波動場の新しい表現 (I)

抄録

In a previous paper¹⁾, a generalization of the Maggi-Rubinowicz theory was developed. The Kirchhoff diffraction integral was expressed as the combined effect of a boundary diffraction wave (represented by a line integral along the boundary of the aperture) and of waves originating in certain special points inside the aperture (singularities of an associated new vector potential).
In this paper a general expression for the vector potential W (r', r) associated with any mono chromatic wave field U(r)e^-iωt is deduced. In terms of W, the integrand vector V(r', r) of the Helmholtz-Kirchhoff integral can be expressed in the form V(r', r)=curl' W(r', r). It is shown that
W(r', r)_??_×_??_e^iκτgradU(r+τ8)dτ+W_∞,
where s=r'-r, _??_=s/s, k=ω/c and W_∞ denotes a certain residual contribution from infinity. This general formula is applied to the case of a spherical wave (created by Maggi and Rubinowicz in a different manner) and the contributions of the singular points of W are examined.