2PA Spectra Research Articles

A Single-Shot Technique for Measuring Broadband Two-Photon Absorption Spectra in Solution.

Applications involving two-photon activation, including two-photon fluorescence imaging, photodynamic therapy, and 3D data storage, require precise knowledge of the two-photon absorption (2PA) spectra of target chromophores. Broadband pump-probe spectroscopy using femtosecond laser pulses provides wavelength-dependent 2PA spectra with absolute cross sections, but the measurements are sometimes complicated by cross-phase modulation effects and dispersion of the broadband probe. Here, we introduce a single-shot approach that eliminates artifacts from cross-phase modulation and enables more rapid measurements by avoiding the need to scan the time delay between the pump and the probe pulses. The approach uses counterpropagating beams to automatically integrate over the full interaction between the two pulses as they cross. We demonstrate this single-shot approach for a common 2PA reference, coumarin 153 (C153), in three different solvents using the output from a Yb:KGW laser. This approach provides accurate 2PA cross sections that are more reliable and easier to obtain compared with scanning pump-probe methods using copropagating laser beams. The single-shot method for broadband two-photon absorption (BB-2PA) spectroscopy also has significant advantages compared with single-wavelength measurements, such as z-scan and two-photon fluorescence.

First-principle study of two-photon absorption in Fe3O4.

Utilizing the length gauge and the electron density operator, we calculate the two-photon absorption (2PA) coefficient of Fe3O4 based on a full ab initio band structure. The pure two-photon interband transitions and those modulated by intraband transitions have been separated explicitly to determine their impact on the 2PA spectrum. A single main absorption peak instead of two will present in the spectrum by including the hybridization of inter- and intra-band transitions, which can be identified easily in future experimental studies. In addition, we find that in almost the whole 2PA-active spectral range, circularly polarized light can be absorbed with a much lower threshold power than the linearly polarized one. But the linearly polarized light is more easily to be manipulated. One can control the magnitude and resonance frequency of the 2PA coefficient by simply adjusting the polarization angle of the incident light. Our findings will deepen the understanding of the 2PA phenomenon in Fe3O4 nanoparticles.

The eXact integral simplified time-dependent density functional theory (XsTD-DFT).

In the framework of simplified quantum chemistry methods, we introduce the eXact integral simplified time-dependent density functional theory (XsTD-DFT). This method is based on the simplified time-dependent density functional theory (sTD-DFT), where all semi-empirical two-electron integrals are replaced by exact one- and two-center two-electron integrals, while other approximations from sTD-DFT are kept. The performance of this new parameter-free XsTD-DFT method was benchmarked on excited state and (non)linear response properties, including ultra-violet/visible absorption, first hyperpolarizability, and two-photon absorption (2PA). For a set of 77 molecules, the results from the XsTDA approach were compared to the TDA data. XsTDA/B3LYP excitation energies only deviate on average by 0.14eV from TDA while drastically cutting computational costs by a factor of 20 or more depending on the energy threshold chosen. The absolute deviations of excitation energies with respect to the full scheme are decreasing with increasing system size, showing the suitability of XsTDA/XsTD-DFT to treat large systems. Comparing XsTDA and its predecessor sTDA, the new scheme generally improves excitation energies and oscillator strengths, in particular, for charge transfer states. TD-DFT first hyperpolarizability frequency dispersions for a set of push-pull π-conjugated molecules are faithfully reproduced by XsTD-DFT, while the previous sTD-DFT method provides redshifted resonance energy positions. Excellent performance with respect to the experiment is observed for the 2PA spectrum of the enhanced green fluorescent protein. The obtained robust accuracy similar to TD-DFT at a fraction of the computational cost opens the way for a plethora of applications for large systems and in high throughput screening studies.

Tuning the linear optical properties and two-photon absorption on the cinnamylideneacetophenone derivatives: The effect of methoxy group by a experimental and theoretical point of view

The present work studied the effect of the methoxy group position in two cinnamylideneacetophenone (CA) derivatives on both one-photon (1PA) and two-photon absorption (2PA) processes. Our outcomes exhibit a dependence on the methoxy group position spectrally and in magnitude for both. A decrease in the lower energy 1PA band of 0.23eV was observed when the methoxy group was moved to the more conjugated part of the cinnamaldehyde molecule. The opposite was also observed for the next higher absorption band. The Quantum Chemical Calculations (QCCs), besides a good agreement between the experimental and simulated 1PA spectra, except for the magnitude of the high energy absorption band, showed that the effect behind the observed experimental red-shift of the lower absorption band is caused by the higher charge transfer when the methoxy group is bounded to the longer conjugated part of the cinnamaldehyde derivative. For experimental 2PA spectra, the higher energy band is strongly affected by the presence of the methoxy group, pointing out an increase of about 56 % in the values of the two-photon absorption cross-section (2PACS). Furthermore, the phenomenological Sum-Over-Essential States (SOS) approach and QCCs were performed for further clarification in the 2PACS experimental results. Hence, our findings demonstrate that changing the methoxy position on opposite sides of the CA may open up a novel insight for designing new organic molecules, particularly when seeking to enhance the values of 2PACS significantly of CA derivatives.

Two- and one-photon absorption spectra of aqueous thiocyanate anion highlight the role of symmetry in the condensed phase.

We present the two-photon absorption (2PA) spectrum of aqueous thiocyanate calculated using high-level quantum-chemistry methods. The 2PA spectrum is compared to the one-photon absorption (1PA) spectrum computed using the same computational protocol. Although the two spectra probe the same set of electronic states, the intensity patterns are different, leading to an apparent red-shift of the 2PA spectrum relative to the 1PA spectrum. The presented analysis explains the intensity patterns and attributes the differences between the 1PA and 2PA spectra to the native symmetry of isolated SCN , which influences the spectra in the low-symmetry solvated environment. The native symmetry also manifests itself in variations of the polarization ratio (e.g., parallel vs. perpendicular cross sections) across the spectrum. The presented results highlight the potential of 2PA spectroscopy and high-level quantum-chemistry methods in studies of condensed-phase phenomena.

Broadband Two-Photon Absorption Spectroscopy with Stimulated Raman Scattering as an Internal Standard.

Two-photon absorption (2PA) spectroscopy provides valuable information about the nonlinear properties of molecules. In contrast with single-wavelength methods, broadband 2PA spectroscopy using a pump-probe approach gives a continuous 2PA spectrum across a wide range of transition energies without tuning the excitation laser. This contribution shows how stimulated Raman scattering from the solvent can be used as a convenient and robust internal standard for obtaining accurate absolute 2PA cross sections using the broadband approach. Stimulated Raman scattering has the same pump-probe overlap dependence as 2PA, thus eliminating the need to measure the intensity-dependent overlap of the pump and probe directly. Eliminating the overlap represents an important improvement because intensity profiles are typically the largest source of uncertainty in the measurement of absolute 2PA cross sections using any method. Raman scattering cross sections are a fundamental property of the solvent and therefore provide a universal standard that can be applied any time the 2PA and Raman signals are present within the same probe wavelength range. We demonstrate this approach using sample solutions of coumarin 153 in methanol, DMSO, and toluene, as well as fluorescein in water.

Beyond Universal Volume Scaling: Tailoring Two-Photon Absorption in Nanomaterials by Heterostructure Design.

Colloidal semiconductor nanomaterials present broadband, with large cross-section, two-photon absorption (2PA) spectra, which turn them into an important platform for applications that benefit from a high nonlinear optical response. Despite that, to date, the only means to control the magnitude of the 2PA cross-section is by changing the nanoparticle volume, as it follows a universal volume scale, independent of the material composition. As the emission spectrum is connected utterly to the nanomaterial dimensions, for a given material, the magnitude of the nonlinear optical response is also coupled to the emission spectra. Here, we demonstrate a means to decouple both effects by exploring the 2PA response of different types of heterostructures, tailoring the volume dependence of the 2PA cross-section due to the different dependence of the density of final states on the nanoparticle volume. By heterostructure engineering, one can obtain 1 order of magnitude enhancement of the 2PA cross-section with minimum emission spectra shift.

Nature of Linear Spectral Properties and Fast Relaxations in the Excited States and Two-Photon Absorption Efficiency of 3-Thiazolyl and 3-Phenyltiazolyl Coumarin Derivatives.

Coumarin-based fluorescent agents play an important role in the manifold fundamental scientific and technological areas and need to be carefully studied. In this research, linear photophysics, photochemistry, fast vibronic relaxations, and two-photon absorption (2PA) of the coumarin derivatives, methyl 4-[2-(7-methoxy-2-oxo-chromen-3-yl)thiazol-4-yl]butanoate (1) and methyl 4-[4-[2-(7-methoxy-2-oxo-chromen-3-yl)thiazol-4-yl]phenoxy]butanoate (2), were comprehensively analyzed using stationary and time-resolved spectroscopic techniques, along with quantum-chemical calculations. The steady-state one-photon absorption, fluorescence emission, and excitation anisotropy spectra, as well as 3D fluorescence maps of 3-hetarylcoumarins 1 and 2 were obtained at room temperature in solvents of different polarities. The nature of relatively large Stokes shifts (∼4000-6000 cm-1), specific solvatochromic behavior, weak electronic π → π* transitions, and adherence to Kasha's rule were revealed. The photochemical stability of 1 and 2 was explored quantitatively, and values of photodecomposition quantum yields, on the order of ∼10-4, were determined. A femtosecond transient absorption pump-probe technique was used for the investigation of fast vibronic relaxation and excited-state absorption processes in 1 and 2, while the possibility of efficient optical gain was shown for 1 in acetonitrile. The degenerate 2PA spectra of 1 and 2 were measured by an open aperture z-scan method, and the maximum 2PA cross-sections of ∼300 GM were obtained. The electronic nature of the hetaryl coumarins was analyzed by quantum-chemical calculations using DFT/TD-DFT level of theory and was found to be in good agreement with experimental data.

Two-photon magneto-optical transitions in quantum rings

We study the effect of the magnetic and Aharonov–Bohm (AB) flux fields on the two-photon absorption (2PA) in a quantum ring (QR) system. The expression of 2PA coefficient is expressed through the two-photon transition probability including both intraband and interband transitions. The effect of the polarization orientation of the incident light breaks the symmetry from the contribution between the AB flux field and the azimuthal quantum number. Magnetic and AB flux fields have a significant effect on the electronic properties of the QR. The 2PA spectra for intraband transitions are in the THz range and have a much higher magnitude compared to those for interband transitions, which are located in the near-infrared range. The increase in the magnetic field results in a blue-shift of the 2PA spectra for both intraband and interband transitions, whereas changes in the azimuthal quantum number only affect the spectra for interband transitions.

Ultrafast Evaluation of Two-Photon Absorption with Simplified Time-Dependent Density Functional Theory.

This work presents the theoretical background to evaluate two-photon absorption (2PA) cross-sections in the framework of simplified time-dependent density functional theory (sTD-DFT). Our new implementation allows the ultrafast evaluation of 2PA cross-sections for large molecules based on a regular DFT ground-state determinant as well as a variant employing our tight-binding sTD-DFT-xTX flavor for very large systems. The method is benchmarked against higher-level calculations for trans-stilbene and typical fluorescent protein chromophores. For eGFP, a quadrupolar chromophore and its branched version, the flavine mono-nucleotide, and the iLOV protein, we compare sTD-DFT 2PA spectra to experimental ones. This includes extension and testing of our all-atom quantum chemistry methodology for the evaluation of 2PA for a system of ∼2000 atoms, providing striking agreement with the experimental spectrum.

New Two-Photon Absorbing Squaraine Derivative with Efficient Near-Infrared Fluorescence, Superluminescence, and High Photostability

The nature of linear photophysical and nonlinear optical properties of a new squaraine derivative 2,4-bis[4-(azetidyl)-2-hydroxyphenyl]squaraine (1) with efficient near-infrared (NIR) emission was comprehensively analyzed based on spectroscopic, photochemical, and two-photon absorption (2PA) measurements, along with quantum chemical analysis. The steady-state absorption, fluorescence, and excitation anisotropy spectra of 1 and its fluorescence emission lifetimes revealed the multiple aspects of the electronic structure of 1, including the relative orientations of the main transition dipoles, effective rotational volumes in solvents of different polarities, and a maximum molar extinction of 1.35 × 10-5 M-1·cm-1, which is unusually small for similar symmetric squaraines. The degenerate 2PA spectrum of 1 was obtained over a broad spectral range under femtosecond excitation, using standard open-aperture Z-scan and two-photon induced fluorescence methods, revealing maximum 2PA cross sections of ∼400 GM. Squaraine 1 exhibited efficient superluminescence emission in the polar solvent (dichloromethane) at room temperature under femtosecond pumping conditions. Quantum chemical analysis of the electronic structure of 1 was performed using the DFT/TD-DFT level of theory and found to be in good agreement with experimental data. The new squaraine derivative 1 displayed high fluorescence quantum yield, efficient NIR superluminescence, large 2PA cross sections, and high photostability with a photodecomposition quantum yield ∼4 × 10-6, suggesting its potential for applications in two-photon fluorescent bioimaging and lasing.

Second- and third-order nonlinear optical properties of mono-substituted terpenoid-like chalcones

Organic molecules exhibiting second and third-order nonlinear optical properties (NLOP) allow several applications in optics and photonics. Among the class of organic compounds, terpenoid-like chalcones derivatives constitute a suitable choice as nonlinear optical materials, given the possibility of obtaining a wide range of compounds that can be used in biophotonic applications. In this way, here we present a study of the first-order molecular hyperpolarizability and the two-photon absorption (2PA) cross-section of several terpenoid-like chalcones derivatives, aiming for applications in the therapeutic window. The 2PA spectra were evaluated employing the femtosecond tunable Z-Scan technique from 480 nm to 850 nm, and the first hyperpolarizability was determined at 1064 nm using the Hyper-Rayleigh scattering (HRS) technique. Moreover, the first-order molecular hyperpolarizability and the 2PA spectra were modeled by the sum-over-states (SOS) approach and undamped phenomenological model, respectively, providing new insights into the properties and compoundś structure relationship. Results showed that substituent features, such as electron-donating or withdrawing ability, were associated with the 2PA cross-section magnitude. Regarding HRS results, it was possible to compare the difference of state dipole moment from both approaches, combining two experimental routes to determine photophysical parameters of non-fluorescent compounds, revealing the structure-relationship aiming the increase of the NLOP at the near-infrared region.

Novel Lipophilic Fluorophores with Highly Acidity-Dependent Two-Photon Response.

Lipophilic fluorophores are widely implemented in nonlinear microscopy; however, few existing membrane-specific probes combine the high brightness of two-photon excited fluorescence (2PEF) with pH sensitivity. Herein we describe four novel two-photon excited fluorophores, based on a coumarin 151 core structure, where lipophilicity is induced by a covalently attached phosphazene moiety. Changing the environmental acidity using trifluoromethanesulfonic (triflic) acid leads to profound changes in the linear fluorescence and 2PEF characteristics, due to chromophores' switching between neutral- and protonated forms. We characterize this dependence by measuring the two-photon absorption (2PA) spectra over the region λ2PA =550-1000 nm, observing 2PA cross sections of σ2PA =10-20 GM, with an associated 2PEF brightness of 10-13 GM, in neutral solutions of both acetonitrile and n-octanol. Although quantum chemical modelling and NMR measurements show that, at high chromophore concentrations, protonation may be accompanied by a dimerization process, these dimers likely do not form at the lower concentrations used in optical spectroscopy.

Dissecting conjugation and electronic effects on the linear and non-linear optical properties of rhenium(I) carbonyl complexes.

Herein, we report a theoretical and experimental analysis of the conjugation and electronic effects on the one-photon (1PA) and two-photon absorption (2PA) properties of a series of Re(I) carbonyl complexes with terpyridine-based ligands. An excellent agreement was obtained between the calculated and experimental 2PA spectra of the κ2N-terpyridine tricarbonyl complexes (1a-b), with 2PA cross sections reaching up to ca. 40 GM in DMF. By stepwise lowering the conjugation length in the terpy ligand and changing the local symmetry around the metal centre, we show that conjugation and delocalisation play a major role in increasing 2PA cross sections, and that the character of the excited states does not directly enhance the non-linear properties of these complexes-contrary to the results observed in 1PA. Altogether, these results give valuable guidelines towards more efficient two-photon-absorbing coordination complexes of Re(I), with potential applications in photodynamic therapy and two-photon imaging.

Electronic Structure of Liquid Alkanes: A Representative Case of Liquid Hexanes and Cyclohexane Studied Using Polarization-Dependent Two-Photon Absorption Spectroscopy.

Two-photon absorption (2PA) spectra of liquid cyclohexane and hexanes are reported for the energy range 6.4-8.5 eV (177-145 nm), providing detailed information about their electronic structures in bulk liquid. Using a broadband pump-probe fashion, we measured the continuous 2PA spectra by simultaneous absorption of a 266 nm (4.6 eV) pump photon and one UV-vis probe photon from the white-light continuum (1.8-3.9 eV). Theoretical one-photon absorption (1PA) and 2PA cross sections of isolated gas phase molecules are computed by the equation of motion coupled-cluster method with single and double substitutions (EOM-CCSD) to substantiate the assignment of the experimental spectra, and the natural transition orbital (NTO) analysis provides visualization of the participating orbitals in a transition. Our analysis suggests that upon solvation transitions at the lowest excitation energy involving promotion of electron to the 3s Rydberg orbitals are blue-shifted (∼0.55 eV for cyclohexane and ∼0.18 eV for hexanes) to a greater extent as compared to those involving other Rydberg orbitals, which is similar to the behavior observed for water and alcohols. All other transitions experience negligible (cyclohexane) or minor red-shift by ∼0.15-0.2 eV (hexane) upon solvation. In both alkanes, the spectra are entirely dominated by Rydberg transitions: the most intense bands in 1PA and 2PA spectra are due to the excitation of electrons to the Rydberg "p" and "d" type orbitals, respectively, although one transition terminating in the 3s Rydberg has significant 2PA strength. This work demonstrates that the gas phase electronic transition properties in alkanes are not significantly altered upon solvation. In addition, electronic structure calculations using an isolated-molecule framework appear to provide a reasonable starting point for a semiquantitative picture for spectral assignment and also to analyze the solvatochromic shifts for liquid phase absorption spectra.

Quantum impedance Lorentz oscillator and its 1- and 2-photon-absorption applications

In this paper, a classical Lorentz oscillator is quantized via Bohr–Sommerfeld quantum theory and 1- and 2-photon absorption (1PA and 2PA) selection rules of quantum mechanics. Based on the Bohr–Sommerfeld model of a hydrogen-like atom in the adiabatic approximation, the computational formulas of the linear and nonlinear parameters and the damping coefficient of the quantized oscillator are derived and further expressed in terms of microphysical quantities, such as electronic charge and mass, Bohr radius, and effective quantum number. In accordance with Boltzmann thermal equilibrium distribution, here, the atom number density in general electric susceptibility is changed to the energy level transition one from the initial to the final state at equilibrium between atomic emission and absorption under light field. A new relationship is proposed to determine the transition eigenfrequency according to the peak frequency and full width at half maximum of an absorption spectrum. Our theoretical simulations of the 1PA spectra of atomic hydrogen and lithium and 1PA and 2PA spectra of two kinds of organic molecules turn out to be in good agreement with the experimental ones. These results suggest that our advancement in the quantization of the Lorentz oscillator is likely successful to make it available for use in the quantitative description of atomic or molecular 1PA and 2PA processes. Generally, the improved Lorentz oscillator may also be more suitable for approximating both linear and nonlinear properties of many dielectric or optoelectronic materials due to its relative simplicity.

Three-Photon Spectroscopy of Porphyrins.

Recent advances in laser technology have made three-photon (3P) microscopy a real possibility, raising interest in the phenomenon of 3P absorption (3PA). Understanding 3PA of organic chromophores is especially important in view of those imaging applications that rely on exogenous probes, whose optical properties can be manipulated and optimized. Here, we present measurements and theoretical analysis of the degenerate 3PA spectra of several phosphorescent metalloporphyrins, which are used in the construction of biological oxygen probes. The effective 3PA cross sections (σ(3)) of these porphyrins near 1700 nm, a new promising biological optical window, were found to be on the order of 1000 GM3 (1 GM3 = 10-83 cm6 s2), therefore being among the highest values reported to date for organic chromophores. To interpret our data, we developed a qualitative four-state model specific for porphyrins and used it in conjunction with quantitative analysis based on the time-dependent density functional theory (TDDFT)/a posteriori Tamm-Dancoff approximation (ATDA)/sum-over-states (SOS) formalism. The analysis revealed that B (Soret) state plays a key role in the enhancement of 3PA of porphyrins in the Q band region, while the low-lying two-photon (2P)-allowed gerade states interfere negatively and diminish the 3PA strength. This study features the first systematic examination of 3PA properties of porphyrins, suggesting ways to improve their performance and optimize them for imaging and other biomedical applications.

The thermochemical, structural, and spectroscopic analyses of the tautomers of sulfur and selenium modified emissive nucleobases

In this study, density functional theory (DFT) and time dependent density functional theory (TD-DFT) are used to investigate the stabilities and spectral properties [IR, UV–vis, and two-photon absorption (2PA)] of two sets of modified RNA nucleobase tautomers. The modifications introduce either a sulfur or selenium atom to form an isothiazolo[4,3-d]pyrimidine or isoselenazolo[4,3-d]pyrimidine heterocyclic core, respectively. The relative stabilities of both sets of modified tautomers determined with B3LYP/6-31++G(d,p) reveal that in water (with a polarizable continuum model), the 6-keto-2-amino tautomer of guanine and the rare 4-imino-2-keto tautomer of cytosine may be present at significant populations, whereas the 6-enol-2-amino tautomer of guanine is more common in the gas phase. The identification of these modified tautomers is possible due to the natural differences in their vibrational modes and hence IR spectra. Furthermore, the photophysical properties of both these sets of modified tautomers indicate that excitation and emission energies are shifted relative to their more abundant form in both one photon absorption and emission and 2PA spectra, as determined at the B3LYP/6-31++G(d,p) and CAM-B3LYP/aug-cc-pVDZ levels of theory, respectively. Even though the 2PA cross sections in water for all of the species are small (0.3–2.3 GM), the modified cytosine tautomer shows promise, as its cross section is larger than the more dominant form. The spectral separation between the dominant form and the tautomers of isoselenazole and isothiazole modified cytosine and guanine are relatively similar, suggesting both modifications could be useful in elucidating the tautomers from their more abundant counterparts.

Two-photon absorption spectrum and characterization of the upper electronic states of the dye IR780

In this work, the full two-photon absorption (2PA) spectrum of cyanine dye IR780 in methanol was measured and some important properties of the upper excited electronic states were investigated. Specifically, two IR780 2PA bands of intensities nearing 140 and 2800 Goeppert-Mayer (GM) were found. In order to determine the optical properties of the upper electronic singlet states, a deconvolution of the absorption peaks in the UV region of the spectrum was made. Based on this, properties such as transition dipole moments, oscillator strengths, absorption maxima in the UV–vis spectra, S2-S1 vibrational couplings and predictions of the lifetime of the second excited state were calculated. Moreover, by combining experimental and computational results, the 2PA transitions were assigned to the upper excited states S2 and S4. Cross-section magnitudes, positions and shapes of the 2PA bands have been satisfactorily explained with a four-state model that comprises the singlet states S1, S2 and S4. From these results, the cyanine investigated in the present work could be used as a novel and interesting moiety for more complex systems that respond to two-photon excitation.

Three-photon absorption spectra and bandgap scaling in direct-gap semiconductors

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 eight-band Kane model (four bands with double spin degeneracy), help to explain the significant disagreements between experiments and theory in the literature to date. 3PA in the eight-band model exhibits quantum interference between the various possible pathways that is not observed in previous two-band theories. We present measurements of degenerate 3PA coefficients in InSb, GaAs, CdTe, CdSe, ZnTe, CdS, ZnSe, ZnO, and ZnS. We examine bandgap, E g , scaling using -band tunneling and perturbation theories that show agreement with the predicted E g − 7 dependence; however, for those semiconductors for which we measured full 3PA spectra, we observe significant discrepancies with both two-band theories. On the other hand, our eight-band model shows excellent agreement with the spectral data. We then use our eight-band theory to predict the 3PA spectra for 15 different semiconductors in their zinc-blende form. These results allow prediction and interpretation of the 3PA coefficients for various narrow to wide bandgap semiconductors.