Refraction of space-time wave packets in a dispersive medium.

Space-time (ST) wave packets are a class of pulsed optical beams whose spatiotemporal spectral structure results in propagation invariance, tunable group velocity, and anomalous refractive phenomena. Here, we investigate the refraction of ST wave packets normally incident onto a planar interface between two dispersive, homogeneous, isotropic media. We formulate a new, to the best of our knowledge, refractive invariant for ST wave packets in this configuration, from which we obtain a law of refraction that determines the change in their group velocity across the interface. We verify this new refraction law in ZnSe and CdSe, both of which manifest large chromatic dispersion at near-infrared frequencies in the vicinity of their band edges. ST wave packets can thus be utilized in nonlinear optics for bridging large group-velocity mismatches in highly dispersive scenarios.

Femtosecond Spectroscopy and Nonlinear Optical Properties of aza-BODIPY Derivatives in Solution.

The fast relaxation processes in the excited electronic states of functionalized aza-boron-dipyrromethene (aza-BODIPY) derivatives (1-4) were investigated in liquid media at room temperature, including the linear photophysical, photochemical, and nonlinear optical (NLO) properties. Optical gain was revealed for nonfluorescent derivatives 3 and 4 in the near infrared (NIR) spectral range under femtosecond excitation. The values of two-photon absorption (2PA) and excited-state absorption (ESA) cross-sections were obtained for 1-4 in dichloromethane using femtosecond Z-scans, and the role of bromine substituents in the molecular structures of 2 and 4 is discussed. The nature of the excited states involved in electronic transitions of these dyes was investigated using quantum-chemical TD-DFT calculations, and the obtained spectral parameters are in reasonable agreement with the experimental data. Significant 2PA (maxima cross-sections ∼2000 GM), and large ESA cross-sections ∼10-20  m2 of these new aza-BODIPY derivatives 1-4 along with their measured high photostability reveal their potential for photonic applications in general and optical limiting in particular.

Transient mid-IR nonlinear refraction in air.

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(λp;λe), 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.

Nonlinear Optics: feature issue introduction.

This joint issue of Optics Express and Optical Materials Express features 18 state-of-the art articles that witness actual developments in nonlinear optics, including those by authors who participated in the international conference Nonlinear Optics held in Waikoloa, Hawaii from July 15 to 19, 2019. As an introduction, the editors provide a summary of these articles that cover all aspects of nonlinear optics, from basic nonlinear effects and novel frequency windows to innovative nonlinear materials and devices, thereby paving the way for new nonlinear optical concepts and forthcoming applications.

Three-photon absorption spectra of zinc blende semiconductors: theory and experiment: erratum.

We provide a correction to the spectral dependence of the three-photon absorption in zinc-blende semiconductors using Kane's 4-band model in Opt. Lett.33, 2626 (2008).OPLEDP0146-959210.1364/OL.33.002626.

Highly Conjugated, Fused-Ring, Quadrupolar Organic Chromophores with Large Two-Photon Absorption Cross-Sections in the Near-Infrared.

The two-photon absorption (2PA) properties are investigated for two series of organic, π-conjugated, fused-ring, quadrupolar A-π-D-π-A chromophores of the type originally developed as nonfullerene acceptors for organic photovoltaics. These molecules are found to exhibit large nondegenerate two-photon absorption (ND2PA) cross-sections (ca. 6-27 × 103 GM) in the near-infrared (NIR). In the first series, involving molecules of varying core size, ND2PA spectra and cross-sections characterized by femtosecond ND2PA spectroscopy in chloroform solutions reveal that increases in core size, and thus conjugation length, leads to substantially red-shifted and enhanced 2PA. In a second series, variation of the strength of the terminal acceptor (A) with constant core size (seven rings, indacene-based) led to less dramatic variation in the 2PA properties. Among the two core types studied, compounds in which the donor has a thieno[3,2-b]thiophene center demonstrate larger 2PA cross-sections than their indacene-centered counterparts, due to the greater electron-richness of their cores amplifying intramolecular charge transfer. Excited-state absorption (ESA) contributions to nonlinear absorption measured by open-aperture Z-scans are deduced for some of the compounds by analyzing the spectral overlap between 2PA bands and NIR ESA transitions obtained by ND2PA and transient absorption measurements, respectively. ESA cross-sections extracted from transient absorption and irradiance-dependent open-aperture Z-scans are in reasonable agreement, and their moderate magnitudes (ca. 10-21 m2) suggest that, although ESA contributions are non-negligible, the effective response is predominantly instantaneous 2PA.

Cationic Polyelectrolyte for Anionic Cyanines: An Efficient Way To Translate Molecular Properties into Material Properties.

In this work, a new phosphonium-containing cationic polyelectrolyte (PE1) has been rationally designed and developed via a facile click-chemistry type postfunctionalization, which can form complexes with highly polarizable anionic cyanines to significantly reduce the strong and random cyanine-cyanine interactions (i.e., aggregation) in the solid-state. This material design strategy enables an efficient translation of the favorable molecular properties of cyanines into macroscopic material properties. One of such complexes exhibits a very large third-order susceptibility over 10-10 esu with low nonlinear optical loss suitable for all optical signal processing.

Nonlinear refraction and absorption measurements of thin films by the dual-arm Z-scan method.

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.

Introduction: Nonlinear Optics (NLO) 2017 feature issue.

The editors introduce the feature issue on "Nonlinear Optics 2017," based on the topics presented at the NLO 2017 conference, which was held in Waikoloa, Hawaii, USA from July 17-21, 2017. This feature issue is jointly published by Optics Express and Optical Materials Express.

Facile Incorporation of Pd(PPh3)2Hal Substituents into Polymethines, Merocyanines, and Perylene Diimides as a Means of Suppressing Intermolecular Interactions.

Compounds with polarizable π systems that are susceptible to attack with nucleophiles at C-Hal (Hal = Cl, Br) bonds react with Pd(PPh3)4 to yield net oxidative addition. X-ray structures show that the resulting Pd(PPh3)2Hal groups greatly reduce intermolecular π-π interactions. The Pd-functionalized dyes generally exhibit solution-like absorption spectra in films, whereas their Hal analogues exhibit features attributable to aggregation.

Dispersion of nondegenerate nonlinear refraction in semiconductors.

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 n2(ωa; ωb) are determined over a broad spectral range for different values of nondegeneracy. In the extremely nondegenerate case, n2(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, n2(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)].

Three-dimensional IR imaging with uncooled GaN photodiodes using nondegenerate two-photon absorption.

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.

Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases: erratum.

We provide an updated comparison of second hyperpolazability of carbon disulfide reported in [Opt. Express23(17), 22224 (2015)10.1364/OE.23.022224Optica3(6), 657 (2016)10.1364/OPTICA.3.000657].

Observation of Nondegenerate Two-Photon Gain in GaAs.

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 2 orders of magnitude is reported. The results point a possible way toward two-photon semiconductor lasers.

Nonlinear Optical Properties of X(C6H5)4 (X = B(-), C, N(+), P(+)): A New Class of Molecules with a Negative Third-Order Polarizability.

Organic π-conjugated materials have been widely used for a variety of nonlinear optical (NLO) applications. Molecules with negative real components Re(γ) of the third-order polarizability, which leads to nonlinear refraction in macroscopic systems, have important benefits for several NLO applications. However, few organic systems studied to date have negative Re(γ) in the long wavelength limit, and all inorganic materials show positive nonlinear refraction in this limit. Here, we introduce a new class of molecules of the form X(C6H5)4, where X = B(-), C, N(+), and P(+), that have negative Re(γ). The molecular mechanism for the NLO properties in these systems is very different from those in typical linear conjugated systems: These systems have a band of excited states involving single-electron excitations within the π-system, several of which have significant coupling to the ground state. Thus, Re(γ) cannot be understood in terms of a simplified essential-state model and must be analyzed in the context of the full sum-over-states expression. Although Re(γ) is significantly smaller than that of other commonly studied NLO chromophores, the introduction of a new molecular architecture offering the potential for a negative Re(γ) introduces new avenues of molecular design for NLO applications.

Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases.

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.

Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction.

We modify the well-known photothermal beam deflection technique to study ultrafast nonlinearities. Using phase-sensitive detection we directly measure the temporal and polarization dynamics of nonlinear refraction (NLR) with sensitivity to optically induced phase changes of approximately λ/20,000. We use the relative polarization dependence of excitation and probe to separate the isotropic and reorientational components of the NLR.

Two-photon absorption spectra of a near-infrared 2-azaazulene polymethine dye: solvation and ground-state symmetry breaking.

Polymethine dyes (PDs) with absorption bands in the near-infrared region undergo symmetry breaking in polar solvents. To investigate how symmetry breaking affects nonlinear optical responses of PDs, an extensive and challenging experimental characterization of a cationic 2-azaazulene polymethine dye, including linear absorption, fluorescence, two-photon absorption and excited-state absorption, has been performed in two solvents with different polarity. Based on this extensive set of experimental data, a three-electronic-state model, accounting for the coupling of electronic degrees of freedom to molecular vibrations and polar solvation, has been reliably parameterized and validated for this dye, fully rationalizing optical spectra in terms of spectral position, intensities and bandshapes. In low-polarity solvents where the dye is mainly in its symmetric form, a nominally forbidden two-photon absorption band is observed, due to a vibronic activation mechanism. Inhomogeneous broadening plays a major role in polar solvents: absorption spectra represent the weighted sum of contributions from states with a variable amount of symmetry breaking, leading to a complex evolution of linear and nonlinear optical spectra with solvent polarity. In more polar solvents, the dominant role of the asymmetric form leads to the activation of two-photon absorption as a result of the symmetry lowering. The subtle interplay between the two mechanisms for two-photon absorption activation, vibronic coupling and polar solvation, can be fully accounted for within the proposed microscopic model allowing a detailed interpretation of the optical spectra of PDs.

Enhanced intersystem crossing rate in polymethine-like molecules: sulfur-containing squaraines versus oxygen-containing analogues.

Two different approaches to increase intersystem crossing rates in polymethine-like molecules are presented: traditional heavy-atom substitution and molecular levels engineering. Linear and nonlinear optical properties of a series of polymethine dyes with Br- and Se-atom substitution, and a series of new squaraine molecules, where one or two oxygen atoms in a squaraine bridge are replaced with sulfur atoms, are investigated. A consequence of the oxygen-to-sulfur substitution in squaraines is the inversion of their lowest-lying ππ* and nπ* states leading to a significant reduction of singlet-triplet energy difference and opening of an additional intersystem channel of relaxation. Experimental studies show that triplet quantum yields for polymethine dyes with heavy-atom substitutions are small (not more than 10%), while for sulfur-containing squaraines these values reach almost unity. Linear spectroscopic characterization includes absorption, fluorescence, quantum yield, anisotropy, and singlet oxygen generation measurements. Nonlinear characterization, performed by picosecond and femtosecond laser systems (pump-probe and Z-scan measurements), includes measurements of the triplet quantum yields, excited state absorption, two-photon absorption, and singlet and triplet state lifetimes. Experimental results are in agreement with density functional theory calculations allowing determination of the energy positions, spin-orbital coupling, and electronic configurations of the lowest electronic transitions.

Optimization of the double pump-probe technique: decoupling the triplet yield and cross section.

The double pump-probe technique (DPP), first introduced by Swatton et al. [Appl. Phys. Lett. 1997, 71, 10], is a variant of the standard pump-probe method but uses two pumps instead of one to create two sets of initial conditions for solving the rate equations, allowing a unique determination of singlet- and triplet-state absorption parameters and transition rates. We investigate the advantages and limitations of the DPP theoretically and experimentally and determine the influence of several experimental parameters on its accuracy. The accuracy with which the DPP determines the triplet-state parameters improves when the fraction of the population in the triplet state relative to the ground state is increased. To simplify the analysis of the DPP, an analytical model is presented, which is applicable to both the reverse saturable and the saturable absorption regimes. We show that the DPP is optimized by working in the saturable absorption regime. Although increased accuracy is in principle achievable by increasing the pump fluence in the reverse saturable absorption range, this can cause photoinduced decomposition in photochemically unstable molecules. Alternatively, we can tune the excitation wavelength to the spectral region of larger ground-state absorption, to achieve similar accuracy. This results in an accurate separation of triplet yield and excited-state absorption cross section. If the cross section at another wavelength is then desired, a second pump-probe experiment at that wavelength can be utilized given the previously measured triplet yield under the usually valid assumption that the triplet yield is independent of excitation wavelength.