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Field Representations in Periodic Artificial Materials Excited by a Source
Published in Filippo Capolino, Theory and Phenomena of Metamaterials, 2017
Filippo Capolino, David R. Jackson, Donald R. Wilton
For some purposes, such as asymptotic analysis and calculation of surface-wave and leaky-wave excitation amplitudes, it is also important to be able to calculate the Fourier transform of the field on an aperture plane. We have shown how the Fourier transform of the field at an aperture plane z = constant can be evaluated via the direct plane-wave expansion and the ASM. Again, the ASM is the more efficient method. In the ASM, the Fourier transform of the field is given directly by the (0,0) Floquet wave in the phased-array problem and is thus relatively easy to numerically calculate, involving a single periodic moment-method solution. In contrast, the direct plane-wave expansion method requires the solution of an infinite number of plane-wave excitation problems (an infinite number of different incident angles) to calculate the Fourier transform of the field for a fixed set of transform wave numbers (kx, ky).
Highly nonlinear dispersion-flattened high-index-core Bragg fibres for supercontinuum generation
Published in Journal of Modern Optics, 2019
Jiajin Zheng, Wenjie Lei, Yao Qin, Hui Zou, Kehan Yu, Wei Wei
Using the plane-wave expansion method, we have solved Maxwell's equations for the propagation of electromagnetic waves. The photonic bandgap structure corresponded to an infinite one-dimensional photonic crystal can be written as Equation (1). where K is Bloch constant, ω is the optical frequency and β is the propagation constant. A and D are related to the structure of optical fibre. K is a real number that Bloch waves can be transmitted when |(A + D)/2|<1. Contrarily, K is an imaginary number that Bloch wave will decay very quickly, which propagates instantaneously in periodic medium and resulting in the bandgap when |(A + D)/2|>1, the boundary is |(A + D)/2|=1. According to the full-vector modal method with shield boundary conditions, the bandgap structures including the spectrum of TE modes and omitting TM modes (15). We have thus applied a relatively simple and fast matrix method that was originally proposed for analysing the leaky modes of a standard silica fibre to obtain the propagation characteristics of the HIC Bragg fibre. In Figure 2, the transverse intensity distribution for the fundamental mode HE11 and first intra-band guided modes TE01 are shown. The light intensity propagated in the HIC and circular symmetry due to the alternating distribution of high and low refractive-index layers.
Three Ways Chip to Chip Communication via a Single Photonic Structure: A Future Paragon of 3D Photonics to Optical VLSI
Published in IETE Journal of Research, 2023
S. Boobalan, P. Venkatesh Kumar, K. Vinoth Kumar, G. Palai
The reflection loss of 3D photonic crystal structure depends on the photonic band gap analysis through the solution electromagnetic wave equation after solving the Maxwell’s differential equation [13]. The photonic band gap of the structure is computed using plane wave expansion method. The reflected signal is a function of photonic band gap because photonic band gap corresponds to the reflection of the signal by the periodic object or structure. Even though the simulation corresponding to all input signal (1.24 m, 1.26 m, 1.28 µm, 1.3 µm, 1.32 µm,1.34 µm, 1.36 µm, 1.38 µm, 1.4 µm, 1.45 µm, 1.5 µm, 1.55 µm, 1.6 µm, 1.65 µm, 1.7 µm, 1.8 µm, 1.9 µm, 2.0 µm, 2.25 µm) is done, the result for 1.24 µm and 2.25 µm is shown in Figure 3(a,b) respectively.
Flexural wave propagation in periodic tunnels with elastic foundations
Published in Mechanics of Advanced Materials and Structures, 2022
Lili Yuan, Zhanhua Cai, Peng Zhao, Yong Ding, Tingfeng Ma, Ji Wang
Herein, one-dimensional PCs consisting of periodic circular tunnel structure on elastic foundation with difference axial prestresses are proposed. The wave equations of flexural wave in periodic circular tunnel structure are established based on Winkler elastic foundation. The band structure and the propagation properties of flexural wave are calculated by the plane wave expansion method. The effects of elastic foundation stiffness, elastic modulus ratio and axial prestress (axial tensile stress, axial compressive stress, periodic axial stress, etc.) on band gap structures are analyzed in detail. The analysis method and results in the paper can provide theoretical bases for the design of tunnel structure with adjustable vibration reduction frequency.