Photonic Band Gap Crystals Research Articles

Omnidirectional photonic band gaps in one-dimensional gradient refractive index photonic crystals considering linear and quadratic profiles

By using the transfer matrix formalism, in this work it is presented the study of the optical properties of 1D photonic structures constructed with M periods of bilayers of dielectric material and slabs with gradient refractive index (GRIN) profile of two types: linear and quadratic. By varying the profile parameters, preserving the average value of the refractive index for the GRIN slab, the results show the formation of new photonic band gaps whose bandwidths depends on the slope and the curvature of the linear and quadratic profile respectively. Also, it can be observed the formation of omnidirectional photonic bandgaps for the TE and TM polarizations, one for the linear profile and three for the quadratic one, for which their bandwidths depend linearly on the slope and the curvature of the GRIN profiles. It is expected that the presented results could be useful in the construction of optical devices based in their optical response under oblique incidence.

High-Q slow light and its localization in a photonic crystal microring

We introduce a photonic crystal ring cavity that resembles an internal gear and unites photonic crystal (PhC) and whispering gallery mode (WGM) concepts. This `microgear' photonic crystal ring (MPhCR) is created by applying a periodic modulation to the inside boundary of a microring resonator to open a large bandgap, as in a PhC cavity, while maintaining the ring's circularly symmetric outside boundary and high quality factor ($Q$), as in a WGM cavity. The MPhCR targets a specific WGM to open a large PhC bandgap up to tens of free spectral ranges, compressing the mode spectrum while maintaining the high-$Q$, angular momenta, and waveguide coupling properties of the WGM modes. In particular, near the dielectric band-edge, we observe modes whose group velocity is slowed down by 10 times relative to conventional microring modes while supporting $Q~=~(1.1\pm0.1)\times10^6$. This $Q$ is $\approx$50$\times$ that of the previous record in slow light devices. Using the slow light design as a starting point, we further demonstrate the ability to localize WGMs into photonic crystal defect (dPhC) modes for the first time, enabling a more than 10$\times$ reduction of mode volume compared to conventional WGMs while maintaining high-$Q$ up to (5.6$\pm$0.1)$\times$10$^5$. Importantly, this additional dPhC localization is achievable without requiring detailed electromagnetic design. Moreover, controlling their frequencies and waveguide coupling is straightforward in the MPhCR, thanks to its WGM heritage. By using a PhC to strongly modify fundamental properties of WGMs, such as group velocity and localization, the MPhCR provides an exciting platform for a broad range of photonics applications, including sensing/metrology, nonlinear optics, and cavity quantum electrodynamics.

Photonic Crystals with a Defect Fabricated by Two-Photon Polymerization for the Infrared Spectral Range

One-dimensional photonic crystals composed of alternating layers with high- and low-density were fabricated using two-photon polymerization from a single photosensitive polymer for the infrared spectral range. By introducing single high-density layers to break the periodicity of the photonic crystals, a narrow-band defect mode is induced. The defect mode is located in the center of the photonic bandgap of the one-dimensional photonic crystal. The fabricated photonic crystals were investigated using infrared reflection measurements. Stratified-layer optical models were employed in the design and characterization of the spectral response of the photonic crystals. A very good agreement was found between the model-calculated and measured reflection spectra. The geometric parameters of the photonic crystals obtained as a result of the optical model analysis were found to be in good agreement with the nominal dimensions of the photonic crystal constituents. This is supported by complimentary scanning electron microscope imaging, which verified the model-calculated, nominal layer thicknesses. Conventionally, the accurate fabrication of such structures would require layer-independent print parameters, which are difficult to obtain with high precision. In this study an alternative approach is employed, using density-dependent scaling factors, introduced here for the first time. Using these scaling factors a fast and true-to-design method for the fabrication of layers with significantly different surface-to-volume ratios. The reported observations furthermore demonstrate that the location and amplitude of defect modes is extremely sensitive to any layer thickness non-uniformities in the photonic crystal structure. Considering these capabilities, one-dimensional photonic crystals engineered with defect modes can be employed as narrow band filters, for instance, while also providing a method to quantify important fabrication parameters.

Enhanced absorption in thin and ultrathin silicon films by 3D photonic band gap back reflectors

Since thin and ultrathin silicon films have limited optical absorption, we explore the effect of a nanostructured back reflector to recycle the unabsorbed light. As a back reflector, we investigate a three-dimensional (3D) photonic band gap crystal made from silicon that is readily integrated with the thin silicon films. We numerically obtain the optical properties by solving the 3D time-harmonic Maxwell equations using the finite-element method, and model silicon with experimentally determined optical constants. The absorption enhancement spectra and the photonic band gap generated current density are obtained by weighting the absorption spectra with the AM 1.5 standard solar spectrum. We study thin films in two different regimes, much thicker (L Si = 2400 nm) or much thinner (L Si = 80 nm) than the wavelength of light. For L Si = 2400 nm thin film, the 3D photonic band gap crystal enhances the spectrally averaged (λ = 680 nm to 880 nm) silicon absorption by 2.22 × (s −pol.) to 2.45 × (p −pol.), which exceeds the enhancement of a perfect metal back reflector (1.47 to 1.56 ×). The absorption is considerably enhanced by the (i) broadband angle and polarization-independent reflectivity in the 3D photonic band gap, and (ii) the excitation of many guided modes in the film by the crystal’s surface diffraction leading to greatly enhanced path lengths. For L Si = 80 nm ultrathin film, the photonic crystal back reflector yields a striking average absorption enhancement of 9.15 ×, much more than 0.83 × for a perfect metal. This enhancement is due to a remarkable guided mode that is confined within the combined thickness of the ultrathin film and the photonic crystal’s Bragg attenuation length. An important feature of the 3D photonic band gap is to have a broad bandwidth, which leads to the back reflector’s Bragg attenuation length being much shorter than the silicon absorption length. Consequently, light is confined inside the thin film and the remarkable absorption enhancements are not due to the additional thickness of the photonic crystal back reflector. We briefly discuss a number of high-tech devices that could profit from our results, including ultrathin film solar cells.

Band gap of silicon photonic crystal with square-lattice and windmill-shaped defects

A new type of 2D square-lattice photonic crystal with different windmill-shaped defects is proposed. Based on the plane wave expansion method and super cell theory, the band gaps of defect models are numerically analyzed according to the symmetry. We aim at further reducing the defect symmetry of photonic crystals compared to previous studies and researching the effect of translation and rotation of different windmill-shaped defect structures on the transverse magnetic (TM) band gap. The results reveal that the translation distance of defects brings great impacts on the band gap of 2D square-lattice photonic crystals and the width of the TM band gap can be further expanded after rotating on the basis of translation. In addition, we discovery that the band gap of the model with even-numbered fan-shaped defects is wider than that of the model with odd-numbered fan-shaped defects. Among the five different defect models (three-wings, four-wings, five-wings, six-wings, rotating-cross), the four-wing windmill defect model produces the largest band gap, which reaches 5.307 × 10−2 (ɷa/2πc). This research is helpful to understand the band gap characteristics of photonic crystals, which will contribute to the design of photonic crystal devices.

Structural Colored Fabrics with Brilliant Colors, Low Angle Dependence, and High Color Fastness Based on the Mie Scattering of Cu2O Spheres.

Compared with conventional textile coloring with dyes and pigments, structural colored fabrics have attracted broad attention due to the advantages of eco-friendliness, brilliant colors, and anti-fading properties. The most investigated structural color on fabrics is originated from a band gap of multilayered photonic crystals or amorphous photonic structures. However, limited by the nature of the color generation mechanism and a multilayered structure, it is challenging to achieve structural colored fabrics with brilliant noniridescent colors and high fastness. Here, we propose an alternative strategy for coloring a fabric based on the scattering of Cu2O single-crystal spheres. The disordered Cu2O thin layers (<0.6 μm) on the surface of fabrics were prepared by a spraying method, which can generate vivid noniridescent structural color due to the strong Mie scattering of Cu2O single-crystal spheres. Importantly, the great mechanical stability of the structural color was realized by firmly binding Cu2O spheres to the fabric using a commercial binder. The structural color can be tuned by changing the diameter of Cu2O spheres. Furthermore, complex patterns can be easily obtained by spray coating Cu2O spheres with different particle sizes using a mask. According to color fastness test standards, the dry rubbing, wet rubbing, and light fastness of the structural color on fabric can reach level 5, level 4, and level 6, respectively, which is sufficient to resist rubbing, photobleaching, washing, rinsing, kneading, stretching, and other external mechanical forces. This coloring method may carve a practical avenue in textile coloring and has potentials in other practical applications of structural color.

Semicomputational calculation of Bragg shift in stratified materials.

The fiber Bragg grating (FBG) may be viewed as a one dimensional photonic band-gap crystal by virtue of the periodic spatial perturbation imposed on the fiber core dielectric material. Similar to media supporting Bloch waves, the engraved weak index modulation, presenting a periodic "potential" to an incoming guided mode photon of the fiber, yields useful spectral properties that have been the basis for sensing applications and emerging quantum squeezing and solitons. The response of an FBG sensor to arbitrary external stimuli represents a multiphysics problem without a known analytical solution despite the growing use of FBGs in classical and quantum sensing and metrology. Here, we study this problem by first presenting a solid mechanics model for the thermal and elastic states of a stratified material. The model considers an embedded optical material domain that represents the Bragg grating, here in the form of an FBG. Using the output of this model, we then compute the optical modes and their temperature- and stress-induced behavior. The developed model is applicable to media of arbitrary shape and composition, including soft matter and materials with nonlinear elasticity and geometric nonlinearity. Finally, we employ the computed surface stress and temperature distributions along the grating to analytically calculate the Bragg shift, which is found to be in reasonable agreement with our experimental measurements.

Impacts of both temperature and condensation on the band gap of photonic crystals around the freezing point

This work investigated the phenomena and cause of photonic band gap (PBG) shift under an open environment at −10 °C ∼ 20 °C for the three-dimensional (3D) photonic crystals (PCs). The 3D PCs were composed of polystyrene spheres using the self-assembly method. The reflective gloss of 3D PC sample underwent non-monotonous color change within the temperature region. PBG of PCs first red-shifted during the cooling from room temperature. Later, the PBG blue-shifted when the temperature decreased from about 0 °C. The average transmittance through the PC sample within the visible range also increased first and then decreased with ambient temperature reduction. Influences from structure dimension, optical constants of involved materials, condensation and its phase change on PBG were all quantitatively investigated.

Photonic Band Gap Material Topological Design at Specified Target Frequency (Adv. Theory Simul. 10/2021)

Photonic Crystals Optimization at Specified Target Frequency To achieve any specified band gap photonic crystal (PhC) structure around the target frequency, a new band gap measuring index and topological design strategy are reported in article number 2100125 by Xiaopeng Zhang, Yangjun Luo, Yi Yan, and co-workers. The cell topology is represented with only 50 design variables through the material-field series-expansion, and the multi-peak optimization problem is solved by the sequential Kriging-based algorithm. The cover shows an ultra-wide band gap PhC device.

Acousto-optic cavity coupling in 2D phoxonic crystal with combined convex and concave holes

A two-dimensional cross-like phoxonic crystal (PxC) model is proposed, which exhibits simultaneously large complete photonic crystal (PtC) and phononic crystal (PnC) bandgaps. The most salient trait of the structure is the wide range of geometrical parameters compatible with large complete bandgaps. After geometrical optimization, photonic and phononic bandgaps with gap-to-midgap ratios of 11.5% and 90.7% are obtained, respectively. These values are close to the best topology-optimized reported values but are obtained with simple shapes compatible with nanoscale fabrication technology. These characteristics make the convex–concave topology a promising candidate for PxC devices. A cavity is then introduced by filling up one cross-like hole in the 7 × 7 super-cell. PtC and PnC bands with defects appear in the respective large complete bandgaps, confining phonons and photons in the same cavity. Acousto-optic (AO) coupling between photonic and phononic defect modes is further investigated by the finite element method, taking both photoelastic and moving interface mechanisms into consideration. The symmetries of both photonic and phononic modes play a dominant role in the coupling strength. Results show that the strongest linear coupling between a photonic transverse magnetic mode and phononic breathing mode is obtained due to the in-phase superposition in the x and y directions. A quadratic nonlinear coupling is observed when photonic modes are coupled with the phononic stretching mode due to the inverse superposition of x and y directions. Finally, the optomechanical coupling rates relative to zero-point motion are estimated.

Photonic Band Gaps and Resonance Modes in 2D Twisted Moiré Photonic Crystal

The study of twisted bilayer 2D materials has revealed many interesting physics properties. A twisted moiré photonic crystal is an optical analog of twisted bilayer 2D materials. The optical properties in twisted photonic crystals have not yet been fully elucidated. In this paper, we generate 2D twisted moiré photonic crystals without physical rotation and simulate their photonic band gaps in photonic crystals formed at different twisted angles, different gradient levels, and different dielectric filling factors. At certain gradient levels, interface modes appear within the photonic band gap. The simulation reveals “tic tac toe”-like and “traffic circle”-like modes as well as ring resonance modes. These interesting discoveries in 2D twisted moiré photonic crystal may lead toward its application in integrated photonics.

Omnidirectional photonic bandgap in one-dimensional photonic crystals containing hyperbolic metamaterials.

We theoretically and experimentally investigate the angle-dependent omnidirectional photonic bandgap (PBG) in one-dimensional photonic crystals (PCs) comprising hyperbolic metamaterials (HMMs) for TM polarization, which is different from blue-shifted PBG in conventional all-dielectric photonic crystals. The frequency range of PBG increases when the incident angles increase, owing to the red-shift and blue-shift of the long-wavelength and short-wavelength band edges, respectively. The red-shifted band edge originates from the phase-variation compensation mechanism between the HMMs and dielectric material. The experimental values are in good agreement with the simulation results. These nanostructures are ideal for fabricating photonic devices such as omnidirectional reflectors.

Angle-insensitive mid-infrared photonic bandgap in one-dimensional photonic crystal containing single-material semiconductor hyperbolic metamaterial layers

Angle-insensitive mid-infrared photonic bandgap in one-dimensional photonic crystal containing single-material semiconductor hyperbolic metamaterial layers

Principles of constructing gyroscopes based on photonic crystal (band-gap) fibers

The gyroscope is a device that makes it possible to measure the change in the orientation angles associated rotation of the body relative to an inertial coordinate system. Photonic crystal fiber gyroscopes are a kind of optical gyroscopes that offer many new features beyond that conventional fiber optic gyroscopes can offer. In any case, the properties of the optical fiber can play a large role in determining the characteristics of the gyroscope. The principle of operation of most optical gyroscopes is based on the Sagnac effect or the Sagnac interferometer, the essence of which is as follows. If two light waves propagate in a closed optical circuit in opposite directions, then in the case of an immovable circuit, the phase incursions of both waves that have passed the entire circuit in opposite directions will be the same. When the contour rotates around an axis normal to the contour plane, the phase incursions of the waves become unequal, and their difference in the general case will be proportional to the angular velocity of the contour rotation, the area covered by the contour, and the frequency of the electromagnetic wave (EMW). Since the area and frequency of the EMW remain unchanged during the operation of the gyroscope, the phase shift will be proportional only to the angular velocity. The use of photonic crystal fiber to increase the sensitivity is very promising; it significantly reduces the drift through thermal polarization, resistance, and the Kerr effect. This article suggests the use of photonic-crystal (hollow-core) fiber in optical gyroscope instead of conventional fibers.

Omnidirectional terahertz photonic band gap broaden effect in one-dimensional photonic crystal containing few-layer graphene

We study the influence of few-layer graphene on omnidirectional photonic band gap (OPBG) in one-dimensional photonic crystal (1DPC) at terahertz frequencies. By periodically introducing few-layer graphene into 1DPC, the width of OPBG can be greatly broadened. As the layer number of introduced graphene increases, the broaden effect of the OPBG becomes stronger. The physical reason behind the broaden effect is that the few-layer graphene acts like an ultrathin metal layer within the frequency range of the OPBG. Besides, the width of the OPBG can be dynamically tuned by the gate voltage of graphene. Compared to 1DPCs containing metal layers, 1DPCs containing few-layer graphene possess lower absorptive loss and more flexible tunability. Our works provides a route and practical way to promote various applications based on tunable terahertz OPBGs.

Transmittance properties of superconductor-dielectric photonic crystal

Using Transfer Matrix Method, we numerically study the transmission behavior of one dimensional superconductor photonic crystal. Superconductor photonic crystal is usually a composite material consisting of superconductor and dielectric material. In this study, we have discussed the photonic band gap of the superconductor-dielectric photonic crystal at different temperatures. The typical transmittance properties of the considered structure have been accessed through the transfer matrix method simulations. The transmission characteristics for superconductor photonic crystal have been examined with different various parametric effects including the thickness of the considered structures, frequency and different temperatures. Moreover, the variations of transmission spectra with respect to thickness and temperature have also been investigated. The findings of the present study support the superconductor photonics structures to possess the potential for tunable filter applications.

Enhancement of sensitivity of silica photonic crystals to carbon dioxide by APTES modification

Abstract The photonic band gap (PBG) of photonic crystals (PCs) has been proven to move in different gas atmospheres. According to this characteristic, silica PCs were used for the detection of different gases with low concentrations from 1 ppb to 100 ppm in our previous work. (3-aminopropyl)-triethoxysilane (APTES) was used as a modifier for the surface modification of SiO2 colloidal spheres, and the amino groups were grafted onto the surface of the colloidal spheres by chemical grafting. In this work, the influence of modifier dosage on gas sensitivity and optical properties was discussed. The results suggest that the PCs modified with APTES has improved the gas-sensitivity of CO2. It was worth noting that the PCs before and after modification have different adsorption behaviors under single gas and mixed gas atmospheres.

Properties of defect modes and band gaps of mirror symmetric metal-dielectric 1D photonic crystals

Inserting of any sort of irregularity in a photonic crystal (PC) with a perfect periodicity can produce defect modes. Great interest has been directed towards defect modes due to many potential applications. In this work, a binary PC consisting of silica (SiO2) and silver (Ag) is assumed. The PC is supposed to have a mirror symmetry with the structure (SiO2/Ag)N(Ag/SiO2)N, where 2 N is the number of periods of the PC. The transmission spectra of the PC are investigated in the visible and IR wavelengths. It is found that when the thickness of Ag layer increases, band gaps are broadened, more band gaps appear starting at low wavelengths and all these band gaps are shifted toward loner wavelengths. Defect modes appear at certain thicknesses of Ag, diminish gradually and then entirely disappear. When the incidence angle increases, band gaps are blue shifted in contrary to their behavior with the increase of the thickness of the metal and SiO2 layers.

Design of asymmetric transmission of photonic crystal heterostructure based on two-dimensional hexagonal boron nitride material

Two-dimensional (2D) hexagonal boron nitride (hBN) possesses many unique properties such as high mechanical strength and excellent chemical and thermal stability. The 2D hBN exhibits a wide bandgap in the UV region and optically-stable ultra-bright quantum emitters that make hBN a promising nanophotonic platform for quantum computing and information processing, especially in the visible wavelength range. Therefore, it is greatly important to build up different nanophotonic devices with different functionalities based on this material platform to achieve the integrated photonic chips. Among the devices, the integratable optical asymmetric transmission devices are important elements for functional quantum computing chips. Since hBN is a dielectric material, photonic crystal (PhC) structure is the most suitable in principle and allows on-chip integration with other photonic devices. In this study, we theoretically design an asymmetric transmission device based on 2D hBN PhC heterostructures in the visible wavelength range for the first time. Due to the relatively low refractive index of 2D hBN material (&lt;i&gt;n&lt;/i&gt; &lt; 2.4), we design a free-standing hBN PhC heterostructure to maximize the light trapping in the structure and minimize the propagation loss. The asymmetric transmission device is composed of two square-lattice 2D PhC structures, namely PhC 1 and PhC 2. We use the plane wave expansion method (PWM) to calculate the iso-frequency contours (EFCs) of the PhC structures to study the light propagation inside of the PhCs, which will propagate along the gradient of direction of the EFCs. We design the PhC structure in the way that the incident light beams from different angles can be self-collimated along the &lt;i&gt;Г-X&lt;/i&gt; direction of the PhC 2 and coupled out. On the other hand, the backward incident light is blocked by the bandgaps of PhC 2. In this way, asymmetric optical transmission is achieved with high forward transmittance and contrast ratio. In addition, we further finely tune the structural parameters, including the lattice constant and column radius of the PhCs to optimize the performance by using the finite difference time domain (FDTD) method. The resulting 2D hBN PhC heterostructure achieves an asymmetric transmission in a wavelength range of 610–684 nm with a peak forward transmittance of 0.65 at a wavelength of 652 nm. Meanwhile, the backward transmittance is controlled to be 0.04. As a result, the contrast ratio can reach up to 0.95. The working bandwidth of the hBN PhC is 74 nm (&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;F&lt;/sub&gt; &gt; 0.5). In addition, the designed asymmetric transmission device has a small size of 11 μm × 11 μm, thus it is suitable for on-chip integration. Our results open up possibilities for designing new nanophotonic devices based on 2D hBN material for quantum computing and information processing. The design principle can be generally used to design other photonic devices based on 2D hBN material.

Ultra-large omnidirectional photonic band gaps in one-dimensional ternary photonic crystals composed of plasma, dielectric and hyperbolic metamaterial

Abstract Owing to the Bragg interference mechanism, photonic band gap (PBG) in all-dielectric one-dimensional photonic crystal (PC) is strongly sensitive to the incident angle, which limits the width of omnidirectional photonic band gap (OPBG). Recently, researchers realized a kind of special PBG called angle-insensitive PBG in one-dimensional binary PC composed of alternating dielectric and hyperbolic metamaterial (HMM) layers. Different from the conventional strongly angle-insensitive PBG, this kind of PBG is angle-insensitive and naturally omnidirectional, providing us an efficient way to achieve ultra-large OPBG. In this paper, by periodically introducing plasma layers into one-dimensional binary PC composed of alternating dielectric and HMM layers with angle-insensitive PBG, we find that the PBG can be efficiently broadened. Although the PBG becomes slightly angle-sensitive since the introduction of plasma layers breaks the phase variation compensation condition, the width of OPBG can still be efficiently broadened. Under the proper design, we achieve an ultra-large OPBG with the width up to 1321 nm (68% relative bandwidth) in the one-dimensional ternary PC composed of alternating plasma, dielectric and HMM layers at near-infrared wavelengths. The whole one-dimensional ternary PC is composed of only three kinds of materials: indium tin oxide (ITO), silicon (Si) and silicon carbide (SiC), which can be fabricated by the atomic layer deposition (ALD) method under the current experimental conditions. This ultra-large OPBG in simple one-dimensional structure could be utilized to design ultra-broadband omnidirectional optical mirror and narrowband optical filter with ultra-large omnidirectional stopband.