria Grimaldi describedthe phenomenon of light wave diffraction, then, the study of thediffraction problem had experienced a long developing process. Inthe1670s, Huygens’ principle, was proposed to determine thedirection of propagation of light waves. In1818, Fresnel combinedYoung’s interference principle developed by him with Huygensmapping method and proposed the Huygens-Fresnel principle, usedto qualitatively explain the diffraction of light wave. In1882,,Kirchhoff obtained Kirchhoff diffraction integral formula andFresnel Kirchhoff diffraction integral formula in Kirchhoffassumption conditions, then the Huygens-Fresnel principle formedKirchhoff’s diffraction theory on a solid mathematical foundation.Sommerfeld selected mirror symmetry of Green’s function,eliminating the part of Kirchhoff’s assumptions which was notself-consistent, and developed into Rayleigh Sommerfeld DiffractionTheory which constituted the spherical wave diffraction theory tosolve the problem of light wave diffraction. Fourier analysis methodwas applied in the early20th century optics field, through thefrequency domain of superposition of plane wave diffraction lightfield distribution, forming the plane wave diffraction theory to solvethe problem of light wave diffraction. In1802, Thomas Yang, a qualitative description of diffraction boundary reflection wave ofideas, in1917, LuBiNuo Veda, according to the Helmholtz Kirchhoffintegral theorem,got LuBiNuo Veda boundary diffraction waveformula and established the boundary diffraction wave theory. Butthe formula applied only when the incident wave is a plane wave orspherical wave, boundary wave diffraction theory is still at thedeveloping stage, the domestic scholars’ researches are still in thediscussion stage, such as boundary wave diffraction experimentobservation, boundary wave diffraction study of meaning, boundarywave diffraction the authenticity of the principle problem, boundarywave diffraction theory formulation of right and wrong, etc. So far,to boundary wave diffraction theory research hasn’t systemreports.Based on the young’s boundary diffraction thought and potentialfield analysis, embarks from the Baker, Kang Pusen special vectorpotential, according to the Helmholtz Kirchhoff integral theoremand Stokes’ theorem, the diffraction light field using the specificvector potential associated with the incident light, respectively gotclosed surface cases and cases of boundary plane wave formula.Based on this, the paper gives all kinds of light wave incident casesof boundary wave formula, so as to establish the boundary wavediffraction theory. Using the boundary wave diffraction theory,diffraction light field simply expresses as boundary light andgeometry of the incident light wave superposition. To a certainextent, it simplifies the study of the diffraction problem. As averification, the paper discusses the hole boundary wave diffractionand straight boundary wave diffraction problem and proves the reliability of the boundary wave diffraction theory. The calculatingsimulation also shows the feasibility of boundary wave diffractiontheory and points out that the real existence of the boundarydiffraction wave and its transfer characteristic, which provides anew solution to solve the problem of light wave diffraction.Simulation results also show that the boundary diffraction wavediffraction theory in the exploration practice, especially the lightfield distribution on the study of the geometrical shadow region, willshow its unique superiority, and has practical value and guidingsignificance to the construction of the diffraction theory.