Three-dimensional Photonic Crystals Research Articles

Geometric anisotropy induced higher-order topological insulators in nonsymmorphic photonic crystals

To a significant extent, the rich physical properties of photonic crystals (PCs) are determined by the underlying geometry, in which the composed symmetry operator and their combinations contribute to their unique topological invariant to characterize the topological phases. In this work, we use geometric anisotropy in the 2D square lattice composed of four rectangle blocks. Due to the presence of glide symmetry, we show a variety of topological phase transitions in designed nonsymmorphic PCs and these transitions shall be understood in terms of the Zak phase and Chern number in synthetic space, as well as the pseudospin-2 concept, combinationally. Furthermore, Zak phase winding in the periodic synthetic parameter space yields high-order Chern number and double interface states. In terms of the extended Zak phase and pseudospin Hall effect, a higher-order topological insulator is constructed in the PC system. Based on the combination of different lattices, this represents a unique system that requires multiple topological concepts and indices for theoretical examination and understanding. The intriguing and abundant topological features are also sustained in the corresponding three-dimensional PC slab, which makes it a very interesting platform to control the flow of optical signals.

Fluid-coupled Lamb waves for self-assembling three-dimensional photonic crystals

Fluid-coupled Lamb waves (LWs) were proposed to facilitate the self-assembling of three-dimensional (3D) photonic crystals (PCs) in this work. Numerical models were constructed for proof-of-concept, and a fabrication set-up was developed for experimental demonstration. LWs were initially generated by a piezoelectric substrate. A couplant altered the propagating direction of these LWs to form the fluid-coupled LWs at a superstrate. The coffee-ring effect (CRE) of a suspension droplet on the superstrate was thus suppressed. The suspended nanospheres formed 3D PCs after the droplet dried out. Diversified PCs were fabricated using the developed set-up. Their transmittance spectra demonstrated the corresponding bandgap clearly. Advantages of utilizing fluid-coupled LWs for self-assembling 3D PCs include flexibility in excitation frequency, fabrication cost-effectiveness, acceptance for a passively oscillating substrate, and enlargement of sample area.

Manipulating Orbital Angular Momentum Entanglement in Three-Dimensional Spiral Nonlinear Photonic Crystals

We propose and theoretically investigate two-photon orbital angular momentum (OAM) correlation through spontaneous parameter down-conversion (SPDC) processes in three-dimensional (3D) spiral nonlinear photonic crystals (NPCs). By properly designing the NPC structure, one can feasibly modulate the OAM-correlated photon pair, which provides a potential platform to realize high-dimensional entanglement for quantum information processing and quantum communications.

Location and Topology of the Fundamental Gap in Photonic Crystals

The fundamental, or first, band gap is of unmatched importance in the study of photonic crystals. Here, we address precisely where this gap can be opened in the band structure of three-dimensional photonic crystals. Although strongly constrained by symmetry, this problem cannot be addressed directly with conventional band-symmetry analysis due to the existence of a photonic polarization vortex at zero frequency. We develop an approach for overcoming the associated symmetry singularity by incorporating fictitious, auxiliary longitudinal modes. Our strategy also enables us to extend recent developments in symmetry-based topological analysis to the fundamental gap of three-dimensional photonic crystals. Exploiting this, we systematically study the topology of the minimal fundamental gaps. This reveals the existence of topological gap-obstructions that push the fundamental gap higher than what a conventional analysis would suggest. Our work demonstrates that topology can play a crucial role in the opening of the fundamental photonic gap and informs future theoretical and experimental searches for conventional and topological band gaps in three-dimensional photonic crystals.

A fast method to compute dispersion diagrams of three-dimensional photonic crystals with rectangular geometry

We propose a method and codes for fast computation of complex dispersion relations in three-dimensional photonic crystals (PCs) with rectangular geometry. The main idea of the method is to convert the eigenproblem to a nonlinear equation equivalent to the zero-determinant condition. This equation is then solved iteratively either by fixed-point iteration or by rational approximation method. Additional mathematical elements include fast-converging continued-fraction expansion to compute the interaction tensor (appearing in the above nonlinear equation) and efficient accounting for the rectangular geometry in matrix-vector multiplications, which are involved in computing the continued fraction coefficients. The method allows one to perform realistic three-dimensional computations on a typical laptop computer, including finding the Bloch wave vector in the band gaps and in evanescent mode bands. This paper is focused on the method and includes its detailed explanation and illustration with examples. The associated computational package contains a detailed user guide and a set of further demonstrations, which can be run with the help of provided scripts. Program summaryProgram title: RectDisp v.1-3CPC Library link to program files:https://doi.org/10.17632/k7nk86cfbs.1Code Ocean capsule:https://codeocean.com/capsule/7141738Licensing provisions: CC BY NC 3.0Programming language: Fortran 2003Nature of problem: The program computes the complex Bloch wave number q as a function of real frequency ω in photonic crystals (PCs) with rectangular geometry. The PC constituents are characterized by complex dispersive permittivities and are non-magnetic. Projection of q onto the XY-plane of the PC is fixed and can be specified by the user, and the projection onto the Z-axis is computed.Solution method: The method converts the eigenproblem of finding q to the nonlinear equation equivalent to the zero-determinant condition for, at most, a 3×3 matrix, and solves the latter by an iterative method (either fixed-point iteration or rational approximation or a combination of the two approaches). Additional features include continued-fraction expansion for computing the coefficients in the nonlinear equation and utilization of variable separability characteristic of the rectangular geometry for fast matrix-vector multiplication.Additional comments including restrictions and unusual features: The current version of the codes computes at most one value of q for each frequency. This excludes spurious modes arising due to the artificial band folding. Such modes are usually not coupled to incident radiation. However, some other modes can be missed. Under most circumstances, this can happen at higher frequencies, i.e., for ωh/c>π, where h is the PC period. Verification of mode coupling to external radiation and exhaustive search for all coupled modes are not currently implemented but we plan to add these features in future releases. If a solution is not found at some frequency, it can potentially be found by fine-tuning input parameters as described in the User Guide.

Structure and Optical Properties of Opal Films Made by an Out-of-Plane Electric Field-Assisted Capillary Deposition Method.

Self-assembled opals that are considered as a promising candidate for three-dimensional photonic crystals often suffer from the existence of internal defects. Defects influence optical properties and limit the applicability of opal films. Directed assembly using external fields may offer a certain degree of tunability in the opal formation process. We investigate the effect of an out-of-plane electric field on the formation and optical properties of opal films deposited using the capillary deposition method. The application of an electric field of intermediate strength (20–30 V/cm) can improve opal quality. The quality of opal films was found to depend on the polarity of the bottom substrate resulting from the beneficial influence of an asymmetry between the growths and the interplay with gravity. The negatively charged bottom substrate results in slightly better opal quality. This finding shows the potential of electric fields to tune opal formation in order to reduce the defect content.

Higher-order Dirac semimetal in a photonic crystal

The recent discovery of higher-order topology has largely enriched the classification of topological materials. Theoretical and experimental studies have unveiled various higher-order topological insulators that exhibit topologically protected corner or hinge states. More recently, higher-order topology has been introduced to topological semimetals. Thus far, realistic models and experimental verifications on higher-order topological semimetals are still very limited. Here, we design and demonstrate a three-dimensional photonic crystal that realizes a higher-order Dirac semimetal phase. Numerical results on the band structure show that the designed three-dimensional photonic crystal is able to host two four-fold Dirac points, the momentum-space projections of which at an edge are connected by higher-order hinge states. The higher-order topology can be characterised with the calculation of the \chi(6) topological invariant at different values of k_z. An experiment at microwave frequencies is also presented to measure the hinge state dispersion. Our work demonstrates the physical realization of a higher-order Dirac semimetal phase and paves the way to exploring higher-order topological semimetals phases in three-dimensional photonic systems.

A UiO-66 3D photonic crystal optical sensor for highly efficient chlorobenzene vapor detection.

Chlorobenzene (C6H5Cl) is a flammable liquid with high vapor activity, which is a severe threat to the environment and human health. Therefore, it is essential to develop a highly efficient sensor to detect C6H5Cl vapor. Herein, we developed a UiO-66 three-dimensional photonic crystal (3D PC) optical sensor and investigated its sensing properties toward the C6H5Cl vapor. The UiO-66 3D PCs optical sensor shows a high sensitivity of C6H5Cl vapor, in the concentrations range of 0-500 ppm, the reflectance intensity response to be 0.06% ppm with a good linear relationship, detection limit can reach 1.64 ppm and the quality factor is 10.8. Additionally, the UiO-66 3D PC optical sensor demonstrated great selectivity with the values of selectivity (S) varying from 2.24 to 10.65 for the C6H5Cl vapor as compared with carbon tetrachloride (CCl4), dichloromethane (CH2Cl2), 1,1,2-trichloroethane (C2H3Cl3), benzene (C6H6), deionized water (H2O), ethanol (C2H5OH) and methyl alcohol (CH3OH) vapors. Moreover, the UiO-66 3D PC optical sensor shows an ultrafast optical response time and recovery times of 0.5 s and 0.45 s with exceptional stability and repeatability to 500 ppm C6H5Cl vapor. These excellent sensing properties are attributed to the efficacy of signal transduction, increased porosity and gas adsorption sites, which are intrinsically endowed by the design of the 3D optical structure. The design and fabrication of this UiO-66 3D PC optical sensor might open up potential applications for the detection of the C6H5Cl vapor.

Manipulating the orbital-angular-momentum correlation of entangled two-photon states in three-dimensional nonlinear photonic crystals

Three-dimensional (3D) nonlinear photonic crystal (NPC) has recently been realized in experiment, which provides a powerful platform for quantum-state engineering. Here, we propose a fork-grating 3D NPC scheme to manipulate orbital-angular-momentum (OAM) correlations of entangled two-photon pairs. The spiral spectra, bandwidths, and generation rates of counterpropagating and copropagating photon pairs are theoretically analyzed. Our results show that 3D NPC is of practical significance to generate high-dimensional OAM entanglement for quantum precision measurement, quantum computing, and quantum communication.

Fabrication of three-dimensional photonic crystals for near-infrared light by micro-manipulation technique under optical microscope observation

We developed a micro-manipulation technique performed under optical microscope observation, which enabled the accurate fabrication of three-dimensional photonic crystals (3D PhCs) for near-infrared light. Thin GaAs plates having an array of rods were picked up with a fine needle by means of the van der Waals force and were mechanically stacked one-by-one by using vertical posts as guides. In spite of the limited spatial resolution in the optical microscope images, the mechanical resolution of the micro-manipulator and the precisely fabricated vertical posts enabled a stacking error that was an order of magnitude smaller than the period of the 3D PhCs. Photoluminescence measurement of a 3D PhC nanocavity containing quantum dots showed a cavity-mode peak in the near-infrared region.

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.

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.

Localized Ferroelectric Domain: Localized Ferroelectric Domains via Laser Poling in Monodomain Calcium Barium Niobate Crystal (Laser Photonics Rev. 15(9)/2021)

In article number 2100088, Leszek M. Mazur and co-workers fabricate two- and three-dimensional nonlinear photonic crystals in the bulk of a single-domain ferroelectric calcium barium niobate (CBN) crystal by employing femtosecond infrared optical pulses to invert spontaneous polarization in CBN. The structures are used to demonstrate nonlinear diffraction via transverse second harmonic generation. This work constitutes the first realization of optically induced spatially localized ferroelectric domains in the bulk of a single-domain crystal and has the potential for applications in nonlinear light processing and frequency conversion.

Blue Phase Liquid Crystals with Tailored Crystal Orientation for Photonic Applications

Blue phase (BP) liquid crystals, which self-assemble into soft three-dimensional (3D) photonic crystals, have attracted enormous research interest due to their ability to control light and potential photonic applications. BPs have long been known as optically isotropic materials, but recent works have revealed that achieving on-demand 3D orientation of BP crystals is necessary to obtain improved electro-optical performance and tailored optical characteristics. Various approaches have been proposed to precisely manipulate the crystal orientation of BPs on a substrate, through the assistance of external stimuli and directing self-assembly processes. Here, we discuss the various orientation-controlling technologies of BP crystals, with their mechanisms, advantages, drawbacks, and promising applications. This review first focuses on technologies to achieve the uniform crystal plane orientation of BPs on a substrate. Further, we review a strategy to control the azimuthal orientation of BPs along predesigned directions with a uniform crystal plane, allowing the 3D orientation to be uniquely defined on a substrate. The potential applications such as volume holograms are also discussed with their operation principle. This review provides significant advances in 3D photonic crystals and gives a huge potential for intelligent photonic devices with tailored optical characteristics.

Transmission properties of microwaves at an optical Weyl point in a three-dimensional chiral photonic crystal.

Microwave transmission measurements were performed for a three-dimensional (3D) layer-by-layer chiral photonic crystal (PhC), whose photonic band structure contains 3D singular points, Weyl points. For the frequency and wavevector in the vicinity of a Weyl point, the transmitted intensity was found to be inversely proportional to the square of the propagation length. In addition, the transmitted wave was well-collimated in the plane parallel to the PhC layers, even for point-source incidence. When a plane wave was incident on the PhC containing metal scatters, the planar wavefront was reconstructed after the transmission, indicating a cloaking effect.

Softness-Enhanced Self-Assembly of Pyrochlore- and Perovskite-like Colloidal Photonic Crystals from Triblock Janus Particles.

It remains extremely challenging to build three-dimensional photonic crystals with complete photonic bandgaps by simple and experimentally realizable colloidal building blocks. Here, we demonstrate that particle softness can enhance both the self-assembly of pyrochlore- and perovskite-like lattice structures from simple deformable triblock Janus colloids and their photonic bandgap performances. Dynamics simulation results show that the region of stability of pyrochlore lattices can be greatly expanded by appropriately increasing softness, and the perovskite lattices are unexpectedly obtained at enough high softness. Photonic calculations show that the direct pyrochlore lattices formed from overlapping soft triblock Janus particles exhibit even larger photonic bandgaps than the ideal nonoverlapping pyrochlore lattice, and proper overlap arising from softness can also dramatically improve the photonic properties of the inverse pyrochlore and perovskite lattices. Our study offers a new and feasible self-assembly path toward three-dimensional photonic crystals with large and robust photonic bandgaps.

Quasi-phase-matching-division multiplexing holography in a three-dimensional nonlinear photonic crystal

Nonlinear holography has recently emerged as a novel tool to reconstruct the encoded information at a new wavelength, which has important applications in optical display and optical encryption. However, this scheme still struggles with low conversion efficiency and ineffective multiplexing. In this work, we demonstrate a quasi-phase-matching (QPM) -division multiplexing holography in a three-dimensional (3D) nonlinear photonic crystal (NPC). 3D NPC works as a nonlinear hologram, in which multiple images are distributed into different Ewald spheres in reciprocal space. The reciprocal vectors locating in a given Ewald sphere are capable of fulfilling the complete QPM conditions for the high-efficiency reconstruction of the target image at the second-harmonic (SH) wave. One can easily switch the reconstructed SH images by changing the QPM condition. The multiplexing capacity is scalable with the period number of 3D NPC. Our work provides a promising strategy to achieve highly efficient nonlinear multiplexing holography for high-security and high-density storage of optical information.

Polymer-stabilized blue phase liquid crystal sensor for sensitive and selective detection of organic vapors

ABSTRACT Polymer-stabilised blue-phase liquid crystal (PS-BPLC) is a soft artificial three-dimensional photonic crystal (PC) functional material for optics and optoelectronics because of its superior optical properties. In this work, we demonstrated that PS-BPLC film could sense and selectively detect the xylene, heptane, cyclohexane, dichloromethane and ethyl alcohol vapours rapidly and accurately. When the PS-BPLC film was alternately exposed to volatile vapours and air, the Bragg reflection wavelength of the PS-BPLC could reversibly and significantly shift because of the adsorption and desorption of the volatile vapours. Different organic vapours could be well discriminated by the linearity and the critical concentration at which the Bragg reflection disappeared. This organic vapour sensor also had a good sensitivity, high repeatability, humidity independence and long-term stability, which promote a widespread use in environmental monitoring, point-of-care biomedical analysis and optical security coatings.

FAME

In this article, we propose the Fast Algorithms for Maxwell’s Equations (FAME) package for solving Maxwell’s equations for modeling three-dimensional photonic crystals. FAME combines the null-space free method with fast Fourier transform (FFT)-based matrix-vector multiplications to solve the generalized eigenvalue problems (GEPs) arising from Yee’s discretization. The GEPs are transformed into a null-space free standard eigenvalue problem with a Hermitian positive-definite coefficient matrix. The computation times for FFT-based matrix-vector multiplications with matrices of dimension 7 million are only 0.33 and 3.6 × 10 − 3 seconds using MATLAB with an Intel Xeon CPU and CUDA C++ programming with a single NVIDIA Tesla P100 GPU, respectively. Such multiplications significantly reduce the computational costs of the conjugate gradient method for solving linear systems. We successfully use FAME on a single P100 GPU to solve a set of GEPs with matrices of dimension more than 19 million, in 127 to 191 seconds per problem. These results demonstrate the potential of our proposed package to enable large-scale numerical simulations for novel physical discoveries and engineering applications of photonic crystals.

The diversity of three-dimensional photonic crystals

Many butterflies, birds, beetles, and chameleons owe their spectacular colors to the microscopic patterns within their wings, feathers, or skin. When these patterns, or photonic crystals, result in the omnidirectional reflection of commensurate wavelengths of light, it is due to a complete photonic band gap (PBG). The number of natural crystal structures known to have a PBG is relatively small, and those within the even smaller subset of notoriety, including diamond and inverse opal, have proven difficult to synthesize. Here, we report more than 150,000 photonic band calculations for thousands of natural crystal templates from which we predict 351 photonic crystal templates – including nearly 300 previously-unreported structures – that can potentially be realized for a multitude of applications and length scales, including several in the visible range via colloidal self-assembly. With this large variety of 3D photonic crystals, we also revisit and discuss oft-used primary design heuristics for PBG materials.