They allow Huygens' Principle
to be realized in fact, with unprecedented control and shaping of the overall wave, at wide bandwidths, with multiple layers if desired.
In modern physics, and following Feynman's developments and using appropriate field operators such as Green's functions, Huygens' principle
also finds exact mathematical expression through the Chapman-Kolmogorov equation, (49) which is the equation of motion of Markov processes.
This is similar to Huygens' Principle
(20), proposed for optics more than three centuries ago.
This is a significant departure from the classical formulation of Huygens' principle
, where a reverse flow of energy on the positive side of the aperture is precluded by the explicit assumption that light does not travel backwards.
The Kirchhoff and Rayleigh-Sommerfeld integral equations (1) and (2) are alternative forms of the theorem of Helmholtz (5), which expresses Huygens' principle
in terms of a scalar wave function U and its normal derivatives without assuming specific attributes of this function, except that it is continuous and twice differentiable with continuous derivatives and obeys the homogeneous wave equation,