Hidden symmetries in N-layer dielectric stacks

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6 Citations (Scopus)


The optical properties of a multilayer system with arbitrary N layers of dielectric media are investigated. Each layer is one of two dielectric media, with a thickness one-quarter the wavelength of light in that medium, corresponding to a central frequency f 0. Using the transfer matrix method, the transmittance T is calculated for all possible 2N sequences for small N. Unexpectedly, it is found that instead of 2N different values of T at f 0 (T 0), there are only discrete values of T 0, for even N, and (N + 1) for odd N. We explain this high degeneracy in T 0 values by finding symmetry operations on the sequences that do not change T 0. Analytical formulae were derived for the T 0 values and their degeneracies as functions of N and an integer parameter for each sequence we call 'charge'. Additionally, the bandwidth at f 0 and filter response of the transmission spectra are investigated, revealing asymptotic behavior at large N.

Original languageEnglish
Article number455303
JournalJournal of Physics Condensed Matter
Issue number45
Publication statusPublished - 2017 Oct 10
Externally publishedYes


  • dielectric stack
  • electromagnetic wave
  • multilayer system
  • transfer matrix

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics


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