Complete Photonic Band Gap Research Articles

Printing of 3D photonic crystals in titania with complete bandgap across the visible spectrum.

A photonic bandgap is a range of wavelengths wherein light is forbidden from entering a photonic crystal, similar to the electronic bandgap in semiconductors. Fabricating photonic crystals with a complete photonic bandgap in the visible spectrum presents at least two important challenges: achieving a material refractive index > ~2 and a three-dimensional patterning resolution better than ~280 nm (lattice constant of 400 nm). Here we show an approach to overcome such limitations using additive manufacturing, thus realizing high-quality, high-refractive index photonic crystals with size-tunable bandgaps across the visible spectrum. We develop a titanium ion-doped resin (Ti-Nano) for high-resolution printing by two-photon polymerization lithography. After printing, the structures are heat-treated in air to induce lattice shrinkage and produce titania nanostructures. We attain three-dimensional photonic crystals with patterning resolution as high as 180 nm and refractive index of 2.4-2.6. Optical characterization reveals ~100% reflectance within the photonic crystal bandgap in the visible range. Finally, we show capabilities in defining local defects and demonstrate proof-of-principle applications in spectrally selective perfect reflectors and chiral light discriminators.

Complete photonic bandgap in a low-index two-dimensional quasicrystalline structure.

A bandgap in the continuum spectrum of photons in addition to its basic physical significance has strong potential for applications. Analogous to semiconductor crystals for electrons, periodic dielectric structures named photonic crystals were proposed to control photon flux propagation. In our search for low refractive index (RI) structures with a photonic bandgap, initial research efforts were focused on photonic crystal design, while aperiodic structures allow lower values of refractive index contrast to sustain a photonic bandgap. Here, we report on a two-dimensional quasicrystalline structure designed as a set of one-dimensional lattices merged into a single binary structure made of two materials with refractive index contrast 2|n1 - n2|/(n1 + n2) = 0.16 and even less in theory. We confirmed the theoretical prediction of bandgap exciting by measuring the radiation suppression of a dipole source placed in the center of the quasicrystalline structure. The full-wave numerical simulations and the experimental study appear to be in good agreement with the theoretical model.

Three-dimensional photonic crystal optical gas sensor for trace detection and ultrafast response of chemical warfare agent in atmospheric humidity

Chemical warfare agents (CWAs) are toxic that pose a threat to the environment and human health, even trace amounts of CWAs can be fatal. In view of this, there is an urgent need to develop gas sensors for trace detection and ultrafast response of CWAs. Herein, an optical gas sensor has been proposed based on metal−organic frameworks (MOFs) three−dimensional (3D) photonic crystal to detect trace CWAs’ simulant (dimethyl methylphosphonate, DMMP) in different atmospheric humidity (RH 20 %, RH 40 %, RH 60 %, RH 80 %). At relative humidity (RH) of 20 %, the sensor shows excellent selectivity of DMMP due to the specific interactions of van der Waals force between UiO−67 and phosphoryl oxygen (OP) group of DMMP (C3H9O3P), the ultrahigh sensitivity (42.7 ppb), ultrafast response (0.5 s) are profit from the ordered superstructure of 3D photonic crystal and its complete photonic bandgap. At higher humidity (RH 40%–80 %), the sensor shows excellent stability, long–term repeatability, and it still keeps ultrahigh sensitivity (12.1 ppb), ultrafast response (0.49 s) for DMMP at RH 80 %. Moreover, an optical gas sensor array has been prepared to solve the problem of cross−sensitive between DMMP and other CWAs at highest humidity (RH ≥ 80 %), the average classification accuracy can reach 98.6 %.

Observation of photonic chiral edge states in penrose quasicrystals

Photonic chiral edge states with one-way propagation and robust topological protection are hallmark features of photonic Chern insulators. To date, photonic chiral edge states have been observed in two-dimensional (2D) periodic and amorphous gyromagnetic photonic crystals. Recent theoretical studies reveal that photonic chiral edge states can also exist in 2D Penrose quasicrystals with long-range order but lack translational symmetry. Here, we report the first experimental observation of photonic chiral edge states in a 2D Penrose-tiled gyromagnetic photonic quasicrystal. By using microwave measurements, we observe a complete photonic band gap in the Penrose photonic quasicrystal despite the absence of bulk Bloch bands in momentum space. Moreover, we directly observe unidirectional backscattering-immune photonic chiral edge states within the photonic bandgap of the 2D Penrose quasicrystal. These results broaden our understanding of photonic chiral edge states and provide a new platform for exploring the intriguing properties of topological photonic quasicrystals.

Diamond-lattice photonic crystals assembled from DNA origami.

Colloidal self-assembly allows rational design of structures on the micrometer and submicrometer scale. One architecture that can generate complete three-dimensional photonic bandgaps is the diamond cubic lattice, which has remained difficult to realize at length scales comparable with the wavelength of visible or ultraviolet light. In this work, we demonstrate three-dimensional photonic crystals self-assembled from DNA origami that act as precisely programmable patchy colloids. Our DNA-based nanoscale tetrapods crystallize into a rod-connected diamond cubic lattice with a periodicity of 170 nanometers. This structure serves as a scaffold for atomic-layer deposition of high-refractive index materials such as titanium dioxide, yielding a tunable photonic bandgap in the near-ultraviolet.

Studies on temperature-dependent bandgap and gap-to-midgap ratio in diamond lattice photonic crystal with biosensing applications

The present study examines the temperature dependence of the photonic bandgap, the corresponding wavelength and the gap-to-midgap ratio in a three-dimensional diamond lattice photonic crystal. The bandgap calculations establish that the structure shows a complete photonic bandgap centered around 1550 nm at 300 K. The thermo-optic effect, observed in silicon, is employed to compute the photonic bandgap, band-edge wavelengths and mid-bandgap wavelength at various temperatures in the range of 300 K–400 K. The gap-to-midgap ratio, for the proposed structure, is also evaluated at different temperatures. It is seen that the upper and lower band-edge wavelengths and the mid-bandgap wavelength show a linear temperature dependence. The sensitivity of the structure is observed to be 0.0518 nm/K, thus supporting temperature sensing applications. It is found that the gap-to-midgap ratio, for the proposed diamond lattice structure, shows linear variation with temperature. The effect of variation of the dielectric constant and the fill factor on the gap-to-midgap ratio for the diamond structure has also been analyzed. The proposed design has also been analyzed as a refractive index sensor with a sensitivity of 254.9 nm/RIU for sensing the different components of blood.

Disentangled Higher‐Orbital Bands and Chiral Symmetric Topology in Confined Mie Resonance Photonic Crystals

AbstractTopological phases based on tight‐binding models have been extensively studied in recent decades. By mimicking the linear combination of atomic orbitals in tight‐binding models based on the evanescent couplings between resonators in classical waves, numerous experimental demonstrations of topological phases have been successfully conducted. However, in dielectric photonic crystals, the Mie resonances' states decay too slowly as , leading to intrinsically different physics between tight‐binding models and dielectric photonic crystals. Here, a confined Mie resonance photonic crystal is proposed by embedding perfect electric conductors between dielectric rods, creating the chiral symmetric band structure which ideally matches tight‐binding models with nearest‐neighbour couplings. As a consequence, disentangled band structure spanned by higher atomic orbitals is observed. Moreover, the result provides an effective route to achieve a 3D photonic crystal with a complete photonic bandgap and third‐order topology. The implementation offers a versatile platform for studying exotic higher‐orbital bands and achieving tight‐binding‐like 3D topological photonic crystals.

Programmed Self‐Assembly of Single Colloidal Gyroids for Chiral Photonic Crystals (Adv. Mater. 23/2023)

Colloidal Self Assembly In article number 2211197, Dwaipayan Chakrabarti and co-workers report on the self-assembly of enantiomorphic single colloidal gyroid crystals in silico from designer chiral patchy spheres. Each of these crystals is shown to support a complete photonic bandgap, whilst also exhibiting rich chiroptical properties. This computational study introduces single colloidal gyroids as attractive targets for chiral photonic crystals operating at optical frequencies. Image credit: Wesley Flavell.

Transverse Magnetic Mode Laser in Photonic Crystal Nanobeam Cavity

We experimentally demonstrate a transverse magnetic (TM) mode laser in a photonic crystal (PhC) slab structure at room temperature. This study proposes a PhC nanobeam (NB) cavity to support a high-quality-factor ($Q$-factor) TM mode. For a large and complete photonic band gap, the PhC NB structures consist of large air holes in a thick dielectric slab. The PhC NB cavity is optimized numerically for a high-$Q$-factor TM mode of over 1 000 000 by reducing the radii of the air holes quadratically from the center to the edge of the PhC NB. A single-TM-mode lasing action is observed in an In-Ga-As-P quantum well (QW)-embedded optimized PhC NB cavity structure at room temperature via optical pulse pumping, where the QW layer is lightly etched. We believe that the TM mode lasers in PhC NB cavities with a lightly etched QW can be good candidates for a surface plasmon excitation source or a highly sensitive optical sensor.

Deep Learning-based Inverse Design of the Complete Photonic Band Gap in Two-Dimensional Photonic Crystals

Background: With the continuous development of computer science, data-driven computing methods have shown their advantages in various fields. In the field of photonics, deep learning (DL) can be used to inversely design the structure of optical devices. Objective: The two-dimensional (2D) photonic crystal (PCs) with adjustable structural parameters and a large complete photonic band gap (CPBG) are inversely designed in terms of DL neural network (NN) tagged to obtain a specified width of CPBG. Methods: The new PCs structure is designed by combining multiple factors that produce a CPBG. Tandem networks are used to speed up the training of the NN and tackle the problem of nonuniqueness that arises in inverse design. Results: After various attempts and improvements, the ideal PCs structure was obtained. It is found that the connecting channel between the primitives in the PCs unit cell has a dominate effect on the CPBG. The use of a tandem network enables better convergence of the network. Finally, suitable NN can be obtained, which can realize the forward prediction of the CPBG and the inverse design of the structure. Conclusion: DL can realize forward prediction and inverse design of 2D PCs targeting the width of the CPBG, which broadens the application scope of DL in the field of PCs.

Programmed Self-Assembly of Single Colloidal Gyroids for Chiral Photonic Crystals.

Gyroid structures are of extensive interest because they provide a rich platform for chiroptics as well as topological photonics. While the double-gyroid morphology as a bicontinuous structure is not uncommon in self-assembled soft materials, direct self-assembly of single-network gyroids has proven elusive. Here, an enantiomorphic pair of single-gyroid crystals comprising colloidal spheres is presented, and two distinct routes are demonstrated for programmed self-assembly of each single colloidal gyroid enantiomorph from rationally designed patchy spheres. The designer colloidal patchy spheres, which closely hew to their synthetic feasibility, are chiral, having either two staggered rectangular patches at opposite poles or four circular patches arranged in a well-defined geometry. The single colloidal gyroid, as well as its inverse structure, is shown to support a wide complete photonic bandgap in addition to exhibiting rich chiroptical properties, making them attractive chiral photonic crystals. The versatility of this single colloidal gyroid, the bottom-up routes devised here in silico, and the robustness of the design space for the chiral colloidal patchy spheres together make a strong case for single colloidal gyroids to supersede colloidal diamond, as a target for programmed self-assembly, in the quest for a photonic crystals operating at opticalfrequencies.

2-Photon Polymerized IP-Dip 3D Photonic Crystals for Mid IR Spectroscopic Applications

Photonic Crystals (PhC) are periodically structured dielectric materials that have been subject to extensive research efforts over the last two decades. PhC are known for the slow-light phenomenon, which increases the interaction time between light and the target gas, thereby enhancing sensitivity when applied to sensors. Slow light is best realized using three-dimensional (3D) PhC with a complete photonic band-gap (PBG). However, they are inherently difficult to fabricate with planar microfabrication techniques. In this work, we present two-photon polymerized (2PP) stereolithographically fabricated 3D PhC targeting mid-infrared (MIR) spectroscopic range. Finite Element Analysis (FEA) was performed on a two-dimensional (2D) PhC waveguide (PhCW) to analyze the significance of PBG and slow light properties. Additional FEA was conducted and validated experimentally using fabricated 3D PhC. The ability to tune PhC to a desired wavelength along with their repeatability and feasibility is experimentally demonstrated. This letter presents the first, to our knowledge, 3D PhC fabricated using 2PP stereolithography operating at this wavelength.

Near-field imaging of optical nanocavities in hyperuniform disordered materials

Hyperuniform disordered photonic materials have recently been shown to display large, complete photonic band gaps and isotropic optical properties, and are emerging as strong candidates for a plethora of optoelectronic applications, making them competitive with many of their periodic and quasiperiodic counterparts. In this work, high quality factor optical cavities in hyperuniform disordered architectures are fabricated through semiconductor slabs and experimentally addressed by scanning near-field optical microscopy. The wide range of confined cavity modes that we detect arise from carefully designed local modifications of the dielectric structure. Previous works on hyperuniform disordered photonic systems have previously identified several Anderson localized states spectrally located at the PBG edges with relatively high quality factors. In this work, by engineering the structural parameters of the cavity, we achieve an experimental quality factor of order 6000 (higher than the one of the Anderson states) and we demonstrate that three types of localized modes of different nature coexist within a small area and in a relatively narrow spectral window of the disordered correlated system. Their compatibility with general boundary constraints, in contrast with ordered architectures that suffer strict layout constraints imposed by photonic crystals' axes orientation, makes optical cavities in disordered hyperuniform patterns a flexible optical insulator platform for planar optical circuits.

Towards complete photonic band gap in a high refractive index nanoparticle-doped blue phase liquid crystal.

Three-dimensional (3D) photonic crystals with complete photonic band gap (PBG) are fascinating due to the possibility of controlling light in all directions. Realizing such photonic crystals is nontrivial due to symmetry requirements and associated fabrication challenges. Liquid crystalline cubic blue phases (BPs) are soft 3D photonic crystals with an incomplete PBG due to the low refractive index contrast (<0.1). The present work attempts to drive a cubic BP towards a complete PBG via a simple approach of high refractive index nanoparticle-doping. The photonic band diagrams and reflection spectra of the nanoparticle-doped BP simulated using the finite element method show an increased PBG width, a parameter that quantifies the complete PBG. The reflection spectra obtained from UV-Vis-NIR spectroscopy show an increase (by a factor of >2) in PBG width for the nanoparticle-doped BP, validating the simulations. The findings are explained based on increased refractive index contrast (∼1.4) due to the nanoparticles getting trapped in the cores of disclination lines that make up the BP lattice. The simulations also indicate effective confinement of electric field eigenmodes in the nanoparticle-doped BP leading to high attenuation of the incident light. Further, the iso-frequency contours extracted from the band diagrams exhibit self-collimation and negative refraction of light.

Pursuing colloidal diamonds.

The endeavor to selectively fabricate a cubic diamond is challenging due to the formation of competing phases such as its hexagonal polymorph or others possessing similar free energy. The necessity to achieve this is of paramount importance since the cubic diamond is the only polymorph exhibiting a complete photonic bandgap, making it a promising candidate in view of photonic applications. Herein, we demonstrate that due to the presence of an external field and delicate manipulation of its strength we can attain selectivity in the formation of a cubic diamond in a one-component system comprised of designer tetrahedral patchy particles. The driving force of such a phenomenon is the structure of the first adlayer which is commensurate with the (110) face of the cubic diamond. Moreover, after a successful nucleation event, once the external field is turned off, the structure remains stable, paving an avenue for further post-synthetic treatment.

Wave propagation and band tails of two-dimensional disordered systems in the thermodynamic limit

Understanding the nature and formation of band gaps associated with the propagation of electromagnetic, electronic, or elastic waves in disordered materials as a function of system size presents fundamental and technological challenges. In particular, a basic question is whether band gaps in disordered systems exist in the thermodynamic limit. To explore this issue, we use a two-stage ensemble approach to study the formation of complete photonic band gaps (PBGs) for a sequence of increasingly large systems spanning a broad range of two-dimensional photonic network solids with varying degrees of local and global order, including hyperuniform and nonhyperuniform types. We discover that the gap in the density of states exhibits exponential tails and the apparent PBGs rapidly close as the system size increases for nearly all disordered networks considered. The only exceptions are sufficiently stealthy hyperuniform cases for which the band gaps remain open and the band tails exhibit a desirable power-law scaling reminiscent of the PBG behavior of photonic crystals in the thermodynamic limit.

Channel switch based on the transformation of two kinds of topological edge states

In this paper, we have constructed a compound triangular lattice in which the optical quantum spin Hall effects and quantum valley Hall effects can simultaneously occur. Through the rotation of the dielectric rods in the lattice, two complete photonic band gaps with nontrivial topology can be created, one of which is due to the band inversion associated with the pseudospin degree of freedom at point in the first Brillouin zone (BZ) and the other due to the gapping out of Dirac cones associated with the valley degree of freedom at K point in the first BZ. The transformation between the two kinds of topological edge states can be also achieved through the rotation of the dielectric rods. A four-channel structure model is proposed to demonstrate the transformation and to achieve the channel switch of the topological edge states.

Complete photonic bandgap in silicon nitride slab assisted by effective index difference between polarizations.

The slab effective index difference between the transverse-electric (TE) and transverse-magnetic (TM) polarizations was utilized to obtain complete photonic bandgap (CPBG) in a silicon nitride (SixNy) photonic crystal slab. For this, coincident frequency range in the TE photonic bandgap (PBG) and TM PBG, which denotes the CPBGs of the slab, must be found with the same structure. Through adjusting the effective index pair of TE and TM polarizations by changing the thickness of the SixNy core layer, and also optimizing the structure parameters within the photonic crystal plane, a large normalized CPBG of 5.62% was theoretically obtained in a slab of SixNy with a refractive index of 2.5. Moreover, based on the obtained CPBG, a microcavity which could support both TE and TM polarization was theoretically demonstrated. The cavity modes for different polarizations were both well confined, which proved the reliability of the CPBG. In addition, using the same method, the lowest refractive index of SixNy on silica slab for a CPBG could be extended to as low as 2. The results indicate that there is potential for development of various high-performance CPBG devices based on SixNy slab technology.

Alternating Gyroid in Block Polymer Blends.

Alternating gyroid is a lower symmetry variant of the double gyroid morphology, where the left-handed and right-handed chiral networks are physically distinct. This structure is of particular interest for photonic applications owing to predictions of a complete photonic band gap subject to the requirement of a large dielectric contrast between the individual networks and sufficient optical matching between one of the networks and the matrix. We provide evidence, via self-consistent field theory (SCFT), that stoichiometric blends of double-gyroid-forming AB and BC diblock copolymers with relatively immiscible A and C blocks should form an alternating gyroid morphology with complementary three-dimensional A and C networks that have a free energy that is nearly degenerate with two phase-separated double gyroid states. Solvent casting offers the potential for trapping this binary mixture of diblock copolymers in this metastable alternating gyroid phase. Theory further predicts that the addition of a minuscule amount (<1%) of ABC triblock terpolymer will open an alternating gyroid stability window in the resulting ternary-phase diagram. The surfactant-like stabilization produced by the triblock is relatively insensitive to its exact composition provided the B-block forms a sufficiently long bridge between the A-rich and C-rich networks. This blending strategy provides significant synthetic and material processing advantages compared to prevailing methods to produce an alternating gyroid phase in block polymers.

Strongly Confining Light with Air-Mode Cavities in Inverse Rod-Connected Diamond Photonic Crystals

Three-dimensional dielectric optical crystals with a high index show a complete photonic bandgap (PBG), blocking light propagation in all directions. We show that this bandgap can be used to trap light in low-index defect cavities, leading to strongly enhanced local fields. We compute the band structure and optimize the bandgap of an inverse 3D rod-connected diamond (RCD) structure, using the plane-wave expansion (PWE) method. Selecting a structure with wide bandgap parameters, we then add air defects at the center of one of the high-index rods of the crystal and study the resulting cavity modes by exciting them with a broadband dipole source, using the finite-difference time-domain (FDTD) method. Various defect shapes were studied and showed extremely small normalized mode volumes (Veff) with long cavity storage times (quality factor Q). For an air-filled spherical cavity of radius 0.1 unit-cell, a record small-cavity mode volume of Veff~2.2 × 10−3 cubic wavelengths was obtained with Q~3.5 × 106.