Absolute Band Gap Research Articles

Experimental observation of resonant filtering in a two-dimensional phononic crystal waveguide

Abstract Transmission of acoustic waves through a two-dimensional composite material made of PVC cylinders surrounded by air is measured experimentally. The spectrum presents a very large absolute band gap in the audible frequency range. A waveguide created inside this phononic crystal by removing a row of cylinders can transmit very efficiently the waves falling inside the stop band. We show the existence of deaf modes in the band structure of the linear waveguide. Resonant filtering is also demonstrated experimentally by coupling the waveguide to a side branch resonator of variable length. Frequency filtering is observed in the form of narrow dips in the transmission spectrum of the waveguide. Most of these observations compare favorably with theoretical calculations of dispersion curves and transmission coefficients of model structures using the plane wave expansion and the finite difference time domain methods. Narrow dips similar to those of the guide with resonator are also observed in the transmission spectrum of a waveguide with a sharp bend.

The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice

The photonic band structures of a two-dimensional photonic crystal consisting of a honeycomb lattice with triangular dielectric rods embedded in air are studied numerically. In a honeycomb lattice, the largest absolute photonic bandgap is achieved by the use of triangular rods which have the same shape as that of the coordination polygon of a lattice point; the reason why triangular dielectric rods in a honeycomb lattice can generate the largest gap is also discussed.

Resonance modes and gap formation in a two-dimensional solid phononic crystal

The resonance modes near the edges of the first absolute band gap of a two-dimensional solid phononic crystal with an epoxy host are investigated in this paper. A rotary resonance mode, induced by the joint effect of the Bragg and Mie scattering, is observed near the bottom of the gap. The gap, resulting from the interaction between the rigid-body resonance and the effective homogeneous medium, coalesces with the Bragg gap, which leads to the formation of a wide gap. Then a simple analytical model is introduced to give a physically intuitive account of the rotary resonance. Finally, the effects of the array and the filling fraction on the band gap are explained by the conditions for occurrence of the resonance.

Absolute luminescence efficiency and photonic band-gap effect of conjugated polymers with top-deposited distributed Bragg reflectors

We study the effects of the deposition of a photonic crystal (PhC) structure, namely a distributed Bragg reflector, on a light-emitting conjugated polymer. The hybrid organic/PhC system is realised by a novel low-temperature reactive electron beam deposition, suitable for the direct fabrication of high-reflective mirrors onto organic soft matter. We investigated the photoluminescence absolute quantum efficiency of the system, finding a yield of 30% after the mirror deposition. We found evidence for the modulation of the output spectra by the photonic band-gap of the coupled PhC, and for the polarisation splitting (as large as 140 meV) of the emitted light.

Role of electronic band structure and resonances on electron-scattering. The case of the hydrogenated polycrystalline diamond

Elastic and inelastic scattering of low energy electrons by hydrogenated and deuterated polycrystalline diamond surfaces was studied by high resolution electron energy loss spectroscopy (HREELS). Energy loss spectra extending up to 800 meV and elastic/inelastic excitation functions, intensity variations of the elastic peak/energy-loss peaks as a function of the incident electron energy, have been measured quasi-continuously over the range 3–17 eV. Their compared behaviors are analyzed taking into account the influence of the electronic band structure of the sample. Electron elastic reflectivities are characterized by an intense broad peak at 13.5 eV incident electron energy, which results from the very high backscattering probability associated with the second absolute band gap of bulk diamond. Excitation functions of the stretching vibration mode of the hydrogen or deuterium terminations present a shoulder at about 4.5 eV and two broad peaks located around 8.0 and 12.8 eV incident electron energy. Significant resonant scattering processes contribute to the vibrational excitation at 4.5 and 8.0 eV: a strong progression of multiple excitation losses has in particular been observed in the energy loss spectrum acquired at the former energy, and a bell shape peak characteristic of a negative ion resonance has been observed at the latter energy in the stretching excitation functions. The peak at 12.8 eV is interpreted as a maximum induced by the resonant electron reflectivity enhancement, which results from the dramatic variation of the density of states corresponding to the diamond second absolute band gap.

Analysis of photonic band gaps in two-dimensional photonic crystals with rods covered by a thin interfacial layer

We investigate different aspects of the absolute photonic band gap (PBG) formation in two-dimensional photonic structures consisting of rods covered with a thin dielectric film. Specifically, triangular and honeycomb lattices in both complementary arrangements, i.e., air rods drilled in silicon matrix and silicon rods in air, are studied. We consider that the rods are formed of a dielectric core (silicon or air) surrounded by a cladding layer of silicon dioxide $({\mathrm{SiO}}_{2})$, silicon nitride $({\mathrm{Si}}_{3}{\mathrm{N}}_{4})$, or germanium $\mathrm{(Ge)}$. Such photonic lattices present absolute photonic band gaps, and we study the evolution of these gaps as functions of the cladding material and thickness. Our results show that in the case of air rods in dielectric media the existence of dielectric cladding reduces the absolute gap width and may cause complete closure of the gap if thick layers are considered. For the case of dielectric rods in air, however, the existence of a cladding layer can be advantageous and larger absolute PBG's can be achieved.

Optical Properties of Nanoparticle‐Based Metallodielectric Inverse Opals

Metallodielectric inverse opals were prepared by co-crystallizing silica-coated gold nanoparticles and polymer spheres, followed by removal of the crystal template. The inverse opals exhibit a distinct reflectance peak, which results from Bragg diffraction due to the highly ordered 3D macroporous structure. Photonic band-structure calculations indicate that the characteristic reflectance peaks observed are signatures of the directional gap at the L point. It is demonstrated that the optical properties (the position and magnitude of the electromagnetic bandgaps) of the gold-silica nanocomposite inverse opals can be engineered by varying the nanoparticle morphology (core size and shell thickness) and/or the nanoparticle volume-filling ratio of the composite. The use of metallodielectric nanoparticles to form inverse opals offers a versatile approach to prepare photonic materials that may exhibit absolute bandgaps.

The effects of shapes and symmetries of scatterers on the phononic band gap in 2D phononic crystals

The phononic band structures of two-dimensional solid phononic crystals consisting of lattices with different symmetry and scatterers of various shapes, orientations, and sizes are studied numerically. Specifically, three types of lattices (triangular, hexagonal and square) and four different shapes of scatterers (hexagon, circle, square and triangle) are considered. Given a lattice symmetry, the largest absolute phononic band gap is achieved when the scatterer has the same shape and orientation as that of coordination polygon of a lattice point; e.g., hexagonal rods in triangular lattices, triangular rods in honeycomb lattices and square rods in square lattices. The band gap can be varied by adjusting the orientation and size of the scatterers; if the maximum allowed filling fraction of scatterers increases after rotation, the normalized gap width will enlarge, otherwise the normalized gap width will decrease.

Band gaps of two-dimensional photonic crystal structure using fullerene films

The concept and method of analysis of photonic crystals and band gaps are introduced into fullerene-film network structure, which is treated theoretically as a photonic crystals. We investigate different aspects of the absolute photonic band gap (PBG) formation for 2D photonic crystals (PC) consisting of air rods drilled into fullerene films. Specifically, square lattices and triangular structure are considered. The formation of PBG is exhibited and confirmed by a calculation of the transfer matrix method (TMM). We find that fullerene based networks could be good candidates for absolute inhibition of transmission in the visible frequency range for given orientations.

Elastic wave propagation along waveguides in three-dimensional phononic crystals

We investigate theoretically using the finite difference time domain method acoustic wave propagation along waveguides in three-dimensional phononic crystals constituted of lead spherical inclusions on a face-centered cubic lattice embedded in an epoxy matrix. The transmission spectra of the perfect phononic crystal for transverse and longitudinal acoustic waves are shown to depend strongly on the direction of propagation. The crystal possesses an absolute band gap. Waveguides oriented along different crystallographic directions, namely the k100l and k111l directions, exhibit pass bands in the phononic crystal band gaps for both transverse and longitudinal polarizations.

Effects of symmetry reduction in two-dimensional square and triangular lattices

We investigate the absolute photonic band gap (PBG) formation in two-dimensional (2-D) photonic crystals designed using symmetry reduction approach. The lattice symmetry, shape and orientation of dielectric scatterers affect the photonic gap parameters. We use symmetry reduction, achieved either by including additional rods into the lattice unit cell or by reorienting noncircular scatterers to engineer the photonic band gaps in 2-D square and triangular structures. The case of air rods drilled into silicon background is considered. We show that for square structures symmetry reduction can be an effective way to enlarge the absolute PBG, but for triangular lattices any modification of the crystal structure considerably reduces the absolute PBG width. We also discuss the practical technological feasibility of the proposed structures.

Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials.

We theoretically investigate the photonic band structure of one-dimensional superlattices composed of alternating layers of right-handed and left-handed materials (RHM and LHM). The dispersion curves are mainly studied by assuming that the dielectric permittivity and magnetic permeability are constant in each layer. It is shown that such structures can exhibit new types of electromagnetic modes and dispersion curves that do not exist in usual superlattices composed only of RHM. In particular, we emphasize the possibility of bands that originate from the interface modes localized at the boundary between a LHM and RHM or from confined modes in one type of layers. These waves are evanescent in both or in one constituent of the superlattice. One of the pass bands may lie below the light lines of the constituting material and go down to the static limit of a vanishing frequency omega, even at a value of the wave vector k(//) (parallel to the layers) that is different from zero. For a given value of the wave vector k(//), the dispersion curves omega versus k(z) (where k(z) is the Bloch wave vector of the periodic system along the axis of the superlattice) may exist only in a limited part of the superlattice Brillouin zone and exhibit a zigzag behavior instead of a monotonic behavior as in usual superlattices. With an appropriate choice of the parameters, we show that it is possible to realize an absolute (or omnidirectional) band gap for either transverse electric (TE) or transverse magnetic (TM) polarization of the electromagnetic waves. A combination of two multilayer structures composed of RHM and LHM is proposed to realize, in a certain range of frequency, an omnidirectional reflector of light for both polarizations.

Three absolute photonic gaps from 2d square compound lattices

AbstractThe photonic band structures of two‐dimensional square compound lattices are calculated by the plane‐wave method. Four air hole cylinders drilled in a square dielectric cylinder which locate at each square lattice site are embedded in a background of air. Three absolute photonic band gaps common to E and H polarized waves are created when given proper structure parameters. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fabrication of Ceramic Photonic Crystals with Diamond Structure for Microwave Applications

A process for fabricating three‐dimensional photonic crystals composed of SiO2–TiO2‐based ceramics with a diamond structure was investigated. An epoxy structure having an inverse diamond configuration was fabricated by stereolithography, a rapid prototyping method. The epoxy structure was infiltrated with a ceramic slurry and then cold isostatically pressed. After sintering at 670°C for 5 h in air, the epoxy was burned off, leaving behind the desired structure of a ceramic photonic crystal. The calculated band diagram indicated that an absolute photonic band gap for all wave vectors existed. The measurement of transmission in the 〈100〉 direction from 10 to 20 GHz showed that a complete band gap formed at about 14.7–18.5 GHz. The magnitude of the maximum attenuation was as large as 30 dB at 17 GHz, which indicated that the fabricated structure worked well as a photonic crystal.

Design for 2D anisotropic photonic crystal with large absolute band gaps by using a genetic algorithm

A 2-state genetic algorithm (GA) approach is used to design a two-dimensional (2D) anisotropic photonic crystal of square lattice with a maximal absolute band gap. The unit cell is devided equally into many small squares, and each filling pattern of squares with two dielectric materials corresponds to a binary number. As a numerical example, the GA gives a 2D Te structure with a relative width of the absolute band gap of about 23%. After a further optimization, a new structure is obtained with a relative width of the absolute band gap of about 28%.

Comparative studies on photonic band structures of diamond and hexagonal diamond usingthe multiple scattering method

Photonic band structures are investigated for both diamond and hexagonal diamondcrystals composed of dielectric spheres, and absolute photonic band gaps (PBGs)are found in both cases. In agreement with both Karathanos and Moroz’scalculations, a large PBG occurs between the eighth and ninth bands in diamondcrystal, but a PBG in hexagonal diamond crystal is found to occur between thesixteenth and seventeenth bands because of the doubling of dielectric spheresin the primitive cell. To explore the physical mechanism of how the photonicband gap might be broadened, we have compared the electric field distributions(|E|2) of the ‘valence’ and ‘conduction’ band edges. Results show that the field intensity for the‘conduction’ band locates in the inner core of the sphere while that of the ‘valence’ bandconcentrates in the outer shell. With this motivation, double-layer spheres aredesigned to enhance the corresponding photonic band gaps; the PBG is increased by35% for the diamond structure, and 14% for the hexagonal diamond structure.

Theoretical studies on the transmission and reflection properties of metallic planar fractals

We describe a systematic finite-difference-time-domain study on the electromagnetic (EM) characteristics of a specific type of planar metallic fractal patterns. These fractals are shown to totally reflect EM waves at a series of frequencies; between any two reflection frequencies there can be total transmission at some particular frequency. We show that both reflection and transmission are induced by local resonances, and develop an effective medium model to reproduce the simulation results. A double stack of 90°-rotated fractals is shown to exhibit absolute band gaps independent of both the polarization and incidence angles. In particular, the size of the band gaps can be significantly enlarged by multilayer stacking, and the fractal sample size can be significantly smaller than the relevant band gap wavelength.

Guide modes at interface of photonic crystal heterostructures composed of different lattices

We have investigated the guide modes in two kinds of two-dimensional photonic crystal heterostructures by using the plane wave expansion method combined with the supercell technique. These heterostructures consist of different air cylinders embedded into host dielectric in different lattices. Namely, One heterostucture is composed of square cylinders in square lattice and hexagon cylinders in triangular lattice (SSTH heterostucture). The other heterostucture is composed of rectangular cylinders in rectangular lattice and circle cylinders in triangular lattice(RRTC heterostucture). We find that the SSTH heterostucture may produce guide modes in absolute photonic band gap (PBG) when introducing relative longitudinal gliding or transverse displacement of the sub-lattices along the interface of the heterostructure. But the RRTC heterostucture can produce guide modes in absolute PBG without any relative longitudinal gliding or transverse displacement. This feature is quite different from other pure dielectric photonic crystals heterostructures.

A two-dimensional photonic crystal formed by a triangular lattice of square dielectric rods with a large absolute band gap

A two-dimensional photonic crystal formed by a triangular lattice of square dielectric rods with a large absolute band gap

Role of electronic band structure and resonances on electron reflectivity and vibrational excitation functions: The case of hydrogenated diamond

We report on an high resolution electron energy loss study of electron surface reflectivity and excitation of the C-H stretch mode of hydrogenated polycrystalline diamond films at low energy. Their specular energy dependences demonstrate that (i) the reflectivity is dominated by the conduction band structure. In particular the second absolute band gap of bulk diamond results in a strong increase of the elastic backscattered intensity around 13.5 eV. (ii) The vibrational excitation is dominated by a negative ion resonance process around 8 eV and a band gap induced scattering enhancement around 13 eV.