Electromagnetic phenomenological study of photonic band structures

Abstract

It is shown, in the case of one-dimensional photonic crystals, that the transmission gaps are caused by the existence of resonance phenomena inside the layers which constitute the crystal. From a mathematical point of view, these resonances are associated with poles and zeros in the complex plane of the wavenumber k. Transmission gaps are located outside these resonance regions. A phenomenological formula allows us to represent quantitatively the transmission inside the gaps. Finally, a synthetic explanation of the properties of doped and non-doped crystals is proposed and it is shown that the transmission peaks inside the gaps of doped photonic crystals are caused by a shift of poles and zeros located inside the resonance regions of non-doped crystals.     

A procedure to obtain the complete electromagnetic scattering properties at discontinuities between integrated optical waveguides

Abstract

A method to obtain the complete electromagnetic scattering properties of discontinuities between arbitrary integrated optical waveguides is presented. The method involves a new generalized scattering matrix concept, together with the generalized telegraphist equations formulism and the modal matching technique. Radiation losses, as well as reflection and transmission coefficients between proper modes, can be obtained. Single and multiple discontinuities in planar and channel optical waveguides have been analysed. Numerical results of complex scattering coefficients are given. The possibilities of the method for analysing waveguide photonic crystals, as well as optical devices in waveguide periodic waveguide structures, are demonstrated.     

Evolution of complete photonic band gap in anisotropic photonic quasicrystals using liquid crystals

Abstract

In this study, we analyse the evolution of complete photonic band gap in two-dimensional photonic structures by arranging the 12-fold symmetric quasicrystalline unit cells on square and triangular lattices. The unit cells composed of circular air holes in anisotropic tellurium background and the air holes are infiltrated with liquid crystal. Using the supercell method based on plane wave expansion, we study the variation of complete band gap by changing the optical axis orientation of liquid crystals.     

Photonic Crystals

Abstract

In this paper, we review the early motivation for photonic crystal research which was derived from the need for a photonic bandgap in quantum optics. This led to a series of experimental and theoretical searches for the elusive photonic bandgap structures: those three-dimensionally periodic dielectric structures which are to photon waves, as semiconductor crystals are to electron waves. We shall describe how the photonic semiconductor can be ‘doped’, producing tiny electromagnetic cavities. Finally, we shall summarize some of the anticipated implications of photonic band structure for quantum electronics and the prospects for the creation of photonic crystals in the optical domain.     

Engineering a light-emitting planar defect within three-dimensional photonic crystals

Abstract

Sandwich structures, constructed from a planar defect of rhodamine-B (RhB)-doped titania (TiO₂) and two photonic crystals, were synthesized via the self-assembly method combined with spin-coating. The modification of the spontaneous emission of RhB molecules in such structures was investigated experimentally. The spontaneous emission of RhB-doped TiO₂ film with photonic crystals was reduced by a factor of 5.5 over a large bandwidth of 13% of the first-order Bragg diffraction frequency when compared with that of RhB-doped TiO₂ film without photonic crystals. The angular dependence of the modification and the photoluminescence lifetime of RhB molecules demonstrate that the strong and wide suppression of the spontaneous emission of the RhB molecules is due to the presence of the photonic band gap.     

Investigation of Absolute Photonic Band Gaps in Two-dimensional Dielectric Structures

Abstract

We examine the photonic band structure of two-dimensional (2D) arrays of dielectric holes using the coherent microwave transient spectroscopy (COMITS) technique. Such 2D hole arrays are constructed by embedding low-index rods (air) in a dielectric background of higher-index Stycast material (n = 3·60). The dispersion relation for electromagnetic wave propagation in these photonic crystals is directly determined using the phase sensitivity of COMITS. We find that both the square and triangular lattice structures exhibit photonic band gaps that are common to both polarizations for all wave-vectors along major symmetry axes. In addition, the connectivity of the high-index dielectric and the opening of a large gap for propagation with E field perpendicular to the hole cylinders are found to be important criteria for generating a large absolute photonic band gap.     

Microassembly of semiconductor three-dimensional photonic crystals

Electronic devices and their highly integrated components formed from semiconductor crystals contain complex three-dimensional (3D) arrangements of elements and wiring. Photonic crystals, being analogous to semiconductor crystals, are expected to require a 3D structure to form successful optoelectronic devices. Here, we report a novel fabrication technology for a semiconductor 3D photonic crystal by uniting integrated circuit processing technology with micromanipulation. Four- to twenty-layered (five periods) crystals, including one with a controlled defect, for infrared wavelengths of 3-4.5 microm, were integrated at predetermined positions on a chip (structural error <50 nm). Numerical calculations revealed that a transmission peak observed at the upper frequency edge of the bandgap originated from the excitation of a resonant guided mode in the defective layers. Despite their importance, detailed discussions on the defective modes of 3D photonic crystals for such short wavelengths have not been reported before. This technology offers great potential for the production of optical wavelength photonic crystal devices.     

Photonic band gap in 1D multilayers made by alternating SiO2 or PMMA with MoS2 or WS2 monolayers

Atomically thin molybdenum disulfide (MoS₂) and tungsten disulfide (WS₂) are very interesting two dimensional materials for optics and electronics. In this work we show the possibility to obtain one-dimensional photonic crystals consisting of low-cost and easy processable materials, as silicon dioxide (SiO₂) or poly methyl methacrylate (PMMA), and of MoS₂ or WS₂ monolayers. We have simulated the transmission spectra of the photonic crystals using the transfer matrix method and employing the wavelength dependent refractive indexes of the materials. This study envisages the experimental fabrication of these new types of photonic crystals for photonic and light emission applications.     

Multipole Dirichlet-to-Neumann map method for photonic crystals with complex unit cells

The periodicity of photonic crystals can be utilized to develop efficient numerical methods for analyzing light waves propagating in these structures. The Dirichlet-to-Neumann (DtN) operator of a unit cell maps the wave field on the boundary of the unit cell to its normal derivative, and it can be used to reduce the computation to the edges of the unit cells. For two-dimensional photonic crystals with complex unit cells, each containing a number of possibly different circular cylinders, we develop an efficient multipole method for constructing the DtN maps. The DtN maps are used to calculate the transmission and reflection spectra for finite photonic crystals with complex unit cells.     

High reflectance materials for photovoltaics applications: analysis and modelling

The paper involves reflectance structures fabricated with application of sol–gel method. High reflectance was obtained through the fabrication of one-dimensional photonic crystals on glass substrate. The paper presents both the results of theoretical analysis as well as the results of experimental studies. Using the 2 × 2 transfer matrix method, we determined reflectance and transmittance characteristics of the analyzed structures as well as power distributions in the photonic crystals. The one-dimensional photonic crystals were fabricated by the successive deposition of quarter-wave layers of silica and titania on glass substrate using the dip-coating method. For the fabricated reflectance structures with four bilayers (TiO₂/SiO₂), for the wavelength ~500 nm we have obtained the reflectance value equal to 0.933, and for the structures with five bi-layers the reflectance was equal to about 0.967. The uniformity of the fabricated structures and the repeatability of the technological process are discussed. We discuss also some slight divergence between theoretical predictions and experimental results.     

Self-collimated waveguide bends and partial bandgap reflection of photonic crystals with parallelogram lattice

The photonic crystal structure with parallelogram lattice, capable of bending a self-collimated wave with free angles and partial bandgap reflection, is presented. The equifrequency contours show that the direction of the collimation wave can be turned by tuning the angle between the two basic vectors of the lattice. Acute, right, and obtuse angles of collimating waveguide bends have been realized by arc lattices of parallelogram photonic crystals. Moreover, partial bandgap reflection of the parallelogram lattice photonic crystals is validated from the equifrequency contours and the projected band structures. A waveguide taper based on this partial bandgap reflection is also designed and proved to have above 85% transmittance over a very wide operating bandwidth of 180 nm.     

Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions

Manipulation of light is in strong demand in information technologies. Among the wide range of linear and nonlinear optical devices that have been used, growing attention has been paid to photonic crystals that possess a periodic modulation of dielectric function. Among many photonic bandgap (PBG) structures, liquid crystals with periodic structures are very attractive as self-assembled photonic crystals, leading to optical devices such as dye lasers. Here we report a new hetero-PBG structure consisting of an anisotropic nematic layer sandwiched between two cholesteric liquid-crystal layers with different helical pitches. We optically visualized the dispersion relation of this structure, displaying the optical diode performance: that is, the non-reciprocal transmission of circular polarized light at the photonic-bandgap regions. Transmittance spectra with circularly polarized light also reveal the diode performance, which is well simulated in calculations that include an electro-tunable diode effect. Lasing action was also confirmed to show the diode effect with a particular directionality.     

High efficiency solution infiltration routes to thin films with photonic properties

A chemical bath deposition (CBD) method has been developed to prepare three-dimensionally-ordered macroporous films of CdS and TiO₂, using colloidal crystals as templates. A series of sequential, short infill/rinse/anneal steps are employed to effect complete infiltration of SiO₂ (opal) thin films with CdS or TiO₂. Removal of templates allows fabrication of macroporous inverse replica structures that exhibit periodic modulation of dielectric behaviour and have potential for use in photonic applications. A study of the photonic properties of films indicates that the multi-step CBD method is a useful approach for infiltration of opal interstices.     

Photonic crystals,amorphous materials,and quasicrystals

Photonic crystals consist of artificial periodic structures of dielectrics, which have attracted much attention because of their wide range of potential applications in the field of optics. We may also fabricate artificial amorphous or quasicrystalline structures of dielectrics, i.e. photonic amorphous materials or photonic quasicrystals. So far, both theoretical and experimental studies have been conducted to reveal the characteristic features of their optical properties, as compared with those of conventional photonic crystals. In this article, we review these studies and discuss various aspects of photonic amorphous materials and photonic quasicrystals, including photonic band gap formation, light propagation properties, and characteristic photonic states.     

Heat transfer in photonic mirrors

The use of secondary mirrors in solar energy concentration is common. However, high concentrated solar radiation heats these mirrors thereby degrading their physical properties. In particular, aluminum mirrors melt because of high temperature due to storage by high radiative heat transfer. In contradistinction photonic crystals could present “perfect reflection” and they can be fabricated using porous silicon which has a higher melting point than aluminum (porous silicon has a melting point higher than 900 K). Porous silicon is a nanostructured semiconductor material which can be fabricated with different porosities and refractive indices. Multilayers of alternating periodic refractive index conform the structure of these photonic crystals. The light that propagates in these structures interacts with its periodic refractive index that generates wavelength gaps of forbidden transmission and so these multilayers conform a mirror. Even these photonic structures are heated when they are exposed to high concentrated solar radiation. In this work we experimentally analyze this heating process and model it using an effective medium approach to explain the increasing temperature behavior.     

Periodic defects in 2D-PBG materials: full-wave analysis and design

In this paper, an accurate and efficient characterization of two-dimensional photonic bandgap structures with periodic defects is performed, which exploits a full-wave diffraction theory developed for one-dimensional gratings. The high convergence rate of the proposed technique is demonstrated. Results are presented for both TE and TM polarizations, showing the efficiencies as a function of wavelength, incidence angle, geometrical and physical parameters. A comparison with other theoretical results reported in the literature is shown with a good agreement. The transmission properties of photonic crystals with periodic defects are studied, investigating the effects of the variation of geometrical and physical parameters; design efficiency maps and formulas are given; moreover, the application of the analyzed structures as filters is discussed.     

Getting effective permittivity and permeability equal to −1 in 1D dielectric photonic crystals

J.B. Pendry (Phys. Rev. Lett., 86 3966 (2000)) mentioned the possibility of making perfect lenses using a slab of left-handed material with relative permeability, permittivity and optical index equal to ?1. This kind of metamaterial has been made in the microwaves domain, using metal and dielectric materials. On the other hand, it has been shown that lenses made using 2D dielectric photonic crystals can generate similar imaging properties, but until now, the image contains only a small part of the incident light. The paper shows, using a very simple analytical model, that 1D dielectric photonic crystals can generate left-handed materials with relative permeability, permittivity and optical index rigorously equal to ?1. Of course, such photonic crystals cannot be used to make perfect lenses, but this conclusion leads to the conjecture that 2D or 3D dielectric photonic crystals could be used in the visible region to realize superlenses.     

Impurity modes in one-dimensional photonic crystals-analytic approach

Abstract

We investigate the impurity problem in one-dimensional photonic crystals using the two-band Bloch wave approximation. The impurity level, as the lasing mode, is described in terms of the width and the dielectric function of the impurity, which are in fair agreement with the numerical data by the transfer matrix method. The maximum field intensity and the strongest spatial localization occur when the impurity mode is at midgap, indicating large gain enhancement of the lasing mode. The threshold gain and the optimal conditions for the impurity are evaluated. Effects of surface variations are also analysed to further improve the efficiency of the lasing system.     

Maximization of Photonic Bandgaps in Two-Dimensional Superconductor Photonic Crystals

In this paper, we investigate the properties of photonic band structures in two-dimensional superconductor photonic crystals (2D-SCPCs) using the frequency dependent plane wave expansion method. We consider two types of 2D-SCPCs, which are composed of superconductor (dielectric) rods embedded into a dielectric (superconductor) background, named type I (type II) SCPCs. We target maximization of the gap-to-mid-gap ratio by varying many parameters, namely, shape of the rods, the operating temperature, the permittivity of the dielectric material, and the threshold frequency of the superconductor. We show that the type II SCPCs have a higher gap-to-mid-gap ratio than the type I SCPCs. In addition, the PBGs can be tuned efficiently by the operating temperature. Moreover, the photonic band structures can be tailored by changing the dielectric constant of the background (rods) in the type I (type II) SCPCs.     

Photonic bandgap calculations with Dirichlet-to-Neumann maps

A simple and efficient method for computing bandgap structures of two-dimensional photonic crystals is presented. Using the Dirichlet-to-Neumann (DtN) map of the unit cell, the bandgaps are calculated as an eigenvalue problem for each given frequency, where the eigenvalue is related to the Bloch wave vector. A linear matrix eigenvalue problem is obtained even when the medium is dispersive. For photonic crystals composed of a square lattice of parallel cylinders, the DtN map is obtained by a cylindrical wave expansion. This leads to eigenvalue problems for relatively small matrices. Unlike other methods based on cylindrical wave expansions, sophisticated lattice sums techniques are not needed.