Complete Photonic Band Gap Research Articles

Miniaturized Bragg-grating couplers for SiN-photonic crystal slabs.

We report on an experimental and theoretical investigation of an integrated Bragg-like grating coupler for near-vertical scattering of light from photonic crystal waveguides with an ultra-small footprint of a few lattice constants only. Using frequency-resolved measurements, we find the directional properties of the scattered radiation and prove that the coupler shows a good performance over the complete photonic bandgap. The results compare well to analytical considerations regarding 1d-scattering phenomena as well as to FDTD simulations.

The Tunable Omnidirectional Reflector Based on Two-Dimensional Photonic Crystals With Superconductor Constituents

The properties of omnidirectional band gap (OBG) in the two-dimensional superconductor photonic crystals (SPCs) with triangular lattices, that are composed of the superconductor (Nb) rods in the dielectric background, are theoretically studied in detail based on the modified plane wave expansion method, as the electromagnetic wave with a off-plane angle. The calculated results demonstrate that not only the complete photonic band gap (PBG) and a flatbands region can be achieved but also the OBG can be observed. The influences of the radius of inserted rod, the dielectric background, the plasma frequency of superconductor, the damping coefficient of the superconductor, and the ambient temperature on the OBG are investigated, respectively. The simulations show that the tunable OBG can be obtained except for changing the damping coefficient of the superconductor. The features of OBG for the complementary structure also are discussed as the anisotropic materials are introduced. The analysis results show that the complete PBG also can be achieved in the large incidence angle region. These values provide the theoretical instructions to realize the omnidirectional reflector by the proposed SPCs.

Complete photonic band gaps and tunable self-collimation in the two-dimensional plasma photonic crystals with a new structure

In this paper, the properties of complete photonic band gaps (CPBGs) and tunable self-collimation in two-dimensional plasma photonic crystals (2D PPCs) with a new structure in square lattices, whose dielectric fillers (GaAs) are inserted into homogeneous and nomagnetized plasma background are theoretically investigated by a modified plane wave expansion (PWE) method with a novel technique. The novel PWE method can be utilized to compute the dispersion curves of 2D PPCs with arbitrary-shaped cross section in any lattices. As a comparison, CPBGs of PPCs for four different configurations are numerically calculated. The computed results show that the proposed design has the advantages of achieving the larger CPBGs compared to the other three configurations. The influences of geometric parameters of filled unit cell and plasma frequency on the properties of CPBGs are studied in detail. The calculated results demonstrate that CPBGs of the proposed 2D PPCs can be easily engineered by changing those parameters, and the larger CPBGs also can be obtained by optimization. The self-collimation in such 2D PPCs also is discussed in theory under TM wave. The theoretical simulations reveal that the self-collimation phenomena can be found in the TM bands, and both the frequency range of self-collimation and the equifrequency surface contours can be tuned by the parameters as mentioned above. It means that the frequency range and direction of electromagnetic wave can be manipulated by designing, as it propagates in the proposed PPCs without diffraction. Those results can hold promise for designing the tunable applications based on the proposed PPCs.

The Optical Transmission Characteristic of Hollow Carbon-Coated <named-content content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX">$\hbox{Fe}_{3}\hbox{O}_{4}$</tex-math></inline-formula></named-content> Colloidal Photonic Crystal

The optical transmission characteristics for the hollow carbon-coated Fe 3 O 4 colloidal photonic crystal have been calculated with the finite-difference time-domain (FDTD) method. We analyze the influence of the factors on the photonic band gap (PBG) that include lattice constant a, the number of the particles in propagating direction N y , the thickness of carbon layer H c and Fe 3 O 4 cluster layer H f , and the thickness ratio of the two layers. The results show that the PBGs red shift and the bandwidth first increases and then decreases with the increasing a. In the situation of increasing N y , the PBG changes from irregular to uniform, followed by the oscillations on both sides of the PBG growing in number and the deepened PBG in the low-frequency region. The PBGs move toward the low frequency direction with the increase of H c , and the optimal value of H c for the uniform color response is 10 nm ~25 nm. The PBGs red shift with the increasing H f , and the first bandwidth increases while the second decreases. The optimal H f for the ideal PBG is 35 nm ~55 nm. The stop bands move to the high-frequency direction with the increasing thickness ratio (H c : H f ), and the best ratio is 10 nm : 55 nm for the complete PBG and wider bandwidth.

Band Structure of Photonic Crystals Fabricated by Two-Photon Polymerization

We study theoretically the band-gap structures of several types of three-dimensional photonic crystals with the fcc lattice symmetry: synthetic opals, inverted yablonovite and woodpile. The samples of inverted yablonovite, inverted yablonovite with a glassy superstructure and woodpile are fabricated by two-photon polymerization through a direct laser writing technique, which allows the creation of complex three-dimensional photonic crystals with a resolution better than 100 nm. A material is polymerized along the trace of a moving laser focus, thus enabling the fabrication of any desirable three-dimensional structure by direct “recording” into the volume of a photosensitive material. The correspondence of the structures of the fabricated samples to the expected fcc lattices is confirmed by scanning electron microscopy. We discuss theoretically how the complete photonic band-gap is modified by structural and dielectric parameters. We demonstrate that the photonic properties of opal and yablonovite are opposite: the complete photonic band gap appears in the inverted opal, and direct yablonovite is absent in direct opal and inverted yablonovite.

Optical Properties of Gyroid Structured Materials: From Photonic Crystals to Metamaterials

The gyroid is a continuous and triply periodic cubic morphology which possesses a constant mean curvature surface across a range of volumetric fill fractions. Found in a variety of natural and synthetic systems which form through self‐assembly, from butterfly wing scales to block copolymers, the gyroid also exhibits an inherent chirality not observed in any other similar morphologies. These unique geometrical properties impart to gyroid structured materials a host of interesting optical properties. Depending on the length scale on which the constituent materials are organised, these properties arise from starkly different physical mechanisms (such as a complete photonic bandgap for photonic crystals and a greatly depressed plasma frequency for optical metamaterials). This article reviews the theoretical predictions and experimental observations of the optical properties of two fundamental classes of gyroid structured materials: photonic crystals (wavelength scale) and metamaterials (sub‐wavelength scale).

Topology optimization of simultaneous photonic and phononic bandgaps and highly effective phoxonic cavity

By using the non-dominated sorting-based genetic algorithm II, we study the topology optimization of the two-dimensional phoxonic crystals (PxCs) with simultaneously maximal and complete photonic and phononic bandgaps. Our results show that the optimized structures are composed of the solid lumps with narrow connections, and their Pareto-optimal solution set can keep a balance between photonic and phononic bandgap widths. Moreover, we investigate the localized states of PxCs based on the optimized structure and obtain structures with more effectively multimodal photon and phonon localization. The presented structures with highly focused energy are good choices for the PxC sensors. For practical application, we design a simple structure with smooth edges based on the optimized structure. It is shown that the designed simple structure has the similar properties with the optimized structure, i.e. simultaneous wide phononic and photonic bandgaps and a highly effective phononic/photonic cavity, see Figures 8(b) and 8(c).

Using microwave and macroscopic samples of dielectric solids to study the photonic properties of disordered photonic bandgap materials.

Recently, disordered photonic materials have been suggested as an alternative to periodic crystals for the formation of a complete photonic bandgap (PBG). In this article we will describe the methods for constructing and characterizing macroscopic disordered photonic structures using microwaves. The microwave regime offers the most convenient experimental sample size to build and test PBG media. Easily manipulated dielectric lattice components extend flexibility in building various 2D structures on top of pre-printed plastic templates. Once built, the structures could be quickly modified with point and line defects to make freeform waveguides and filters. Testing is done using a widely available Vector Network Analyzer and pairs of microwave horn antennas. Due to the scale invariance property of electromagnetic fields, the results we obtained in the microwave region can be directly applied to infrared and optical regions. Our approach is simple but delivers exciting new insight into the nature of light and disordered matter interaction. Our representative results include the first experimental demonstration of the existence of a complete and isotropic PBG in a two-dimensional (2D) hyperuniform disordered dielectric structure. Additionally we demonstrate experimentally the ability of this novel photonic structure to guide electromagnetic waves (EM) through freeform waveguides of arbitrary shape.

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Recently, disordered photonic materials have been suggested as an alternative to periodic crystals for the formation of a complete photonic bandgap (PBG). In this article we will describe the methods for constructing and characterizing macroscopic disordered photonic structures using microwaves. The microwave regime offers the most convenient experimental sample size to build and test PBG media. Easily manipulated dielectric lattice components extend flexibility in building various 2D structures on top of pre-printed plastic templates. Once built, the structures could be quickly modified with point and line defects to make freeform waveguides and filters. Testing is done using a widely available Vector Network Analyzer and pairs of microwave horn antennas. Due to the scale invariance property of electromagnetic fields, the results we obtained in the microwave region can be directly applied to infrared and optical regions. Our approach is simple but delivers exciting new insight into the nature of light and disordered matter interaction. Our representative results include the first experimental demonstration of the existence of a complete and isotropic PBG in a two-dimensional (2D) hyperuniform disordered dielectric structure. Additionally we demonstrate experimentally the ability of this novel photonic structure to guide electromagnetic waves (EM) through freeform waveguides of arbitrary shape.

Comparison of photonic bandgaps of two-dimensional periodic and quasi-periodic photonic crystals with different relative permittivity dielectric

Photonic bandgaps (PBGs) of two-dimensional (2D) triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals (PCs) have been analyzed, with a given scatterer radius and dielectric relative permittivity changing from 1 to 30 within air-cylinders-in-dielectric and dielectric-cylinders-in-air constructions. The results have shown that 2D quasi-periodic PC is more likely to generate PBG and complete PBG than 2D periodic PC. For the given scatterer radius and two constructions, PBG widths of the two types of 2D PCs vary little, whereas the corresponding center frequencies decrease in smooth “hyperbola-like” curves with dielectric relative permittivity increasing monotonically. The present results will guide the design of PBG-type microstructure photonic devices.

Three-dimensional photonic crystals created by single-step multi-directional plasma etching.

We fabricate 3D photonic nanostructures by simultaneous multi-directional plasma etching. This simple and flexible method is enabled by controlling the ion-sheath in reactive-ion-etching equipment. We realize 3D photonic crystals on single-crystalline silicon wafers and show high reflectance (>95%) and low transmittance (<-15dB) at optical communication wavelengths, suggesting the formation of a complete photonic bandgap. Moreover, our method simply demonstrates Si-based 3D photonic crystals that show the photonic bandgap effect in a shorter wavelength range around 0.6 μm, where further fine structures are required.

Study on the Properties of Switching Bandgap and Surface Plasmon Modes in 3-D Plasma Photonic Crystals With Pyrochlore Lattices in Core-Shell Structure

The interesting properties of surface plasmon modes and switching bandgap of 3-D photonic crystals (PCs) with pyrochlore lattices that are composed of the core isotropic and positive-index dielectric spheres surrounded by the plasma shells inserted in the air, are theoretically investigated in detail on the basis of the plane wave expansion method. Numerical simulations show that the proposed core-shell structure can obtain the complete photonic bandgaps (PBGs) and a flatbands region. Compared with the conventional lattices, such as diamond, face-centered cubic, body-centered cubic, and simple cubic lattices, the larger PBG can be achieved in the pyrochlore arrangement. The flatbands region is determined by the existence of surface plasmon modes. If the thickness of plasma shell is larger than a threshold value, the dispersive curves of such 3-D PCs will be similar to those obtained from the same structure containing the pure plasma spheres. In this condition, the inserted core spheres also will not affect the band structures. It is also provided that the upper edge of flatbands region does not depend on the topology of PCs. Our results also demonstrate that the PBG can be manipulated appropriately by the radius of core dielectric sphere and the plasma frequency, respectively. Thus, the PBG can be obtained by replacing the pure plasma spheres with proposed core-shell structures to fabricate possibly and save the material in the realization.

The Properties of Surface Plasmon Modes and Switching Gap for Extraordinary Mode in the 3-D Magnetized Plasma Photonic Crystals Based on the Voigt Effects

The properties of surface plasmon modes and switching gaps for extraordinary mode in the 3-D magnetized plasma photonic crystals (MPPCs) with body-centered-cubic lattices, that are composed of the core tellurium (Te) spheres with surrounded by the magnetized plasma shells inserted in the air, are theoretically investigated in detail by the plane wave expansion method, as the magneto-optical Voigt effects of magnetized plasma are considered (the incidence electromagnetic wave vector is perpendicular to the external magnetic field at any time). Our computing results show that the complete photonic bandgaps for extraordinary mode and two flatbands regions can be observed. The optical switching can be realized by such MPPCs, which can be tuned by the radius of core Te sphere, the plasma density and the external magnetic field, respectively. The flatbands regions are determined by the existence of surface plasmon modes. The numerical simulations also demonstrate that the interesting properties of surface plasmon modes can be found. If the thickness of magnetized plasma shell is larger than a threshold value, the band structures for extraordinary mode will be similar to those obtained from the same structure containing the pure magnetized plasma spheres. In this condition, the inserted core sphere also has no effect on the band structures. It is worth to be noticed that the upper edge frequencies of two flatbands regions will not depend on the topology of lattice. However, to the different topologies of lattices, if the thickness of magnetized plasma shell is close to zero, the frequencies of lower edges will be convergence to two different constants.

Template-assisted chemical synthesis of Au opal photonic crystal film with complete photonic band gaps in the visible

Three-dimensionally (3D) ordered Au sphere array (opal) films are fabricated through a combination of templating synthesis and chemical reduction deposition. First, large area crack free silica inverse opal films are prepared by the co-assembly of polystyrene (PS) colloidal spheres and silica precursor, followed by a thermal treatment to remove the PS and transform the precursor to silica; then Au is infiltrated into the void spaces of the silica inverse opal by chemical reduction deposition. Subsequent removal of the silica template produces 3D periodic arrays of Au spheres. The prepared Au opal photonic crystal film composed of~510nm diameter Au spheres possesses two complete photonic band gaps in the visible region.

The properties of unusual surface plasmon modes and switching gaps in the three-dimensional photonic crystals composed of plasma-coated spheres

In this paper, the surface plasmon modes and switching gaps of three-dimensional (3D) photonic crystals (PCs) with diamond lattices, which are composed of core isotropic dielectric spheres surrounded by plasma shells inserted in air, are theoretically investigated in detail based on a modified plane wave expansion method. The equations for computing band structures for such 3D PCs are presented. Our analyses show that the proposed double-shell structure can produce the complete photonic band gaps (PBGs) which can be worked as an optical switching by manipulating the parameters of such PCs. However, the switching state cannot be tuned by the plasma collision frequency. Numerical results also demonstrate that a flatbands region and the stop band gaps (SBGs) in the (1 0 0) and (1 1 1) directions which are above the flatbands region can be achieved. The SBGs also can be tuned by the parameters as mentioned above. There is also a threshold value for the thickness of plasma shell, which can make the band structures of the 3D PCs with double-shell structures similar to those obtained from the same PC structure containing the pure plasma spheres. In this case, the dielectric function of the inserted core sphere will not affect the band structures. It means that the PBGs can be achieved by replacing the pure plasma spheres with such double-shell structures to make fabrication possible and save the material in the realization. It is also noticed that the flatbands region is determined by the existence of surface plasmon modes, and the upper edge of flatbands region does not depend on the topology of lattice.

The properties of the extraordinary mode and surface plasmon modes in the three-dimensional magnetized plasma photonic crystals based on the magneto-optical Voigt effects

In this paper, the properties of the extraordinary mode and surface plasmon modes in the three-dimensional (3D) magnetized plasma photonic crystals (MPPCs) with face-centered-cubic lattices that are composed of the core tellurium (Te) spheres with surrounded by the homogeneous magnetized plasma shells inserted in the air, are theoretically investigated in detail by the plane wave expansion method, as the magneto-optical Voigt effects of magnetized plasma are considered (the incidence electromagnetic wave vector is perpendicular to the external magnetic field at any time). The optical switching or wavelength division multiplexer can be realized by the proposed 3D MPPCs. Our analyses demonstrate that the complete photonic band gaps (PBGs) and two flatbands regions for the extraordinary mode can be observed obviously. PBGs can be tuned by the radius of core Te sphere, the plasma density and the external magnetic field. The flatbands regions are determined by the existence of surface plasmon modes. Numerical simulations also show that if the thickness of magnetized plasma shell is larger than a threshold value, the band structures of the extraordinary mode will be similar to those obtained from the same structure containing the pure magnetized plasma spheres. In this case, the band structures also will not be affected by the inserted core spheres. It is also provided that the upper edges of two flatbands regions will not depend on the topology of lattice. However, the frequencies of lower edges of two flatbands regions will be convergent to the different constants for different lattices, as the thickness of magnetized plasma shell is close to zero.

Geometric Modeling of Ceramics Dendrites to Modulate Energy and Material Flows by Using Stereolithography

Through computer aided design, manufacturing and evaluation, various ceramics dendrites with spatially ordered micro cavities were successfully fabricated by utilizing stereolithography. Micrometer order ceramic lattices were propagated spatially in computer graphic space. Ceramics nanoparticles were dispersed in to photo sensitive liquid resins to obtain thixotropic slurries. The paste material was spread on a grass substrate by using a mechanical knife edge, and an ultra violet micro pattern was exposed to create cross sectional solid layer. After the layer stacking process, the obtained composite precursor was dewaxed and sintered in an air atmosphere. By the micro patterning stereolithography, solid electrolyte dendrites of yttria stabilized zirconia with spatially ordered porous structures were fabricated for fuel cell miniaturizations. Gaseous fluid profiles and pressure distributions in the formed ceramic lattices with various porosity percent were visualized and analyzed by a finite element method. Subsequently, alumina micro photonic crystals with a diamond lattice structure were fabricated. Electromagnetic wave properties were measured by using a terahertz time domain spectroscopy. A complete photonic band gap was exhibited, and a localized mode to select the wavelength was obtained by introducing a defect cavity.

Angled etching of (001) rutile Nb–TiO2 substrate using SF6-based capacitively coupled plasma reactive ion etching

We demonstrated the plasma etching of a (001) rutile Nb–TiO2 substrate using SF6 plasma. A vertical etching profile and a smooth etched surface were obtained. In addition, the angled etching of a (001) rutile Nb–TiO2 substrate was achieved in a conventional SF6 reactive ion etching system for the first time. The etching angle was determined by the angle of the groove of the holder. We believe that our simple dry etching technique is suitable for the formation of a three-dimensional photonic crystal with complete photonic bandgap (CPBG) and optical waveguides.

Study on the anisotropic photonic band gaps in three-dimensional tunable photonic crystals containing the epsilon-negative materials and uniaxial materials

In this paper, the properties of anisotropic photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) composed of the anisotropic positive-index materials (the uniaxial materials) and the epsilon-negative (ENG) materials with body-centered-cubic (bcc) lattices are theoretically studied by a modified plane wave expansion (PWE) method, which are the uniaxial materials spheres inserted in the epsilon-negative materials background. The anisotropic photonic band gaps (PBGs) and one flatbands region can be achieved in first irreducible Brillouin zone. The influences of the ordinary-refractive index, extraordinary-refractive index, filling factor, the electronic plasma frequency, the dielectric constant of ENG materials and the damping factor on the properties of anisotropic PBGs for such 3D PCs are studied in detail, respectively, and some corresponding physical explanations are also given. The numerical results show that the anisotropy can open partial band gaps in such 3D PCs with bcc lattices composed of the ENG materials and uniaxial materials, and the complete PBGs can be obtained compared to the conventional 3D PCs containing the isotropic materials. The calculated results also show that the anisotropic PBGs can be manipulated by the parameters as mentioned above except for the damping factor. Introducing the uniaxial materials into 3D PCs containing the ENG materials can obtain the larger complete PBGs as such 3D PCs with high symmetry, and also provides a way to design the tunable devices.

Optical switching realized in three-dimensional unusual surface-plasmon-induced photonic crystals composed of plasma-coated spheres

In this paper, the dispersive properties and switching state of three-dimensional (3D) photonic crystals (PCs) with face-centered-cubic lattices, which are composed of core anisotropic dielectric (tellurium) spheres surrounded by non-magnetized plasma shells inserted in the air, are theoretically investigated in detail based on a modified plane wave expansion method. The equations for calculating the band structures for such 3D PCs are deduced. Our analyses show that the proposed double-shell structures can produce the complete photonic band gaps (PBGs) which can work as the optical switching by manipulating the radius of core dielectric sphere and the plasma frequency. However, the switching state of PCs cannot be tuned by the thickness of the plasma shell and plasma collision frequency as the radius of the core dielectric sphere is certain. Numerical simulations also demonstrate that a flatbands region, and the stop band gaps (SBGs) in the (100) and (111) directions which are above the flatbands region can be achieved. The SBGs in the (100) and (111) directions can also be tuned by the parameters as mentioned above. There is also a threshold value for the thickness of plasma shell, which makes the band structures of such 3D PCs with double-shell structures to be similar to those obtained from the same PCs containing the pure plasma spheres. In this condition, the dielectric function of inserted core sphere will not affect the band structures. It means that the PBGs can be achieved by replacing the pure plasma spheres with such double-shell structures to make fabrication possible and save the material in the realization. It is also noted that the flatbands region is determined by the existence of surface plasmon modes, and the upper edge of flatbands region does not depend on the topology of lattice. The proposed 3D PCs with double-shell structures offer a novel way to realize the tunable optical switching.