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We develop a common path interferometer to measure the refractive index in liquids. This technique can measure the refractive index from the visible to infrared. In this work, we present experimental data in four wavelengths for several organic solvents.

This paper presents three-photon absorption (3PA) measurement results for nine direct-gap semiconductors, including full 3PA spectra for ZnSe, ZnS, and GaAs. These results, along with our theory of 3PA using an 8-band Kane model (4 bands with double spin degeneracy), help to explain the significant disagreements between experiments and theory in the literature to date. 3PA in the 8-band model exhibits quantum interference between the various possible pathways that is not observed in previous 2-band theories. We present measurements of degenerate 3PA coefficients in InSb, GaAs, CdTe, CdSe, ZnTe, CdS, ZnSe, ZnO, and ZnS. We examine bandgap, Eg, scaling using 2-band tunneling and perturbation theories that show agreement with the predicted Eg^-7 dependence; however, For those semiconductors for which we measured full 3PA spectra, we observe significant discrepancies with both 2-band theories. On the other hand, our 8-band model shows excellent agreement with the spectral data. We then use our 8-band theory to predict the 3PA spectra for 15 different semiconductors in their zincblende form. These results allow prediction and interpretation of the 3PA coefficients for various narrow to wide bandgap semiconductors., 20 pages

By exciting in both the Near-IR and Mid-IR and probing in the mid-IR, using the polarization-resolved Beam Deflection Technique, the bound electronic nonlinear refractive index of air is measured below the ionization threshold.

We present measurements of the nonlinear absorption and refraction of GaAs/AlGaAs quantum wells, and explore the fitness of this material system for nonlinear photonic devices.

We present 3-photon-absorption (3PA) measurements of 9 direct-gap semiconductors, including the 3PA spectra of ZnS, GaAs, and ZnSe and use a Kane 4-band model to fit the spectra and show the bandgap dependence.

Gold dipole nanoantennas embedded in an organic molecular film provide strong local electromagnetic fields to enhance both the nonlinear refractive index (n2) and two-photon absorption (2PA) of the molecules. An enhancement of 53× for 2PA and 140× for nonlinear refraction is observed for BDPAS (4,4′-bis(diphenylamino)stilbene) at 600 nm with only 3.7% of gold volume fraction. The complex value of the third-order susceptibility enhancement results in a sign change of n2 for the effective composite material relative to the pure BDPAS film. This complex nature of the enhancement and the tunability of the nanoantenna resonance allow for engineering the effective nonlinear response of the composite film.

Typically, strong gain saturation and gain dynamics play a crucial role in semiconductor laser mode-locking. While there have been several investigations of the ultrafast gain dynamics in vertical-external-cavity surface-emitting lasers (VECSELs), little is known about the associated refractive index changes. Yet, such refractive index changes do not only have a profound impact on the pulse formation process leading to self-phase modulation, which needs to be compensated by dispersion, but they are also of particular relevance for assessing the feasibility of Kerr-lens mode-locking of VECSELs. Here, we measure both refractive index as well as gain dynamics of a VECSEL chip using the ultrafast beam deflection method. We find that, in contrast to the gain dynamics, the refractive index dynamics is dominated by an instantaneous ($\sim$100~fs) and a very slow component ($\sim$100~ps). The time-resolved measurement of nonlinear refraction allows us to predict a pulse-length dependent, effective nonlinear refractive index $n_{2,eff}$, which is shown to be negative and in the order of $10^{-16}$ $m^2/W$ for short pulse lengths ($\sim$100~fs) . It becomes positive for large excitation fluences and large pulse lengths (few ps). These results agree with some previous reports of self-mode-locked VECSELs for which the cavity design and pulse properties determine sign and strength of the nonlinear refractive index when assuming Kerr-lens mode-locking.

We present femtosecond pump-probe measurements of the nondegenerate (1960$\,$nm excitation and 1176--1326$\,$nm probe) two-photon absorption spectra of 8 $\,$nm GaAs/12$\,$nm Al$_{0.32}$Ga$_{0.68}$As quantum well waveguides. Experiments were performed with light pulses co-polarized normal and tangential to the quantum well plane. The results are compared to perturbative calculations of transition rates between states determined by the $\mathbf{k}\cdot\mathbf{p}$ method with an 8 or 14 band basis. We find excellent agreement between theory and experiment for normal polarization, then use the model to support predictions of orders-of-magnitude enhancement of nondegenerate two-photon absorption as one constituent photon energy nears an intersubband resonance., 13 pages, 8 figures

We present beam deflection measurements to study the nondegenerate nonlinear refraction of highly doped semiconductors at epsilon-near-zero (ENZ) for several different pump and probe polarizations. Beam deflection is sensitive to induced optical path length as small as 1/20,000 of a wavelength, which enables us to resolve NLR in the presence of large nonlinear absorption backgrounds. The optically induced index changes in these materials can be both very large (on the order of unity) and fast (on the order of 100 fs). Our results show that carrier redistribution effects dominate the nonlinear refraction, and by independently tuning the pump and probe wavelengths, we find that the strong wavelength dependence of nonlinearities around the ENZ point is different for pump and probe waves. These nonlinear optical properties, where the ultrafast index change can be larger than the linear index, offer new paradigms for dynamically switchable diffractive elements that respond to structured light, allowing manipulation of optical beams in transmission and reflection not only along the two spatial dimensions but also in time. This is a revolutionary change in the field of nonlinear optics allowing a myriad of potential applications, ranging from rapid all-optical beam steering and switching, to spectral scanning, spatial mode conversion, as well as pulse shaping and suppression, all on sub-picosecond time scales.

Fast optical limiters are needed to protect sensors from intense short laser pulses. An optical limiter design based on a conducting-oxide grating with a large nonlinear refractive index at the plasma frequency is proposed and investigated.

We present measurements of nonlinear refraction and absorption in transparent conductive oxides (TCO), which are essentially highly-doped semiconductors, at Epsilon-Near-Zero (ENZ). In this spectral region, where the real part of the permittivity crosses zero, materials demonstrate interesting nonlinear properties such as enhanced harmonic generation, nonlinear absorption (NLA), and nonlinear refraction (NLR). We find that induced changes in the refractive index of Indium Tin Oxide, can be very large with respect to the initial index. This means that the even the Fresnel coefficients are highly irradiance-dependent. Therefore, the nonlinear transmission, reflection, and absorption of the material will be significantly different from conventional materials which means that it is challenging to use conventional methods such as Z-Scan and time-resolved transmission and reflection techniques to accurately determine the underlying nonlinear optical coefficients. We have studied optical nonlinearities of TCOs using the Beam-Deflection (BD) method to independently characterize the temporal dynamics and polarization dependence of the NLR. This method enables us to resolve NLR in the presence of large NLA backgrounds. In addition, we can also study the dependence on relative polarization and incidence angle of excitation and probe waves to characterize the enhancement mechanism and the physical origin of the nonlinear response. We conduct these BD measurements in conjunction with Z-Scan and transient reflection and transmission at different wavelengths, incidence angle, and polarization. Our measurements reveal that there is a strong wavelength dependence of nonlinearities around the ENZ point. We find that the wavelength dependence is quite different for excitation and probe waves.

info:eu-repo/semantics/published

We used the polarization-resolved beam-deflection technique to separate the bound-electronic and molecular-rotational components of the transient nonlinear refraction (NLR) of ambient air in the Mid-infrared spectral range below the ionization threshold.

We use the polarization-sensitive, time-resolved Beam-Deflection technique to measure the nonlinear refraction of air, exciting in both the near and mid-IR and probing in the mid-IR. This gives us the first measurements for air using both excitation and probe in the mid-IR, and we find no dispersion of the bound-electronic nonlinear refractive index, n2,el(λ p ;λ e ), assuming, as has been shown earlier, that the nuclear rotational nonlinear refraction is nearly dispersionless. From these data, we can model the pulsewidth dependence of the effective nonlinear refractive index, n2,eff, i.e., as would be measured by a single beam. Interestingly, n2,eff is maximized for a pulsewidth of approximately 0.5 ps. The position of this maximum is nearly independent of pressure while its magnitude decreases with increasing pressure and temperature. From the measurements and modeling, we predict the nonlinear refraction in the atmosphere at different altitudes.

We recently demonstrated orders of magnitude enhancement of two-photon absorption (2PA) in direct gap semiconductors due to intermediate state resonance enhancement for photons of very different energies. It can be expected that further enhancement of nondegenerate 2PA will be observed in quantum wells (QWs) since the intraband matrix elements do not vanish near the band center as they do in the bulk, and the density of states in QWs is larger near the band edge. Here we present a perturbation-theory based theoretical description of nondegenerate 2PA in semiconductor QWs, where both frequency and polarization of two incident waves can vary independently. Analytical expressions for all possible permutations of frequencies and polarizations have been obtained, and the results are compared with degenerate 2PA in quantum wells along with degenerate and nondegenerate 2PA in bulk semiconductors. We show that using QWs in place of bulk semiconductors with both beams in the TM-polarized mode leads to an additional order of magnitude increase in the nondegenerate 2PA. Explicit calculations for GaAs QWs are presented., Comment: 24 pages, 13 figures

Materials exhibiting near zero refractive index are shown to have interesting nonlinear optical properties such as enhanced second and third harmonic generation, and large nonlinear refraction (NLR) due to their unique interplay between linear and nonlinear optical features. In particular, the NLR of highly doped semiconductors such as Indium Tin Oxide and Aluminum doped Zinc Oxide is enhanced in the near-infrared spectral regions, where the real part of the permittivity crosses zero with the advantage of having a tunable zero crossover frequency by controlling the doping level. This is also known as the epsilon near zero (ENZ) regime, where the refractive index is very small. We have used the Beam-Deflection (BD) method to directly characterize the temporal dynamics and polarization dependence of the nondegenerate (ND) NLR of doped semiconductors at ENZ. The origin of the nonlinear optical response of these materials is different than for the case of bound electronic nonlinearities which depend upon the third-order susceptibility. The ND BD technique has the potential to study the dependence on relative polarization of excitation and probe waves to accurately determine the instantaneous electronic nonlinearities separately from the non-instantaneous mechanisms such as carrier redistribution effects, however, the carrier nonlinearities are dominant in such materials. This method also reveals the effect of tuning the wavelength of excitation or probe waves through ENZ separately. BD has sensitivity to induced optical path length as small as 1/20,000 of a wavelength, which enables the possibility to resolve NLR in the presence of large nonlinear absorption backgrounds.

Transient nondegenerate nonlinear refraction of Indium Tin Oxide has been characterized in the near-infrared using femtosecond Beam-Deflection with independently tuned excitation and probe. ENZ enhancement depends more strongly on the probe wavelength than the excitation.

The third-order optical nonlinearities of Si and GaAs have been characterized throughout the near-infrared spectral region (1.1-2 μm) using multiple ultrafast spectroscopic techniques. These results have been independently confirmed at two different laboratories.

Dispersion of nondegenerate nonlinear refraction in semiconductors is measured using the Beam-Deflection technique. With large nondegeneracy, n2 is greatly enhanced and exhibits a strong nonlinear dispersion, which rapidly switches sign to negative near the bandgap. Potential applications including nondegenerate all-optical switching and pulse shaping are discussed.

Many materials exhibit nonlinear refraction (NLR) and absorption (NLA) that has multifaceted temporal dynamics. As a result, measurements at one laser pulse width may not be fully predictive of the behavior at other pulse widths. We have recently developed a method, Nonlinear Beam Deflection, (BD) that allows sensitive time-resolved measurement of nonlinear refraction (NLR) and absorption (NLA) by using an excitation beam to create an index gradient deflecting a probe beam onto a quad-cell detector. The method has a demonstrated sensitivity to induced phase changes as small as 1/20,000 of a wavelength, which is sensitive enough to measure NLR in gases. By changing the relative polarization of the beams we can separate the bound-electronic response from the slower and different-symmetry nuclear contributions. In gases and liquids where reorientational nonlinearities are important, measurements at the magic angle allow isolation of the ultrafast nonlinearities. In isotropic solids the bound-electronic symmetry dictates a ratio of 1/3 for parallel to perpendicular polarizations which measurements confirm. This method also allows for measurements of nonlinearities using very different wavelengths for the excitation and probe. We have used this method to characterize the impulse response function for third-order nonlinearities in many transparent organic solvents. This allows accurate prediction of the nonlinear refraction for any pulse width longer than that used for the BD characterization. The method proves to be very useful in organic materials that may show strong nonlinear absorption, as it is able to resolve NLR in the presence of strong NLA better than other methods, such as Z-scan.

We have shown both experimentally and theoretically that the effect of intermediate-state resonance enhancement causes highly nondegenerate 2-photon absorption, 2PA, to be strongly enhanced in direct-gap semiconductors. Calculations indicate an additional 10x increase in this enhancement is possible for quantum-well semiconductors. This enhancement leads to interesting applications of 2PA, such as mid-infrared detection, where uncooled, large-gap photodiodes can rival the sensitivity of cooled MCT detectors (for short pulses). Additionally, mid-IR imaging and tomography based on this effect have been shown. Even larger enhancement of 3PA is calculated and observed. In the case of optically-pumped semiconductors, we have now demonstrated that the complementary process of nondegenerate 2-photon stimulated emission can be observed. Theoretically, this results in 2-photon gain (2PG) that is enhanced as much as 2PA, leading to the possibility of large gap devices with tunable mid-infrared gain. However, the effect of nondegenerate enhancement of 3PA can be detrimental to the observation of this gain. Additionally, by causality, Kramers-Kronig relations predict that the enhancement of 2PA is accompanied by an enhancement of the nonlinear refractive index, n2, which is very highly dispersive in the region of 2PA. Our latest experimental results confirm this enhancement and strong dispersion.

We extend our recently developed Beam-Deflection (BD) method which we used to determine the sign, magnitude, and ultrafast dynamics of bound electronic and nuclear nonlinear optical responses, to measure elements of the third-order nonlinear optical susceptibility tensor with longitudinal field components. In these measurements, in contrast to the conventional BD technique where excitation and probe beams are nearly collinear, the interaction geometry involves orthogonal propagation of excitation and probe beams. This cross-propagating BD method enables probing with the electric field polarized parallel to the wavevector of the excitation beam as well as conventional parallel and perpendicular polarizations as in most other experimental methods. This technique may be of use in detecting possible magneto-electric contributions to the nonlinear susceptibility. The ratio between parallel and perpendicular bound-electronic responses in this method is shown to be larger than the factor of 3 predicted by theory and measured in the conventional configuration.

Using Beam-Deflection measurements we directly measure the temporal dynamics of nonlinear refraction and transmittance of an ITO thin film in the e-near-zero regime, and find a nonlinear index 5000 times that of glass.

High-spectral-irradiance infrared supercontinuum with fundamental Gaussian spatial profile was generated in Krypton gases. We demonstrate its usefulness for Z-scan nonlinear spectroscopy in the 800-1600nm spectral range using GaAs and CS2.

Weakly focused, near mJ, 1800nm femtosecond pulses in a 1.8m Krypton gas chamber generates a high-spectral-irradiance, Gaussian spatial profile continuum for nonlinear spectroscopy in the 800-1600nm range. We demonstrate its usefulness with Z-scans on GaAs.

We extend the recently developed dual-arm Z-scan to increase the signal-to-noise ratio (SNR) for measuring the nonlinear refraction (NLR) of thin films on thick substrates. Similar to the case of solutes in solution, the phase shift due to NLR in a thin film can often be dominated by the phase shift due to NLR in the much thicker substrate. SNR enhancement is accomplished by simultaneously scanning a bare substrate and the film plus substrate in two separate but identical Z-scan arms. The subtraction of these signals taken simultaneously effectively cancels the nonlinear signal from the substrate, leaving only the signal from the film. More importantly, the SNR is increased since the correlated noise from effects such as beam-pointing instabilities cancels. To show the versatility of the dual-arm Z-scan method, we perform measurements on semiconductor and organic thin films, some less than 100 nm thick and with thicknesses up to 4 orders of magnitude less than the substrate.

We review several experimental methodologies for the determination of nonlinear absorption coefficients of organic chromophores in either solution or thin film form. The goal here is to also be able to identify and quantify the nonlinear absorption process or processes, e.g. the essentially instantaneous two-photon absorption (2PA) or the cumulative excited-state absorption (ESA). These methods include the direct methods of nonlinear transmission and Z-Scan, along with the indirect methods of two-photon-induced fluorescence, exciteprobe approaches, and Degenerate Four-Wave Mixing. We also discuss both frequency degenerate and frequency nondegenerate processes with emphasis on 2PA. It is important to note that a single method is generally incapable of both measuring and identifying the source of the nonlinearity, thus it is usually necessary to employ more than a single method to determine the sign, magnitude and physical processes involved. For example, single beam experiments cannot give the temporal response of the nonlinearity while excite-probe methods do; however, single beam measurements lend themselves better to absolute calibration. In addition we include information on nonlinear refraction, which always accompanies nonlinear absorption processes. For example, the nondegenerate bound-electronic nonlinear refraction and ultrafast nondegenerate nonlinear absorption come from the real and imaginary parts of the nondegenerate third-order nonlinear susceptibility and are related by Kramers-Kronig relations via causality.

Two-photon absorption, 2PA, in semiconductors is enhanced by two orders of magnitude due to intermediate-state resonance enhancement, ISRE, for very nondegenerate (ND) photon energies. Associated with this enhancement in loss is enhancement of the nonlinear refractive index, n2. Even larger enhancement of three-photon absorption is calculated and observed. These large nonlinearities have implications for applications including ND two-photon gain and twophoton semiconductor lasers. Calculations for enhancement of ND-2PA in quantum wells is also presented showing another order of magnitude increase in 2PA. Potential devices include room temperature gated infrared detectors for LIDAR and all-optical switches.

We present measurements of the temporal and polarization dependence of the nonlinear optical (NLO) response of selected organic solvents using our beam deflection (BD) method. These measurements allow us to separately determine the bound-electronic and nuclear responses which then determines the NLO response function. With this NLO response function the outcome of other experiments such as Z-scan as a function of pulse-width can be predicted. By performing similar measurements on the gas phase of these solvents we can compare the hyper-polarizabilities in the two phases.

We utilize the recently demonstrated orders of magnitude enhancement of extremely nondegenerate two-photon absorption in direct-gap semiconductor photodiodes to perform scanned imaging of three-dimensional (3D) structures using IR femtosecond illumination pulses (1.6 µm and 4.93 µm) gated on the GaN detector by sub-gap, femtosecond pulses. While transverse resolution is limited by the usual imaging criteria, the longitudinal or depth resolution can be less than a wavelength, dependent on the pulsewidths in this nonlinear interaction within the detector element. The imaging system can accommodate a wide range of wavelengths in the mid-IR and near-IR without the need to modify the detection and imaging systems.

The simple figures of merit for optical switching that were introduced by George Stegeman in the early 1990s are still widely used and have helped to drive research into nonlinear optical materials research over the past two decades. Coincidentally, his work on this occurred around the time we were working on the relationship between nonlinear refraction and nonlinear absorption, which led to increased collaboration between our groups. The speaker will describe the time when we were working on this and discuss how this has impacted the field of nonlinear optics since then.

Two-photon lasers require materials with large two-photon gain (2PG) coefficients and low linear and nonlinear losses. Our previous demonstration of large enhancement of two-photon absorption in semiconductors for very different photon energies translates directly into enhancement of 2PG. We experimentally demonstrate nondegenerate 2PG in optically excited bulk GaAs via femtosecond pump-probe measurements. 2PG is isolated from other pump induced effects through the difference between measurements performed with parallel and perpendicular polarizations of pump and probe. An enhancement in the 2PG coefficient of nearly two orders-of-magnitude is reported. The results point a possible way toward two-photon semiconductor lasers., Comment: 5 pages, 5 figures

Here we study the third-order susceptibility of TiN thin films using the dual-arm Z-scan technique at 780 nm and 1550 nm. Due to its refractory nature, TiN is a promising metallic nonlinear component.

The nonlinear optical (NLO) response functions of 24 widely used organic solvents are measured, including both bound-electronic and nuclear contributions. The response function establishes a self-consistent reference for predicting the outcomes of various NLO experiments.

Identifying strong and fast nonlinearities for today’s photonic applications is an ongoing effort 1 . Materials 2–5 and devices 6–9 are typically sought to achieve increasing nonlinear interactions. We report large enhancement of two-photon absorption through intrinsic resonances using extremely non-degenerate photon pairs. We experimentally demonstrate two-photon absorption enhancements by factors of 100–1,000 over degenerate two-photon absorption in direct-bandgap semiconductors. This enables gated detection of sub-bandgap and sub-100 pJ mid-infrared radiation using large-bandgap detectors at room temperature. Detection characteristics are comparable in performance to liquid-nitrogen-cooled HgCdTe (MCT) detectors. The temporal resolution of this gated detection by two-photon absorption is determined by the gating pulse duration.

The influence of quantum confinement on the one- and two-photon absorption spectra (1PA and 2PA) of PbS and PbSe semiconductor quantum dots (QDs) is investigated. The results show 2PA peaks at energies where only 1PA transitions are predicted and 1PA peaks where only 2PA transitions are predicted by the often used isotropic k x p four-band envelope function formalism. The first experimentally identified two-photon absorption peak coincides with the energy of the first one photon allowed transition. This first two-photon peak cannot be explained by band anisotropy, verifying that the inversion symmetry of the wave functions is broken and relaxation of the parity selection rules has to be taken into account to explain optical transitions in lead-salt QDs. Thus, while the band anisotropy of the bulk semiconductor plays a role in the absorption spectra, especially for the more anisotropic PbSe QDs, a complete model of the absorption spectra, for both 1PA and 2PA, must also include symmetry breaking of the quantum confined wave functions. These studies clarify the controversy of the origin of spectral features in lead-salt QDs.

A polarization-resolved beam deflection technique is used to separate the bound-electronic and molecular rotational components of nonlinear refractive transients of molecular gases. Coherent rotational revivals from N(2), O(2), and two isotopologues of carbon disulfide (CS(2)), are identified in gaseous mixtures. Dephasing rates, rotational and centrifugal distortion constants of each species are measured. Polarization at the magic angle allows unambiguous measurement of the bound-electronic nonlinear refractive index of air and second hyperpolarizability of CS(2). Agreement between gas and liquid phase second hyperpolarizability measurements is found using the Lorentz-Lorenz local field correction.

We present data indicating two-photon gain using extremely nondegenerate (END) photons in optically excited GaAs. These results are consistent with our demonstration of END two-photon absorption enhancement and points a possible way to two-photon lasing.

We present a theoretical study of extremely nondegenerate two-photon absorption in direct-gap quantum well semiconductors. We predict large enhancement in nondegenerate two-photon absorption for TM-TM polarized light over bulk semiconductors.

Nanophotonic devices offer an unprecedented ability to concentrate light into small volumes which can greatly increase nonlinear effects. However, traditional plasmonic materials suffer from low damage thresholds and are not compatible with standard semiconductor technology. Here we study the nonlinear optical properties in the novel refractory plasmonic material titanium nitride using the Z-scan method at 1550 nm and 780 nm. We compare the extracted nonlinear parameters for TiN with previous works on noble metals and note a similarly large nonlinear optical response. However, TiN films have been shown to exhibit a damage threshold up to an order of magnitude higher than gold films of a similar thickness, while also being robust, cost-efficient, bio- and CMOS-compatible. Together, these properties make TiN a promising material for metal-based nonlinear optics.

We present theoretical calculations and experimental measurements of the nondegenerate three-photon absorption coefficient of GaAs, which is enhanced by >3 orders of magnitude over the degenerate case.

We use the beam-deflection method to measure nondegenerate nonlinear refractive indices of ZnO and ZnSe and show, in agreement with theory, extremely nondegenerate nonlinear refraction is significantly larger than in the degenerate or near-degenerate case.

Transparent ceramics gain much attention as an alternative medium for high power ultra-short lasers because of its superior thermal properties over single crystals. Measurement of nonlinear refractive index is essential to understand the limit of such material for ultra-short laser generation. Dual arm Z-scan technique was employed to measure n2 for single crystal and ceramic at the same time to avoid any uncertainty due to different measuring times.

We measure the temporal dynamics of nonlinear absorption (NLA) and refraction (NLR) in crystalline and hydrogenated-amorphous silicon at 1550 nm. The effect of relative polarization on NLA and NLR are also reported.

We demonstrate a scanning 3-D IR imaging technique using extremely nondegenerate two-photon absorption in an uncooled GaN photodiode, and obtain ∼2 μm depth resolution at a wavelength of ∼5 μm in buried semiconductor structures.