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.     

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.     

Diamond-structured photonic crystals

Certain periodic dielectric structures can prohibit the propagation of light for all directions within a frequency range. These 'photonic crystals' allow researchers to modify the interaction between electromagnetic fields and dielectric media from radio to optical wavelengths. Their technological potential, such as the inhibition of spontaneous emission, enhancement of semiconductor lasers, and integration and miniaturization of optical components, makes the search for an easy-to-craft photonic crystal with a large bandgap a major field of study. This progress article surveys a collection of robust complete three-dimensional dielectric photonic-bandgap structures for the visible and near-infrared regimes based on the diamond morphology together with their specific fabrication techniques. The basic origin of the complete photonic bandgap for the 'champion' diamond morphology is described in terms of dielectric modulations along principal directions. Progress in three-dimensional interference lithography for fabrication of near-champion diamond-based structures is also discussed.     

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 bandgaps of different unit cells in the basic structural unit of germanium-based two-dimensional decagonal photonic quasi-crystals

Based on the infrared optical material germanium, in the basic structural unit of a two-dimensional decagonal photonic quasi-crystal, photonic bandgaps of four square unit cells with a scattering radius in the range of [0,0.3a] have been calculated within two cases of construction (i.e., air cylinders arranged in germanium and germanium cylinders arranged in air) by using the plane wave expansion method. In considering the Bragg-like scattering effect in two-dimensional photonic quasi-crystals as the elastic collision in physics, we put forward the photonic bandgap impact function F=q(1)q(2)q(3)επr(2) for the first time, to the best of our knowledge. A certain unit cell structure shares some similar photonic bandgap properties with a periodic structure. For a certain structure of the unit cell, the center frequency change trends of the photonic bandgap and the type of photonic bandgap generated are not related with the period of the photonic crystal, but with the relative dielectric constant and the construction, respectively. Different unit cell structures own different photonic bandgap structures. This occurs because the high degree of rotational symmetry of the quasi-periodic structure and weak long-range order of the basic structural unit lead to different Bragg-like scattering effects within the unit cell structures.     

非空气-石英结构PCF的带隙特性分析

光子晶体光纤是近十来年兴起的一个新兴的研究领域,是现今纤维光学的研究重点,光子带隙特性是光子晶体光纤区别传统光纤的主要特征。本文利用全矢量平面波展开法对非空气-石英结构PCF的带隙特性进行分析,并且重点讨论空气孔内填充介电材料对光子带隙存在的影响。     

Direct laser writing of three-dimensional photonic-crystal templates for telecommunications

The past decade has witnessed intensive research efforts related to the design and fabrication of photonic crystals. These periodically structured dielectric materials can represent the optical analogue of semiconductor crystals, and provide a novel platform for the realization of integrated photonics. Despite intensive efforts, inexpensive fabrication techniques for large-scale three-dimensional photonic crystals of high enough quality, with photonic bandgaps at near-infrared frequencies, and built-in functional elements for telecommunication applications, have been elusive. Direct laser writing by multiphoton polymerization of a photoresist has emerged as a technique for the rapid, cheap and flexible fabrication of nanostructures for photonics. In 1999, so-called layer-by-layer or woodpile photonic crystals were fabricated with a fundamental stop band at 3.9 microm wavelength. In 2002, a corresponding 1.9 microm was achieved, but the important face-centred-cubic (f.c.c.) symmetry was abandoned. Importantly, fundamental stop bands or photonic bandgaps at telecommunication wavelengths have not been demonstrated. In this letter, we report the fabrication--through direct laser writing--and detailed characterization of high-quality large-scale f.c.c. layer-by-layer structures, with fundamental stop bands ranging from 1.3 to 1.7 microm.     

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.     

Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups

The promise of photonic crystals and their potential applications has attracted considerable attention towards the establishment of periodic dielectric structures that in addition to possessing robust complete bandgaps, can be easily fabricated with current techniques. A number of theoretical structures have been proposed. To date, the best complete photonic bandgap structure is that of diamond networks having Fd3m symmetry (2-3 gap). The only other known complete bandgap in a face-centred-cubic (f.c.c.) lattice structure is that of air spheres in a dielectric matrix (8-9 gap; the so called 'inverse-opal' structure). Importantly, there is no systematic approach to discovering champion photonic crystal structures. Here we propose a level-set approach based on crystallography to systematically examine for photonic bandgap structures and illustrate this approach by applying it to the 11 f.c.c. groups. This approach gives us an insight into the effects of symmetry and connectivity. We classify the F-space groups into four fundamental geometries on the basis of the connectivity of high-symmetry Wyckoff sites. Three of the fundamental geometries studied display complete bandgaps--including two: the F-RD structure with Fm3m symmetry and a group 216 structure with F43m symmetry that have not been reported previously. By using this systematic approach we were able to open gaps between the 2-3, 5-6 and 8-9 bands in the f.c.c. systems.     

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．     

Multidirectional lateral gradient films with position-dependent photonic signatures made from porous silicon

We describe here the fabrication of laterally graded porous silicon films which display gradients of photonic reflectance peaks spanning the optical spectrum. We demonstrate that up to three of these gradients can be overlayed to produce multidirectional photonic gradients with position-dependent spectral bar-codes. Each gradient is generated by asymmetric anodisation of silicon using temporal variations (sinusoidal or square-wave) in current density affording rugate and Bragg reflectors, respectively. The fabricated optical structures and the quality of the photonic resonances are characterised by optical reflectivity measurements and scanning electron microscopy. We finally remove the pSi gradient layers from the silicon substrate by applying an electropolishing current and embed the free-standing pSi membranes in polydimethylsiloxane to form flexible and foldable photonic films.     

Recent developments in the design and fabrication of visible photonic band gap waveguide devices

In this paper, we present the design, fabrication and initial optical testing of dielectric waveguide devices which incorporate photonic crystals with photonic band gaps (PBG) in the visible region of the spectrum. In the design of our devices we use a full three-dimensional plane wave analysis to solve the photonic band structure simultaneously with the dielectric waveguide boundary conditions for a fixed lattice and waveguide geometry. This takes into account the finite thickness of the waveguide core, and the evanescent wave in the dielectric cladding layers. Furthermore, we explain how the effective Bloch mode index can be extracted from the results. This enables us to tackle important problems associated with mode coupling between the input waveguide and guided Bloch modes within the porous PBG region, such as Fresnel reflections at the interface and up-scattering from the holes. Finally, we present the recent fabrication of quasi-periodic photonic crystals and PBG waveguide bends.     

Observation and tuning of hypersonic bandgaps in colloidal crystals

Composite materials with periodic variations of density and/or sound velocities, so-called phononic crystals, can exhibit bandgaps where propagation of acoustic waves is forbidden. Phononic crystals are the elastic analogue of the well-established photonic crystals and show potential for manipulating the flow of elastic energy. So far, the experimental realization of phononic crystals has been restricted to macroscopic systems with sonic or ultrasonic bandgaps in the sub-MHz frequency range. In this work, using high-resolution Brillouin spectroscopy we report the first observation of a hypersonic bandgap in face-centred-cubic colloidal crystals formed by self-assembly of polystyrene nanoparticles with subsequent fluid infiltration. Depending on the particle size and the sound velocity in the infiltrated fluid, the frequency and the width of the gap can be tuned. Promising technological applications of hypersonic crystals, ranging from tunable filters and heat management to acousto-optical devices, are anticipated.     

Tunable photonic bandgap in a one-dimensional superconducting-dielectric superlattice

The transmittance of one-dimensional photonic crystals consisting of superconductor and lossless dielectric has been systematically studied through the transfer-matrix method. Obviously, the shift of the photonic bandgap (PBG) becomes more noticeable by adjusting the thicknesses of the dielectric layers than that of superconductor layers. Furthermore, the number of PBGs can be controlled by varying the thicknesses of dielectric layers. Compared to the thicknesses of the dielectric layers, the width of the PBGs is more sensitive to the thicknesses of the superconductor layers. However, the width of the first PBG promptly varies when the thicknesses of the dielectric layers increase from 0 to 40?nm. If the contribution of the normal conducting electrons of the superconductor is nonnegligible, the temperature of the superconductor has no influence on the width of the PBGs. Moreover, the damp coefficient does not affect the PBGs under low-temperature conditions.     

Highly engineered mesoporous structures for optical processing

Arranging periodic, or quasi-periodic, regions of differing refractive index in one, two, or three dimensions can form a unique class of mesoporous structures. These structures are generally known as photonic crystals, or photonic quasicrystals, and they are the optical analogue of semiconducting materials. Whereas a semiconductor's band structure arises from the interaction of electron or hole waves with an arrangement of ion cores, the photonic crystal band structure results from the interaction of light waves with an arrangement of regions of differing refractive index.What makes photonic crystals highly attractive to the optical engineer is that we can actually place the regions of differing refractive index in a pattern specifically tailored to produce a given optical function, such as an extremely high dispersion, for example. That is, we can define the geometrical arrangement of the dielectric foam to provide us with the form of band structure we require for our optical functionality.In this paper, the optical properties and applications of these highly engineered mesoporous dielectrics will be discussed.     

Organic light-emitting diode microcavities from transparent conducting metal oxide photonic crystals

We report herein on the integration of novel transparent and conducting one-dimensional photonic crystals that consist of periodically alternating layers of spin-coated antimony-doped tin oxide nanoparticles and sputtered tin-doped indium oxide into organic light emitting diode (OLED) microcavities. The large refractive index contrast between the layers due the porosity of the nanoparticle layer led to facile fabrication of dielectric mirrors with intense and broadband reflectivity from structures consisting of only five bilayers. Because our photonic crystals are easily amenable to large scale OLED fabrication and simultaneously selectively reflective as well as electronically conductive, such materials are ideally suited for integration into OLED microcavities. In such a device, the photonic crystal, which represents a direct drop-in replacement for typical ITO anodes, is capable of serving two necessary functions: (i) as one partially reflecting mirror of the optical microcavity; and (ii) as the anode of the diode.     

Stabilization and operation of porous silicon photonic structures from near-ultraviolet to near-infrared using high-pressure water vapor annealing

The effects of high-pressure water vapor annealing (HWA), electrochemical oxidation, and substrate resistivity on the properties of porous silicon Bragg mirrors and photoluminescent cavities have been investigated. The photonic structures treated by HWA show very good stability upon ageing in air whereas as-formed structures exhibit significant drifts in their optical properties. Using HWA with lightly doped porous silicon, the structure transparency is enhanced sufficiently to enable the possible photonic operation in the near-ultraviolet. However, the index contrast achievable with these structures is very low in the visible and near-infrared. Useful index contrasts in this range can be achieved with either lightly doped porous silicon treated by electrochemical oxidation and HWA or heavily doped porous silicon treated by HWA.     

Large complete bandgaps in a two-dimensional square photonic crystal with isolated single-atom dielectric rods in air

It is well known that the square lattice of isolated single-atom dielectric rods in air does not give rise to complete bandgaps even when asymmetry is introduced to lift some degeneracy. However, in this paper, a new kind of two-dimensional square photonic crystal with isolated single-atom dielectric rods in air formed by holographic lithography is proposed, and the relation between their photonic bandgap properties and their specific holographic design are systematically analyzed. In addition to the large complete relative bandgap, namely 9.68% gap/midgap ratio for the dielectric constant contrast of 13.6:1, this structure has very large tolerance on the system parameters and fabrication conditions. This fact can greatly relax the experimental requirements. This work may demonstrate the unique feature and advantages of photonic crystals made by the holographic method and provide a guideline for their design and fabrication.     

Hybrid colloidal plasmonic-photonic crystals

We review the recently emerged class of hybrid metal-dielectric colloidal photonic crystals. The hybrid approach is understood as the combination of a dielectric photonic crystal with a continuous metal film. It allows to achieve a strong modification of the optical properties of photonic crystals by involving the light scattering at electronic excitations in the metal component into moulding of the light flow in series to the diffraction resonances occurring in the body of the photonic crystal. We consider different realizations of hybrid plasmonic-photonic crystals based on two- and three-dimensional colloidal photonic crystals in association with flat and corrugated metal films. In agreement with model calculations, different resonance phenomena determine the optical response of hybrid crystals leading to a broadly tuneable functionality of these crystals.     

One-dimensional photonic crystals with an amplitude-modulated dielectric constant in the unit cell

Photonic band structures of one-dimensional photonic crystals with an amplitude-modulated dielectric constant in the unit cell were studied. With this structure two bandgaps in the visible and one in the IR region were predicted. Experimental measurements of the two photonic bandgaps in the visible spectrum were made in a photonic crystal recorded in a holographic emulsion. Good agreement between experimental and theoretical results was obtained.