By Obayya, Salah
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Additional info for Computational Liquid Crystal Photonics : Fundamentals, Modelling and Applications
6 Applications of PhCs The PhC can manipulate the photons and thus has received great interest in different applica‑ tions, such as sub‐wavelength imaging, scanning photon tunneling microscopy, phase shifters, logic gates, and optical routers. The design of PhC‐based applications is based on the bandgap or defect engineering. In this regard, the light can be controlled by introducing a defect in the periodic structure. If a line defect is introduced, the light can be transmitted through such a small waveguide along the defect only .
He showed that the propagation of un‐scattered waves in such media is gov‑ erned by a periodic envelope function multiplied by a plane wave. The proposed methodol‑ ogies by Bloch in quantum mechanics can be used in electromagnetism by formulating Maxwell’s equations as an eigenvalue problem in analogy with Schrödinger’s equation. 6) where ε is the dielectric permittivity function ε (x, y, z) and c is the light speed. 7) The two curls equal somewhere to the “kinetic energy” and 1/ε to the “potential” (compared with the Schrödinger Hamiltonian).
Electromagnetic modes with wavelengths lying within the PBG cannot propagate through the PhCs due to the Computational Liquid Crystal Photonics: Fundamentals, Modelling and Applications, First Edition. Salah Obayya, Mohamed Farhat O. F. Areed. © 2016 John Wiley & Sons, Ltd. Published 2016 by John Wiley & Sons, Ltd. 18 Computational Liquid Crystal Photonics reflection and refraction at the boundaries of the alternating materials. Periodic dielectric structures with bandgaps have many comprehensive applications in different branches of wave optics, such as filters, mirrors, resonators, sensors, and lasers and microwaves.