Formation of all fourteen Bravais lattices of three-dimensional photonic crystal structures by a dual beam multiple-exposure holographic technique

We make use of a dual beam multiple-exposure (DBME) holographic technique for the formation of all 14 Bravais lattices of three-dimensional photonic crystal microstructures. For simplicity of experimental implementation, the DBME method has been modified such that, prior to each exposure, once the proper angle between the wave vectors of the interfering beams is chosen, a single axis rotation of the recording medium gives the desired results. The parameters required for the generation of the lattice structures have been derived by appropriate modification of interference of four noncoplanar beams (IFNB) analysis for corresponding implementation in the DBME technique, and the results have been verified by computer simulations. After giving a comparative study of the results with the IFNB method, recording geometries for the DBME approach are also proposed in order to realize all 14 Bravais lattices experimentally.     

Nanoimprinting lithography of a two-layer phase mask for three-dimensional photonic structure holographic fabrications via single exposure

We report a combined holographic and nanoimprinting lithography technique to produce three-dimensional woodpile photonic crystal templates through only one single exposure. The interference lithography process uses an integratable diffractive optical element for large throughout 3D pattern manufacturing. The diffractive optical element consists of two layers of phase grating separated by an intermediate layer, fabricated by repeated nanoimprinting lithography, followed by an SU8 photoresist bonding technique. Grating periods, relative orientation, diffraction angle, and efficiency, as well as layer to layer phase delay, are well designed during manufacturing. By thermally optimizing the thickness of the intermediate layer, this paper demonstrates the fabrication of interconnected 3D photonic structures with arbitrary symmetry through a single laser exposure. The two-layer phase mask approach enables a CMOS-compatible monolithic integration of 3D photonic structures with other integrated optical elements and waveguides.     

Fabrication and characterisation of CdSe photonic structures from self-assembled templates

We demonstrate here a method to fabricate CdSe photonic crystal from a very cheap fabrication route of templated self-assembly. The hexagonal close-packed photonic crystals are formed by the electrochemical growth of CdSe through the interstitial spaces between polymer nano/micro sphere templates. The confocal voids containing photonic crystals can be made either interconnected or well separated, with high uniformity. Structural and optical characterisation confirms the good quality of electrochemically grown CdSe. These cheaply fabricated 2D photonic crystals provide a wide range of opportunities for optoelectronic devices.     

Synthesis of green emitting and transparent zn2siO4:mn2+ thin film phosphors on 2D photonic crystal patterned quartz substrates

Zn2SiO4:Mn2+ thin film phosphors (TFPs) have been synthesized by RF magnetron sputtering, using a single multicomponent stoichiometric target. And 2D photonic crystal patterns were introduced on a quartz substrate to enhance the light extraction efficiency. In order to introduce 2D photonic crystal patterns on a quartz substrate, nanosphere lithography was used. Polystyrene spheres, with diameter of 330 nm, were transferred on the quartz substrate and subsequently were served as an etch mask. Quartz substrates were patterned by CF4 gas-based reactive ion etching. Zn2SiO4:Mn2+ were deposited on that 2D photonic crystal patterned quartz substrate and the effect of height of photonic crystal layers were investigated. The light extraction efficiency of Zn2SiO4:Mn2+ thin film phosphors deposited on the photonic crystal patterned quartz substrate was enhanced three times to compared with that of flat Zn2SiO4:Mn2+ thin film phosphors due to the Bragg diffraction and leaky mode caused by PCLs. Transmittance of Zn2SiO4:Mn2+ TFPs deposited on the photonic crystal patterned substrate was high enough, above 70% in the visible light region with respect to that of quartz substrate.     

Tailored complex 3D vortex lattice structures by perturbed multiples of three-plane waves

As three-plane waves are the minimum number required for the formation of vortex-embedded lattice structures by plane wave interference, we present our experimental investigation on the formation of complex 3D photonic vortex lattice structures by a designed superposition of multiples of phase-engineered three-plane waves. The unfolding of the generated complex photonic lattice structures with higher order helical phase is realized by perturbing the superposition of a relatively phase-encoded, axially equidistant multiple of three noncoplanar plane waves. Through a programmable spatial light modulator assisted single step fabrication approach, the unfolded 3D vortex lattice structures are experimentally realized, well matched to our computer simulations. The formation of higher order intertwined helices embedded in these 3D spiraling vortex lattice structures by the superposition of the multiples of phase-engineered three-plane waves interference is also studied.     

Pattern-integrated interference lithography: single-exposure fabrication of photonic-crystal structures

Multibeam interference represents an approach for producing one-, two-, and three-dimensional periodic optical-intensity distributions with submicrometer features and periodicities. Accordingly, interference lithography (IL) has been used in a wide variety of applications, typically requiring additional lithographic steps to modify the periodic interference pattern and create integrated functional elements. In the present work, pattern-integrated interference lithography (PIIL) is introduced. PIIL is the integration of superposed pattern imaging with IL. Then a pattern-integrated interference exposure system (PIIES) is presented that implements PIIL by incorporating a projection imaging capability in a novel three-beam interference configuration. The purpose of this system is to fabricate, in a single-exposure step, a two-dimensional periodic photonic-crystal lattice with nonperiodic functional elements integrated into the periodic pattern. The design of the basic system is presented along with a model that simulates the resulting optical-intensity distribution at the system sample plane where the three beams simultaneously interfere and integrate a superposed image of the projected mask pattern. Appropriate performance metrics are defined in order to quantify the characteristics of the resulting photonic-crystal structure. These intensity and lattice-vector metrics differ markedly from the metrics used to evaluate traditional photolithographic imaging systems. Simulation and experimental results are presented that demonstrate the fabrication of example photonic-crystal structures in a single-exposure step. Example well-defined photonic-crystal structures exhibiting favorable intensity and lattice-vector metrics demonstrate the potential of PIIL for fabricating dense integrated optical circuits.     

Three-dimensional power splitter based on self-imaging effect in multimode layer-by-layer photonic crystal waveguides

The self-imaging effect based on symmetrical interference in multimode layer-by-layer photonic crystal waveguides (PhCWs), is numerically studied with finite-difference time-domain simulations. With the properties of twofold images, a kind of three-dimensional (3D) PhCW-based power splitters with an ultracompact size using complete photonic bandgaps is proposed, calculated, and analyzed. The presented structure can be extended for the design of M×N power splitters for 3D photonic integrated circuits applications.     

Layer‐by‐Layer Approach to (2+1)D Photonic Crystal Superlattice with Enhanced Crystalline Integrity

Large‐area polystyrene (PS) colloidal monolayers with high mechanical strength are created by a combination of the air/water interface self‐assembly and the solvent vapor annealing technique. Layer‐by‐layer (LBL) stacking of these colloidal monolayers leads to the formation of (2+1)D photonic crystal superlattice with enhanced crystalline integrity. By manipulating the diameter of PS spheres and the repetition period of the colloidal monolayers, flexible control in structure and stop band position of the (2+1)D photonic crystal superlattice has been realized, which may afford new opportunities for engineering photonic bandgap materials. Furthermore, an enhancement of 97.3% on light output power of a GaN‐based light emitting diode is demonstrated when such a (2+1)D photonic crystal superlattice employed as a back reflector. The performance enhancement is attributed to the photonic bandgap enhancement and good angle‐independence of the (2+1)D photonic crystal superlattice.     

Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams

A newly reported method of making three-dimensional microstructures or photonic crystals by holographic lithography has some obvious advantages over other techniques with the same purpose. A systematic and comprehensive analysis of interference of four noncoplanar beams (IFNB) is provided. It shows that all 14 Bravais lattices can be formed by means of IFNB and gives explicit relationships between each lattice and the corresponding recording geometry. The concept of pattern contrast is extended to the case of IFNB, and it is indicated that a uniform contrast for each interference term can be obtained by properly choosing the beam ratio and polarization. A calculation algorithm is then developed to optimize the direction of polarization of each beam to ensure maximum uniform contrast. These results, verified by computer simulations, may lay a theoretical foundation for fabrication of photonic crystals with the approach of IFNB.     

Patterned when wet: environment-dependent multifunctional patterns within amphiphilic colloidal crystals

A simple integration of molecular and colloidal self-assembly approaches with photopatterning is shown to produce multifunctional patterns of amphiphilic colloidal crystals. These crystals display binary spatial patterns of wettability by water and a single photonic stop-band in air. Upon exposure to water, the uniform stop-band is replaced by a pattern of coexisting stop-bands that reflect the underlying pattern of surface wetting. These hydration-dependent photonic patterns within single colloidal crystals form because of near-complete water rejection from the three-dimensionally disposed nanoscale interstices in hydrophobic regions and its exclusive permeation within the hydrophilic regions. This water permeation pattern is further structured by the three-dimensional (3D) distribution and contiguity of the nanoscale interstices between individual colloids, allowing 3D patterned organization of functional units in secondary self-assembly processes, as illustrated using quantum dots, metal nanoparticles, and fluorescent probes.     

Single-beam holography for Ag nanoparticle-embedded two-dimensional binary metallodielectric photonic crystals

Absolute photonic bandgaps of photonic crystals can be increased by reducing the structural symmetry and/or by enhancing the refractive index contrast. We have experimentally demonstrated a single-beam holography for creating Ag nanoparticle-embedded 2D binary photonic microstructures by adding a different diameter rod in the center of each original 2D honeycomb lattice for simultaneously realizing both symmetry reduction and the enhancement of the index contrast of PC structures.     

Area scalable optically induced photorefractive photonic microstructures

A convenient approach to fabricate area scalable two-dimensional photonic microstructures was experimentally demonstrated by multi-face optical wedges. The approach is quite compact and stable without complex optical alignment equipment. Large-area square lattice microstructures are optically induced inside an iron-doped lithium niobate photorefractive crystal. The induced large-area microstructures are analyzed and verified by plane wave guiding, Brillouin-zone spectroscopy, angle-dependent transmission spectrum, and lateral Bragg reflection patterns. The method can be easily extended to generate other more complex area scalable photonic microstructures, such as quasicrystal lattices, by designing the multi-face optical wedge appropriately. The induced area scalable photonic microstructures can be fixed or erased even re-recorded in the photorefractive crystal, which suggests potential applications in micro-nano photonic devices.     

A novel structure of photonic crystal fibre for dispersion compensation over broadband range

This paper studies a novel structure of photonic crystal fibre (PCF) for dispersion compensation at broadband wavelengths. The application of broadband is investigated using a design model based on combination of modal properties and dispersion compensation. The newly designed PCF with defect introduced is recorded over transmission spectrum range 146.7–256.98 THz, i.e., 1.16–2.04 µm. The modal characteristics and dispersion compensation of 2D PCF with circular air holes defect introduced are investigated and compared to those of conventional hexagonal 2D PCF. Changes in bandwidth behaviour are also observed by changing refractive index and geometric parameter of PCF.     

Analysis of a two-dimensional photonic bandgap structure fabricated by an interferometric lithographic system

An interferometric lithographic technique and double exposure method are applied to theoretically and experimentally investigate several kinds of 2D periodic structures. The shape, lattice symmetries, and lattice constants of the 2D structures, for different substrate rotational angles, are obtained from the simulated predictions. The shape of the 2D structures can be varied by controlling the rotational angle of the substrate and the development process, and they are validated experimentally. The variation of the lattice symmetry of the 2D structure with the substrate rotational angle is discussed in detail in relation to the axial angle and lattice constant. It is found that square, circular, rectangular, and elliptical scatterers which are arranged in parallelogram, triangular, and square lattices (with different lattice constants) can be obtained. The photonic bandgaps for each condition are also investigated. When the substrate rotational angles are the same, the normalized frequency (omega a/2 pi c) of photonic bandgap structures with an equal filling factor are very similar regardless of the interference angle. The results are helpful in designing the forbidden frequency when the lattice constant and the scatterer shape can be controlled by the interferometric lithographic technique.     

Enhancement of Faraday rotation in 3D/Bi:YIG/1D photonic heterostructures

We suggest a new design of magnetophotonic crystals. Microcavity-type magnetic photonic heterostructures exhibiting enhanced magneto-optical Faraday rotation have been fabricated. Such a heterostructure comprises an opal film (3D photonic crystals), a bismuth substituted iron garnet (Bi:YIG) spacer film acting as the defect layer, and a dielectric multilayer (1D photonic crystal). Localized mode was shown to exist in the photonic band gap as a result of resonant interference in heterostructures. The observed enhancement of Faraday rotation was more than three times as compared with that of the Bi:YIG constituent. We have also found that the heterostructures exhibit an unusual polarization-dependent response.     

Five-beam interference pattern controlled through phases and wave vectors for diamondlike photonic crystals

We demonstrate, for what is believed to be the first time, the design of diamondlike photonic crystals made by holographic lithography based on five-beam interference. All five beams are launched from the same half-space, and the exposure can easily be realized by a single diffractive optical element. The photonic structure can be constructed through the translation of the interference pattern controlled by the phase shift of laser beams. The proposed holographic lithography is capable of creating series photonic crystals with large photonic bandgaps by adjusting the phase and the wave vector of interfering beams.     

Rapid fabrication of 2D and 3D photonic crystals and their inversed structures

In this paper a new technique is proposed for the fabrication of two-dimensional (2D) and three-dimensional (3D) photonic crystals using monodisperse polystyrene microspheres as the templates. In addition, the approaches toward the creation of their corresponding inversed structures are described. The inversed structures were prepared by subjecting an introduced silica source to a sol-gel process; programmed heating was then performed to remove the template without spoiling the inversed structures. Utilizing these approaches, 2D and 3D photonic crystals and their highly ordered inversed hexagonal multilayer or monolayer structures were obtained on the substrate.     

Mie resonances and Bragg-like multiple scattering in opacity of two-dimensional photonic crystals

The lowest (main) and high-order Mie resonances and the Bragg-like multiple scattering of electromagnetic (EM) waves are determined as three mechanisms of formation and frequency position of two opaque bands, with narrow peaks in one of the bands in the transmission spectra of 2D photonic crystals composed of dielectric cylinders arranged parallel to the EM wave's electric vector in the square lattice. The main Mie resonance in a single cylinder defines the frequency position of the main gap whose formation results from the Bragg-like scattering. An additional gap with narrow transmission peaks opens in the spectrum of a cylinder layer and becomes pronounced with the number of layers. It is argued that higher-order Mie resonances are responsible for the transmission peaks within the additional band of a perfect crystal. It is shown that 2D photonic crystals with a filling factor ranging from 3% to 20% at a fixed crystal period may be a good zero approximation to study wave transmission through a localizing 2D dense random medium slab.     

Heterostructure photonic crystals: theory and applications

A hybrid structure combining square and hexagonal photonic crystal lattices is presented. This structure, which we refer to as heterostructure, offers the ability to tailor, optimize, and match the band structure of different lattices. The availability of heterostructures in photonic crystals opens abroad range of possibilities for optical device development. In particular, heterostructure photonic crystals are well suited for the application of optical beam splitting (Y coupler) and combining. Numerical experiments performed by use of the finite-difference time-domain method are shown to illustrate the device implemented in both unistructure and heterostructure lattices.     

Rigorous analysis of diffraction gratings of arbitrary profiles using virtual photonic crystals

A new approach is developed to calculate diffraction efficiency for a dielectric grating with an arbitrary refractive index profile. By treating a one-dimensional grating as a segment of a virtual two-dimensional (2D) photonic crystal, we exploit a rigorous theory of photonic crystal refraction and calculate the diffraction efficiencies. We expand, analytically in many cases, the dielectric function of the grating into 2D Fourier series. We find the eigenmodes for the virtual photonic crystal, and then use these eigenmodes to match the boundary conditions by solving a set of linear equations. In two such simple steps, the diffraction efficiencies can be computed rigorously without slicing the grating into thin layers.