Reflectance spectra and photonic band gaps of a one-dimensional photonic crystal based on a silicon-air periodic structure

The reflectance spectra of a one-dimensional photonic crystal based on a silicon-air periodic structure are calculated. A map of photonic band gaps is plotted, which makes it possible to deliberately choose the geometric parameters of the structure (the thickness of silicon partitions D _Si and the period A) for different ranges of the wavelength λ. To obtain structures with a photonic band gap in the range A/λ=0.15–0.5, the main region (as rule, corresponding to the lowest frequencies) can be used, and, taking into account the secondary photonic band gaps, the range A/λ can be extended to 1 and even more. In addition, it is found that, in the range D _Si/A=0.4–0.9, the secondary band gaps may be wider than the main ones (on the frequency scale). The influence of the filling factor D _Si/A on the formation of the edges of spectral bands is revealed.     

Resonant tunneling effect in one-dimensional twinned lattice photonic crystal under total reflection conditions

Under total reflection conditions, it typically seems as though light waves will be reflected completely on the interface; in actuality, the waves can penetrate the medium as evanescent waves. In this paper, we present a twinned lattice photonic crystal with a unit cell composed of AB layers and their mirror. We assume that the refractive index n ₀ of the input and output end is equal to n _B and larger than n _A . We first demonstrate the dependence of band structure on the incidence angle and normalized wavelength, in which the resonant tunneling bands are exposed. We then draw a comparison of bands between ABBA and AB. To conclude, we discuss the resonant tunneling effect in the twinned lattice photonic crystal under the total reflection conditions. As incidence angle increases, the resonant tunneling band ultimately vanishes completely.     

Dielectric photonic crystal with a near-zero effective refractive index in the microwave range

The microwave propagation in a 3D dielectric photonic crystal at the frequency range from 8.5 to 12GHz has been investigated. A frequency range where effective refractive index n _ef of the crystal approaches zero is found. In the frequency range where n _ef <0.2, themicrowave beam becomes collimated, sharpened, and free of diffraction noise. An excitation of a surface wave, propagating along the external surface of the structure, is revealed in same frequency range. This property of the photonic crystal structure can be used to screen and mask objects scanned by external radiation.     

Modified multicomponent band pass optical reflection filters at oblique incidence

Reflection and transmission characteristics of a modified long-wavelength cutoff filter using a three-component system with an angular dependence are studied. In this case, a layer of high refractive index is sandwiched between edge layers of equivalent refractive index with the base structure [G(0.5AB0.5A)]^N; then, an optimized structure of the form [(0.5AB0.5A)^N?X (0.5AB0.5A)^X (0.5AB0.5A)^N?X] is taken and its spectral properties are studied. In the case of a short-wavelength three-component cutoff filter, a layer of low refractive index is sandwiched between two edge layers of high equivalent refractive index with a base structure [G(0.5BA0.5D)]^N and its spectral characteristics are studied. Then, the structure is optimized [(0.5BA0.5B)^{N? X}(0.5BA0.5B)^X(0.5BA0.5B)^N?tX] and spectral characteristics of this structure are also studied. Spectral properties of band pass optical reflection filters of the type [G(XY)A] whose components are the proposed long-wavelength cutoff [(0.5AB0.5B)^{N? X}(0.5AB0.5A)^X(0.5BA0.5B)^N?X] and short-wavelength cutoff [(0.5BA0.5B)^N?X(0.5BA0.5B)^X(0.5BA0.5B)^N?X] filter structures are studied with angular dependences. No increase in the bandwidth with the least oscillatory components at the edges can be precisely formed by known classes of a two-component system at normal incidence. It is shown that the use of reflection and transmission filters with oblique bands yields an ideal polarizer. Angular dependences of the filter and the transmission and reflection band shapes on the parameters of a high-reflectance multilayer coating, such as the thickness, refractive indices, and the number of layers, are analyzed in detail.     

Amplitude-phase reflectance spectra of amorphous silicon-based Bragg structures

Amplitude-phase spectra of light reflection from distributed Bragg reflectors and Fabry-Pérot microcavities based on a-Si: H/a-SiO_x: H thin films have been studied. The frequency dependence of the phase difference between the amplitude p-and s-light reflection coefficients within the photonic band gap is measured. The phase spectrum exhibits predominantly a monotonic, close-to-linear frequency behavior, except for spectral regions near the stop band edges and near the singularities related to the microcavity eigenmodes. The experimental spectra are compared with theoretical calculations based on the transfer matrix method and approximate analytical relations. A method based on analyzing amplitude-phase reflectance spectra is proposed for structural characterization of multilayer microcavity systems.     

Dependence of the refractive index on crystal thickness due to a Pekar extra light wave

Transmission spectra of CdS crystals of different thickness are calculated in the region of A _n =1 exciton using the Pekar theory taking into account an extra light wave. It is shown that the dependence of the refractive index variance on the thickness of superthin crystals at low temperatures, which has been observed earlier, is associated with interference of the extra light wave, to which the crystal is opaque, with the fundamental wave transmitted by the crystal.     

Electromagnetic-field amplification in finite one-dimensional photonic crystals

The electromagnetic-field distribution in a finite one-dimensional photonic crystal is studied using the numerical solution of Maxwell’s equations by the transfer-matrix method. The dependence of the transmission coefficient T on the period d (or the wavelength λ) has the characteristic form with M–1 (M is the number of periods in the structure) maxima with T = 1 in the allowed band of an infinite crystal and zero values in the forbidden band. The field-modulus distribution E(x) in the structure for parameters that correspond to the transmission maxima closest to the boundaries of forbidden bands has maxima at the center of the structure; the value at the maximum considerably exceeds the incident-field strength. For the number of periods M ~ 50, more than an order of magnitude increase in the field amplification is observed. The numerical results are interpreted with an analytic theory constructed by representing the solution in the form of a linear combination of counterpropagating Floquet modes in a periodic structure.     

Self-diffraction at a dynamic photonic crystal formed in a colloidal solution of quantum dots

Self-diffraction at a one-dimensional dynamic photonic crystal formed in the colloidal solution of CdSe/ZnS quantum dots has been discovered. This self-diffraction appears simultaneously with self-diffraction at induced transparency channels at the resonant excitation of the main electron–hole (excitonic) transition of quantum dots by two laser beams with a Gaussian intensity distribution over the cross section. It is shown that a nonlinear change in the absorption of colloidal quantum dots results in the formation of a transparency channel and an induced amplitude diffraction grating, and a significant nonlinear change in the refractive index (Δn ≈ 10^?3) in the absorbing medium is responsible for the formation of the dynamic photonic crystal. Self-diffracted laser beams are revealed propagating not only in directions corresponding to self-diffraction at the induced diffraction grating but also in directions satisfying the Laue condition.     

Photonic crystals with a specified bandgap width

A new method is proposed for the production of photonic crystals with a thoroughly controlled photonic bandgap. The method is based on the synthesis of an A_1?x B _x photonic crystal with controlled parameter x based on two isostructural A and B photonic crystals such that the photonic bandgap of the A crystal is smaller and that of the B crystal is greater than the required bandgap. The method is exemplified in a (100 ? x) mol % SiO₂?x mol % ZnO inverse opal, in which the relative stop-band width monotonically increases with parameter x.     

Polarization-dependent suppression of Bragg reflections in light reflection from photonic crystals

This paper reports on an experimental and theoretical study of the spectra of Bragg reflection of light from opal-like photonic crystals near the critical angle of incidence ? _c , at which the Bragg reflection in the p polarization of reflected light disappears The objects studied were polymer photonic-crystal structures made up of polystyrene particles. It is shown that Bragg reflection for the electromagnetic TM mode becomes totally suppressed at an angle of incidence ? _c , which depends on the geometric parameters and dielectric constants of the spatially periodic structure.     

Slow light engineering in a photonic crystal slab waveguide through optofluidic infiltration and geometric modulation

In this paper, a new type of flat-band slow light structure with high group index (n _g) and large normalized delay-bandwidth product (NDBP) in a silicon on insulator (SOI) based photonic crystal (PC) slab waveguide with a triangular lattice of circular holes is demonstrated. The dispersion engineering is performed by infiltrating optical fluids with different refractive indices n _f in the first row and shifting the second row of air holes adjacent to the PC waveguide (PCW) in the longitudinal direction. In the optimized case, a high NDBP of 0.32 with a group index of 54.55 and a bandwidth of 9.13 nm could be obtained. Furthermore, an ultra-low group velocity dispersion (GVD) in the range of 10^–20 s²/m is achieved in all of the structures. These results are obtained by numerical simulations based on three-dimensional (3D) plane wave expansion (PWE) method.     

An optical study of vacuum evaporated amorphous Ge<Subscript>20</Subscript>Te<Subscript>80−<Emphasis Type="Italic">x</Emphasis></Subscript>Bi<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> thin films using transmission and reflection spectra

The present paper reports the effect of Bi addition on the optical behavior (optical band gap and refractive index) of Ge₂₀Te_80?x Bi _x (where x=0, 1.5, 2.5, 5.0) glassy alloys by analyzing the transmission and reflection spectra of their thin films in the 900–2400 nm range. Films are deposited on glass substrate using a thermal evaporation technique under vacuum. Various optical parameters viz. refractive index, extinction coefficient, absorption coefficient, optical band gap, etc. are determined and the effect of Bi incorporation on these parameters is studied. The refractive index has been found to increase with increasing Bi content over the entire spectral range and this behavior is due to the increased polarizability of the larger Bi atomic radius (1.46 Å) compared to Te atomic radius (1.36 Å). Dispersion energy, E _d , average energy gap, E ₀ and static refractive index, n ₀ is calculated using Wemple–DiDomenico model. Optical band gap is estimated using Tauc’s extrapolation and is found to decrease from 0.86 to 0.73 eV with the Bi addition. This behavior of the optical band gap is interpreted in terms of the electronegativity difference of the atoms involved and the cohesive energy of the system.     

基于光纤的三维可调胶体光子晶体

用改进的垂直沉积法在光纤端面制备了高质量的SiO₂胶体光子晶体,经过烧结、固化构成胶体光子晶体-光纤结构. 用扫描电子显微镜确定了样品为面心立方密排结构,其密排面平行于光纤基底表面. 利用全光纤传感网络测试了该胶体光子晶体,反射峰中心位于845 nm处,与Bragg理论计算值符合很好. 将该样品浸入不同折射率的液体中,反射光谱的峰值位置随着液体折射率的改变而发生偏移,近似呈线性关系,实现了峰位可调. 对于不同浓度引起的液体折射率的变化,基于光纤的胶体光子晶体结构也能够很好地分辨出来. 关键词： 可调胶体光子晶体 2微球')" href="#">SiO₂微球 Bragg反射 光纤     

Luminescence of Tl<Superscript>+</Superscript> ions in a KZnF<Subscript>3</Subscript> crystal

The luminescence spectra of a KZnF₃: Tl⁺ crystal are investigated in the energy range from 4.75 to 5.9 eV at temperatures of 10–300 K upon excitation into the A absorption band (5.7–6.3 eV). At T=300 K, the luminescence spectra exhibit an intense band with a maximum at 5.45 eV, which is attributed to single Tl⁺ ions substituted for K⁺ ions. The 5.723-eV intense narrow band observed at T<20 K is assigned to the ³Γ_1u-¹Γ_1g zero-phonon transition, which is weakly allowed by the hyperfine interaction. The luminescence decay is studied as a function of temperature. The main characteristics of the luminescence spectra are adequately described in terms of the semiclassical theory based on the Franck-Condon principle and the Jahn-Teller effect for an excited sp configuration of the Tl⁺ ion with the use of the parameters obtained earlier from analyzing the absorption spectra of the system under investigation.     

Electronic band structure and x-ray spectra of boron nitride polytypes

The electronic band structures of boron nitride crystal modifications of the graphite (h-BN), wurtzite (w-BN), and sphalerite (c-BN) types are calculated using the local coherent potential method in the cluster muffin-tin approximation within the framework of the multiple scattering theory. The specific features of the electronic band structure of 2H, 4H, and 3C boron nitride polytypes are compared with those of experimental x-ray photoelectron, x-ray emission, and K x-ray absorption spectra of boron and nitrogen. The features of the experimental x-ray spectra of boron nitride in different crystal modifications are interpreted. It is demonstrated that the short-wavelength peak revealed in the total densities of states (TDOS) in the boron nitride polytypes under consideration can be assigned to the so-called outer collective band formed by 2p electrons of boron and nitrogen atoms. The inference is made that the decrease observed in the band gap when changing over from wurtzite and sphalerite to hexagonal boron nitride is associated with the change in the coordination number of the components, which, in turn, leads to a change in the energy location of the conduction band bottom in the crystal.     

Dispersion of light in opal photonic crystal

The selective reflection spectra of films prepared from the photonic crystal, i.e., synthetic opal, are investigated. It is revealed that the refractive index changes at the boundaries of the photonic band gap. The wave vector is renormalized as a result of the interaction of the light wave with the periodic structure of the crystal, and the dependence of the frequency on the photon wave vector deviates from a linear behavior. The band gap determined from these data is approximately equal to 1.7 × 10¹⁴ Hz.     

Isotope effects in the vibrational spectrum of the SF<Subscript>6</Subscript> molecule

The IR absorption spectra of solutions of SF₆ in liquid argon are studied at a temperature of 93 K in the concentration interval 10^?5–10^?7 mole fractions. A sample with a natural abundance of isotopes and a monoisotope ³⁴SF₆ sample are studied. The frequencies, half-widths, and relative intensities of bands in the vibrational spectrum of all isotopomers of the molecule are determined. For the ³⁴SF₆ molecule, the ratio of integral absorption coefficients of fundamental bands A(ν₄)/A(ν₃)=0.07(6) is larger than ³²SF₆:A(ν₄)/A(ν₃)=0.66(4) for the ³²SF₆ molecule, which corresponds to the same signs of P′₃ and P′₄. The change in the intensity of the ν₂+ν₆ and ν₅+ν₆ bands upon isotopic substitution is explained by the change in the resonance contributions of due to the isotope shift of the ν₃ band.     

Analysis of optical characteristics of holey photonic crystal devices with the extended coupled-mode formalism

Presented here is a new approach for analysis of the so-called holey photonic crystals—a class of electro-optical components, in which periodicity of air holes in dielectric media is used for confinement of light. This class includes several kinds of microstructured fibers, semiconductor lasers etc. Accurate evaluation of optical characteristics of those devices is usually a complicated problem due to the large dimensions and the fine structure of their refractive index distribution. Furthermore, usually, only numerical solutions for this class of optical components are available. The overwhelming majority of the physical models, suitable for analysis of holey photonic devices, proceed from the “natural” assumption: the devices are considered as arrays of air holes, surrounded by dielectric material. In this work we propose another model. Namely, we treat them as arrays of dielectric spots (waveguides), embedded in the air (cladding material). This model allows utilization of the extended coupled-mode theory (a relatively new approach designed for analysis of infinite arrays of coupled waveguides and previously considered inapplicable to holey optical components) for calculations of the latter. In this sense, we present a new method for analysis of holey photonic crystals. On the one hand, our method allows analytical evaluation of some optical characteristics of holey optical components (such as the number of photonic bands and bandwidth). On the other hand, accurate numerical computation of the photonic band structure of the holey photonic devices, incorporating a large number of holes, can be done with this technique on a timescale of several minutes.     

Optical characterization of natural and synthetic opals by Bragg reflection spectroscopy

The Bragg reflection of light from natural and synthetic opals was studied experimentally, and the samples were characterized by atomic-force microscopy. The reflection spectra were theoretically calculated within the model of a planar, periodically layered medium. A comparison of the experimental and calculated data made it possible to determine the parameters of the crystal structure of synthetic opals (lattice constants and sintering coefficients of a-SiO₂ particles). It was concluded that the pores in the structure of natural opals are filled by a material with a refractive index close to that of a-SiO₂.     

Multi-channel biosensor based on photonic crystal waveguide and microcavities

An ultrasensitive two-dimensional photonic crystal biosensor is theoretically demonstrated in this paper. Such device consists of a waveguide and high Q-value microcavities which are realized by introducing line and point defects into the photonic crystal respectively. The band structures and the transmission spectra are obtained from the Finite-Difference –Time-Domain (FDTD) method. The simulation results showed that such device is strongly sensitive to the refractive index of the analyte injected into the point defect. The designed device can be applied for measurements of the refractive index and detection of protein-concentrations.