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Hidden symmetries in N-layer dielectric stacks

When a light hits the interface of a medium, some part of the light's energy is reflected and another part is transmitted to a different medium. When the light comes to a multilayer of dielectric media shown in Figure 1, the light will experience multi reflection inside the random multilayer structure, making the light inside the structure act in chaos.

Recent work at Tohoku University has revealed that the light properties of multilayer structures are not as random as previously thought. A team of researchers used a N-layer structure consisting of two different dielectric media shown as A and B in Figure 1 to investigate how light behaves in multilayer structures.

Figure 1. The light coming to a multilayer system consisting of two kinds of media, A and B. > (modified from the published figures) credit: Muhammad Shoufie Uktary.

If the thickness of each layer of the structure is determined by the quarter of light wavelength, it was found that the transmission probability of light (T) is not random and instead of 2N different values of T, There are only N/2+1 or N+1 discrete values for an even or odd number of N, respectively. For example, if we have N = 6, there will be 64 possible sequences, but we get only 4 different values of T.

Even for N = 10, where there are 1,024 possible sequences, there are only 6 different values of T. This implies there are symmetry operations acting on the sequences that do not change the value of T. Five symmetry operations were found and Figure 2 shows three of them. We call this phenomenon: "hidden symmetries in dielectric multilayer structures".

Figure 2. The symmetry operations acting on the sequences that do not change the T values. > (modified from the published figures) credit: Muhammad Shoufie Uktary.

This concept provides an impact for optics, in which many optical properties can be expressed by the new integer parameter called "charge".

This study was selected to be in the Journal of Physics: Condensed Matter highlights of 2017. The collection includes outstanding articles published in the journal during 2017. Articles were selected on the basis of a range of criteria including referee endorsements, presentation of outstanding research and popularity with the online readership.

Publication Details:

Authors: L. Haihao, M. Shoufie Ukhtary, and R. Saito
Title: Hidden symmetries in N - layers dielectric stacks
Journal: Journal of Physics: Condensed Matter
DOI: 10.1088/1361-648X/aa865c

Press release in Japanese


Muhammad Shoufie Ukhtary
Department of Physics, Tohoku University

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