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Properties of Electromagnetic Density of Mode in Acoustically Perturbed Photonic Crystal
Published in Narendra Kumar, Bhuvneshwer Suthar, Advances in Photonic Crystals and Devices, 2019
Ayush Aman, Yogesh Sharma, Surendra Prasad, Vivek Singh
In order to calculate the transmission coefficient (t), we have used transfer matrix method (TMM) (Yariv and Yeh 1983), which is widely used to study the optical properties of layered media. According to TMM, the final matrix of the structure can be written as follows: () M=∏j=1k[cosδjiNjsinδji⋅Njsinδjcosδj]=∏j=1kMj=[m11m12m21m22]
Quantum Corrections to Semiclassical Approaches
Published in Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck, Computational Electronics, 2017
Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck
Equation 8.99, which represents a system of coupled ordinary differential equations, can be solved by several approaches such as the transfer matrix method [140,141], the finite element method [142], and the basis expansion method [143]. Each method has its own advantages and disadvantages. The transfer matrix method uses analytical expressions for the eigenvalues and eigenvectors and is computationally faster. However, a tedious step is to express the wave vector along the confinement direction in terms of the in-plane components for each subband. The finite difference method is much simpler in formulation, yet it is computationally time consuming because of a large number of unknowns. The basis expansion method combines the two approaches by finding a certain number of band-edge wavefunctions at K|| = 0 and expanding the wavefunctions at finite values of the in-plane wave vector in terms of those at K|| = 0, and solving a new set of eigenvalue equations. In this work, the finite difference method has been employed because of its conceptual simplicity and its numerical stability with respect to the transfer matrix method that is inherently unstable and requires the truncation of a number of evanescent states [144].
Electron–Photon Interaction
Published in Joachim Piprek, Handbook of Optoelectronic Device Modeling and Simulation, 2017
In free space or homogeneous matter, plane waves E0ei(q⋅r−ωt) are solutions to Maxwell's equations [4]. Any light field may be expanded in plane waves. The transfer matrix method uses this to express the light field as a plane wave in every layer of a microstructure and appropriately match the conditions at the interfaces.
Designing a phononic crystal with a defect for target frequency matching using an analytical approach
Published in Mechanics of Advanced Materials and Structures, 2022
In band-structure analysis, a PnC that includes both the defect and the array of unit cells is called a supercell, which is distinct from a unit cell [50, 51]. The process to derive the dispersion relations (normalized wavenumber-frequency relations) for a supercell is known as the supercell technique [52, 53]. To date, many methods have been developed to calculate band structures of a unit cell or a supercell, including the plane-wave expansion method [54], multiple scattering method [55], wavelet method [56], and finite element method [57]. Among them, the transfer matrix method is used in this work since it is an analytical approach that is based on the explicit solutions to the governing equations of the elastic waves [58, 59]. In this paper, for a given one-dimensional structure, the transfer matrix refers to a 2 × 2 matrix that transforms a vector of an axial velocity and force at one end into that at the other end.
Ultrasonic guided wave technique for monitoring cure-dependent viscoelastic properties of carbon fiber composites with toughened interlaminar layers
Published in Advanced Composite Materials, 2021
Koichi Mizukami, Takahiro Ikeda, Keiji Ogi
The transfer matrix method is a semi-analytical method for determining the complex phase velocity of a guided wave propagating through a stratified medium [27]. Once the complex phase velocity is known, the energy velocity and attenuation can be calculated. Figure 6 shows the analytical model for the transfer matrix method. It was assumed that the guided wave propagated in a four-layer laminate consisting of a bottom release film, unidirectional CFRP with interlayers, top release film, and vacuum bag. Because the breather had low acoustic impedance, the bottom surface of the release film was assumed to be a free surface [18]. The x1 direction is the direction of the propagation of the guided wave, and the x3 direction is the thickness direction. It was assumed that the model was infinitely long in the x2 direction. Only the Lamb wave was considered as the guided wave mode propagating in the material. The calculation procedures of the transfer matrix method are shown in Appendix B. The transfer matrix method produces a dispersion equation with respect to the complex phase velocity of the guided wave at a specific frequency. Once the complex phase velocity is known, the energy velocity and attenuation of the guided wave can be calculated [28,29].
Matrix method for two-dimensional waveguide mode solution
Published in Journal of Modern Optics, 2018
Baoguang Sun, Congzhong Cai, Balajee Seshasayee Venkatesh
When the waveguide structure sometimes becomes anisotropic, derivative free method also can be used (23). This method is efficient and works well for varieties isotropic and anisotropic waveguide structures and it is based on the dispersion equation which is derived from the transfer matrix method. In other words, the transfer matrix method is also efficient for anisotropic waveguide structures. The transfer matrix method can also be used for the analysis of the wave propagation of quantum particles (24), such as electrons, and of electromagnetic waves, acoustic waves and elastic waves. Once the technique is developed for one type of wave, it can easily be applied to any other wave problems.