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.     

Enhanced third-order nonlinear optical response of photonic bandgap materials

Abstract

We calculate the nonlinear phase shift acquired by a laser beam in propagating through a one-dimensional photonic bandgap material, that is a material in which the linear refractive index is periodically modulated along the direction of propagation. We find that the nonlinear phase shift shows resonances for laser frequencies close to the edge of the stop band of the photonic bandgap structure. Enhancements of the nonlinear phase shift compared with that of a homogeneous nonlinear optical material by a factor of approximately five are predicted under realistic laboratory conditions. We find that similar enhancements of the two-photon absorption rate can occur for a material with an imaginary nonlinear susceptibility. We also treat the case of a photonic bandgap material containing a ′defect,' that is a central region somewhat too thick to conform to the periodicity of the system, and find that the nonlinear phase shift can be enhanced by a factor of approximately thirty.     

Photonic band gaps in quasicrystal-related approximant structures

Abstract

We propose a method for a systematic investigation of quasicrystal-related approximant structures in view of photonic bandgap applications. A detailed study is presented in the case of approximants formed by dielectric cylinders and constructed from a two-dimensional quasiperiodic lattice with octagonal symmetry. We show that isotropic photonic bandgaps are obtained even for the lowest order approximants generated by successive hyperspace shear. The main Fourier components of the dielectric function, responsible for the first photonic bandgap opening, are derived from the main component set of the quasiperiodic lattice. The magnitudes of the corresponding Brillouin zone vectors are shown to be directly related to the average distance between the planes passing by the dielectric cylinders. In other words, the approximant gap position is rather determined by the fundamental lattice parameters common to the quasiperiodic and approximant structures than by the approximant period. We also show that structure point symmetry is not indispensable for the band gap opening.     

Analysis of the Filling Pattern Dependence of the Photonic Bandgap for Two-dimensional Systems

Abstract

We investigate in this paper different aspects of the absolute photonic bandgap (PBG) formation for a two-dimensional periodic dielectric structure. In particular we examine how the symmetry of the filling pattern in a periodic dielectric material influences the photonic gap parameters. We present the results of the calculations and discuss the existence of the absolute PBG, the maximization of its width as a function of the parameters of a two-dimensional dielectric crystal as well as the practical technological feasibility of these optimized structures.     

The design of two-dimensional photonic quasicrystals by means of a fourier transform method

Abstract

We report a method of designing aperiodic photonic quasicrystals. The method is based on the recognition that the Fourier transform of the dielectric structure has a direct influence on the mode spectrum, and can be chosen to enhance the properties of the system. The diffraction of light by, and the band structure of, such modified photonic quasicrystals is investigated and compared to the properties of conventional photonic quasicrystals.     

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.     

Concurrent bandgap narrowing and polarization enhancement in epitaxial ferroelectric nanofilms

Abstract

Perovskite-type ferroelectric (FE) crystals are wide bandgap materials with technologically valuable optical and photoelectric properties. Here, versatile engineering of electronic transitions is demonstrated in FE nanofilms of KTaO₃, KNbO₃ (KNO), and NaNbO₃ (NNO) with a thickness of 10–30 unit cells. Control of the bandgap is achieved using heteroepitaxial growth of new structural phases on SrTiO₃ (001) substrates. Compared to bulk crystals, anomalous bandgap narrowing is obtained in the FE state of KNO and NNO films. This effect opposes polarization-induced bandgap widening, which is typically found for FE materials. Transmission electron microscopy and spectroscopic ellipsometry measurements indicate that the formation of higher-symmetry structural phases of KNO and NNO produces the desirable red shift of the absorption spectrum towards visible light, while simultaneously stabilizing robust FE order. Tuning of optical properties in FE films is of interest for nanoscale photonic and optoelectronic devices.     

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.     

光子晶体的能带结构、潜在应用和制备方法

光子晶体是指具有光子能带和能隙的一类新型材料,它具有奇特的调节光子传播状态的特性．本文将从光子晶体的能带结构、潜在应用和制备方法三方面对其进行综述性介绍．由于光子晶体有着非常广阔的应用前景,这一领域已成为当今世界范围内的研究热点．     

Spontaneous emission from a double V-type four-level atom in a double-band photonic crystal

Abstract

Quantum interferences in spontaneous emission from a double V-type four-level atom in a double-band photonic crystal have been investigated. The double V-type transitions from the two upper levels to the two lower levels can interact not only with modes near the edges of a double-band photonic band gap, but also with free vacuum modes. The resulting two types of quantum interferences give rise to not only dark lines, but also a narrow spontaneous line in the spectrum from the transition coupled to the free vacuum modes. The dark lines and narrow spontaneous line are shown to be dependent on the width of the forbidden gap, relative position of the upper levels from the band edges, coupling constants, and initial coherent superposition state of the system.     

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.     

Electric-Field-Regulated Energy Transfer in Chiral Liquid Crystals for Enhancing Upconverted Circularly Polarized Luminescence through Steering the Photonic Bandgap

Circularly polarized luminescent materials with high dissymmetry factor (g_lum) have been attracting increasing attention due to their distinctive photonic properties. In this work, by incorporating upconversion nanoparticles (UCNPs) and CsPbBr₃ perovskite nanocrystals (PKNCs) into a chiral nematic liquid crystal (N*LC), enhanced upconverted circularly polarized luminescence (UC-CPL) based on a radiative energy transfer (RET) process from UCNPs to CsPbBr₃ PKNCs is successfully implemented. By locating the emission peak of CsPbBr₃ PKNCs at the center of the photonic bandgap of N*LC, the maximum g_lum value of UC-CPL can be amplified to an extremely large value of 1.1. Meanwhile, upconverted emission of UCNPs can be significantly enhanced due to the band edge enhancement effect of the N*LC, subsequently enhancing the emission of the CsPbBr₃ PKNCs through the RET process. In addition, an applied electric field can switch the upconverted emission of the UCNPs, as well as the RET process, enabling an electric-field-controlled UC-CPL switch.     

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.     

A Polarized Transfer Matrix for Electromagnetic Waves in Structured Media

Abstract

The study of electromagnetic systems with dielectric or magnetic properties that vary spatially on or below the scale set by the wavelength of the radiation considered is of interest both in the field of photonic band gap materials and in that of random multiple scattering media. A key calculation technique in both areas is the transfer matrix. We derive a new transfer matrix, written in the language of scattering between transverse polarized wave states. This could be used in either photonic band calculations or in disordered media calculations. We demonstrate the use of the new transfer matrix to describe transport through a layered random dielectric in the Rayleigh scattering regime. This problem has considerable similarities to that of non-interacting electrons in a one-dimensional random potential. A complete solution for one polarization can be given by the use of group theoretical results. The other polarization exhibits pronounced dipole effects which can easily be calculated to lowest order.     

Large-area 2D periodic crystalline silicon nanodome arrays on nanoimprinted glass exhibiting photonic band structure effects

Two-dimensional silicon nanodome arrays are prepared on large areas up to 50 cm2 exhibiting photonic band structure effects in the near-infrared and visible wavelength region by downscaling a recently developed fabrication method based on nanoimprint-patterned glass, high-rate electron-beam evaporation of silicon, self-organized solid phase crystallization and wet-chemical etching. The silicon nanodomes, arranged in square lattice geometry with 300 nm lattice constant, are optically characterized by angular resolved reflection measurements, allowing the partial determination of the photonic band structure. This experimentally determined band structure agrees well with the outcome of three-dimensional optical finite-element simulations. A 16% photonic bandgap is predicted for an optimized geometry of the silicon nanodome arrays. By variation of the duration of the selective etching step, the geometry as well as the optical properties of the periodic silicon nanodome arrays can be controlled systematically.     

Dispersion relation of surface plasmons near photonic band gaps: Influence of the interaction with light

Abstract

We present an experimental and theoretical study of the photonic band gap in the propagation of surface plasmons (SPs) on periodically corrugated surfaces. Our main purpose is to investigate the case where the band gap width is larger than the energy distance between the SP dispersion curve for a flat surface and the light line. We introduce a physical model of the interaction of light waves with SPs and derive an analytical expression for the SP wave vector near band gaps based on the coupled-mode approach involving three interacting modes (two of them are SP modes and one is a light mode). By using the interferometric measurement we have studied, for the first time, the SP propagation parameters in the vicinity of the photonic band gap (10 μm wavelength region). The predictions of our theory are in good agreement with the experimental data.     

Effect of photonic bandgap on upconversion emission in YbPO4:Er inverse opal photonic crystals

We obtained upconversion (UC) light-emitting photonic materials (YbPO(4):Er) with an inverse opal structure by the self-assembly technique in combination with a solgel method. The effect of the photonic stopband on the UC luminescence of the (2)H(11/2), (4)S(3/2)→(4)I(15/2), and (4)F(9/2)→(4)I(15/2) transitions of Er(3+) has been observed in the inverse opals of the Er(3+)-doped YbPO(4). Significant suppression of the UC emission was detected if the photonic bandgap overlapped with the Er(3+) ions emission band, while enhancement of the UC emission occurs if the emission band appears at the edge of the bandgap.     

Symmetry properties of two-dimensional anisotropic photonic crystals

A theoretical study of two-dimensional photonic crystals made of anisotropic material is presented. Detailed computation principles including a treatment of the TE and TM polarizations are given for a photonic crystal made of either uniaxially or biaxially anisotropic materials. These two polarizations can be decoupled as long as any one of the principal axes of the anisotropic material is perpendicular to the periodic plane of the photonic crystal. The symmetry loss due to the anisotropy of the material and the variation of the Brillouin zones relative to the tensor orientations are also analyzed. Furthermore, the symmetry properties of the two-dimensional photonic band structure are studied, and the resulting effect on the photonic bandgap and the dispersion properties of photonic crystal are analyzed as a function of the orientation of the anisotropic material.     

Layer‐by‐Layer Approach to (2+1)D Photonic Crystal Superlattice with Enhanced Crystalline Integrity

Large‐area polystyrene (PS) colloidal monolayers with high mechanical strength are created by a combination of the air/water interface self‐assembly and the solvent vapor annealing technique. Layer‐by‐layer (LBL) stacking of these colloidal monolayers leads to the formation of (2+1)D photonic crystal superlattice with enhanced crystalline integrity. By manipulating the diameter of PS spheres and the repetition period of the colloidal monolayers, flexible control in structure and stop band position of the (2+1)D photonic crystal superlattice has been realized, which may afford new opportunities for engineering photonic bandgap materials. Furthermore, an enhancement of 97.3% on light output power of a GaN‐based light emitting diode is demonstrated when such a (2+1)D photonic crystal superlattice employed as a back reflector. The performance enhancement is attributed to the photonic bandgap enhancement and good angle‐independence of the (2+1)D photonic crystal superlattice.     

Two-dimensional penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes

Abstract

We report measurements of the diffraction pattern of a two-dimensional photonic quasicrystal structure. Using a set of plane waves defined by the diffraction pattern we introduce a theoretical approach for the calculation of the band structure which captures the rotational and inflational properties of the quasicrystal. Based on this model we find that the density of modes of the quasicrystal displays a fractal character and a depleted region analogous to the band gap in a periodic system.