Tuning the band gap of self-assembled superparamagnetic photonic crystals in colloidal magnetic fluids using external magnetic fields

The model of tunable superparamagnetic photonic crystals self-assembled in colloidal magnetic fluids under externally applied magnetic fields is established. The mechanisms, which are in charge of the tunability of the band gaps with magnetic fields are clarified. The band structures of the triangularly-arrayed two-dimensional photonic crystals with limited heights of magnetic columns are calculated with the experimental data of structures and refractive indices in the literatures. The field-dependent properties of the first band gaps are gained for the z-odd and z-even modes, respectively. Simulation results indicate that the mid frequencies of the first band gaps of the z-odd modes can be easily tuned by the external magnetic fields, while those of the z-even modes bear relatively weak dependence on the external magnetic fields. Simultaneously, the first band gaps of both kinds of modes become wide along with the increase of the magnetic fields. The results presented in this work give a guideline for realizing the tunable photonic crystals with magnetically colloidal materials and magnetic stimuli.     

Periodic thin-film interference filters as one-dimensional photonic crystals

We review the photonic band gap-related properties of a simple periodic system of thin dielectric layers. Properties associated with forbidden and allowed bands of such one-dimensional photonic crystals are presented. A revision of the properties of forbidden bands leads to an omnidirectional Bragg mirror design. The anisotropy of allowed bands suggests the formation of photon-focusing caustics in one-dimensional photonic crystals.     

Uncoupled photonic band gaps

We theoretically investigated the symmetry properties of the modes in two-dimensional square lattice photonic crystals in order to study phenomena that would enable new frontiers in the applications of photonic crystals. Using group theory, symmetry analysis of the photonic crystals bands has been done. Particular attention was given to the search for the uncoupled B modes that cannot be excited by the external plane wave because they are symmetry forbidden. The existence of the uncoupled modes enabled to define new physics phenomena: uncoupled photonic band gaps. For the frequency ranges inside the uncoupled photonic band gaps, zero transmission is obtained. Therefore, there are two different types of photonic gaps in the photonic crystals: photonic band gaps and uncoupled photonic band gaps. The appearance of uncoupled photonic band gaps in photonic crystals could at least improve the application of the existing photonic materials and structures or even enable the usage of new ones for devices like waveguides, filters, and lasers.     

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.     

Tuning of the photonic band gaps and the reflection spectra of a one-dimensional photonic crystal based on silicon and a liquid crystal

The reflection spectra and the photonic band gaps of a one-dimensional composite photonic crystal are calculated for different filling factors (the ratio of the thickness of a silicon layer to the lattice constant A). A change in the refractive index of the filler in a photonic crystal leads to the shift of both edges for certain side photonic bands. It is shown that, with a change in the refractive index from 1.49 to 1.69, the shift of the edges (the tuning effect) can reach the value A/λ = 0.04 for the main photonic band and 0.08 for a side band. An additional criterion for designing a photonic crystal is the estimation of the sharpness of the edges of photonic bands in the reflection spectra.     

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.     

EPR and optical absorption studies of V O ions in L-asparagine monohydrate

Electron paramagnetic resonance (EPR) studies of V O²⁺ ions in L-asparagine monohydrate single crystals are reported at room temperature. It is found that the V O²⁺ ion takes up an interstitial site. The angular variations of the EPR spectra in three mutually perpendicular planes are used to determine the principal g and A values and their direction cosines. The values of g and A parameters are: g_x=1.9011, g_y=2.1008, g_z=1.9891 and A_x=100, A_y=78, A_z=126 (×10⁻⁴) cm⁻¹. The optical absorption spectrum of V O²⁺ ions in L-asparagine monohydrate is also studied at room temperature. The band positions are calculated using the energy expressions and compared with the observed band positions to confirm the transitions. The best-fit values of the crystal field (Dq) and tetragonal (Ds and Dt) parameters are evaluated from the observed band positions.     

Dispersion properties of two-dimensional plasma photonic crystals with periodically external magnetic field

Dispersion properties of two types of two-dimensional periodically magnetized plasma array structures with square lattices have been investigated by using plane wave expansion method. It is found that two different regions of flatbands and photonic band gaps occur in the TE polarization due to the external magnetic field. The two types of system can be seen as a kind of unusual plasma photonic crystals. The results show that not only the location of flatbands but also the position and bandwidth of photonic band gaps can be tuned by external magnetic field. The cutoff frequency decreases as external magnetic field increases. The edge of two different of flatbands regions and cutoff frequency shift downward to lower frequencies obviously with increasing plasma collision frequency, while they shift upward to higher frequencies notably with increasing plasma frequency. The filling factor has little effect on the location of flatbands regions. The width of flatbands regions and photonic band gaps are almost unchanged by increasing filling factor, but the number of ominidirectional photonic band gap for type-1 structure plasma photonic crystals can be effectively controlled by adjusting filling factor. It is worth to be noted that the first band gaps above the cutoff frequencies in Г–X and Г–M direction for two types of PPCs can be modulated by the parameters as mentioned above, and the relative bandwidth of band gap in Г–X direction is wider than the one in Г–M direction. The results may provide theoretical instructions to design new tunable photonic crystals devices.     

一维光子晶体的透射谱特性

利用传输矩阵法研究了一维光子晶体的透射谱特性,数值模拟得到了可见光波段一维光子晶体中的透射谱特性,计算结果表明可见光波段入射波长变化时,透射谱禁带宽度发生变化。研究结果为可见光波段一维光子晶体器件的设计提供了理论依据。     

Optical properties of one-dimensional photonic crystals containing graded materials

The optical properties of an one-dimensional photonic crystal containing graded materials are studied theoretically. The graded layers have space dispersive permittivity and magnetic permeability which vary along the direction perpendicular to the surface of the layer. The gradation profiles of permittivity are studied in detail. We show that the structure possesses forbidden band gaps in its transmission spectra and the gradation profiles of permittivity affect the band gaps significantly. For the exponential gradation profile ε₁(x) = α e^βx, the number of the band gaps increases and the total frequency region corresponding to the gaps becomes large with increasing parameter β. On the other hand, the position of band gaps can be changed by the adjustment of the gradation profiles even if possessing same volume-average permittivity in the graded layers. Therefore, we can achieve suitable photonic band gaps by choosing gradation profiles of permittivity.     

Spin waves in periodic magnetic structures—magnonic crystals

Propagation of spin waves (SWs) through a periodic multilayered magnetic structure is analyzed. It is assumed that the structure consists of ferromagnetic layers having the same thickness but different magnetizations. The wave spectrum obtained contains forbidden zones (stop bands) in which wave propagation is prohibited. Introduction into the structure of the ferromagnetic layer with a different thickness breaks the structural symmetry and leads to a localization of the SW mode with the frequency lying in the stop band. Reflection of the wave by the structure of the finite length and transmission of the wave through the structure are also investigated. Numerical calculations of the wave dispersion and the transmission coefficients for symmetrical periodic structures as well as the structures with a defect are presented. Drawing an analogy from photonic crystals known in optics, such magnetic structures can be called one-dimensional (1-D) magnonic crystals (MCs). The possibilities of existence of the 2-D MCs are also discussed.     

First-principles study on electronic structures of BaWO4 crystals containing F-type color centers

The electronic structures of BaWO₄ crystals containing F-type color centers are studied within the framework of the fully relativistic self-consistent Dirac-Slater theory, using a numerically discrete variational (DV-Xα) method. It is concluded that F and F⁺ color centers have donor energy level in the forbidden band. The optical transition energies are 2.449 and 3.101 eV, which correspond to the 507 and 400 nm absorption bands, respectively. It is predicted that 400-550 nm absorption bands originate from the F and F⁺ color centers in BaWO₄ crystals.     

The reversibility of the Goos–Hänchen shift near the band-crossing structure of one-dimensional photonic crystals containing left-handed metamaterials

We perform a theoretical investigation on the Goos–Hänchen (GH) shift in one-dimensional photonic crystals (1DPCs) containing left-handed metamaterials (LHMs). We find an unusual effect of the GH shift near the photonic band-crossing structure, which is located at the condition, ?k _z ^(A) d _A =k _z ^(B) d _B =m π (m=1,2,3,…), under the inclined incident angle, here A denotes the LHM layer and B denotes the dielectric layer. Above the frequency of the band-crossing point (BCP), the GH shift changes from negative to positive as the incident angle increases, while the GH shift changes reversely below the BCP frequency. This effect is explained in terms of the phase property of the band-crossing structure.     

On the nature of energy bands in tetracyanoplatinates

Optical data and band calculations are presented for a series of tetracyanoplatinates with varying Pt—Pt-distance R. The band gap energies decrease according to R^-3 with decreasing R. The energy bands which determine the optical and electrical properties for E6 c originate from (Pt5d_z², 6s) and (Pt6p_z, CNπ¹) hybrid molecular states.     

Applications of the finite difference mode solution method to photonic crystal structures

The finite difference waveguide mode solution method, which has been popularly employed in the study of waveguide modes on various optical and dielectric waveguides, is utilized to calculate the modal characteristics of photonic crystal fibers (PCFs) and planar photonic crystal waveguides and the band diagrams of two-dimensional photonic crystals. Vector guided modes on both PCFs based on the total internal reflection guiding mechanism ('holey fibers') and those resulting from photonic band gap effect are accurately computed, with their effective indexes and field distributions compared with other methods. Calculated dispersion of a single-core holey fiber and coupled-power behavior of a two-core holey fiber are found to agree with measured results. For applications to band diagram calculation and planar photonic crystal waveguide analysis, the finite difference scheme is modified simply by imposing suitable periodic boundary condition. Numerical results for air-column crystals and dielectric-rod crystals are both found to agree well with calculations using other methods.     

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.     

Quantum Monte Carlo Investigation of the magnetic properties of weakly interacting antiferromagnetic chains with an alternating exchange interaction with spin S = 1/2

An approximation dependence of the spontaneous magnetic moment at a site, σ/σ(0) ? 1 = and the antiferromagnet-singlet state phase boundary, J ₂/J ₁ = 0.52(3)δ, are determined by the quantum Monte Carlo method in the self-consistent sublattice molecular field approximation for weakly inter-acting (J ₂) antiferromagnetic chains with spin S = 1/2 and alternating exchange interaction (J ₁ ± δ). The Néél temperature and a number of critical temperatures which could be related with the filling energy of two singlets (ΔS ^z = 0) and one triplet (ΔS ^z = 1) spin bands, each of which is split by the sublattice field (h ^{x, y} ≠ h ^z into two subbands, are determined on the basis of the computed correlation radii of the two-and four-spin correlation function, the squared total spin 〈 (S ^z)²〉 with respect to the longitudinal components, the dimerization parameter, and the correlation functions between the nearest neighbors with respect to longitudinal and transverse spin components. On the basis of the Monte Carlo calculations, the critical temperatures and possible energy gaps at the band center are determined for the antiferromagnets CuWO₄ and Bi₂CuO₄ and for the singlet compounds (VO)₂P₂O₇ and CuGeO₃, agreeing satisfactorily with existing results, and new effects are also predicted.     

一维光子晶体带隙结构对不同偏振态的角度和波长响应

用传输矩阵法计算了一维光子晶体带隙结构对不同偏振态入射光的角度和波长响应. 结果表明，对P偏振态，带隙的宽度明显小于S偏振态. 对于角度响应，两种偏振态有相同的变化趋势，但变化量不同. 而对于波长响应，两种偏振态表现出不同的变化趋势. 引入了“广义布儒斯特角”的概念. 理论分析表明，当光以此角射入光子晶体时，S偏振态入射光的禁带完全保留，而P偏振态入射光的禁带完全消失，从而可以在S偏振态入射光的禁带背景中用P偏振态入射光获得受主掺杂模式. 同时还给出了实验验证结果. 关键词： 体积全息图 光子晶体 偏振     

A wide band-pass filter of broad angle incidence based on one-dimensional metallo-dielectric ternary photonic crystal

A wide band-pass filter has been presented based on one-dimensional metallo-dielectric ternary photonic crystal. ZnS, Ag and MgF₂ are used as the materials of the photonic crystal. The forbidden and allowed bands of the photonic crystal are determined by using the band-edge analysis. The result indicates that the filter has a wide pass band in the visible region and it can block ultraviolet and infrared light. Simulation of the transmission spectra shows that the filter has decent transmittance in the pass band at broad angle incidence ranging from 0° to 70°, which can meet the need of practical use.     

Phenomenological description of the microwave surface impedance and complex conductivity of high-T c single crystals

Measurements of the microwave surface impedance Z _s (T) = R _s (T) + iX _s (T) and the complex conductivity σ_s(T) in the ab-plane of high-quality high-T _c YBCO, BSCCO, TBCCO, and TBCO single crystals are analyzed. Experimental data of Z _s (T) and σ_s(T) are compared with calculations based on a modified two-fluid model that includes a temperature-dependent quasiparticle scattering and a unique temperature variation of the density of superconducting carriers. We describe the agreement and disagreement of our analysis with the salient features of the experimental data. We review the existing microscopic models based on unconventional symmetry types of the order parameter and on novel quasiparticle relaxation mechanisms.