3D Photonic Band Gap Research Articles

Stealthy and hyperuniform isotropic photonic band gap structure in 3D.

In photonic crystals, the propagation of light is governed by their photonic band structure, an ensemble of propagating states grouped into bands, separated by photonic band gaps. Due to discrete symmetries in spatially strictly periodic dielectric structures their photonic band structure is intrinsically anisotropic. However, for many applications, such as manufacturing artificial structural color materials or developing photonic computing devices, but also for the fundamental understanding of light-matter interactions, it is of major interest to seek materials with long range nonperiodic dielectric structures which allow the formation of isotropic photonic band gaps. Here, we report the first ever 3D isotropic photonic band gap for an optimized disordered stealthy hyperuniform structure for microwaves. The transmission spectra are directly compared to a diamond pattern and an amorphous structure with similar node density. The band structure is measured experimentally for all three microwave structures, manufactured by 3D laser printing for metamaterials with refractive index up to . Results agree well with finite-difference-time-domain numerical investigations and a priori calculations of the band gap for the hyperuniform structure: the diamond structure shows gaps but being anisotropic as expected, the stealthy hyperuniform pattern shows an isotropic gap of very similar magnitude, while the amorphous structure does not show a gap at all. Since they are more easily manufactured, prototyping centimeter scaled microwave structures may help optimizing structures in the technologically very interesting region of infrared.

Symmetries and wave functions of photons confined in three-dimensional photonic band gap superlattices

We perform a computational study of confined photonic states that appear in a three-dimensional (3D) superlattice of coupled cavities, resulting from a superstructure of intentional defects. The states are isolated from the vacuum by a 3D photonic band gap, using a diamondlike inverse woodpile crystal structure, and they exhibit “Cartesian” hopping of photons in high-symmetry directions. We investigate the confinement dimensionality to verify which states are fully 3D-confined, using a recently developed scaling theory to analyze the influence of the structural parameters of the 3D crystal. We create confinement maps that trace the frequencies of 3D-confined bands for select combinations of key structural parameters, namely the pore radii of the underlying regular crystal and of the defect pores. We find that a certain minimum difference between the regular and defect pore radii is necessary for 3D-confined bands to appear, and that an increasing difference between the defect pore radii from the regular radii supports more 3D-confined bands. In our analysis, we find that their symmetries and spatial distributions are more varied than electronic orbitals known from solid-state physics. We surmise that this difference occurs since the confined photonic orbitals derive from global Bloch states governed by the underlying superlattice structure, whereas single-atom orbitals are localized. Based on this realization, we suggest that the extent symmetries of “photonic orbitals” could possibly translate to novel macroscopic behaviors of “photonic solid-state matter,” never before seen in the standard electronic solid-state systems. We also discover pairs of degenerate 3D-confined bands with p-like orbital shapes and mirror symmetries matching the symmetry of the superlattice. Finally, we investigate the enhancement of the local density of optical states for cavity quantum electrodynamics applications. We find that donorlike superlattices, i.e., where the defect pores are smaller than the regular pores, provide greater enhancement in the air region than acceptorlike structures with larger defect pores, and thus offer better prospects for doping with quantum dots and ultimately for 3D networks of single photons steered across strongly coupled cavities. Published by the American Physical Society 2024

Unsupervised machine learning to classify the confinement of waves in periodic superstructures.

We propose a rigorous method to classify the dimensionality of wave confinement by utilizing unsupervised machine learning to enhance the accuracy of our recently presented scaling method [Phys. Rev. Lett.129, 176401 (2022)10.1103/PhysRevLett.129.176401]. We apply the standard k-means++ algorithm as well as our own model-based algorithm to 3D superlattices of resonant cavities embedded in a 3D inverse woodpile photonic band gap crystal with a range of design parameters. We compare their results against each other and against the direct usage of the scaling method without clustering. Since the clustering algorithms require the set of confinement dimensionalities present in the system as an input, we investigate cluster validity indices (CVIs) as a means to find these values. We conclude that the most accurate outcome is obtained by first applying direct scaling to find the correct set of confinement dimensionalities, and subsequently utilizing our model-based clustering algorithm to refine the results.

High Performance Biosensor for Detection of the Normal and Cancerous Liver Tissues Based on 1D Photonic Band Gap Material Structures

High Performance Biosensor for Detection of the Normal and Cancerous Liver Tissues Based on 1D Photonic Band Gap Material Structures

Two-stage neural network via sensitivity learning for 2D photonic crystal bandgap maximization.

We propose a two-stage neural network method to maximize the bandgap of 2D photonic crystals. The proposed model consists of a fully connected deep feed-forward neural network (FNN) and U-Net, which are employed, respectively, to generate the shape function and learn the sensitivity. The shape is generated by the FNN during the entire optimization process, and obtaining the sensitivity can be split into two steps. In the first step of the optimization, the sensitivity is calculated by finite element analysis (FEA) and the result is used as a sample to train the U-Net. Second, the optimization procedure is adopted instead of FEA, where a trained U-Net is used to generate the corresponding sensitivity. The main advantage of such an approach is that the shape function and sensitivity can be obtained by neural networks without solving a partial differenital equation. Therefore, the computational cost can be reduced by the proposed method without using large training sets. The effectiveness of the proposed method is verified in the numerical experiments in terms of the optimized shape and time consumption.

Entanglement of three-level atomic system and spontaneous emission fields in a vacuum and near the 1D photonic crystal band gap

Entanglement of three-level atomic system and spontaneous emission fields in a vacuum and near the 1D photonic crystal band gap

Over 200 °C Broad-Temperature Lasers Reconstructed from a Blue-Phase Polymer Scaffold.

Blue-phase liquid crystal (BPLC) lasers have received extensive attention and have potential applications in sensors, displays, and anti-counterfeiting, owing to their unique 3D photonic bandgap. However, the working temperature range of such BPLC lasers is insufficient, and investigations are required to elucidate the underlying mechanism. Herein, a broad-temperature reconstructed laser is successfully achieved in dye-doped polymer-stabilized blue-phase liquid crystals (DD-PSBPLCs) with an unprecedented working temperature range of 25-230 °C based on a robust polymer scaffold, which combines the thermal stability and the tunability from the system. The broad-temperature lasing stems from the high thermal stability of the robust polymerized system used, which affords enough reflected and matched fluorescence signals. The temperature-tunable lasing behavior of the DD-PSBPLCs is associated with the phase transition of the unpolymerized content (≈60 wt%) in the system, which endows with a reconstructed characteristic of BP lasers including a U-shaped lasing threshold, a reversible lasing wavelength, and an obvious lasing enhancement at about 70 °C. This work not only provides a new idea for the design of broad-temperature BPLC lasers, but also sets out important insight in innovative microstructure changes for novel multifunctional organic optic devices.

Light dynamics around an exceptional point in a 1D photonic bandgap waveguide

Exceptional points (EP) in a system parameter space at which eigenvalues and corresponding eigenvectors coalesce are ubiquitous in non-Hermitian systems. Many unconventional applications have been proposed while encircling around the EPs. One of the unique application is the direction-dependent mode conversion. Here the appearance of an EP has been investigated in a planar 1D Bragg reflection waveguide(BRW) geometry, which has provided an additional degree of freedom to explore EP-based exotic light dynamics. A planar 1D BRW consists of periodic dielectric arrays and a defect dielectric layer forming the core. An inhomogeneous customized gain-loss profile is incorporated in the core region to couple two quasi-guided transverse electric (TE) modes so that the waveguide hosts an EP of order two. Here, we propose a dynamical EP encirclement scheme and corresponding asymmetric mode conversion phenomenon between two photonic bandgap quasi-guided TE modes in a 1D photonic bandgap-guided structure. Our findings will be potentially important to open up a fertile platform using the paradigm of non-Hermitian coupling to meet a wide range of exotic integrated chip-scale applications in the context of mode selectivity for switching and conversion.

Targeted Positioning of Quantum Dots Inside 3D Silicon Photonic Crystals Revealed by Synchrotron X-ray Fluorescence Tomography.

It is a major outstanding goal in nanotechnology to precisely position functional nanoparticles, such as quantum dots, inside a three-dimensional (3D) nanostructure in order to realize innovative functions. Once the 3D positioning is performed, the challenge arises how to nondestructively verify where the nanoparticles reside in the 3D nanostructure. Here, we study 3D photonic band gap crystals made of Si that are infiltrated with PbS nanocrystal quantum dots. The nanocrystals are covalently bonded to polymer brush layers that are grafted to the Si–air interfaces inside the 3D nanostructure using surface-initiated atom transfer radical polymerization (SI-ATRP). The functionalized 3D nanostructures are probed by synchrotron X-ray fluorescence (SXRF) tomography that is performed at 17 keV photon energy to obtain large penetration depths and efficient excitation of the elements of interest. Spatial projection maps were obtained followed by tomographic reconstruction to obtain the 3D atom density distribution with 50 nm voxel size for all chemical elements probed: Cl, Cr, Cu, Ga, Br, and Pb. The quantum dots are found to be positioned inside the 3D nanostructure, and their positions correlate with the positions of elements characteristic of the polymer brush layer and the ATRP initiator. We conclude that X-ray fluorescence tomography is very well suited to nondestructively characterize 3D nanomaterials with photonic and other functionalities.

Optical properties of 87Rb atomic vapor near the 1D photonic crystal bandgap and all-optical switching of transmitted light

We investigate the steady-state and dynamic behavior of the optical properties of the laser pulse in a GaAs/AlAs 1D photonic crystal (1DPC) with an atomic vapor defect layer. We chose the atomic vapor of the 87Rb as a defect layer by driving the probe field on the D2 transition between 52P3/2 - 52S1/2 levels through the 1DPC. The effect of the photonic bandgap (PBG) on the absorption and dispersion properties of the probe field is discussed. Moreover, the transmission and reflection coefficient of the 1DPC is controlled by applying the various value of the intensity of the coupling field. By comparing these results in the vacuum and near the PBG, we find that the absorption/dispersion and transmission/reflection properties are strongly affected by the PBG. We find that all-optical properties of atomic vapor in the surrounding of 1DPC are improved due to PBG. Furthermore, the effect of the intensity of the coupling field on the all-optical switching is studded. The proposed model may provide some new possibilities for technological applications as an all-optical device based on the photonic crystal in quantum information science, quantum computing, signal processing, and quantum communications.

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.

Complete two-dimensional photonic bandgap in refractive-index ratio 2.1 photonic crystals due to high-order bands.

We find that in a suitably designed photonic crystal (PC) certain high-order photonic bands are less affected by the refractive-index ratio (RIR) than low-order bands, enabling the realization of a robust and complete two-dimensional (2D) photonic bandgap in a moderate refractive-index-ratio PC. A detailed theoretical investigation of low- and high-order bandgaps in a series of PCs with different configurations is performed that shows that high-order bands may favor substantial complete photonic bandgaps (CPBGs) for systems with a moderate RIR. Furthermore, the importance of the geometry and structural parameters on achieving a high-order CPBG is found. Specifically, a hexagonal lattice PC of annular-hole-peripheral connecting rods is proposed, which can support a CPBG with a refractive-index ratio (RIR) as low as nhigh:nlow=2.1; to the best of our knowledge, this is the lowest RIR used to obtain a 2D CPBG in a PC.

Realization of all-optical logic gates using a single design of 2D photonic band gap structure by square ring resonator

The interference method is used to achieve all-optical logic gate operations. This has been realized with a single design of photonic crystal ring resonator at different wavelengths rather than designing separate for all the logic gates. Such a single design can be used to perform all optical operations as AND, OR, and XOR logic gates at different wavelengths. Further operating wavelength, contrast ratio (CR), response time (RT), and bit rate have been analyzed for all three logic gates. The highest CR is obtained as about 22.06 dB with fast RT about 0.14 ps and high bit rate of 7.14 Tb / s for proposed XOR logic gate in comparison to all the other logic gates with single-design structure, which may lead us to construct on-chip logic circuits.

Topology optimization of 3D photonic crystals with complete bandgaps.

The design of photonic crystals with complete bandgaps has recently received considerable research focus for numerous reasons. This work leverages well-known nonlinear programming techniques to alleviate the non-smoothness caused by degenerate eigenvalues such that topology optimization problems can be solved with the open-source IPOPT software. A fully-vectorial plane wave expansion technique is used with an iterative eigensolver to efficiently predict dispersion properties of candidate structures. Nonlinear programming is employed to solve the inverse problem of designing three-dimensional periodic structures that exhibit complete two-dimensional (2D) and three-dimensional (3D) photonic bandgaps. Mesh refinement is performed to alleviate the large computational burden of designing and analyzing photonic crystals, and a periodic density filter is implemented to impose a minimum feature size for manufacturability considerations.

Video-Rate Identification of High-Capacity Low-Cost Tags in the Terahertz Domain.

In this article, we report on video-rate identification of very low-cost tags in the terahertz (THz) domain. Contrary to barcodes, Radio Frequency Identification (RFID) tags, or even chipless RFID tags, operate in the Ultra-Wide Band (UWB). These THz labels are not based on a planar surface pattern but are instead embedded, thus hidden, in the volume of the product to identify. The tag is entirely made of dielectric materials and is based on a 1D photonic bandgap structure, made of a quasi-periodic stack of two different polyethylene-based materials presenting different refractive indices. The thickness of each layer is of the order of the THz wavelength, leading to an overall tag thickness in the millimetre range. More particularly, we show in this article that the binary information coded within these tags can be rapidly and reliably identified using a commercial terahertz Time Domain Spectroscopy (THz-TDS) system as a reader. More precisely, a bit error rate smaller than 1% is experimentally reached for a reading duration as short as a few tens of milliseconds on an 8 bits (~40 bits/cm2) THID tag. The performance limits of such a tag structure are explored in terms of both dielectric material properties (losses) and angular acceptance. Finally, realistic coding capacities of about 60 bits (~300 bits/cm2) can be envisaged with such tags.

Elusive photonic crystals come a step closer

Researchers have long sought materials in which light behaves the way electrons do in semiconductors. A workable approach for growing such materials in bulk now seems at hand, and could lead to advances in computing. Key step towards production of 3D photonic bandgap crystals.

Micrometric Monodisperse Solid Foams as Complete Photonic Bandgap Materials.

Solid foams with micrometric pores are used in different fields (filtering, 3D cell culture, etc.), but today, controlling their foam geometry at the pore level, their internal structure, and the monodispersity, along with their mechanical properties, is still a challenge. Existing attempts to create such foams suffer either from slow speed or size limitations (above 80 μm). In this work, by using a temperature-regulated microfluidic process, 3D solid foams with highly monodisperse open pores (PDI lower than 5%), with sizes ranging from 5 to 400 μm and stiffnesses spanning 2 orders of magnitude, are created for the first time. These features open the way for exciting applications, in cell culture, filtering, optics, etc. Here, the focus is set on photonics. Numerically, these foams are shown to open a 3D complete photonic bandgap, with a critical index of 2.80, thus compatible with the use of rutile TiO2. In the field of photonics, such structures represent the first physically realizable self-assembled FCC (face-centered cubic) structure that possesses this functionality.

Local density of optical states in the three-dimensional band gap of a finite photonic crystal

A three-dimensional (3D) photonic band gap crystal is an ideal tool to completely inhibit the local density of optical states (LDOS) at every position in the crystal throughout the band gap. This notion, however, pertains to ideal infinite crystals, whereas any real crystal device is necessarily finite. This raises the question as to how the LDOS in the gap depends on the position and orientation inside a finite-size crystal. Therefore, we employ rigorous numerical calculations using finite-difference time-domain (FDTD) simulations of 3D silicon inverse woodpile crystals filled with air or with toluene, as previously studied in experiments. We find that the LDOS versus position decreases exponentially into the bulk of the crystal. From the dependence on dipole orientation, we infer that the characteristic LDOS decay length $\ell_{\rho}$ is mostly related to far-field dipolar radiation effects, whereas the prefactor is mostly related to near-field dipolar effects. The LDOS decay length has a remarkably similar magnitude as the Bragg length for directional transport, which suggests that the LDOS in the crystal is dominated by vacuum states that tunnel from the closest interface towards the position of interest. Our work leads to design rules for applications of 3D photonic band gaps in emission control and lighting, quantum information processing, and in photovoltaics.

Reflectivity of three-dimensional GaAs photonic band-gap crystals of finite thickness

We study the optical reflectivity of three-dimensional (3D) photonic band gap crystals with increasing thickness. The crystals consist of GaAs plates with nanorod arrays that are assembled by an advanced stacking method into high-quality 3D woodpile structures. We observe intense and broad reflectivity peak with stop bands that correspond to a broad gap in the photonic band structures. The maximum reflectivity quickly reaches high values even for a few crystal layers. Remarkably, the bandwidth of the stop bands hardly decreases with increasing crystal thickness, in good agreement with FDTD simulations. This behavior differs remarkably from the large changes observed earlier in weakly interacting 3D photonic crystals. The nearly constant bandwidth and high reflectivity are rationalized by multiple Bragg interference that occurs in strongly interacting photonic band gap crystals, whereby the incident light scatters from multiple reciprocal lattice vectors simultaneously, in particular from oblique ones that are parallel to a longer crystal dimension and thus experience hardly any finite size effects. Our new insights have favorable consequences for the application of 3D photonic band gap crystals, notably since even thin structures reveal the full band gap functionality, including devices that shield quantum bits from vacuum fluctuations.

Experimental probe of a complete 3D photonic band gap.

The identification of a complete three-dimensional (3D) photonic band gap in real crystals typically employs theoretical or numerical models that invoke idealized crystal structures. Such an approach is prone to false positives (gap wrongly assigned) or false negatives (gap missed). Therefore, we propose a purely experimental probe of the 3D photonic band gap that pertains to any class of photonic crystals. We collect reflectivity spectra with a large aperture on exemplary 3D inverse woodpile structures that consist of two perpendicular nanopore arrays etched in silicon. We observe intense reflectivity peaks (R>90%) typical of high-quality crystals with broad stopbands. A resulting parametric plot of s-polarized versus p-polarized stopband width is linear ("y=x"), a characteristic of a 3D photonic band gap, as confirmed by simulations. By scanning the focus across the crystal, we track the polarization-resolved stopbands versus the volume fraction of high-index material and obtain many more parametric data to confirm that the high-NA stopband corresponds to the photonic band gap. This practical probe is model-free and provides fast feedback on the advanced nanofabrication needed for 3D photonic crystals and stimulates practical applications of band gaps in 3D silicon nanophotonics and photonic integrated circuits, photovoltaics, cavity QED, and quantum information processing.