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We demonstrate scanning 3-D IR imaging using non-degenerate two-photon absorption (2PA) in an uncooled GaN photodetector. The SNR of the technique should improve for longer imaging wavelengths due to increased nondegeneracy, which enhances 2PA.

We modify the "photothermal" beam deflection technique to study ultrafast optical nonlinearities. We measure the temporal and polarization dynamics of nonlinear refraction with sensitivity of λ/5500 while separating the isotropic and reorientational components.

We modify the photothermal beam deflection technique for the sensitive measurement of ultrafast nonlinear refraction (λ/5000 sensitivity to nonlinearly-induced phase changes). This allows direct measurement of the temporal dynamics and polarization dependence of nonlinear refraction.

We observe CW Mid-IR detection using GaN or GaAs p-i-n detetctors with extremely nondegenerate two-photon absorption. Current from the Urbach tail absorption limits the minimum detectable power of the IR beam.

We report nonlinear-refractive indices of ZnO films on relatively thick substrates using the dual-arm Z-scan method to remove the substrate signals and obtain values agreeing with bulk ZnO, thus verifying the sensitivity of the technique.

Cascading is the process by which the exchange of energy between optical beams interacting via second order nonlinearities (χ(2)) leads to various effects such as nonlinear phase shifts, the generation of new beams, all-optical transistor action, the formation of soliton-like (solitary) waves, etc. Here we review the fundamentals of the processes and discuss experimental verification of the effects and various related applications.

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.

We use our recently developed beam-deflection technique to measure the dispersion of the nondegenerate nonlinear refraction (NLR) of direct-gap semiconductors. The magnitude and sign of the NLR coefficient nsub2/sub(ωa; ωb) are determined over a broad spectral range for different values of nondegeneracy. In the extremely nondegenerate case, nsub2/sub(ωa; ωb) is positively enhanced near the two-photon absorption (2PA) edge and is significantly larger than its degenerate counterpart, suggesting applications for nondegenerate all-optical switching. At higher photon energies within the 2PA regime, nsub2/sub(ωa; ωb) switches sign to negative over a narrow wavelength range. This strong anomalous nonlinear dispersion provides large phase modulation of a femtosecond pulse with bandwidth centered near the zero-crossing frequency. The measured nondegenerate dispersion closely follows our earlier predictions based on nonlinear Kramers-Kronig relations [Sheik-Bahae et. al, IEEE J. Quant. Electron. 30, 249 (1994)].

Polarization dependent degenerate-four-wave-mixing experiments on semiconductors (ZnSe, CdS) and dielectrics (NaCl, PbF/sub 2/) reveal the essential mechanisms of the bound-electronic /spl chi//sup (3)/. We show, for the first time, that the observed anomalous dispersion of the polarization dependent phase-conjugate reflectivity can be explained using a simple 3-band model. The near vanishing reflectivity in the two-photon coherence geometry is shown to be a consequence of the interference between transitions originating from heavyand light-hole valence bands. We also present measurements on the polarization dichroism of the nonlinear refractive index (n/sub 2/), in good agreement with this simple theory. >

Numerical simulations are employed to elucidate the physics underlying the enhanced femtosecond supercontinuum generation previously observed during optical filamentation in noble gases and in the presence of a weak seed pulse. Simulations based on the metastable electronic state approach are shown not only to capture the qualitative features of the experiment, but also reveal the relation of the observed enhancement to recent developments in the area of sub-cycle engineering of filaments.

This note corrects author affiliations, errors in one equation, and two equation callouts of J. Opt. Soc. Am. B33, 780 (2016)10.1364/JOSAB.33.000780JOBPDE0740-3224.

Materials with a large nonlinear refractive index (n2) and relatively small linear and nonlinear absorption losses, namely, two-photon absorption (2PA, of coefficient α2), have long been sought after for applications such as all-optical switching (AOS). Here we experimentally determine the linear and 2PA properties of several organic molecules, which we approximate as centrosymmetric, and use a simplified essential-state model (quasi-three-level model) to predict the dispersion of n2. We then compare these predictions with experimental measurements of n2 and find good agreement. Here “quasi”-three-level means using a single one-photon allowed intermediate state and multiple (here two) two-photon allowed states. This also allows predictions of the figure-of-merit (FOM), defined as the ratio of nonlinear refractive phase shift to the 2PA fractional loss, that determines the viability for such molecules to be used in device applications. The model predicts that the optimized wavelength range for a large FOM lies near the short wavelength linear absorption edge for cyanine-like dyes where the magnitude of n2 is quite large. However, 2PA bands lying close to the linear absorption edge in certain classes of molecules can greatly reduce this FOM. We identify two molecules having a large FOM for AOS. We note that the FOM is often defined as the ratio of real to imaginary parts of the third-order susceptibility (χ(3)) with multiple processes leading to both components. As explained later in this paper, such definitions require care to only include the 2PA contribution to the imaginary part of χ(3) in regions of transparency.

An ongoing problem in characterizing organic nonlinearities in the presence of large solvent backgrounds can be eradicated by performing identical and simultaneous Z-scans on two samples (solvent and solvent plus solute).

We compare GaAs and GaN for IR detection using extremely non-degenerate two-photon absorption. While the small gap material has larger ND-2PA and hence better sensitivity to IR, unwanted background from degenerate 2PA outweighs this advantage.

The plasmon resonance is found to broaden and red-shift under strong femtosecond/picosecond irradiation. Using a standard two-temperature model we find a correlation mapping the electron gas and lattice temperatures to the Drude damping coefficient.

Replacing oxygen with sulfur in a squaraine bridge compound leads to a large increase in triplet yield (and triplet-state absorption) while maintaining the already enhanced two-photon absorption as well as the singlet excited-state absorption.

Performing identical and simultaneous Z-scans on two samples (solvent and solvent plus solute), the effects of solvent n2 can be essentially eliminated, thus overcoming a longstanding problem in organic dye nonlinear characterization.

We perform a theoretical and experimental study of extreme nondegenerate two-photon stimulated emission in bulk GaAs. We calculate two-photon gain coefficient for various photon energies. A three beam experiment is conducted to observe two-photon gain.

We show how the semiconductor band structure influences the size dependence trends of two-photon absorption in quantum dots. We demonstrate, via two-photon spectroscopy, that parity symmetry does not hold in small lead-chalcogenides quantum-dots

We measure the nonlinear optical properties of solutions of a bisbenzethiozole-substituted thiophene compound (BBTDOT) and didecyloxy substituted polyphenyl (DDOS) using the Z -scan technique with 532 nm picosecond pulses. Both compounds exhibit two-photon absorption (2PA) and excited-state absorption (ESA) from the 2PA generated excited states. We measure the magnitude and sign of the real (refractive) and imaginary (2PA) parts of the third-order hyperpolarizability, and the excited-state absorptive and refractive cross sections. We observe third-order self-focusing in BBTDOT and self-defocusing in DDOS while both show excited-state defocusing. All these effects were previously observed and modeled in semiconductors giving insight into the nonlinearities occurring in these organic materials.

We describe the application of single beam propagation methods, namely Z-scan and EZ-scan, for the determination of nonlinear refractive indices in materials including thin films. In these experiments the transmittance of a sample is measured either through a finite aperture (Z-scan) or around an eclipsing disk (EZ-scan) placed in the far-field as the sample is moved along the propagation path (Z) of a focused beam. Both methods can also be used to separately measure the nonlinear absorption so that both the real and imaginary parts of the nonlinear susceptibility are determined along with their signs. The sensitivity to induced phase distortion depends on the sensitivity of the measuring apparatus to transmittance changes ΔT. For the 10 Hz repetition rate Nd:YAG lasers used in our experiments, we can detect ΔT≃10−3. This leads to a sensitivity to optical path length changes of λ/103 for the Z-scan and λ/104 for the EZ-scan where λ is the wavelength. This interferometric sensitivity, using a single beam, allows measurement of nonlinear refraction in thin films without the need for using a waveguiding geometry.

Two-photon absorption (2PA) spectra with pairs of extremely nondegenerate photons are measured in several direct-gap semiconductors (GaAs, CdTe, ZnO, ZnS and ZnSe) using picosecond or femtosecond pulses. In ZnSe, using photons with a ratio of energies of ~12, we obtain a 270-fold enhancement of 2PA when comparing to the corresponding degenerate 2PA coefficient at the average photon energy (ηω1 + ηω2)/2. This corresponds to a pump photon energy of 8% of the bandgap. 2PA coefficients as large as 1 cm/MW are measured. Thus, by using two widely different wavelengths we are able to access the large 2PA observed previously only in narrow gap semiconductors. We also calculate the corresponding enhancement of nonlinear refraction, consisting of two-photon, AC-Stark and Raman contributions. The net effect is a smaller enhancement, but exhibits very large dispersion within the 2PA regime.

Femtosecond gated detection of low power mid-IR radiation using ultraviolet gating pulses in a GaN detector at room temperature is demonstrated by utilizing two-to-three orders of magnitude enhancement from nondegenerate two-photon absorption.

Our observation of two-to-three orders of magnitude enhancement of nondegenerate two-photon absorption in direct-gap semiconductors has led to gated detection of subgap femtosecond pulses, e.g. measurement of 200fs 5.6μm pulses in a GaN photodiode.

The time dynamics of the photoexcited carriers and carrier-multiplication efficiencies in PbS quantum dots (QDs) are investigated. In particular, we report on the carrier dynamics, including carrier multiplication, as a function of QD size and compare them to the bulk value. We show that the intraband 1P→1S decay becomes faster for smaller QDs, in agreement with the absence of a phonon bottleneck. Furthermore, as the size of the QDs decreases, the energy threshold for carrier multiplication shifts from the bulk value to higher energies. However, the energy threshold shift is smaller than the band-gap shift and, therefore, for the smallest QDs, the threshold approaches 2.35 Eg, which is close to the theoretical energy conservation limit of twice the band gap. We also show that the carrier-multiplication energy efficiency increases with decreasing QD size. By comparing to theoretical models, our results suggest that impact ionization is sufficient to explain carrier multiplication in QDs.

The two-photon absorption, 2PA, cross sections of PbS quantum dots, QDs, are theoretically and experimentally investigated and are shown to be enhanced with increasing quantum confinement. This is in contrast to our previous results for CdSe and CdTe QDs where the reduced density of states dominated and resulted in a decrease in 2PA with a decrease in QD size. Qualitatively this trend can be understood by the highly symmetric distribution of conduction and valence band states in PbS that results in an accumulation of allowed 2PA transitions in certain spectral regions. We also measure the frequency nondegenerate 2PA cross sections that are up to five times larger than for the degenerate case. We use a k·p four-band envelope function formalism to model the increasing trend of the two-photon cross sections due to quantum confinement and also due to resonance enhancement in the nondegenerate case.

The double pump-probe method allows determination of singlet and triplet excited state parameters, but we show that this method has limitations. We describe how to overcome such limitations allowing unambiguous determination of the triplet yield.

We observe spectral enhancement of femtosecond supercontinua in krypton gas using weak, nJ to μJ, seed pulses with the order of ∼mJ pump pulses resulting in > 3× total energy enhancement and spectral broadening.

We measure a fourfold increase in femtosecond supercontinuum integrated spectral irradiance using extremely weak seeding (~10^-3) in Kr gas. We present data on the effect of seeding on supercontinuum in other gases, liquids, and solids.

The dispersion of the nonlinear refractive index, “n2”, of carbon disulfide by femto-, pico-, and nano-second pulses, and its two-photon absorption spectrum are measured. The pulsewidth dependence of “n2” is also determined.

We are investigating the nonlinear optical properties of noble metal nanoparticles immersed in various host materials. Changes in the permittivity of the nanoparticles under large irradiances are measured in pump-probe experiments. A two-temperature model is used to fit the data and obtain a correlation between the electron gas and lattice temperatures and the Drude-type electron damping of the metal. The enhanced two-photon absorption (2PA) of silver nanospheres suspended in carbon disulfide (CS2) is measured by Z-Scan. The sample showed a combined signal of 2PA and saturable absorption (SA) which can be decoupled using the temperature-electron-damping mapping.

We investigate enhancement of femtosecond supercontinua (SC) in various nonlinear media including solvents by seeding the SC with nanojoule to microjoule visible pulses. Increasing enhancement for decreasing nonlinear refraction is observed.

Two-to-Three orders of magnitude enhancement of nondegenerate two-photon absorption (2PA) compared to degenerate 2PA are observed. Femtosecond gated detection of low power mid-IR radiation using ultraviolet gating pulses using a GaN detector at room temperature is demonstrated.

We present results of optical limiting experiments designed to study optical geometries for increasing the dynamic range over which limiters function without incurring optical damage. Specifically, we investigate a tandem geometry with two passive nonlinear elements, one placed in the focal plane of a lens and the second placed “upstream” of the focal position to protect the material at focus from damage. To provide a proof-of-principle demonstration of this geometry, simple limiters consisting of combinations of reverse saturable absorber dyes and a carbon black suspension in thin cells were tested. Our results show that a substantial increase in device performance can be achieved by use of a tandem limiter geometry. Simple modelling predicts that the dynamic range of a separate-element tandem limiter is given by the product of the dynamic ranges of the individual component limiting elements, in agreement with our experimental results.

Subpicosecond time-resolved white-light continuum measurements of the nondegenerate two-photon absorption spectra of ZnSe, ZnS and ZnO, with pump photon energy 1.76 eV, are reported. The spectra presented cover a photon energy range of 1 eV. The results are found to agree well both in absolute value and frequency dependence with a model for the two-photon transition probability incorporating the Kane band structure and nonparabolicity.

We discuss the characterization of nonlinear optical processes that give rise to changes in the absorption coefficient and refractive index. We primarily concentrate on methods for determining the dominant nonlinearities present in condensed matter and the responsible physical mechanisms. In extensive studies of a wide variety of material, we have found that there is seldom a single nonlinear process occurring. Often several processes occur simultaneously, sometimes in unison, sometimes competing. It is necessary to experimentally distinguish and separate these processes in order to understand and model the interaction. There are a variety of methods and techniques for determining the nonlinear optical response, each with its own weaknesses and advantages. In general, it is advisable to use as many complementary techniques as possible over a broad spectral range in order to unambiguously determine the active nonlinearities. Here we concentrate on the use of nonlinear transmittance, Z-scan and degenerate four-wave mixing experiments as applied to polycrystalline and single crystal semiconductors and dielectric materials.

The nonlinear absorption spectrum of InSb was measured using a combination of tunable $\ensuremath{\sim}160\text{ }\text{fs}$, $\ensuremath{\sim}10\text{ }\text{ps}$, and $\ensuremath{\sim}150\text{ }\text{ns}$ IR sources along with a cryostat for controlling the sample temperature to vary the band gap energy from 0.17 to 0.23 eV. The measured nonlinear optical properties in InSb are consistent with those predicted by the models which include two- and three-photon absorption (2PA and 3PA), multiphoton generated free-carrier absorption (FCA) and various recombination mechanisms. Temperature-dependent Z-scan and nonlinear transmission measurements yield information on the temperature and spectral dependence of 2PA, FCA, and carrier recombination processes of Shockley-Read-Hall, and Auger mechanisms. We find good agreement between the measured and the modeled nonlinear properties is possible only when the recently predicted temperature dependence of the FCA is considered. The wavelength- and temperature-dependent 2PA and 3PA coefficients in InSb were experimentally obtained. The inferred values of the 2PA and 3PA are consistent with the scaling rules of a simple two-parabolic band model. We further determine recombination rates from nonlinear transmittance of nanosecond pulses of ${\text{CO}}_{2}$ laser.

Efficient Pd-catalyzed Heck coupling methodology was employed to provide two new fluorene derivatives with phosphonate (2) and nitro (3) electron-withdrawing functionalities. Both derivatives exhibit two-photon absorption (2PA), as determined by nonlinear absorption measurements using a femtosecond pump/white light continuum probe “NLO spectrometer”. Both fluorene derivatives have high 2PA cross sections (650 and 1300 × 10-50 cm4 s photon-1 molecule-1 for compounds 2 and 3, respectively).

We present an experimental and theoretical investigation of the linear and nonlinear optical properties of a series of acceptor-pi-acceptor symmetrical anionic polymethine dyes with diethylamino-coumarin-dioxaborine terminal groups and different conjugation lengths. Two-photon absorption (2PA) cross sections (delta(2PA)) are enhanced with an increase of pi-conjugation length in the investigated series of dyes. 2PA spectra for all dyes consist of two well-separated bands. The first band, located within the telecommunications window, occurs upon two-photon excitation into the vibrational levels of the main S(0) --S(1) transition, reaching a large delta(2PA) = 2200 GM (1 GM = 1 x 10(-50) cm(4) s/photon) at 1600 nm for the longest conjugated dye. The position of the second, and strongest, 2PA band for all anionic molecules corresponds to the second-excited final state, which is confirmed by quantum-chemical calculations and excitation anisotropy measurements. Large delta(2PA) values up to 17,000 GM at 1100 nm are explained by the combination of the large ground- and excited-state transition dipole moments. The three shortest dyes show good photochemical stability and surprisingly large fluorescence quantum yields of approximately 0.90, approximately 0.66, and approximately 0.18 at the red to near-IR region of approximately 640, approximately 730, and approximately 840 nm, respectively. The excited-state absorption spectra for all samples are also studied and exhibit intense bands throughout the visible wavelength region with peak cross section close to 5 x 10(-16) cm(2) with a corresponding red shift with increasing conjugation lengths.

Understanding the nonlinear optical processes in semiconductor nanostructures leads to possible applications in areas including laser amplifiers, optical switches, and solar cells. Here we present a study of the frequency degenerate twophoton absorption (2PA) spectrum of a series of PbS and PbSe quantum dots (QDs). The influence of the quantum confinement is analyzed using a four-band model which considers the mixing of valence and conduction bands. In contrast to our observations of CdSe QDs, the present results point to an increase of the 2PA cross-section (normalized by the QD volume) as the quantum dot size is made smaller. This is explained by the symmetry between the valence and conduction bands which allows the density of states to remain high even for small QDs. A study of the ultrafast carrier dynamics of the PbS quantum dots is also presented. Through nondegenerate femtosecond pump-probe experiments we show evidence of multi-exciton generation with quantum yield (number of excitons generated per absorbed photon) up to 170% for excitation with hω > 3 Eg (where Eg is the bandgap energy).

In the past few years, applications built around two-photon absorption (2PA) have emerged, which require new materials to be designed and characterized in order to discover new applications and to advance the existing ones. This chapter describes the nonlinear optical processes and characterization techniques along with design strategies and structure-property relations of cyanine and cyanine- like molecular structures with the goal of enhancing 2PA in the near-IR for multiphoton fluorescence sensing applications. Specifically, a detailed analysis of the linear and nonlinear optical properties of several classes of polymethine dyes, which include symmetrical and asymmetrical combinations of p-conjugated bridges with electron donating (D) or electron accepting (A) terminal groups, are presented. These structures are: D-p-D, A-p-A, D-p-A, and a quadrupolar type arrangement of D-p-A-p-D. The results of this research combined with the growing literature on structure- property relations in organic materials is moving us closer to the ultimate goal of developing a predictive capability for the nonlinear optical properties of molecules.

Gold dipole nanoantennas which have strong local electromagnetic fields are used to enhance two-photon absorption. A 30 to 40 times enhancement is observed for BDPAS (4,4'-bis(diphenylamino)stilbene) at 600 nm.

Efficiency of singlet oxygen generation is investigated for a series of new sulfur-containing squaraines molecules. Experimental results, in agreement with quantum calculations, show both large triplet quantum yield and quantum yield of singlet oxygen generation.

We measure the size dependent two-photon absorption (2PA) and multi-exciton generation (MEG) efficiency in lead-salt quantum dots (QD). The results are discussed in view of the uniquely symmetric band structure of these materials.

We report the two-photon absorption spectrum of single crystals of an asymmetric cyanine-like dye in comparison to its spectrum in solution. The 2PA peak magnitude is comparable to bulk semiconductors of similar absorption edge.

We present an experimental and theoretical study of self-trapping that includes self-focusing and the production of plasma for supercontinuum generated in noble gases using ultra-short laser pulses.

We performed frequency non-degenerate pump-probe experiments in several direct-gap semiconductors using femtosecond and picosecond pulses. Tuning the long wavelength photons in the IR region, we observed a 125-fold enhancement of the two-photon absorption coefficient.

We review dispersion relations, which relate the real part of the optical susceptibility (refraction) to the imaginary part (absorption). We derive and discuss these relations as applied to nonlinear optical systems. It is shown that in the nonlinear case, for self-action effects the correct form for such dispersion relations is nondegenerate, i.e. it is necessary to use multiple frequency arguments. Nonlinear dispersion relations have been shown to be very useful as they usually only require integration over a limited frequency range (corresponding to frequencies at which the absorption changes), unlike the conventional linear Kramers-Kronig relation which requires integration over all absorbing frequencies. Furthermore, calculation of refractive index changes using dispersion relations is easier than a direct calculation of the susceptibility, as transition rates (which give absorption coefficients) are, in general, far easier to calculate than the expectation value of the optical polarization. Both resonant (generation of some excitation that is long lived compared with an optical period) and nonresonant ‘instantaneous’ optical nonlinearities are discussed, and it is shown that the nonlinear dispersion relation has a common form and can be understood in terms of the linear Kramers-Kronig relation applied to a new system consisting of the material plus some ‘perturbation’. We present several examples of the form of this external perturbation, which can be viewed as the pump in a pump-probe experiment. We discuss the two-level saturated atom model and bandfilling in semiconductors among others for the resonant case. For the nonresonant case some recent work is included where the electronic nonlinear refractive coefficient,n2, is determined from the nonlinear absorption processes of two-photon absorption, Raman transitions and the a.c. Stark effect. We also review how the dispersion relations can be extended to give alternative forms for frequency summation which, for example, allows the real and imaginary parts ofχ(2) to be related.