Hidden symmetries inN-layer dielectric stacks

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 . Using the transfer matrix method, the transmittance T is calculated for all possible 2 sequences for small N. Unexpectedly, it is found that instead of 2 different values of T at f (T ), there are only [Formula: see text] discrete values of T, for even N, and (N + 1) for odd N. We explain this high degeneracy in T values by finding symmetry operations on the sequences that do not change T. Analytical formulae were derived for the T values and their degeneracies as functions of N and an integer parameter for each sequence we call 'charge'. Additionally, the bandwidth at f and filter response of the transmission spectra are investigated, revealing asymptotic behavior at large N.

Tunable optical absorption in undoped graphene sandwiched between multilayer dielectric stacks with mirror symmetry

“…The description of light propagation is encapsulated by the matrix equations known as the transfer matrix method [31,32]. This is a simple and accurate method for describing wave propagation inside several connected media and has been frequently applied in photonics and quantum transport research fields [18,[31][32][33]. Within this method, E (+) and E (−) are expressed in terms of E ″(+) and E ″(−) .…”

“…where i is an imaginary number and k = 2nπ/λ represents the wavevector of light with a wavelength of λ. Here, we configure each layer's thickness to be a quarter of the wavelength to ensure there are no reflections when the light propagates through the layer [33]. Therefore, P n can be simplified to:…”

“…The reflected electric field -E 0 ( ) is calculated by solving equation (15). It is important to note that Liu et al have shown that the = -E 0 0 ( ) for the mirrored structure, owing to the symmetry of the structure [28,33]. Furthermore, the repetition of the unit layers is represented by the (r − 1)th power of the matrices J 2 and J 3 , as defined in equations (7) and (12).…”