Methods of measuring the nonlinear-optical coefficients of the refractive index of nonlinear media

A cousistent analysis of a method of measuring the coefficient n ₂ of the Kerr nonlinearity and the two-photon absorption coefficient in presented. The method is based on the study of the dependence of the nonlinear transmittance with respect to the far-field axial intensity of the laser beam on the position of the layer of the nonlinear medium on the z (longitudinal) coordinate of this beam (z scanning). The possibility for the measurement of n ₂ and the two-photon (multiphoton) absorption coefficient based on the study of the far-field variations in the spatial profile of the beam having passed through the nonlinear medium is also analyzed. The calculations prove the efficiency of the new method for measuring n ₂ and the two-photon (multiphoton) absorption coefficient.     

Nonlinear responses and optical limiting behavior of fast green FCF dye under a low power CW He-Ne laser irradiation

The nonlinear responses and optical limiting performance of a dye type acid, called fast green FCF, are investigated under irradiation of 35 mW continuous wave He-Ne Laser. The second order refractive index and nonlinear absorption coefficient are measured by use of z-Scan technique. The optical limiting behavior is investigated by transmission measurement through the sample. Linear absorption coefficient (α), nonlinear absorption coefficient (β) and second order refractive index (n₂) of fast green FCF are measured at different concentrations.     

Resonance in the infra-red spectrum of N−

The free-free continuous absorption coefficient of N^- is calculated using multichannel theory and Hartree-Fock target functions. The ³P^e shape resonance due to e-N interactions gives rise to a resonance feature in the absorption coefficient.     

Optical absorption in a heavily doped semiconductor with a narrow forbidden band

The coefficient of interband absorption in a heavily doped, strongly compensated semiconductor with a narrow forbidden band was calculated for emission frequencies ?ω which are smaller than the width? _g of the forbidden band. If the width of the forbidden band is smaller than the characteristic energy w₀ of the random field produced by randomly distributed impurities, the optical absorption gap is missing and the coefficient of absorption increases with the frequency, with the increase being basically proportional toω.     

Optical properties of microphytobenthic biofilms (MPBOM): Biomass retrieval implication

Microphytobenthos Optical Model (MPBOM) provides the optical properties, absorption coefficient and refractive index, of a laboratory simulated microphytobenthic biofilm using the reflectance measurements derived from HySpex laboratory images, with the final aim of estimating photosynthetically active biomass. The high correlation between this biomass, expressed in chlorophyll a (mg Chl a m⁻²) and the absorption coefficient at the corresponding absorption wavelength of Chl a (673 nm) made possible the estimation of biomass for any absorption coefficient calculated from reflectance measurements of any other data set. The latter was validated for an independent data set which performed an acceptable estimation of biomass in comparison with the biomass measured by HPLC (R²=0.93). Finally, this model is designed to be applied to hyperspectral images, like airborne or satellite, in order to map biomass in the field.     

Optical limiting properties of trimeric metallo-phthalocyanines/polymer composite films

The nonlinear absorption and optical limiting properties of two trimeric metallo-phthalocyanines namely, 2,4,6-tris[2-oxa-9,10,16,17,23,24-hexa(hexylthio) phthalocyaninato M(II)]-s-triazine (M=Zn for compound ZnPc and Cu for compound CuPc) doped polyvinyl chloride (PVC) thin film in the nanosecond regime were investigated by using the open-aperture Z-scan technique. The measurements were performed using 4 ns pulses generated from a frequency-doubled Nd:YAG laser at 532 nm wavelength. OL parameters of the ratio of the excited state to ground state absorption cross-sections κ, the effective nonlinear absorption coefficient β_eff, the linear absorption coefficient α₀ and the saturation density or energy density F_sat values were determined. The results show that MPc/PVC composite displays much larger nonlinear absorption coefficient and lower saturable fluence for optical limiting when compared to the same Pc molecules in solution. The results indicated that both compounds exhibited good OL performances. ZnPc shows slightly better OL parameters than that of CuPc.     

Oscillator strength of electron-type color centers in KCl single crystals irradiated with electrons and protons

The absorption spectra of KCl single crystals irradiated with electrons and protons at energies of 15 and 100 keV and a particle flux ranging from 5×10¹² to 10¹⁵ cm^?2 are investigated. The absorption bands attributed to simple (F, F _a, K) and complex (M, R ₂, R ₄, N) color centers are identified in the spectra. The correlation dependences of the absorption coefficients for M, R ₂, and R ₄ centers on the absorption coefficient of F centers and the correlation dependences of the absorption coefficients for R ₂ and R ₄ centers on the absorption coefficient of M centers are established. The oscillator strengths are calculated for M, R ₂, and R ₄ color centers.     

Thermal annealing effect of on optical constants of vacuum evaporated Se75S25−xCdx chalcogenide thin films

Chalcogenide glasses are interesting materials due to their infrared transmitting properties and photo induced effects exhibited by them. Thin films with thickness of 3000 Å of the glasses Se₇₅S_25−xCd_x with x=6, 8 and 10 at% prepared by melt quench technique were evaporated by thermal evaporation onto glass substrates under a vacuum of 10⁻⁶ Torr. The optical constants (absorption coefficient, refractive index and extinction coefficient) of as-prepared and annealed films have been studied as a function of photon energy in the wave length region 400-1000 nm. Analysis of the optical absorption data shows that the rule of non-direct transitions predominates. It has been found that the absorption coefficient and optical band gap increase with increasing annealing temperatures. The refractive index (n) and the extinction coefficient (k) were observed to decrease with increasing annealing temperature.     

The effect of spatial dispersion on the attenuation of exciton polaritons in semiconducting films

We calculate the effective light absorption coefficient K(ω) and the frequency-integrated absorption I = ∫ K(ω) dω caused by spatially dispersive excitons in a semiconductor film. A sharp decrease of I is found for small masses and long lifetimes of the exciton. Oscillations of I as a function of thickness are also reported.     

Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption

The authors have investigated self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption. The field distribution in the medium is expressed in terms of beam-width parameter f, decentred parameter b and absorption coefficient k_i. The differential equation for f parameter is established by following Wentzel–Kramers–Brillouin (WKB) and paraxial approximations through parabolic wave equation approach and analytical solution is obtained for the same. The behavior of f parameter with the normalized distance of propagation η is studied at various values of b with different absorption levels in the medium. The results are presented graphically and discussed.     

X-ray absorption intensity at high-energy region

We theoretically discuss X-ray absorption intensity in high-energy region far from the deepest core threshold to explain the morphology-dependent mass attenuation coefficient of some carbon systems, carbon nanotubes (CNTs), highly oriented pyrolytic graphite (HOPG) and fullerenes (C₆₀). The present theoretical approach is based on the many-body X-ray absorption theory including the intrinsic losses (shake-up losses). In the high-energy region the absorption coefficient has correction term dependent on the solid state effects given in terms of the polarization part of the screened Coulomb interaction W_p. We also discuss the tail of the valence band X-ray absorption intensity. In the carbon systems C 2s contribution has some influence on the attenuation coefficient even in the high energy region at 20 keV.     

Nonextensive black-body distribution function and Einstein's coefficients A and B

The nonextensive statistics of a boson gas within the dilute gas approximation is applied to black-body radiation. Einstein's spontaneous emission coefficient A₂₁, stimulated emission coefficient B₂₁, and absorption coefficient B₁₂ are studied in connection with this new statistical mechanics. Relations including nonextensivity between these coefficients are obtained.     

Origin of the generally defined absorption edge of non-stoichiometric lithium niobate crystals

The ultraviolet absorption edges of LiNbO₃ crystals with different Li₂O contents and MgO doping concentrations were investigated. The generally defined absorption edges at absorption coefficient α=15 or 20 cm⁻¹ of all these crystals fit the Urbach rule perfectly. The origin of this absorption edges in non-stoichiometric LiNbO₃ crystals is attributed to the presence of Li vacancies.     

Acoustic design of small rectangular rooms: Normal frequency statistics

The subject of discrete modes in small rectangular rooms has been considered. A new procedure for selecting optimum geometric proportions of rooms has been proposed, taking into account the eigenfrequencies up to the Schroeder frequency and considering also the surface averaged sound absorption coefficient (α) of a given room. This new procedure leads to a series of plots describing the geometric proportions of small rectangular rooms corresponding to the smoothest frequency response for different absorption conditions. When taking α into account, the range of the acceptable dimension ratios X:Y has proved relatively wide, so the standard deviation calculated for the distances between subsequent modes does not exceed 1.5 (as in Bolt’s work). However, the range of the acceptable dimension ratios decreases with decreasing α and for mean absorption coefficient lower or equal 0.3 there are only a few of the ratios for which a uniform distribution of eigenmodes is obtained.     

Z-scan measurements of optical nonlinearity in acid blue 29 dye

The third order nonlinear optical properties of acid blue 29 solutions have been studied using Z-scan technique. Experiments are performed using a CW He–Ne laser at 632.8 nm wavelength and 3 mW power. The linear absorption coefficient α₀, nonlinear absorption coefficient β, nonlinear refractive index n₂, Re χ³, and Im χ³ are measured at three different concentrations. Our results show that higher concentration gives better nonlinear optical properties. Also, it was found that there is an increasing trend in the value of the nonlinear refractive index n₂ as the concentration increases.     

Optical characterization of radiative semiconductors

This paper describes a direct photoluminescent method of characterizing high quantum efficiency semiconductors in terms of an “effective absorption coefficient” which is a function of the absorption coefficient and of the diffusion length of excess minority carriers injected optically.The results obtained by this method indicate that the diffusion lengths in unintentionally doped (pure) and n and p-type GaAs can be in excess of 0.03 cm at room temperature, and that surface and bulk radiation processes in these materials can be separated.     

Effect of position-dependent effective mass on linear and nonlinear optical properties of a cubic quantum dot

In this paper, we first obtain an analytic relation for studying the position-dependent effective mass in a GaAs/Al_xGa_1−xAs cubic quantum dot. Then, the effect of position-dependent effective mass on the intersubband optical absorption coefficient and the refractive index change in the quantum dot are studied. Our numerical calculations are performed using both a constant effective mass and the position-dependent effective mass. We calculate the linear, nonlinear and total intersubband absorption coefficient and refractive index change as a function of the incident optical intensity and structural parameters such as dot length. The results obtained from the present work show that spatially varying electron effective mass plays an important role in the intersubband optical absorption coefficient and refractive index change in a cubic quantum dot.     

IR absorption in p-type pb0.97Sn0.03Se

IR absorption in p-type melt grown Pb_0.97Sn_0.03Se crystals is reported. The results for the room temperature absorption coefficient (α) in the wavelength region 2–15 μm are analysed. The indirect absorption edge is found to be at 0.26 eV for this ternary alloy. In the longwavelength region α is found to be proportional to λ², in agreement with the classical free carrier absorption expression. The conductivity effective mass of holes is found to be 0.067 m₀ at 300°K.     

Oscillation dependence of two-wave mixing gain for unidirectional ring resonator in photorefractive materials

Dependence of the coupling strength of two-wave mixing gain in photorefractive materials for the single unidirectional ring resonator on oscillation conditions has been analyzed in the strong nonlinear regime. In this regime, difference between the frequency of the pump beam and oscillating beam is proportional to the cavity-length detuning, which can be explained in terms of the photorefractive phase-shift. This phase-shift results due to slightly non-degenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for the steady-state oscillation. The presence of such a phase-shift allows the possibility of the nonreciprocal steady-state energy transfer between the pump and oscillating beams. If the gain due to the beam coupling is large enough to overcome the cavity losses then the signal beam is amplified in the presence of material absorption. Such amplification is responsible for the oscillations. For the single unidirectional ring resonator, the effects of cavity-length detuning, energy coupling coefficient, crystal thickness of the material, reflectivity of the cavity mirrors and material's absorption coefficient on the frequency and intensity of oscillations have also been studied in detail. It has been found that for the smaller value of absorption coefficient (α) of the photorefractive crystal, the unidirectional ring resonator can oscillate at almost any cavity-length detuning (ΔΓ) whereas for the larger value of α oscillation occurs only when the cavity-length detuning is limited to small region (around ΔΓ=0). But reverse of the case is found for energy coupling coefficient (γ₀).     

Bound-to-extended state absorption in quantum wells confined byδ-like barriers

Within the framework of a simple envelope function and effective mass approximation, by including the spatial variation of effective mass and nonparabolicity effects, we have investigated the energy spectrum and intersubband optical absorption in a quantum well with additional thin and higher (δ -like) cladding barriers on either side of the well. The dependence of the absorption coefficient on the structure parameters, doping level, photon energy and temperature has been investigated. The absorption coefficient and spectrum strongly depend on the cladding barrier tunnel transparency. The peak absorption wavelength is shifted towards the high energies as the barrier transparency decreases. The temperature shift of the absorption peak is very small. The results are compared with experiments of Schneider et al. taking into account the broadening induced by well width fluctuations.