Analytical solution for the field in photonic structures containing cubic nonlinearity

In this work, we consider the exact solution of the stationary cubic nonlinear equation in a semi-infinite nonlinear medium in contact with a one-dimensional photonic crystal. Two kinds of analytical solutions are found for an arbitrary magnitude of the nonlinearity: a standing-wave-like one containing the inverse elliptic function Eli(?∣m), and a one-wave-type solution for transmitted TE-polarized waves. An approximate two-wave solution is proposed to describe the field propagation through the nonlinear film covering the photonic crystal. It is shown that the problem of a mixed linear-nonlinear structure may be reduced to a transcendental kernel equation determining the field inside the nonlinear part of the medium. The light reflection from a Si/SiO₂ layered structure in contact with an optically nonlinear medium is calculated. The angular-frequency photonic band diagram and power dependency are investigated. Local interface waveguide modes are considered.     

Enhanced omni-directional reflection frequency range in Si-based one dimensional photonic crystal with defect

In the present communication, we study omni-directional reflection in one-dimensional photonic crystal (PC) based on Si/SiO₂ multilayered structure. It has been shown numerically that it is possible to enhance the range of omni-directional reflection in one-dimensional photonic crystal appreciably by introducing a defect in the multilayered structure.     

Large range of omni-directional reflection in 1D photonic crystal heterostructures

A simple design of one-dimensional omni-directional reflector based on photonic crystal heterostructures structure has been proposed. The proposed structure consists of a periodic array of alternate layers of SiO₂ and Te as the materials of low and high refractive indices, respectively. The structure considered here has three stacks of periodic structures having five layers each. The lattice period of successive stack is increased by a certain multiple (say gradual constant, δ) of the lattice period of the just preceding stack. For numerical computation, the method of transfer matrix method (TMM) has been employed. It is found that such a structure has wider reflection bands in comparison to a conventional dielectric PC structure and the width of the omni-directional reflection (ODR) bands can be enlarged by increasing the value of the gradual constant δ.     

One dimensional photonic band gap material as an omnidirectional reflector

In this article, the reflection properties in one-dimensional dielectric-dielectric photonic band gap (PBG) structure have been studied. We have used SiO₂ as material of low refractive index and Te as a high refractive index material. Reflectivity of proposed PBG structure is plotted as a function of wavelength and angle of incidence and omni-directional PBGs are computed theoretically. To obtain reflectance, we used transfer matrix method for solving Maxwell’s equations for electromagnetic wave in PBG structures. For a large range of frequency, the PBG structure is found to exhibit omni-directional reflection which can be exploited in devices such as optical resonators, mirrors, etc.     

Impact of organic contamination on laser-induced damage threshold of high reflectance coatings in vacuum

The influence of organic contamination in vacuum on the laser-induced damage threshold (LIDT) of coatings is studied. TiO₂/SiO₂ dielectric mirrors with high reflection at 1064 nm are deposited by the electron beam evaporation method. The LIDTs of mirrors are measured in vacuum and atmosphere, respectively. It is found that the contamination in vacuum is easily attracted to optical surfaces because of the low pressure and becomes the source of damage. LIDTs of mirrors have a little change in vacuum compared with in atmosphere when the organic contamination is wiped off. The results indicate that organic contamination is a significant reason to decrease the LIDT. N₂ molecules in vacuum can reduce the influence of the organic contaminations and prtectect high reflectance coatings.     

Omni directional reflectance properties of superconductor-dielectric photonic crystal

The omnidirectional reflection properties in one dimensional superconductor-dielectric photonic crystal have been studied theoretically. In this present communication, the superconductor-dielectric photonic crystal in one dimension having alternate regions of superconductor-dielectric. The reflectance behaviors from these periodic multilayered structures are calculated for different angles of incidence. The reflectance and band structure is obtained by solving a Maxwell's equation using a translational matrix method. The study of reflectance bands of such superconductor-dielectric photonic crystal show that it can be used as broad band reflector.     

Equations for filling factor estimation in opal matrix. Addendum to “Deep level emission of ZnO nanoparticles deposited inside UV opal”, [Opt. Commun. 259 (1) (2006) 378-384]

We consider two equations for the filling factor estimation of infiltrated zinc oxide (ZnO) in silica (SiO₂) opal and gallium nitride (GaN) in ZnO opal. The first equation is based on the effective medium approximation, while the second one—on Maxwell-Garnett approximation. The comparison between two filling factors shows that both equations can be equally used for the estimation of the quantity of infiltrated nanoparticles inside opal photonic crystal.     

Large forbidden band in one-dimensional multi-layered structure containing exponentially graded materials

In the present communication, we have presented band spectra and reflectance properties of one-dimensional multi-layered structure containing dielectric exponentially graded and simple dielectric layers. This study has been performed theoretically by using transfer matrix method. In this paper we have taken the multi-layered structure where refractive index of odd layers is varying continuously along the direction perpendicular to the surface of the layer in exponential form. The effect of the graded profiles are studied and compared with the conventional multi-layered structure of suitable contrast of refractive indices in detail. In this study the materials are considered as non-magnetic and layers other than the graded are taken to be homogeneous and isotropic dielectric medium of constant refractive index. It has been found that the introduction of graded layers enhanced the forbidden band gaps and affects the reflectance of electromagnetic wave spectra significantly. By changing the grading profiles and the contrast, we obtained the forbidden band gaps and the reflectance of such structural change accordingly. Therefore, introducing a graded exponential layer of dielectric in the one-dimensional multi-layered structure provides possible mechanism for enhancing the reflectance as well as the forbidden gap in the optical region. Such multi-layered structure may be useful in the design of a broadband filter.     

Photonic band structure and effect of ε and μ on the reflectivity of one-dimensional magnetic photonic crystal structure

In this paper, we study the photonic band structure and reflection properties in one-dimensional magnetic photonic crystals (MPCs). Investigation of dispersion characteristics shows that in the case of MPCs, photonic band gaps arise due to the contrast in the wave impedance, not due to the contrast in the refractive index, while contrast in the refractive index of the two layers decides the position and number of the band gaps. We also study the effect of permittivity and permeability on reflection bands, which shows that the structure that has larger values of magnetic permeability (μ) than dielectric permittivity (ε) have wider TM-reflection bands, whereas the structure for which ε is greater than μ has wider TE-reflection bands. But the gap to mid-gap frequency ratio for TM-reflection bands is larger than TE-reflection bands. Thus, magnetic permeability has greater impact on the reflectivity of MPCs than dielectric permittivity. Finally, the analysis of the omni-reflectance in MPCs has also been studied.     

Optical properties and photonic bands of GaAs photonic crystal waveguides with tilted square lattice

Reflectance measurements at variable angle of incidence are performed on GaAs photonic crystal waveguides with unconventional square lattices. The technique yields the dispersion of photonic bands for the investigated lattices, as first shown by Astratov et al. [Phys. Rev. B 60, R16225 (1999)]. A sample with a square lattice of air rings and small air fraction yields narrow resonant structures and a dispersion of photonic modes close to that of free photons. Another sample with a square lattice of dielectric squares and large air fraction leads to broader structures and to a dispersion of photonic modes which differs strongly for the two polarizations of light: this sample has a pseudo-gap around 1 micron wavelength. The experimental results are in good agreement with theoretical calculations of the reflectance and of the photonic mode dispersion in the photonic crystal slabs. Received 16 January 2002     

Quantum electron plasma in one-dimensional metallic–dielectric photonic crystal

The interaction of the electromagnetic radiation with one-dimensional photonic crystal consisting of metal and transparent dielectric medium is studied numerically. Dielectric permeabilities of the electron plasma in the metal are considered both in the quantum Mermin and in the classical Drude–Lorentz approaches. It is shown that the reflection, transmission and absorption-frequency zones of electromagnetic radiation appear in the photonic crystal. In addition, the reflectance, transmittance and absorptance optical coefficients for such photonic crystal in the quantum approach differ from those coefficients in the Drude–Lorentz approach.     

Isotropic photonic bandgap in Penrose textured metallic mircocavity

Photonic microcavity has modified photonic modes that have intense localized electric field, which can couple strongly with the embedded emission centers. In this work, we fabricated 2D photonic microcavities with Penrose quasicrystal pattern with 10-fold symmetry. Organic luminescence material tris(8-hydroxyquinoline) aluminum (Alq₃) was embedded into the microcavity and the angle resolved transmission (ART) and photoluminescence (ARPL) spectra of the microcavity were measured. The results showed that the normal Gaussian photoluminescence spectrum of Alq₃ has been strongly modified by the microcavity dispersion characteristic. In addition, omni-directional photonic band gap exists in the microcavity. The higher symmetry of Penrose quasicrystal pattern means that there was minimal difference in the directional dispersion characteristics.     

Optical properties of organic-inorganic hybrid films prepared by the two-step growth process

Thin films of microcrystalline (C₈H₁₇NH₃)₂PbBr₄ have been prepared by the two-step growth process as follows: (1) precipitation of nanometer-sized PbBr₂ particles on substrates by vapor deposition and then (2) growth of (C₈H₁₇NH₃)₂PbBr₄ films by exposing PbBr₂ particles to C₈H₁₇NH₃Br vapor. Atomic force microscope observations reveal that the substrate is fully covered with nanometer-sized rodlike precipitates. X-ray diffraction studies suggest that (C₈H₁₇NH₃)₂PbBr₄ films are found to be microcrystalline form, single phase and highly oriented with the c-axis perpendicular to the substrate surface. (C₈H₁₇NH₃)₂PbBr₄ films show a clear exciton absorption and free-exciton emission even at room temperature. At low temperatures below 40 K, the emission band separates into three bands at 3.07 (A-band), 3.14 (B-band) and 3.20 (C-band) eV, respectively. Both A- and C-bands correspond to the free-exciton emission with large binding energies. On the contrary, time-resolved PL spectra indicate that the B-band is attributed to phosphorescence formed by the intersystem crossing.     

A comparative study of dispersion relation of EM waves in ternary one-dimensional plasma photonic crystals having two different structures

In this paper, a rigorous theoretical analysis has been made to study the dispersion relation of EM waves in periodic ternary one-dimensional photonic crystal having two different structures. In one case we have chosen glass-plasma and ZnS in one unit cell and in other case we have considered glass-plasma and M_gF₂ in one unit cell. Using Kronig-Penney model the dispersion relation for proposed structures has been obtained and numerical results are presented in the form of dispersion curves. The dependence of photonic band gap (PBG) characteristics on plasma frequency, plasma width and the width of dielectric media are discussed in the light of frequency gap and cutoffs of binary one-dimensional plasma photonic crystal. An attempt has been made to show how the PBG characteristic of a particular structure changes when the dielectric materials of its unit cell is changed by the other dielectric material. It is found that the structure having glass-plasma-ZnS in unit cell is more useful for broad band filtering and other plasma functioning devices compared to the structure having glass-plasma-MgF₂ in one unit cell.     

Polarization catastrophe in nanostructures doped in photonic band gap materials

In the presence of the dipole-dipole interaction, we have studied a possible dielectric catastrophe in photonic band gap materials doped with an ensemble of four-level nanoparticles. It is found that the dielectric constant of the system has a singularity when the resonance energy lies within the bands. This phenomenon is known as the dielectric catastrophe. It is also found that this phenomenon depends on the strength of the dipole-dipole interaction.     

Multilayer dielectric cylindrical mirrors based on omnidirectional reflection from a one-dimensional photonic crystal

A multilayer dielectric cylindrical mirror (MDCM) based on the one-dimensional omnidirectional reflection of a photonic crystal is presented. In this case, the refractive indices of the two materials are 1.6 (polystyrene) and 4.6 (tellurium), and the corresponding optimized thicknesses are 0.75a and 0.25a. A very high reflectance over a wide frequency range is observed. In this case, a is the lattice constant of the photonic crystal. In this band, the MDCM has good reflection and focal properties. Therefore, it is feasible to use the MDCM for integrated waveguide devices. As an example, an etched diffraction grating demultiplexer based on the MDCM is also proposed. Both the operational principle and design of the device are introduced. This provides a method for designing compact integrated waveguide devices.     

The theory of cylindrical photonic wires

The energy modes for a photonic nanowire have been studied and calculated. We model our photonic crystals after Noda et al. (1999) [18] where logs of semiconductor material are stacked to produce photonic band gaps in both the near and far infrared regions. A nominal dispersion relation was adopted in order to achieve qualitatively useful results. Photonic wires were modeled in two schemes, each with two specific geometries. In the first scheme, a pillar of one photonic crystal is embedded in a larger photonic crystal to produce a wire. This pillar was modeled as having either a square or a circular cross-section. The photonic crystals considered consisted of varying proportions of Ga_xAl_1−xAs, so that the wire could be adjusted. The second scheme investigated was a dielectric material for the central pillar, rather than a photonic crystal. Again, circular and square cross sections were considered. It was found that many more modes fit into the near infrared band gap than the far infrared band gap, and that a circular cross-section permits fewer modes. Finally, a dielectric pillar allows for a wire which is physically much smaller than a wire with a photonic crystal in the middle. As many photonic devices include such wires, these qualitative results could be useful in their design.     

Optimization of two-photon absorption enhancement in one-dimensional photonic crystals with defect states

One-dimensional photonic crystals with a defect layer of CdS were fabricated. The observed enhancement of two-photon absorption (TPA) in the CdS layer can be attributed to the intensified optical field confined within the defect layer of the photonic crystal. The results show that the enhancement of TPA coefficient depends basically on the number of periods of the photonic crystal and the defect mode position in the photonic band gap. The observation agrees qualitatively with the expectations of a computation by matrix transfer formulation.     

Broad Stopband Characteristic of Dielectric Chiral Photonic Crystals

In this paper, a novel chiral photonic crystal structure is presented. The formula of reflection coefficient of multi-layer chiral media is applied to dielectric-chiral photonic crystal structure, which is composed of thin chiral layers sandwiched by conventional media. To compare with previous literature, we consider the dielectric structure with alternate glass and GaAs layers. The power reflectance as a function of wavelength for this photonic crystal structure has been calculated. The results are in good agreement with that of Reference. However, our method is simpler. From these graphs, it is found that 100% reflectance is only in finite wavelength ranges, and reflection bandwidth is also small for conventional photonic crystal structure. For chiral photonic crystal, the results show that the chiral photonic band gap (PBG) structure gives nearly 100% reflections in the near-infrared region in addition to some parts of the visible region of the wavelengths. Therefore, it can be used as a broadband reflector and filter.     

Localized interface phonon polaritons in superlattice with a structural defect consisting of ternary mixed crystal

Using a transfer matrix method, we investigate the existence and characteristics of the localized interface phonon-polariton modes (IPPMs) in superlattice (SL) with a structural defect consisting of ternary mixed crystal (Al_xGa_1−xAs). The results show that the introduction of two-mode behavior of the ternary mixed crystal leads to the rich and varied localized IPPMs spectra with new features. The characteristics and positions of the localized IPPMs in the Reststrahlen region are strongly dependent on the concentration x of the ternary mixed crystal. Moreover, it is found that the localized IPPMs are sensitive to the thicknesses of the defect and constituent layers as well as to the transverse wavenumber q_∥.