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4Merging of defect modes in one-dimensional photonic crystals
with two defect layers
A.O. Kamenev12*, A.A. Malinchenko1, N.A. Vanyushkin1, I.M. Efimov1, S.S. Golik12, V.G. Chigrinov3, A.H. Gevorgyan1
1- Far Eastern Federal University, Institute of High Technologies and Advanced Materials, 690922 Vladivostok,
Russia
2- Institute of Automation and Control Processes, Far East Branch, Russian Academy of Sciences, 690041
Vladivostok, Russia
3- Foshan University, School of Physics and Optoelectronic Engineering, 528011 Foshan, China
With the development of optics and photonics, research into the possibilities of photonic crystals (PCs) is becoming increasingly popular. A well-known property of such structures is their ability to control the light passing through them due to the so-called photonic bandgap (PBG). In one-dimensional (1D) PCs, defect modes (DMs) represent resonant peaks in the transmission spectra. The number of DMs within the PBG is determined by the number of defect layers (DLs) in the structure of the PC and their optical thicknesses. The parameters of the DL directly influence the position of the DMs in the spectra, which is the basis for the operation of 1D PC-based sensors. Over the past few decades, many different optical sensors based on 1D PCs with DLs have been developed for a wide range of applications. Additionally, many papers have been published on the optimization of 1D PCs and their properties [1-3]. However, the application potential of PCs with several defects in the structure is not well investigated. In particular, no paper presents a condition for the merging of two DMs appearing in such structures. That is why we have studied this question in more detail. Here we have derived the condition for the merging of two DMs in 1D PCs with two DLs. This condition is demonstrated by formula 1:
A^ = ln
rnr^l 2-|rn|2+2Vl-|rn|2 7111*1* |rn|4
^2, (1)
where A^ = — is the phase difference, r is the reflection coefficients for each of the three PCs in the structure, f is the reflection coefficient for each of the three PCs when the wave is incident from
2n
the right, i.e., from the DL side, q2 e Z, 2 = ~r^d12^d12 are the changes of phase of the wave at a
' A ' '
single passage through the first and second DLs in the structure, nd1 and nd2 are the refractive indices of two DLs, dd1 and dd2 are their thicknesses. Using this formula, we have found such PC parameters at which the DMs merge and a large localization of the electromagnetic field in the DLs and at the wavelength of the merging of two DMs in the 1D PC with two DLs is observed.
[1] I.M. Efimov, et al, Sensor with enhanced performance based on photonic crystal with a defect layer, Computer Optics, vol. 47, pp. 57279, (2023).
[2] I.M. Efimov, N.A. Vanyushkin, A.H. Gevorgyan, Peculiarities of the Electromagnetic Field Distribution Inside a 1D Photonic Crystal with a Defect Layer, Bulletin of the Russian Academy of Sciences: Physics, vol. 86, pp. 60-65, (2022).
[3] A.O. Kamenev, et al, On the sensitivity of defect modes outside the first photonic bandgap in optical sensors based on defected 1D photonic crystals, Physica Scripta, vol. 99(4), pp. 045521, (2024).
