Analysis of Leaky Modes in Photonic Crystal Fibers Using the Surface Integral Equation Method

Abstract

A fully vectorial algorithm based on the surface integral equation method for the modelling of leaky modes in photonic crystal fibers (PCFs) by solely solving the complex propagation constants of characteristic equations is presented. It can be used for calculations of the complex effective index and confinement losses of photonic crystal fibers. As complex root examination is the key technique in the solution, the new algorithm which possesses this technique can be used to solve the leaky modes of photonic crystal fibers. The leaky modes of solid-core PCFs with a hexagonal lattice of circular air-holes are reported and discussed. The simulation results indicate how the confinement loss by the imaginary part of the effective index changes with air-hole size, the number of rings of air-holes, and wavelength. Confinement loss reductions can be realized by increasing the air-hole size and the number of air-holes. The results show that the confinement loss rises with wavelength, implying that the light leaks more easily for longer wavelengths; meanwhile, the losses are decreased significantly as the air-hole size d/Λ is increased.

An Ultrashort Wavelength Multi/Demultiplexer via Rectangular Liquid-Infiltrated Dual-Core Polymer Optical Fiber

“…Photonic crystal fibers (PCFs) are a special class of optical fibers characterized by a periodical arrangement of microcapillaries that form the fiber’s cladding around a solid or hollow defect core [16,17,18]. Since then, various fiber types such as honeycomb PCF [19], triangular PCF [20], rectangular PCF [21,22,23,24], D-shape PCF [25], side-polished PCF [26], and metal-coated PCF [27] have been demonstrated and applied in the fields of pharmaceutical drug testing, astronomy, communication, and biomedical engineering and sensing [28,29,30,31,32,33,34,35,36,37]. Compared with conventional optical fibers, the unique features of PCFs, such as flexibility of design, endless single-mode wavelength [21], high birefringence [22,23,24], and adjustable dispersion and nonlinearity [38,39], can be obtained by manipulating lattice period, air hole size and shape, refractive index of the materials, and type of lattice.…”

Numerical Modeling of Guided Mode for Negative Curvature Hollow-core Fibers

“…In this study, a new vectorial algorithm is derived from the VBEM (19)(20)(21)(22) for modeling guided modes in an NCHCF by simply solving the propagation constants corresponding to the supported modes of the NCHCF structure. To our knowledge, this is the first time an approach based on the boundary element method has been used for a hollow-core photonic crystal fiber.…”

“…Two homogeneous regions describe a hollow-core fiber: the air of the fiber core and the capillaries. We denote E as an arbitrary function in the rectangular coordinate system that is the solution of the Helmholtz equation in each region as follows: (22) 2 2…”

“…The differential equation Eq. ( 1) is converted to the following integral equation by using Green's identities: (22) ( , , )…”

Design of Polarization Splitter via Liquid and Ti Infiltrated Photonic Crystal Fiber

“…At present, refractive index guided PCF is the most mature and widely used optical fiber. PCF technology has made great progress in pharmaceutical drug testing, astronomy, communication, and biomedical engineering and sensing [2][3][4][5][6][7][8]. In recent years, the PCFs filled with materials have attracted great interests, because PCFs could provide excellent properties by filling different functional materials into the air holes [9][10][11][12][13][14].…”