Analysis of the diffraction by the gratings generated in the materials with a nonlinear response

Diffraction by a thick transmission phase grating being illuminated by a plane wave at the first, second and third Bragg angles is analyzed using the rigorous coupled-wave theory for the materials having a nonlinear response to the holographic illumination. It is shown that in the case of nonlinear holographic recording the two-wave approximation can be applied with the use of the effective value of the amplitudes of the refractive index modulation (n_1ef, n_2ef, and n_3ef). The applicability conditions of such approximation are defined. The analytical dependencies of n_1ef, n_2ef, and n_3ef on the amplitudes of the first, second and third harmonics of spatial frequency of the refraction index modulation amplitude n₁, n₂ and n₃ are derived and the criteria of their applicability are established here. The resulting expressions for the diffraction efficiencies are given for readout at three Bragg angles. The results of analytical and numerical methods are compared. The obtained formulas are used for the calculation of n₁, n₂ and n₃ of the holographic gratings generated in the photopolymer material.     

Microwave Photonic Crystal from Spirals

Features of microwave propagation through a two-dimensional periodic structure of cylindrical spiral coils were studied in the frequency range from 8.5 to 12 GHz. The frequency dependence of the effective refractive index n_ef of the structure is measured. The features of measurements are noted and the structure reflectance is estimated in various regions of the frequency range under study. In the frequency range where n_ef ~ 0, a surface wave propagating around the structure is detected.     

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.     

2D Periodic Structure for Acoustic and Electromagnetic Radiation

The propagation of microwaves in the frequency range from 8.5 to 12GHz and acoustic radiation in the frequency range from 8.5 to 14 kHz in the same 2D periodic crystal formed by cylindrical spiral coils has been investigated. The frequency ranges in which the effective refractive index n_ef of the crystal is close to zero are found. In these ranges, microwaves are collimated and concentrated in a narrow lobe with an FWHM of about 9?. Focusing of divergent microwave and acoustic beams by a flat periodic structure has been observed in the frequency range where the effective refractive index of this structure is negative.     

Effects of Pb addition and heat treatment on optical properties of thermally evaporated Ge1−xSe2Pbx thin films

Thin chalcogenide films of Ge_1−xSe₂Pb_x (x=0, 0.2, 0.4, 0.6 and 0.8) have been prepared by the thermal evaporation technique, from previously synthesized bulk samples. The X-ray diffraction showed the amorphous nature for the as-deposited films and the partially crystalline for the annealed films. The optical constants (the refractive index, n, and absorption index k) were determined for as-deposited and annealed Ge_1−xSe₂Pb_x films of different thicknesses by using spectrophotometeric measurements of the transmittance and reflectance at normal incidence in the spectral range 200-2500 nm. The obtained values of both n and k were found to be independent of the film thickness. The optical absorption edges are described using both the Urbach rule and the indirect transition. In transparent region, the spectral dependences of refractive index were interpreted in the frame of a single oscillator model.     

Linear optical properties of γ-modification of bismuth borate BiB3O6

The refractive index dispersion of the ??-BiB₃O₆ crystal in the wavelength range 0.43?C0.81 ??m has been measured. It has been shown that the principal refractive indices n ₁, n ₂, and n ₃ are on average higher than those of ??-BiB₃O₆, but are slightly lower than those of ??-BiB₃O₆. The temperature dependences of the rotation angle ??(T) of the optical indicatrix and birefringence ??n ₂(T) = (n ₁ ? n ₃)(T) have been studied in the temperature range 100?C963 K. It has been shown that the ??-BiB₃O₆ crystal is stable in this temperature region.     

Wavelength modulation absorption spectrometry from optically saturated collision-broadened transitions

A theoretical investigation of the influence of optical saturation on wavelength modulation absorption spectrometry (WMAS) signals from collision-broadened transitions is presented. Expressions are derived for the nth Fourier coefficient of the analytical detector signal, and thereby also for the nth harmonic signal from a WMAS instrumentation (i.e. the nf-WMAS signal), from a wavelength modulated collision-broadened transition exposed to optical saturation. The flux- (or irradiance-) and modulation-amplitude dependences of the nf-WMAS signal on resonance are scrutinized in detail. It is shown that the nth Fourier coefficient of the wavelength modulated analytical detector signal from an optically saturated collision-broadened transition can be written as a product of a flux-dependent (φ) bleaching function, given by (1+φ/φ_sat)^-1 and identical to that appearing for ordinary, unmodulated absorption spectrometry (AS), and a flux-, detuning-, and modulation-amplitude-dependent wavelength modulated peak-normalized saturation-broadened Lorentzian lineshape function, specific for the WMAS technique. It is found that the nf-WMAS signal on resonance decreases faster than an ordinary AS signal as a function of laser flux when smaller-than-optimum modulation amplitudes are used, but slower when larger-than-optimum modulation amplitudes are used. When optimum (or close-to-optimum) modulation amplitudes are being used, on the other hand, the flux dependence of the WMAS signal resembles to a large degree that of ordinary AS. The conditions for when WMAS from collision-broadened transitions has the same flux dependence as ordinary AS are identified.     

The effect of impurity on temperature variations in the refractive indices and thickness of TGS crystals

Temperature dependences of optical path difference δΔ_? and the relative changes in thickness δl_?/l of TGS crystals doped with L-valine are studied. Temperature dependences of the relative changes in refractive indices δn_?/(n–1) are calculated. The anisotropy coefficients of refractive indices А_n–1(Т) and linear expansion Аα(Т) are calculated, and a characteristic minimum of these dependences is found near the phase transition temperature.     

Composition-tuned refractive index and oscillator parameters in TlGaxIn1−xS2 layered mixed crystals (0≤x≤1)

The optical properties of TlGa_xIn_1?xS₂ mixed crystals have been studied through transmission and reflection measurements in the wavelength range 400–1100 nm. These measurements allowed determination of the spectral dependence of the refractive index for all compositions of the mixed crystals studied. The dispersion of the refractive index is discussed in terms of the Wemple–DiDomenico single-effective-oscillator model. The compositional dependences of the refractive index dispersion parameters (oscillator energy, dispersion energy and zero-frequency refractive index) were revealed.     

Interrelation between optical, refractometric, and lattice parameters of Cu6P(S1−x Sex)5I crystals

The influence of the compositional disordering on the energy of the fundamental absorption edge and the refractive index dispersion of the crystalline solid solutions Cu₆P(S_1?x Se_x)₅I is studied. It is shown that the concentration dependences of the optical pseudogap width, the refractive index, and the lattice parameter in these crystalline solid solutions are interrelated.     

Nonlinear refractive index measurements and self-action effects in Roselle-Hibiscus Sabdariffa solutions

We report the observation of self-action phenomena, such as self-focusing, self-defocusing, self-phase modulation and beam fanning in Roselle-Hibiscus Sabdariffa solutions. This material is found to be a new type of natural nonlinear media, and the nonlinear reflective index coefficient has been determined using a Z-scan technique and by measuring the critical power for the self-trapping effect. Z-scan measurements show that this material has a large negative nonlinear refractive index, n ₂ = 1 × 10^?4 esu. A comparison between the experimental n ₂ values and the calculated thermal value for n ₂ suggests that the major contribution to nonlinear response is of thermal origin.     

Optical coefficients of Hg1 − x − y Cd x Eu y Se crystals

Optical properties of Hg_{1 ? x ? y} Cd _x Eu _y Se crystals grown by the Bridgman method have been investigated based on the independent reflectance and transmittance measurements, which were performed on a Nicolet 6700 spectrometer at T = 300 K in the wavelength range 0.9 ≤ λ ≤ 26.6 μm. The values of refractive index n, absorption index k, and absorption coefficient α have been determined for the crystals studied. Based on the dependences α = f(hν), the presence of direct allowed interband optical transitions in the crystals is established and the band-gap values are determined. The influence of temperature on the transmittance and band gap are investigated in the range T = 114–300 K.     

Simulation of elasto optical properties of K2SO4 crystals

The electronic optical spectra of the mechanically free and stressed crystals of potassium sulfate, K₂SO₄, in the orthorhombic phase Pnma have been calculated by the Cambridge Serial Total Energy Package (CASTEP) code. On the basis of these calculations, the components of stress elasto optical tensors based on the changes of refractive index n (π_im) and birefringence Δn () (i, k, m=1, 2, …, 6) have been obtained for the indices i, k ,m=1, 2, 3. Absolute magnitudes of the calculated tensor π_im are probably underestimated because the magnitudes of the calculated elastic stiffness tensor c_rm are found to be overestimated about two times. Features of the spectral dependences n(E) and k(E) of refractive and absorption indices of the mechanically free and stressed potassium sulfate crystals have been analyzed.     

The Lorentz-Lorenz function of five gaseous and liquid saturated hydrocarbons

The refractive indices of compressed gaseous and liquid ethane, propane,n-butane,n-pentane, and liquidn-hexane were measured on up to seven isotherms at temperatures between 290 K and 500 K. Densities ranged from 0.2 g/cm³ to 0.7 g/cm³ at pressures up to 170 bar. The refractive index valuesn were combined with simultaneously measured density values ?, to compute the Lorentz-Lorenz function LL =(n ²-1)M/(n ²+2) ?=A _n+B_n(?/M), whereM is the molar mass andA _n andB _n are the first and second refractive index virial coefficients. Additionally, the functions LL/z (z=pV/nRT is the compressibility factor) of ethane, propane, andn-butane were computed to determine the second refractive index virial coefficientsB _n(T). The relative uncertainty of the measured LL functions is 0.1% in most cases. At constant temperature (LL?A _n)/A_n is ≦5·10^?3 for ethane, propane, andn-butane and ≦0.02 forn-pentane andn-hexane. The greatest deviations of the LL functions from theA _n value were measured at the temperatures near the critical points. TheA _n-values show a temperature dependence which increases with increasing molar mass (maximum value: ΔA _n/ΔT=0.0044 cm³/mol · K). The slopes of the LL-function become lower and the LL maxima become smaller with increasing distance of the temperature from the critical point. TheB _n values increase linearly with reciprocal temperature.     

Differences between surface and bulk refractive indices of a-InxSe1−x

Thin films of amorphous indium selenide compounds (a-In_xSe_1−x) are important, e.g. for photovoltaics. The feature of merit in such applications is also the real part of refractive index n of this material. The data on n in literature are divergent. In this paper, the results of investigations on n in the bulk as well as in the interface layers of thin films of a-In_xSe_1−x are presented. The measurements had been performed using optical transmittance and reflectance in spectral range from 1.24 to 1.96 eV of linear polarized radiation that hit the samples with angles of incidence from 0° to 80°. Investigations had been done for sample temperatures from 80 to 340 K. It was found that the refractive index for areas at the free surface n_f is bigger than the refractive index n_b at the interface of thin film-substrate. The averaged over thin film thickness value of real part refractive index have the biggest value in all spectral range. Values of these coefficients increase with increasing the temperature.     

Optical parameters of epitaxial GaN thin film on Si substrate from the reflection spectrum

A method has been proposed for determining the optical properties of a thin film layer on absorbing substrates. The film optical parameters such as thickness, refractive index, absorption coefficient, extinction coefficient and the optical energy gap of an absorbing film are retrieved from the interference fringes of the reflection spectrum at normal incidence. The envelopes of the maxima of the spectrum E_M and of the minima E_m are introduced in analytical forms to find the reflectance amplitudes at the interfaces and approximate values of the thin film refractive index. Then, the interference orders and film thickness are calculated to get accurate values of the needed optical parameters. There are no complex fitting procedures or assumed theoretical refractive index dispersion relations. The method is applied to calculate the optical properties of an epitaxial gallium nitride thin film on a silicon (1 1 1) substrate. Good agreement between our results and the published data are obtained.     

Refractive index behavior of SiO2-P2O5 glass in optical fiber application

The refractive index of SiO₂-P₂O₅ glass prepared by a modified chemical vapor deposition method is measured using an interference microscope. It is found that the refractive index in bulk form increases linearly at 9.5×10^-4 (mol.%)^-1 as the P₂O₅ concentration increases. It is also found that quenching at extremely high speed reduces the refractive index over 2 mol.% P₂O₅. The wavelength dispersion of the refractive index dn/dλ is constant up to 5 mol.% P₂O₅ producing a refractive index difference of 5×10^-3 compared with fused silica. Consequently, this glass materials is thought to be suitable for wide band-width optical fiber applications.     

Changes in fluorescence lifetimes induced by variation of of the radiating molecules' optical environment

We report results of experiments with about 30 nm thick evaporated layers of an europium-chelate fluorescing at λ = 612 nm: i.) For layers on different substrates S₁ in air the lifetime decreases with increasing refractive index n₁ of S₁. ii.) For a layer on a substrate S₁ the lifetime decreases when the width d of an air gap between the layer and a second plate S₂ is reduced from d å λ to d = 0. Theoretically, we derived analytic expressions for the spontaneous emission rates of electric and magnetic dipole transitions taking place in an atomic system embedded in a very thin layer of refractive index n₀ and optical thickness $\text{n}{}_0\text{d}{}_0\text{« λ/8}$, which is sandwiched between two dielectric loss-free media of refractive indices n₁ and n₂. Comparison of theory and experiment allows to determine the absolute quantum efficiency of the emitting state.     

Effect of annealing on structure and optical properties of Ga5Se95 films

To investigate the effect of annealing on the structural and optical properties of a binary compound Ga₅Se₉₅, thin films of Ga₅Se₉₅ have been deposited on quartz substrates at room temperature by the thermal evaporation technique. X-ray diffraction patterns showed that the films before and after annealing at 573 K have polycrystalline texture and exhibit tetragonal structure. The dependences of the optical constants, the refractive index n and extinction coefficient k were studied in the spectral range of 200 nm to 2500 nm. The normal dispersion of the refractive index of the films could be described using the Wemple–DiDomenco single-oscillator model. Analysis of absorption index data reveals that as-deposited Ga₅Se₉₅ films has indirect transitions with optical energy gap of 1.685 eV.     

The effects of external applied voltage on the nonlinear refractive index and the birefringence of a dye-doped nematic mixture

The nonlinear refractive index, n₂, and the birefringence, Δn, of a nematic liquid crystal mixture (denoted as 1294-1b) doped with a anthraquinone derivative (denoted as AQ) dye were measured as a function of an external ac applied voltage. The self-phased modulation effect was used to measure the nonlinear refractive index of homeotropical-aligned samples. The change of the dyed liquid crystal nonlinearity, which is the direct impact of the applied voltage on the dye molecules orientation, was not observed for the nonlinear response of the pure liquid crystal. Planar (homogeneous) aligned samples were used for birefringence measurements by taking into account the absorption coefficients of the dye. The birefringence decreased to a limiting value in the high voltage region for both pure and dye-doped samples, although in the presence of the absorbing dye the birefringence of the liquid crystal was not approximately changed.The polarized absorption spectra of the dye in nematic mixture were recorded in parallel-aligned liquid crystal cell and its dichroic ratio R and the order parameter S_d were obtained. The electro-optical effect of the guest-host system was also using polarized spectroscopic method.