I show that the reflection coefficient of any stratified planar structure can be obtained by using a complex generalization of Einstein's addition theorem for parallel velocities. This result also applies to multiple quantum wells. It provides a new mathematical tool in optics and in quantum theory and may lead to useful algorithms in computing. It may also give a new insight into special relativity. The composition law of velocities, in fact, no longer appears as a specific result of special relativity but rather as the expression, in the particular case of kinematics, of a more general law of physics. The possible use of the composition law of probability amplitude in quantum theory is also presented.
© 1992 Optical Society of America
Original Manuscript: July 17, 1991
Revised Manuscript: March 10, 1992
Manuscript Accepted: January 23, 1992
Published: August 1, 1992
J. M. Vigoureux, "Use of Einstein’s addition law in studies of reflection by stratified planar structures," J. Opt. Soc. Am. A 9, 1313-1319 (1992)