Abstract
In a new theoretical investigation, we study light transmission through a photonic crystal (PC) slab with limited boundaries at width. By using a tight binding model, photon dispersion relation and photon Green function for a perfect system are obtained. Then, based on the Lippmann-Schwinger formalism, we calculate the effects of disordering on light transmission in the PC channel. We found that the ratio of the electric field for a defected system with respect to a perfect system at a peculiar frequency is maximized for the wave vector corresponding to the first Brillouin zone (BZ) edge showing photon localization. The electric field difference of the first and second neighboring sites with respect to the defect site on the first BZ edges are depicted in several plots indicating frequency dependence which can be applicable in frequency filtering or resonating cavity studies.
Highlights
The design of two-dimensional (2D) or three-dimensional periodic dielectric arrangements with proper choice of materials, lattice symmetry, embedded defect creation, and boundary situations in photonic crystals (PCs) enables the control of light flow at an elevated level
Based on the first-order perturbation theory and Lippmann-Schwinger formalism, we have presented a new treatment for light transmission through a PC slab which introduces a new equation by including disorders of the system
The equation has a general form and is applicable to 2D PC systems with different polarizations, but we simplify it for transverse magnetic (TM) modes and extend the method to investigate effects of a point defect on the light transmission along a boundary-limited slab length in which the slab system is mapped to a quasi-1D system
Summary
The design of two-dimensional (2D) or three-dimensional periodic dielectric arrangements with proper choice of materials, lattice symmetry, embedded defect creation, and boundary situations in photonic crystals (PCs) enables the control of light flow at an elevated level. More attention has been given to photon localization in PC microcavities and wave guides [3,4,5], nanocavities [6], and disordered or amorphous PCs [7,8,9]. In the last step, defected system electric field is related to the perfect system electric field by applying an equation based on the Lippmann-Schwinger formalism. In the‘Results and discussion’ section, application of this equation is investigated by several plots of the electric field and intensity at the defect site and its neighboring sites for different cases, followed by the the ‘Conclusions’ section
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