Band-structure properties of photonic superlattices

The band structure of a one-dimensional periodic array composed of two different layers of dimensions a and b characterized by refractive indices n ₁ and n ₂, respectively, is investigated. Refractive indices may take on positive as well as negative values. Within the Maxwell framework and using a transfer matrix technique for one dimensional periodic eigen-problems, we have determined a general equation, which governs the photonic band structure and the density of states (DOS) of one-dimensional photonic crystals. In addition to the well-known existence of the band gaps, we show that, depending on the width relationship b/a between the layer materials, super-lattices with null photonic band gap may exist and the conditions for such occurrences are established. Furthermore, we have been able to study the so-called 〈n〉 = 0 non-Bragg gap, ground ω₀, for which the average refraction felt by the propagating radiation is null. The text was submitted by the authors in English.     

The nonlinear optical susceptibility and electro-optic tensor of ferroelectrics: first-principle study

The nonlinear optical properties of some ABO₃ materials (BaTiO₃, KNbO₃, LiTaO₃ and LiNbO₃) are studied by density functional theory (DFT) in the local density approximation (LDA) expressions based on first-principle calculations. Our goals are to give the details of the calculations for linear and nonlinear optical properties, including the linear electro-optic (EO) tensor for some ABO₃ structures with oxygen octahedral structures using first-principles methods. These results can then be used in the study of the physics of ferroelectrics, specifically, we present calculations of the second harmonic generation response coefficient X _ijk ⁽²⁾ (−2ω, ω, ω) over a large frequency range for ABO₃ crystals. The electronic linear EO susceptibility X _ijk ⁽²⁾ (−ω, ω,0) is also evaluated below the band gap. These results are based on a series of the LDA calculations using DFT. Results for X _ijk ⁽²⁾ (−ω, ω,0) are in agreement with experiments below the band gap. The results are compared with the theoretical calculations and the available experimental data.     

Optical properties of MgxZn1−xO nanowire photonic crystals

We investigate the optical properties of two-dimensional periodic arrays of well-aligned Mg_xZn_1−xO nanowires, i.e., Mg_xZn_1−xO nanowire photonic crystals. The nanowire photonic crystal can exhibit a photonic band gap in the visible range. As the mole fraction of Mg, x, increases, the edge frequencies of the band gap increase and the band gap size decreases. The characteristics of relative band gap and vacant point defect mode are also studied with varying x. From the finite-difference time-domain simulations, we show that the light extraction from nanowires can be controlled by varying the distance between optically excited nanowires and a waveguide, and the mole fraction of Mg. Controlling the light extraction from nanostructures can be useful in the implementation of nanoscale light emitting devices.     

Analysis of photonic band gaps in a two-dimensional photonic crystal with centrifugal core-shell rods

The absolute photonic band gap (PBG) in two-dimensional (2D) photonic crystal with excentric core-shell rods is studied in this paper. The core rod shifts away from the core-shell rod center, and its position is decided by two new introduced parameters — the shift angle θ and the offset ρ. We use the FDTD algorithm to calculate the photonic bands of the photonic crystal, and analyze how the offset and shift angle affect the photonic bang gap of excentric core-shell photonic crystal for different core rod size. It has been shown that the variation of the photonic band gap is quite peculiar.     

Space-time dispersion of graphene conductivity

We present an analytic calculation of the conductivity of pure graphene as a function of frequency ω, wave-vector k, and temperature for the range where the energies related to all these parameters are small in comparison with the band parameter γ≃3 eV, but much larger than the collision rate τ^-1. The simple asymptotic expressions are given in various limiting cases. For instance, the conductivity for kv₀≪ T≪ω is equal to σ(ω,k)=e²/4ħ and independent of the band structure parameters γ and v₀. Our results are also used to explain the known dependence of the graphite conductivity on temperature and pressure.     

A local moment approach to the gapped Anderson model

We develop a non-perturbative local moment approach (LMA) for the gapped Anderson impurity model (GAIM), in which a locally correlated orbital is coupled to a host with a gapped density of states. Two distinct phases arise, separated by a level-crossing quantum phase transition: a screened singlet phase, adiabatically connected to the non-interacting limit and as such a generalized Fermi liquid (GFL); and an incompletely screened, doubly degenerate local moment (LM) phase. On opening a gap (δ) in the host, the transition occurs at a critical gap δ_c, the GFL [LM] phase occurring for δ<δ_c [ δ>δ_c] . In agreement with numerical renormalization group (NRG) calculations, the critical δ_c = 0 at the particle-hole symmetric point of the model, where the LM phase arises immediately on opening the gap. In the generic case by contrast δ_c > 0, and the resultant LMA phase boundary is in good quantitative agreement with NRG results. Local single-particle dynamics are considered in some detail. The major difference between the two phases resides in bound states within the gap: the GFL phase is found to be characterised by one bound state only, while the LM phase contains two such states straddling the chemical potential. Particular emphasis is naturally given to the strongly correlated, Kondo regime of the model. Here, single-particle dynamics for both phases are found to exhibit universal scaling as a function of scaled frequency ω/ω_m ⁰ for fixed gaps δ/ω_m ⁰, where ω_m ⁰ is the characteristic Kondo scale for the gapless (metallic) AIM; at particle-hole symmetry in particular, the scaling spectra are obtained in closed form. For frequencies |ω|/ω_m ⁰ ≫δ/ω_m ⁰, the scaling spectra are found generally to reduce to those of the gapless, metallic Anderson model; such that for small gaps δ/ω_m ⁰≪ 1 in particular, the Kondo resonance that is the spectral hallmark of the usual metallic Anderson model persists more or less in its entirety in the GAIM.     

First-principles study of the optical properties of PbFX (X = Cl,Br, I) compounds in its matlockite-type structure

We present the results of the ab initio theoretical study of the optical properties for PbFX (X = Cl, Br, I) compounds in its matlockite-type structure using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code. We employed generalized gradient approximation (GGA), which is based on exchange-correlation energy optimization to calculate the total energy. Also we have used the Engel-Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. Our calculations show that the valence band maximum (VBM) and conduction band minimum (CBM) are located at Z resulting in a direct energy gap. We present calculations of the frequency-dependent complex dielectric function ε( ω) and its zero-frequency limit ε₁ ( 0 ). We find that the values of ε₁ ( 0 ) increases with decreasing the energy gap. The reflectivity spectra and absorption coefficient has been calculated and compared with the available experimental data. The optical properties are analyzed and the origin of some of the peaks in the spectra is discussed in terms of the calculated electronic structure.     

Investigation of luminescence properties in SiO2: Tb,Yb upconversion inverse opal

The SiO₂: Tb, Yb inverse opals with photonic band gap at 465 or 543 nm were prepared, and an effect of photonic band gap on upconversion spontaneous emission from Tb³⁺ was investigated. The results show that the photonic band gap has a significant influence on the upconversion emission of the SiO₂: Tb, Yb inverse opals. The upconversion luminescence of the Tb³⁺ ions is suppressed in the inverse opal compared with the luminescence of that of the reference sample.     

Pressure-tuned resonance Raman scattering and photoluminescence studies on MBE grown bulk GaAs at theE 0 gap

Hydrostatic pressure has been used to tune in resonance Raman scattering (RRS) in bulk GaAs. Using a diamond anvil cell, both the photoluminescence peak (PL) and the 2 LO and LO-phonon Raman scattered intensities have been monitored, to establish RRS conditions. When theE ₀ gap of GaAs matchesħω _S orħω _L, the 2 LO and LO-phonon intensity, respectively, exhibit resonance Raman scattering maxima, at pressures determined byħω _L. With 647.1 nm radiation (ħω _L = 1.916 eV), a sharp and narrow resonance peak at 3.75 GPa is observed for the 2 LO-phonon. At this pressure the 2 LO-phonon goes through its maximum intensity, and falls right on top of the PL peak, revealing thatħω _S(2 LO) =E ₀. This is the condition for “outgoing” resonance. Experiments with other excitation energies (ħω _L) show, that the 2 LO resonance peak-pressure moves to higher pressure with increasingħω _L, and the shift follows precisely theE ₀ gap. Thus, the 2 LO RRS is an excellent probe to follow theE ₀ gap, far beyond the Γ-X cross-over point. A brief discussion of the theoretical expression for resonance Raman cross section is given, and from this the possibility of a double resonance condition for the observed 2 LO resonance is suggested. The LO-phonon resonance occurs at a pressure whenħω _L ≈E ₀, but the pressure-induced transparency of the GaAs masks the true resonance profile.     

Design of sharp transmission filters using band-edge resonances in one-dimensional photonic crystal hetero-structures

This paper presents a design of sharp transmission filters using band edge resonance effects in a hetero-structure composed of one-dimensional photonic crystals with different periods. Assuming that the photonic crystals are made of identical pairs of transparent materials, the band-edge resonance occurs when the periods are distributed in a geometrical progression with a common ratio, r=r _c , where r _c is a known function of refractive-index modulation, incident angle and the polarization of light. The band-edge resonance results in sharp resonant peaks in the transmission spectrum, with the full width at half maximum of the peaks increasing with an increase in the number of unit cells in each photonic crystal. Furthermore, if M photonic crystals are used to construct the hetero-structure, M−1 resonant peaks with the spacing between kth (1<k<M) and (k−1)th peaks equal to the band gap of the kth photonic crystal form in the transmission spectrum.     

Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods

The plane-wave expansion method is used to calculate photonic band gaps for two structures with hollow anisotropic tellurium (Te) rods. Both structures are found to have absolute band gaps at the low- and high-frequency regions. Compared with the photonic crystal with solid Te rods, the photonic crystal with hollow Te rods has a large absolute band gap at the high-frequency region: for the triangular lattice of oval hollow Te rods, there is an absolute band gap of 0.058w_e (w_e=2πc/a), and for the square lattice of square hollow Te rods, there is an absolute band gap of 0.056w_e.     

Manipulating electromagnetic wave with the magnetic surface plasmon based metamaterials

In this work, we have investigated the optical properties of the magnetic metamaterials (MMs) consisting of periodically/randomly arranged ferrite rods. By calculating the photonic band diagrams and transmittance, we have identified a photonic band gap originating from the magnetic surface plasmon (MSP) resonance. In addition, by tuning the external magnetic field (EMF), an MM slab can be used as an optical switch. Our simulated results also suggest that the optical properties of the MMs are robust against the position disorder and the size fluctuation of the ferrite rods. Moreover, by examining the relation between the transmittance and the EMF, we can optimize the EMF to realize the best switching effect. With the retrieved effective constitutive parameters ε _eff and μ _eff obtained from the effective-medium theory, the optimal EMF can be understood in a more clear manner.     

Analysis and design of optically transparent antenna on photonic band gap structures

An optically transparent microstrip patch antenna is designed on photonic bandgap structures and its radiation characteristics are computed and analyzed in the visible spectrum region. The proposed antenna consists of indium tin oxide, a transparent conducting material used both as a radiating patch and a ground plane separated by the 5 μm thin glass substrate. The introduction of periodic cylindrical air cavity structures in the glass substrate leads to the formation of photonic band gap. The patch thickness is carefully selected based on the analysis of the optical transmission coefficient with respect to patch thickness. The effective dielectric constant of the photonic band gap loaded glass substrate is computed using the effective medium approach. The refractive index of the proposed antenna is presented and discussed. The radiation efficiency of the antenna is shown to improve significantly due to insertion of proposed photonic band gap structures. The proposed design has yielded a bandwidth of 2–2.3 THz for a return loss (S₁₁) of less than −15dB and achieved a peak gain of 4.97dB at 2.27 THz.     

Effect of biaxial strain on the band gap of wurtzite AlxGa1?xN

First-principles calculations are applied to investigate the effect of biaxial strain on the band gap of wurtzite Al _x Ga_1−x N. The band gap and band gap bowing parameter increase with compressive strain and decrease with tensile strain. The strain-induced changes in the band gap of Al _x Ga_1−x N are linear in the strain range of about −1% to 1% while the linearity is invalid out of the range. The linear coefficient B(x), characterizing the relationship between the band gap and the biaxial stress, with a quadratic form is obtained. The value of the band gap bowing parameter decreases from 1.0 eV for −2% strain to 0.91 eV for unstrained and to 0.67 eV for 2% strain.     

Fabrication of polaritonic structures in LiNbO<Subscript>3</Subscript> and LiTaO<Subscript>3</Subscript> using femtosecond laser machining

Fabrication of patterned materials in ferroelectric LiNbO₃ and LiTaO₃ crystals using femtosecond laser micromachining is presented and discussed. Damage feature sizes in the 10–100 μm range were achieved using 800-nm, 50-fs (FWHM) ultra-fast laser pulses with energies ranging from 10 μJ up to 350 μJ. Fabrication of polaritonic devices such as waveguides, resonators, focusing reflectors, diffractive and dispersive elements, photonic band gap materials, and other microstructures is demonstrated. PACS 77.84.Dy; 42.62.Cf; 71.36.+c     

Evolution of the optical properties of single-crystal La1−x SrxMnO3

An ellipsometric method is used to study the dispersion of the real ɛ ₁(ω) and imaginary ɛ ₂(ω) parts of the complex dielectric permittivity of single-crystal La_1−x Sr_xMnO₃ (x=0.1, 0.2, and 0.3) for energies from 100 meV to 5 eV at room temperature. It is found that, when lanthanum is replaced by strontium, the optical spectrum changes fundamentally. A shift in the main features of the spectrum of initial LaMnO₃ at 1.9 and 4.7 eV to lower energies takes place, as well as a partial redistribution of the optical-conductivity spectral weight in the band gap region E<1.7 eV. For compositions with x=0.2 and 0.3, a fine structure of the interband absorption is observed against a background of non-Drude optical conductivity at low energies. Fiz. Tverd. Tela (St. Petersburg) 41, 1445–1449 (August 1999)     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Applicability of the empirical Varshni relation for the temperature dependence of the width of the band gap

We have carried out a comparison of relations used to describe the temperature dependence of the width of the band gap in crystals. It is shown that for kT≫ℏω the well-known Varshni relation can be obtained from the non-empirical Fan expression in explicit form taking account of the phonon statistics. We have calculated the temperature coefficient bof the width of the band gap for a number of materials in the range where the high-temperature condition is not met. We have found that the Varshni relation overestimates β, whereas calculations based on the Fan expression agree with experiment. Fiz. Tverd. Tela (St. Petersburg) 41, 994–998 (June 1999)     

Holographic design of hexagonal photonic crystals of irregular columns with large full band gap

The shape and size of the dielectric columns or particles (“atoms”) of photonic crystals (PhCs) formed by holographic lithography are determined by the isointensity surfaces of the interference field; consequently the PhCs’ photonic band gap (PBG) properties are closely related to their fabrication design. Here we have proposed a new structure of two-dimensional (2-D) hexagonal lattice with irregular columns, which can yield a 2-D complete relative band gap of 24.0% in case of the dielectric columns of ε = 13.6 in air, about 27% increase compared with that of the same lattice with regular triangular columns. This band gap size is among the largest for all the possible 2-D PhCs reported until now. The relationship between band gap properties of resultant structure and the specific fabrication conditions such as structure design and the choice of optimum intensity threshold and filling ratio are systematically discussed. The optical design for making this structure by two exposures is explained. This work may demonstrate the unique feature and advantages of photonic crystals made by holographic method and provide a guideline for their design and experimental fabrication.