### Abstract

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 2^{N} sequences for small N. Unexpectedly, it is found that instead of 2^{N} 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 language | English |
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Article number | 455303 |

Journal | Journal of Physics Condensed Matter |

Volume | 29 |

Issue number | 45 |

DOIs | |

Publication status | Published - 2017 Oct 10 |

Externally published | Yes |

### Keywords

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

### ASJC Scopus subject areas

- Materials Science(all)
- Condensed Matter Physics

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## Cite this

*Journal of Physics Condensed Matter*,

*29*(45), [455303]. https://doi.org/10.1088/1361-648X/aa865c