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

UR - http://www.scopus.com/inward/record.url?scp=85037736808&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037736808&partnerID=8YFLogxK

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 -