Dielectric and optical behaviors in relaxor ferroelectric Pb(In1/2Nb1/2)1−xTixO3 crystal

Dielectric permittivities (ε′,ε″) have been measured as functions of temperature (140-535 K) and frequency (500 Hz-2.0 MHz) in a (001)-cut Pb(In_1/2Nb_1/2)_0.7Ti_0.3O₃ (PINT30%) single crystal grown by the modified Bridgman method with Pb(Mg_1/3Nb_2/3)_0.71Ti_0.29O₃ (PMNT29%) seed crystal. A diffused phase transition was observed in the temperature region of ∼430-460 K with strong frequency dispersion. Above the Burns temperature T_B≅510 K, the dielectric permittivity was found to follow the Curie-Weiss behavior, ε′=C/(T−T_C), with parameters C=3.9×10⁵ and T_C=472 K. Below T_B≅510 K, polar nanoclusters are considered to appear and are responsible for the diffused dielectric anomaly. Optical transmission, refractive indices, and the Cauchy equations were obtained as a function of wavelength at room temperature. The unpoled crystal shows almost no birefringence, indicating that the average structural symmetry is optically isotropic. The crystal exhibits a broad transparency in the wavelength range of ∼0.4-6.0 μm.     

Relaxation of Dielectric Loss Peak over Intermediate Temperature Range in Bi5TiNbWO15 Intergrowth

A dielectric loss peak with relaxation-type characteristic is observed in Bi5TiNbWO15 over 200-400℃. The modified Cole-Cole relation by introducing relaxation strength as another important fitting parameter is used to describe this temperature-dependent behaviour of dielectric relaxation process. This peak is considered to be associated with the oxygen vacancies inside the grains and with its activation energy by relaxation determined to be 0.76eV. The obtained broadening factor α is around 0.4, which indicates a strong correlation between those relaxation units. It is confirmed that the behaviour of this peak is due to the combined effects of the dielectric relaxation and electrical conduction by the thermal motion of oxygen vacancies. These results axe further confirmed in Bi5TiNbWO15 samples through oxidization atmosphere treatment and Nd modification respectively.     

Dielectric Properties of GaN in THz Frequencies

The complex refractive indices and the dielectric function of GaN for frequencies ranging from 0.25 to 1.22THz are obtained using THz time-domain spectroscopy. The real part of the dielectric function first decreases from 0.25 to 0.42THz and then oscillates from 0.42 to 1.22THz, whereas the imaginary part of the dielectric function is oscillating within the whole range of frequency. The simple Drude model is extended to take into account the effect of defects on the dielectric function. The extended model is in agreement with the experimental data.     

Correlation of the left- and the right-handed circularly polarized waves in an anisotropic crystal

An optical torque is induced by incidence of the linearly polarized light and propagating through an anisotropic crystal, which results in self-modulation of the ordinary and the extraordinary waves and causes an energy splitting of the resultant left-, and the right-handed elliptically polarized waves. The optical torque originates from the angular momentum of light, which causes the correlation of the left- and the right-handed circularly polarized waves in the crystal.     

Entanglement of the l- and the r-photons in an anisotropic crystal

Light incident onto an anisotropic crystal is divided into the ordinary and the extraordinary waves which vibrate in two perpendicular directions. Because of the tensor property of the dielectric constant, the direction of the electric displacement is not parallel to the vector of the incident electric field. An optical torque is induced by incidence of the linearly polarized light and propagating through the crystal. The optical torque tends to rotate the directions of eigenvibration which results in self-modulation of the ordinary and the extraordinary waves, and causes an energy splitting of the left (l)-, and the right (r)-handed circularly polarized waves in the crystal. The l- and the r-photons are correlated through the optical torque, which are found to be in an entanglement state.     

The structure and optical properties of evaporated Samarium fluoride films

Samarium fluoride (SmF₃) films have been deposited on quartz, silicon and germanium substrates by vacuum evaporation method. The crystal structure of the films deposited on silicon substrate is examined by X-ray diffraction (XRD). The films deposited at 100 °C, 150 °C and 250 °C have the (1 1 1) preferred growth orientation, but the film deposited at 200 °C has (3 6 0) growth orientation. The surface morphology evolution of the films with different thickness is investigated with optical microscopy. It is shown that the microcrack density and orientation of thin film is different from that of thick film. The transmission spectrum of SmF₃ films is measured from 200 nm to 20 μm. It is found that this material has good transparency from deep violet to far infrared. The optical constants of SmF₃ films from 200 nm to 12 μm are calculated by fitting the transmission spectrum of the films using Lorentz oscillator model.     

General theory for the interference of two-photon and one-photon processes in semiconductor heterostructures

We develop a general theory for the dynamics of multi-photon processes in semiconductor heterostructures. The resulting effective multi-band Bloch equations describe the dynamics of electrons in the reduced set of bands between which the optical pulses induce quasi-resonant transitions. The model is specialized to the case of interfering one- and two-photon transitions across the band gap. The withdrawn bands are included as intermediate states for an effective interaction that is quadratic in the electromagnetic fields. The benefit of this perturbative approach is to lead to equations of motion for slowly varying quantities only, in the spirit of the rotating wave approximation. Coulomb interaction and relaxation can also easily be included. Finally, a general expression for the time dependent polarization current that is consistent with the approximations involved by the effective multi-band Bloch equations is derived.     

Classical light dispersion theory in a regular lattice

We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by all the other particles, and to the radiation reaction expressed according to the Lorentz-Dirac equation. Exact normal mode solutions, describing the propagation of plane electromagnetic waves through the lattice, are obtained for the complete linearized system of infinitely many oscillators. At variance with all the available results, our method is valid for any values of the frequency, or of the ratio between wavelength and lattice parameter. A remarkable feature is that the proper inclusion of radiation reaction in the dynamics of the individual oscillators does not give rise to any extinction coefficient for the global normal modes of the lattice. The dispersion relations resulting from our solution are numerically studied for the case of a simple cubic lattice. New predictions are obtained in this way about the behavior of the crystal at frequencies near the proper oscillation frequency of the dipoles.     

Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background

We analyze the band gap spectra of two-dimensional photonic crystals created by square, triangular and honeycomb lattices of air rings with different geometrical shapes and orientations in anisotropic tellurium background. Specifically, five different shapes of rings (circular, hexagonal, elliptical, rectangular and square) are considered. Using the numerical plane wave method, we discuss the maximization of the absolute photonic band gap width as a function of air ring parameters with different shapes and orientations in three types of lattices.     

Negative magnetic permeability of split ring resonators in the visible light region

Negative magnetic permeability of split ring resonator (SRR) is theoretically investigated in the visible light region. In our calculations, we considered the delay of the current inside the metal SRR in order to estimate the permeability of the SRR precisely. From the results, the silver SRR array with small capacitance exhibits negative permeability in all the visible range. The dependence of the permeability on the filling factor of the SRR elements is also discussed.     

Theoretical investigation of chirped mirrors in semiconductor lasers

This paper reports a theoretical design of chirped mirrors in 1.3-μm double-section semiconductor lasers to achieve high reflectivity and dispersion compensation over a broad bandwidth. Analytic expressions for reflectivity, group delay and group delay dispersion are derived. We use for the first time chirped air/semiconductor layer pairs as mirrors for higher-order dispersion compensation in semiconductor lasers. Our optimised calculations demonstrate that the broad-band mirrors designed consist of a total of only 12 air/semiconductor layers and achieve a reflectivity higher than 99.8%, a smooth group delay and almost stable dispersion in the laser cavity over a 100-nm bandwidth. Due to a high index contrast of both types of the layers, n _l = 1, n _h~ 3.5, a high-reflectivity bandwidth of > 700 nm is obtained in 1.3-μm semiconductor lasers. We also compare our results with that of a commercial simulation program and show a good agreement between them. As a conclusion, we assume from the theoretical results that air/semiconductor layer pairs with varying thicknesses used at one end of double-section semiconductor lasers can lead to femtosecond optical pulse generation using mode-locking techniques. An erratum to this article can be found at .     

The pressure influence on the incommensurate-commensurate ferroelectric phase transition in [4-NH2C5H4NH][SbCl4]

The dielectric properties of the [4-NH₂C₅H₄NH] SbCl₄ (abbreviated as 4-APCA) crystal were investigated under hydrostatic pressure up to 300 Mpa. The pressure-temperature phase diagram was given. The paraelectric-ferroelectric phase transition (II→III) temperature (T_c) increases linearly with increasing pressure with a slope dT_c/dp=21×10⁻² K/MPa. The pressure dependence of Curie-Weiss constants has been evaluated also. In the paraelectric phase (II) the Curie constant (C₊) was pressure dependent whereas the C₋ constant over the ferroelectric phase (III) was almost constant. The results are interpreted in terms of improper and displacive type phase transition model with a soft phonon at a zone boundary.     

Investigations on the soft-mode mechanism of the ferroelectric phase transition in

Dielectric and Raman spectroscopic measurements have been performed to investigate the ferroelectric phase transition in . Single crystals were grown by the zone melting method. The frequency dependence of the dielectric permittivity from 1 MHz to 1 GHz has been studied in a temperature range between 265 and 285 K. A Debye like dielectric dispersion was found, showing a critical slowing down around K. Polarized Raman spectra have been taken between 220 and 310 K. Two softening modes have been found, one of A- and another one of B / B g-symmetry. The phase transition mechanism in can be classified as partially order-disorder and partially displacive, confirming former structural results. It resembles strongly that of monoclinic . Received: 7 April 1998 / Revised: 5 June 1998 / Accepted: 16 June 1998     

Slowing down of the relaxational dynamics at the ferroelectric phase transition in one-dimensional (TMTTF)2AsF6

We present measurements of the dielectric response of quasi one-dimensional system (TMTTF)₂AsF₆ in a wide temperature and frequency range. We provide a thorough characterization of the relaxational dynamics observed close to the ferroelectric-like transition at T_c=100 K. Our measurements, extending up to 100 MHz, reveal a continuous slowing down of the mean relaxation time when approaching T_c from high as well as from low temperatures. The simultaneous critical rise of the dielectric constant and relaxation time point to an explanation of the transition in terms of a classic ferroelectric scenario.     

Influence of grooves in the electromagnetic transmission of a periodic metallic grating filter

The light transmittance of metal film with periodic slits and grooves structure has been investigated. It was demonstrated that the grooves significantly affect the transmittance of the metal film. The structure excavating two grooves symmetric to the central slit in a cell of a period grating displays a dent in the transmission spectrum comparing with the structure with only one slit in the cell. Deepening the grooves moves the dents to the longer wavelengths in the transmission spectrum. An analytical equation is also provided to approximately locate the dents. The grooves in the grating filter supply the advantage of removing the needless transmission of certain frequency.     

Giant optical activity and circular dichroism in the terahertz region based on bi-layer Y-shaped chiral metamaterial

We present a bi-layer Y-shaped chiral metamaterial (CMM) that can realize a giant optical activity and circular dichroism (CD) effect to the incident linear polarization wave in the terahertz (THz) region. Numerical simulation results exhibit that the pronounced CD effect with a great difference between the transmission coefficients for the circularly polarized waves can be obtained at 5.06 THz, meanwhile the 90°-polarization rotation can be observed at 5.2 THz when a y-polarized wave is incident to this CMM propagating along the −z-axis. The mechanism of the optical activity and giant CD effect is illustrated by simulated surface current distributions. Further, the influences of the structural parameters of the proposed CMM to the optical activity and CD effect have been investigated numerically.     

Determination of size and concentration of copper nanoparticles dispersed in glasses using spectroscopic ellipsometry

For the generation of particular optical properties the melt of a commercially manufactured glass is doped with copper compounds. The glass obtained is opaque black at the usual thickness and looks dark red after making it into bulbs of incandescent lamps. It is generally assumed that copper particles cause this colouring. A proof in a spectrophotometric way fails due to the very high absorbance even for a sample thickness below 20 μm. It will be shown that in these cases spectroscopic ellipsometry is a suitable method of investigation. The pseudo-optical constants of this material were determined as a function of wavelength in the range from 350 nm to 700 nm by ellipsometric measurements. They can be reproduced very well by those of a model that consists of a roughness layer situated on a substrate of glass containing spherical copper particles with a Gaussian size distribution with =6.5 nm and σ=0.24 and a volume concentration of 2.4×10^-3. For this modelling the dielectric function of the roughness layer was approximated by Bruggeman effective-medium theory and that of the copper-containing glass substrate was calculated on the basis of the theory of Gans and Happel. The results were verified by transmission electron microscope investigations. Received: 1 July 2001 / Published online: 10 October 2001     

Effect of Cu-stoichiometry on the dielectric and electric properties in CaCu3Ti4O12 ceramics

CaCu_3+yTi₄O₁₂ (y=0, ±0.025, ±0.05, ±0.1 and −0.15) ceramics are prepared by the conventional solid-state reaction technique under sintering condition of 1050 ^°C, 10 h. X-ray diffraction shows that they all have the good crystalline structure. Cu-deficient ceramics exhibit the microstructures of uniform grain size distribution, whereas both Cu-stoichiometric and Cu-rich ceramics display microstructures of bimodal grain size distribution. The largeness of low-frequency dielectric permittivity at room temperature is found to be very sensitive to the Cu-stoichiometry. Upon raising the measuring temperature, all of the ceramics present commonly three semicircles in the complex impedance plane. It indicates that there exist three distinct contributions, which are ascribed to arising from domains, grain boundaries and domain boundaries. In addition, the influence of CuO segregation on the dielectric and electrical properties is also discussed.     

Focal Shift of Paraxial Gaussian Beams in a Left-Handed Material Slab Lens

Focal shift is inevitable in conventional lens systems due to the Fresnel number and angular aperture. In this Letter, we demonstrate that there is no focal shift when a paraxial Gaussian beam passes through a left-handed material slab lens without absorption or gain. However, the effect is exhibited in the presence of absorption or gain, and becomes larger as the absorption or gain increases. When the absorption is equal to the gain, the phenomenon of the focal shift caused by the gain is more obvious. In addition, the field distribution is not affected by the absorption or gain and always remains Gaussian both in internal and external focus planes.     

Copropagation of two pulses of different frequencies and modulation instabilities induced by cross-phase modulation in metamaterials

Nonlinear coupled equations describing the copropagation of two light pulses of different central frequencies in metamaterials (MMs) are derived. Based on the derived equations and the Drude model for dispersive MMs, the modulation instabilities (MIs) induced by cross-phase modulation (XPM) for different combination of the signs of refractive index experienced by the two optical pulses, respectively, are analyzed. It is shown that, in the absence of group-velocity mismatch, the property of MI only depends on the sign of group-velocity dispersion the two pulses experience, irrespective of the sign of refractive index. The group-velocity mismatch plays an important role in the occurrence of MI, especially when the central frequencies of the two pulses near the electric or magnetic plasma frequency of the MM. The theoretical results are confirmed by numerical simulations.