The transmission coefficient for the amplitude of an electromagnetic field that propagates through a one-dimensional N-layer medium is obtained from summing the coefficients that belong to the individual transmitted light-paths. The medium does not have to be periodic; the layers can have arbitrary physical lengths and arbitrary field response parameters. As compared to the traditional transfer-matrix derivation for the transmission coefficient, the sum-over-all-paths derivation results in a transparent representation that reveals that the presence of the medium can effectively be described as a self-interaction of the field.

R. Uitham, B. Hoenders, "Transmission coefficient of a one-dimensional layered medium from a light-path sum", J. Europ. Opt. Soc. Rap. Public. 08013 Vol 3 (2008)

10.2971/jeos.2008.08013

Click here to see articles that refer to this one