Abstract
One of the methods for calculating electromagnetic wave dispersion in multi-layer structures is the transfer matrix method. In this paper, we use the transfer matrix method for second harmonic generation in a nonlinear multilayer structure. The nonlinear photonic crystals investigated in this paper are as one-dimensional multi-layered structures including ferroelectric materials such as LiTaO3. Our goal is to investigate the effect of the disorder on the transmission spectrum of electromagnetic waves. Our results showed that positional disorder has different effects on the transmitting band and the gap band. The disorder in the transmitting band reduces the transmission coefficient of the waves and increases the transmission coefficient of the waves in the gap band. Such work has not yet been done on nonlinear photonic crystals producing the second harmonic.
Highlights
In recent decades, the study of the transmission of waves in random systems has been highly studied because it plays an important role in understanding the optical, mechanical, magnetic, and electrical properties of materials
We investigate a random binary structure constructed of N lithium tantalite (LiTaO3) layers
To calculate the Transmission coefficient quantity, averaging operations are performed on 3000 systems with different ordering (Figure 2)
Summary
The study of the transmission of waves in random systems has been highly studied because it plays an important role in understanding the optical, mechanical, magnetic, and electrical properties of materials. For example a one-dimensional system with the periodic period consisting of two parts is known as a random-dimer model [4] [5] In this type of system, there are modes that disorder does not affect them. The last model that produces non-localized states, unlike the one-dimensional Anderson model prediction, is called the “necklace” model [10] This model has been used in a multilayer dielectric structure [11]. A periodic structure with a transmission spectrum that does not have any propagating modes in certain frequency regions is called the photonic crystal [12]. By placing a positional disorder in a multilayer structure, when the optical length of layer is equal to a quarter wavelength, a series of transmission modes through the photonic band gap are created [15]. We study the effect of the positional disorder on the transmission of an electromagnetic wave that collides vertically on the surface of the structure, so that during the initial wave propagation
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