The bound electronic nonlinear refractive index, n/sub 2/, and two-photon absorption (2PA) coefficient, /spl beta/, are measured in a variety of inorganic dielectric solids at the four harmonics of the Nd:YAG laser using Z scan. The specific materials studied are: barium fluoride (BaF/sub 2/), calcite (CaCO/sub 3/), potassium bromide (KBr), lithium fluoride (LiF), magnesium fluoride (MgF/sub 2/), sapphire (Al/sub 2/O/sub 3/), a tellurite glass (75%TeO/sub 2/+20%ZnO+5%Na/sub 2/O) and fused silica (SiO/sub 2/). We also report n/sub 2/ and /spl beta/ in three second-order, /spl chi//sup (2)/, nonlinear crystals: potassium titanyl phosphate (KTiOPO/sub 4/ or KTP), lithium niobate (LiNbO/sub 3/), and /spl beta/-barium berate (/spl beta/-BaB/sub 2/O/sub 4/ or BBO). Nonlinear absorption or refraction can alter the wavelength conversion efficiency in these materials. The results of this study are compared to a simple two-parabolic band model originally developed to describe zincblende semiconductors. This model gives the bandgap energy (E/sub g/) scaling and spectrum of the change in absorption. The dispersion of nl as obtained from a Kramers-Kronig transformation of this absorption change scales as E/sub g//sup -1/. The agreement of this theory to data for semiconductors was excellent. However, as could be expected, the agreement for these wide bandgap materials is not as good, although general trends such as increasing nonlinearity with decreasing bandgap energy can be seen.

Infrared to ultraviolet measurements of two-photon absorption and n/sub 2/ in wide bandgap solids

We report experimental values for the nonlinear optical coefficients of AlGaAs, in the half-band-gap spectral region. The dispersion of the nonlinear refractive-index coefficient, n/sub 2/, is measured for both TE- and TM-polarized light. We observe n/sub 2/(TE)>n/sub 2/(TM) and a ratio of cross-phase modulation to self-phase modulation (TE) of /spl sim/0.95, as predicted from band structure calculations. The spectral dependence of the two- and three-photon absorption coefficients are also measured. Finally, the implications for all-optical switching and spatial soliton propagation are discussed.

The nonlinear optical properties of AlGaAs at the half band gap

Organometallic trihalide perovskites are solution-processed semiconductors that have made great strides in third-generation thin film light-harvesting and light-emitting optoelectronic devices. Recently, it has been demonstrated that large, high-purity single crystals of these perovskites can be synthesized from the solution phase. These crystals’ large dimensions, clean bandgap, and solid-state order have provided us with a suitable medium to observe and quantify two-photon absorption in perovskites. When CH3NH3PbBr3 single crystals are pumped with intense 800 nm light, we observe band-to-band photoluminescence at 572 nm, indicative of two-photon absorption. We report the nonlinear absorption coefficient of CH3NH3PbBr3 perovskites to be 8.6 cm GW–1 at 800 nm, comparable to epitaxial single-crystal semiconductors of similar bandgap. We have leveraged this nonlinear process to electrically autocorrelate a 100 fs pulsed laser using a two-photon perovskite photodetector. This work demonstrates the viability ...

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Two-Photon Absorption in Organometallic Bromide Perovskites

Nonlinear polarization rotation and generation of a polarization component orthogonal to the input beam were observed along fourfold axes of YVO4 and BaF2 crystals. We demonstrate experimentally that in both crystals the angle of rotation is proportional, at low intensities, to the square of the product of the input intensity and the crystal length and is the result of simultaneous action of two third-order processes. This type of nonlinear polarization rotation is driven by the real part of the cubic susceptibility. The recorded energy exchange between the two orthogonal components can exceed 10%. It is to our knowledge the highest energy-conversion efficiency achieved in a single beam nonresonant χ(3) interaction. A simple theoretical model is elaborated to describe the dependence of nonlinear polarization rotation and orthogonal polarization generation on the intensity of the input beam at both low- and high-intensity levels. It reveals the potential contributions from the real and the imaginary parts of the susceptibility tensor. Moreover, this kind of measurement is designed to permit the determination of the magnitude and the sign of the anisotropy of the real part of third-order nonlinearity in crystals with cubic or tetragonal symmetry on the basis of polarization-rotation measurements. The χxxxx(3) component of the third-order susceptibility tensor and its anisotropy sign and amplitude value for BaF2 and YVO4 crystals are estimated and discussed.

Nonlinear polarization rotation and orthogonal polarization generation experienced in a single-beam configuration

An analysis of the dispersion of two-photon absorption and Kerr nonlinearity of indirect semiconductors below the indirect bandgap is presented Similar to the case of linear absorption, third-order nonlinear processes are found to be mediated by phonon-assisted transitions The Kerr coefficient n/sub 2/ is positive below the indirect gap, and the dispersion of the third-order nonlinearities is reduced relative to direct semiconductors The results are compared with existing experimental data in silicon

Dispersion of phonon-assisted nonresonant third-order nonlinearities

The imaginary parts of all of the independent two-photon-resonant susceptibility tensor elements in GaAs and CdTe are determined by using a two-beam coupling technique to measure the anisotropy of the two-photon absorption coefficient p as a function of crystal orientation and probe polarization. Anisotropy parameters of -0.76 and -0.46 are measured for GaAs and CdTe, respectively, at a wavelength of 950 nm. These correspond to a 45% variation in /spl beta/ for GaAs, between 19 and 30 cm/GW, for radiation polarized along the [001] and the [111] crystallographic axes, respectively, and a 25% variation between 14 and 18 cm/GW for CdTe. By invoking intrinsic and zincblende symmetry, we present macroscopic expressions that accurately account for the dependence of single-beam two-photon absorption on the orientation of the crystal with respect to the polarization of the light and also expressions that describe the two-photon absorption of a probe when it is polarized either perpendicular or parallel to the pump in degenerate-four-wave-mixing experiments. Finally, we discuss the microscopic origins of this anisotropy of two-photon absorption in terms of simple k/spl middot/p models of the band structure, and we find the anisotropy to be caused predominantly by the mixing of the valence band with a higher conduction hand. This simple theory produces magnitudes consistent with experimental results and predicts that the anisotropy scales linearly with the ratio of the lower bandgap to the higher bandgap: E/sub g//E'/sub g/. >

W. A. Schroeder

Papers

Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors