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Embedded Liquid Crystal Defect with Graphene Layers in Asymmetric One-Dimensional Photonic Crystal as Sensor Application
Published in Narendra Kumar, Bhuvneshwer Suthar, Advances in Photonic Crystals and Devices, 2019
Pawan Singh, Krishan Pal, Khem B. Thapa, Narinder Kumar, Devesh Kumar
PCs can be categorized into one dimensional (1D), two dimensional (2D), and three dimensional as shown in Figure 8.1. 1D PCs are periodic structure of dielectric materials in which the modulation of dielectric permittivity in only one direction is considered, which are very easy to fabricate. Its optical properties can be investigated using transfer matrix method (TMM), which can be satisfied with experiments. The optical properties of 2D PCs can be investigated using plane wave expansion (PWE) method, beam propagation method (BPM), finite element method (FEM), and finite difference time domain (FDTD) method, usually used in waveguides.
The Modal Method
Published in Andrei V. Lavrinenko, Jesper Lægsgaard, Niels Gregersen, Frank Schmidt, Thomas Søndergaard, Numerical Methods in Photonics, 2018
Andrei V. Lavrinenko, Jesper Lægsgaard, Niels Gregersen, Frank Schmidt, Thomas Søndergaard
We observe that the implementation of the absorbing boundary condition in the plane-wave expansion technique simply requires the inclusion of one additional Toeplitz matrix F¯¯ in the eigenproblem formulation.
Propagation and Focusing of the Beam
Published in Yasuo Kokubun, Lightwave Engineering, 2018
On the other hand, although the Hermite–Gaussian function was derived in this section as the solution for the Helmholtz equation, the plane wave as another orthogonal function is also a solution. Therefore, expansion using a plane wave is also possible. In particular, when the paraxial approximation cannot be applied, a more accurate understanding of the optical beam propagation may be possible using the plane wave expansion.
Unidirectional weak visibility in bandgap and singular scattering in conduction band of one-dimensional -symmetry photonic crystal
Published in Waves in Random and Complex Media, 2022
In Figure 3, we present the complex band structures for different values of the imaginary relative permittivity . In our calculation, plane wave expansion method is applied, in our work, 61 plane waves are used to expand the electromagnetic field. For small values of , e.g. in Figure 3(a,b), the eigenfrequencies for all the bands remains real. When is increased to a critical value, the second bandgap starts to vanish and the 2nd and 3rd bands begin to coalesce, in which case an exceptional point emerges at the center of the Brillouin zone. As is further increased, this exceptional point is split in two, e.g. in Figure 3(c,d). These points are located at either sides of the Brillouin center; between these two exceptional points the complex eigenfrequencies emerge, which are conjugate to each other. The band region with complex eigenfrequencies forms the -broken phase, while the band region with real eigenfrequencies corresponds to the -exact phase. These properties agree with non-Hermitian quantum mechanics.