TY - JOUR
T1 - Hidden symmetries in N-layer dielectric stacks
AU - Liu, Haihao
AU - Shoufie, Ukhtary M.
AU - Saito, Riichiro
N1 - Funding Information:
H L worked as a participant in the 2016 Nakatani RIES: Research & International Experiences for Students Fellowship program, sponsored by the Nakatani Foundation and organized by Rice University, and thanks J Kono, S R Phillips, C J Stanton, K Packard, K Ogawa and U Endo for making the program possible. M S U is supported by the MEXT scholarship. R S acknowledges JSPS KAKENHI Grant Numbers JP 25107005 and JP 25286005.
Publisher Copyright:
© 2017 IOP Publishing Ltd.
PY - 2017/10/10
Y1 - 2017/10/10
N2 - 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.
AB - 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.
KW - dielectric stack
KW - electromagnetic wave
KW - multilayer system
KW - transfer matrix
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U2 - 10.1088/1361-648X/aa865c
DO - 10.1088/1361-648X/aa865c
M3 - Article
C2 - 28809756
AN - SCOPUS:85037736808
VL - 29
JO - Journal of Physics Condensed Matter
JF - Journal of Physics Condensed Matter
SN - 0953-8984
IS - 45
M1 - 455303
ER -