Lattice Constant Of Photonic Crystal Research Articles

Stretchable, stable, and structural color reversible enabled by mesoscopic regulation and design for flexible photonic crystal mechanical sensors

This paper reports a flexible mechanical sensor developed by combining an opal photonic crystal and a flexible medium through UV curing technology. Under the action of external force, the deformation of the flexible medium causes the change of the photonic crystal lattice constant, which leads to the displacement of the reflection peaks, thus realizing the detection of the deformation of the film. The flexible medium is mixed by photoinitiators and polymer monomers, and its mechanical properties are directly related to the mass fraction of photoinitiators and polymer monomers. The results show that the film can reach a maximum strain of about 180% when the mass fraction of photoinitiator is 3% and the volume ratio of the polymer functional monomers is 8:2. In addition, for the responsiveness test of the sensor under tensile, the results show that at 0%, 26%, and 78% of tensile strain, its structural color is blue-shifted sequentially, and its spectral peaks are 668 nm, 535 nm, and 488 nm, respectively. Finally, the sensor is applied to the detection of acoustic waves in air, and it is found that its spectral response peaks can be obtained for acoustic waves of different frequencies (250–650 Hz), and a spectral peak at 500 Hz. This flexible photon sensor has the potential to match the acoustic resistance of water. It will greatly expand the response research of ocean exploration in the low frequency range.

Design of GaN-based photonic crystal surface emitting lasers with top TiO2 photonic crystals

We designed GaN-based blue photonic crystal surface emitting lasers (PCSELs) by incorporating a TiO2 photonic crystal (PhC) layer on top of the GaN surface. An AlGaN cladding layer was designed under the active region to form a waveguide-like cap layer. The dimension of the cap layer, the lattice constant of PhC, the hole radius, and the layer thickness were investigated to optimize the structure design in view of the PhC confinement factor and gain threshold. With a depth of 100 nm of the PhC layers, a hole radius of 40 nm, and a thickness of 100 nm of GaN layers above and below multiple quantum wells (MQWs), the PhC confinement factor of greater than 10% and the gain threshold below 400 cm−1 can be realized. Furthermore, the photonic band diagram is calculated, which shows that the designed PCSELs are operated at the Γ1 band edge with the lowest pump energy. This work demonstrates the potential of excellent properties in the future surface emitting blue laser sources.

Size-controllable nanopyramids photonic crystal selectively grown on p-GaN for enhanced light-extraction of light-emitting diodes

Size-controllable p-GaN hexagonal nanopyramids (HnPs)-photonic crystal (PhC) structures were selectively grown on flat p-GaN layer for the elimination of total internal reflection of light-emitting diodes (LEDs). The LEDs with HnPs-PhC of 46.3% bottom fill factor (PhC lattice constant is 730 nm) showed an improved light output power by 99.9% at forward current of 350 mA compared to the reference LEDs with flat p-GaN layer. We confirmed the effect of HnPs-PhC with different bottom fill factors and the effect of nanopyramid-shaped and nanocolumn-shaped PhC on the light-extraction of LEDs was also investigated by using three-dimensional finite-difference time-domain simulations.

Transmission line model for extraction of transmission characteristics in photonic crystal waveguides with stubs: optical filter design

A simple and efficient transmission line model is proposed here to study how the transmission characteristics of photonic crystal waveguides are tailored by introduction of stubs patterned in the photonic crystal lattice. It is shown that band-pass and band-stop optical filters can be easily designed and optimized when stubs of appropriate length are brought in. Since the lengths of the designed stubs are not necessarily integer multiples of the photonic crystal lattice constant, a geometric shift in a portion of the photonic crystal structure is shown to be essential. The proposed model is verified by using a rigorous numerical method. An excellent agreement is observed between the numerical results and the transmission characteristics as extracted by the proposed model.

Observation of unconventional optical diffraction in α-Fe2O3/Si two-dimensional photonic crystal slab fabricated by sol-gel method

The α-Fe2O3/Si two-dimensional (2D) photonic crystal (PC) with hexagonal honeycomb structure was fabricated by self-assembly and solution-dipping method based on colloidal monolayer template with 780 and 470 nm diameter polystyrene (PS) spheres. Optical diffraction measurement was carried out under wavelengths of 800, 532 and 400 nm. An interesting dispersion phenomenon with a hexagonal diffraction pattern composed of six elliptical spots is observed under specific wavelengths. Both theoretical and experimental calculations reveal that the diffraction can only occur when the incident wavelength is smaller than \(\sqrt{3}/2\) of lattice constant, and both the shape and distribution of these spots can be modified by the PC lattice constant and the incident wavelength. All these results reveal that optical properties of these 2D PC slabs are different from conventional diffractive devices.

Higher order modes in photonic crystal slabs

We present a detailed investigation of higher order modes in photonic crystal slabs. In such structures the resonances exhibit a blue-shift compared to an ideal two-dimensional photonic crystal, which depends on the order of the slab mode and the polarization. By fabricating a series of photonic crystal slab photo detecting devices, with varying ratios of slab thickness to photonic crystal lattice constant, we are able to distinguish between 0th and 1st order slab modes as well as the polarization from the shift of resonances in the photocurrent spectra. This method complements the photonic band structure mapping technique for characterization of photonic crystal slabs.

GaN-based surface-emitting laser with two-dimensional photonic crystal acting as distributed-feedback grating and optical cladding

We demonstrate GaN-based distributed-feedback surface-emitting lasers grown on sapphire substrates with a two-dimensional (2D) square-lattice photonic crystal (PhC) that forms a high-aspect-ratio void array (void diameter: 65 nm and depth: 220 nm). The 2D PhC layer acts as both distributed-feedback grating and p-type optical cladding of a separate confinement heterostructure. To form the 2D PhC in the nitride semiconductor layers, we developed an embedding process that uses mass-transport phenomena. Crystallographic facets appeared on the inner walls of the embedded voids. Room-temperature lasing action was observed at 406.0 nm for a PhC lattice constant of 162.5 nm. The threshold current density was 9.7 kA/cm2 for a 120-μm-square p-contact electrode.

Design of low-loss tapered waveguide by applying photonic-crystal-based microlenses in telescopic structure

In this paper, the design of low-loss tapered waveguides by applying photonic-crystal-based microlenses is presented. The microlenses are realized by using two-dimensional photonic crystal (PhC) structures with a hexagonal periodic lattice of air-holes. In order to make the PhC structures behave as homogeneous and isotropic microlenses, the PhC structures are designed to operate in the low-frequency domain with light wavelength sufficiently larger than the PhC lattice constant. The effective indices of the PhC are calculated and the structures are properly arranged in microlenslike shapes. By monolithically integrating the effective microlenses in the tapered area between the two optical waveguides with different core dimensions, the wavefront of the eigenmode can be coupled from the larger core to the smaller core effectively and also the radiation loss in the tapered area between the two connected optical waveguides can be effectively suppressed. The results show that the PhC-based microlens in the telescopic structure can serve as an optical element in the tapered waveguide with the advantages of low loss, high efficiency and compactness.

Structural Effects on Highly Directional Far-Field Emission Patterns of GaN-Based Micro-Cavity Light-Emitting Diodes With Photonic Crystals

This study theoretically and experimentally investigates the highly directional far-field emission patterns of GaN photonic crystal (PhC) micro-cavity light-emitting diodes (MCLEDs) depending on varying structural parameters. Angular-spectra-resolved electroluminescence measurements reveals the behavior of guided-mode extraction which is significantly affected by the structural parameters of GaN PhC MCLEDs, where the GaN cavity thickness decides the extracted guided mode numbers, PhC lattice constant influences the distribution of far-field emission, and PhC hole depth affects the interaction with guided modes. The proposed GaN ultrathin MCLED (uMCLED) with PhC lattice constant of 420 nm and deep hole depth of 250 nm exhibited a maximum output light extraction efficiency of 248% under one-watt input power compared to GaN non-PhC uMCLED and produced a directional far-field emission pattern at half intensity near 17^ . The present results indicate that highly directional light extraction enhancement could contribute to developments of many applications, especially for etendue-limited applications such as pico- projectors.

Spectral, amplitude and phase sensitivity of a plasmonic gas sensor in a metallic photonic crystal slab geometry: Comparison of the near and far field phase detection strategies

Using finite-difference time-domain method, we investigate phase and amplitude reflective properties of a metallic photonic crystal slab comprising a two-dimensional array of gold disks placed on top of a thin gold film resting on a dielectric substrate. Photonic crystal slab overcladding is a gaseous analyte. Throughout the paper we discuss prospectives of application of such photonic crystal slabs to sensing of changes in the gas refractive index. We start by studying the field distributions and spectral positions of two types of surface plasmons supported by such PhCs as a function of the photonic crystal lattice period, the gold film thickness, and the gold disk size. First, we find that the spectral positions of plasmon peaks depend almost linearly on the photonic crystal lattice constant, which is a manifestation of the delocalized nature of a plasmon extending over the PhC lattice. This is possible due to connectivity between metallic disks via an underlying thin metallic film. Second, we find that the width of plasmonic peaks is highly sensitive to the relative size of the metallic disks compared to the lattice period. This can be well explained via interaction between the localized plasmons situated at the disc edges in the adjacent unit cells. We therefore find that plasmons in the metallic PhC slabs featuring metallic discs connected by a metallic film exhibit both strong local and non-local properties. Third, we find that, generally, there are two types of plasmons supported by such metallic PhCs. One type is a plasmon with a large fraction of its field located in the gas overcladding, which is most suitable for sensing. In contrast, another plasmon type has its field concentrated at the interface between a thin metal film and a substrate; such plasmons are only weakly sensitive to the refractive index of the sensor overcladding, and, therefore, can serve as convenient references for the sensor measurements. Finally, we report sensor sensitivities to changes in the real part of the gas refractive index when using amplitude and phase-based detection strategies. We start by demonstrating that when measured in the sensor far field, the phase sensitive detection provides much lower detection limit ( 1.8 × 1 0 − 6 RIU) compared to that of the amplitude-based detection ( 1.5 × 1 0 − 4 RIU). We then find that sensor phase and amplitude sensitivities can be considerably enhanced when performing measurements using point detectors placed in the near field of a sensor. Particularly, we have established that both phase and amplitude sensitivities are maximal when measured in the sensor near field along the normal to the sensor surface going through the point of the highest symmetry of a photonic crystal unit cell ( Γ point). Sensor resolution as high as 2.2 × 1 0 − 7 RIU for the phase-based detection and 7.4 × 1 0 − 5 RIU) for the amplitude-based detection are found, with the most dramatic enhancement observed for the phase detection approach. We believe that experimental verification of the sensor sensitivity enhancement using phase detection in the sensor near field can be accomplished by using scanning near-field optical microscopy.

Study of GaN-Based Photonic Crystal Surface-Emitting Lasers (PCSELs) With AlN/GaN Distributed Bragg Reflectors

GaN-based 2-D photonic crystal (PC) surface-emitting lasers (PCSELs) with AlN/GaN distributed Bragg reflectors are fabricated and investigated. A clear threshold characteristic under the optical pumping at room temperature is observed at about 2.7 mJ/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with PC lattice constant of 234 nm. Above the threshold, only one dominant peak appears at 401.8 nm with a linewidth of 0.16 nm. The laser emission covers whole circular 2-D PC patterns of 50 mu m in diameter with a small divergence angle. The lasing wavelength emitted from 2-D PC lasers with different lattice constants occurs at the calculated band edges, showing different polarization angles due to the light diffracted in specific directions, corresponding exactly to Gamma -, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -directions in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> space. The PCSEL also shows a spontaneous emission coupling factor beta of 5 times 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and a characteristic temperature of 148 K. Furthermore, the coupled-wave model in 2-D hexagonal lattice is applied to distinguish the discrepancy in threshold power and the corresponding coupling coefficient. The results show that the lasing actions within Gamma, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> , and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> modes have a substantial relation between the threshold energy density and the coupling coefficient.

Fabrication of Metallodielectric Photonic Crystals with a Diamond Structure and their Microwave Properties

Three‐dimensional (3D) metallodielectric photonic crystals with a diamond structure were fabricated in order to investigate the formation of stop bands and the absorption ability for microwaves with the dielectric absorbing media embedded into the 3D metal lattice. First, the metallic photonic crystals were prepared by filling the epoxy molds formed by stereolithography with a metal alloy having a low melting point of 70°C, followed by removal of the molds. The metallodielectric photonic crystals were then fabricated by infiltrating the porous metal crystal with a SiC/polyester mixture. The lattice constant of photonic crystals was 15 mm. The effects of different aspect ratios of diamond lattice rods, number of metallic lattice units along Γ‐L 〈1 1 1〉, Γ‐X 〈1 0 0〉, and Γ‐K 〈1 1 0〉 directions, and metallodielectric samples along the Γ‐X 〈1 0 0〉 direction on the formation of stop band and microwave absorption ability were investigated in the frequency range from 3 to 30 GHz. Metallodielectric photonic crystals formed showed good absorption ability. The measured transmission spectra of the metallic and metallodielectric crystals agreed well with the simulation of the transmission line modeling method.

Multichannel Photonic Crystal Wavelength Filter Array for Near-Infrared Wavelengths

Multichannel wavelength filters consisting of 2-D photonic crystal (PhC) for the near-infrared wavelength region (~800 nm) are demonstrated. The filter is a thin-film wavy multilayer structure and is fabricated by the autocloning method, which is based on a radio frequency bias sputtering process. Twelve long-pass-type filter regions are integrated on a common silica substrate. Sharp cutoff characteristics and almost equal channel spacing are experimentally verified. To precisely control the effective lattice constant of PhC, a modulated lattice structure on the substrate is utilized

Structure Dependence of Mode Edges in Photonic CrystalWaveguide with Silicon on Insulator

The mode edges of photonic crystal waveguide with triangular latticebased on a silicon-on-insulator slab are investigated by combination ofthe effective index method and the two-dimensional plane wave expansionmethod. The variations of waveguide-mode edges with the structureparameters of photonic crystal are deduced. When the ratio of theradius of air holes to the lattice constant, r/Λ, is fixedand the lattice constant of photonic crystal, Λ, increases, thewaveguide-mode edges shift to longer wavelengths. When Λ is fixedand r/Λ increases, the waveguide-mode edges shift to shorterwavelengths. Additionally, when r/Λ and Λ are both fixed,the radius of the two-row air holes adjacent to the waveguideincreases, the waveguide-mode edges shift to shorter wavelengths.

Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure

A vertical-cavity surface-emitting laser with a two-dimensional photonic crystal (PC) structure has been investigated for single lateral mode operation. The PC confined mode can be controlled by the lattice constant, the hole diameter, the etching depth, and the defect structure. A seven-point defect structure is proposed to enhance the confinement effect, which is diluted by finite hole depth of the PC structure. We obtained a pure PC confined mode under room-temperature cw conditions with a PC lattice constant of 2 μm, hole diameters of 1.0 and 1.4 μm, and depths of 1.85 and 1.92 μm, respectively.