Three-photon Cross Sections Research Articles

Measurement of third order coherence by in situ autocorrelation for determining three-photon cross-sections.

We show theoretically that the third order coherence at zero delay can be obtained by measuring the second and third order autocorrelation traces of a pulsed laser. Our theory enables the measurement of a fluorophore's three-photon cross-section without prior knowledge of the temporal profile of the excitation pulse by using the same fluorescent medium for both the measurement of the third order coherence at zero delay as well as the cross-section. Such an in situ measurement needs no assumptions about the pulse shape nor group delay dispersion of the optical system. To verify the theory experimentally, we measure the three-photon action cross-section of Alexa Fluor 350 and show that the measured value of the three-photon cross-section remains approximately constant despite varied amounts of chirp on the excitation pulses.

In Vivo Deep-Brain Structural and Hemodynamic Multiphoton Microscopy Enabled by Quantum Dots.

Visualizing deep-brain vasculature and hemodynamics is key to understanding brain physiology and pathology. Among the various adopted imaging modalities, multiphoton microscopy (MPM) is well-known for its deep-brain structural and hemodynamic imaging capability. However, the largest imaging depth in MPM is limited by signal depletion in the deep brain. Here we demonstrate that quantum dots are an enabling material for significantly deeper structural and hemodynamic MPM in mouse brain in vivo. We characterized both three-photon excitation and emission parameters for quantum dots: the measured three-photon cross sections of quantum dots are 4-5 orders of magnitude larger than those of conventional fluorescent dyes excited at the 1700 nm window, while the three-photon emission spectrum measured in the circulating blood in vivo shows a slight red shift and broadening compared with ex vivo measurement. On the basis of these measured results, we further demonstrate both structural and hemodynamic three-photon microscopy in the mouse brain in vivo labeled by quantum dots, at record depths among all MPM modalities at all demonstrated excitation wavelengths.

Two- and Three-Photon Partial Photoionization Cross Sections of Li+, Ne8+ and Ar16+ under XUV Radiation

In this work, we present the photon energy dependence of the two- and three-photon cross sections of the two-electron Li+, Ne8+ and Ar16+ ions, following photoionization from their ground state. The expressions for the cross sections are based on the lowest-order (non-vanishing) perturbation theory for the electric field, while the calculations are made with the use of an ab initio configuration interaction method. The ionization cross section is dominated by pronounced single photon resonances in addition to peaks associated with doubly excited resonances. In the case of two-photon ionization, and in the non-resonant part of the cross section, we find that the 1D ionization channel overwhelms the 1S one. We also observe that, as one moves from the lowest atomic number ion, namely Li+, to the highest atomic number ion, namely Ar16+, the cross sections generally decrease.

Nonlinear-Optical Response of Prussian Blue: Strong Three-Photon Absorption in the IR Region.

The nonlinear-optical properties of Prussian Blue nanoparticles have been evaluated with the use of femtosecond Z-scan measurements in the 1350-1750 nm range. This well-known inorganic pigment having interesting magnetic and electrochemical properties was found to be an efficient near-IR three-photon absorber. The maximum of the effective three-photon cross section is as high as 4.5 × 10-78 cm6 s2 at 1375 nm. By a comparison of the three-photon molar-mass-normalized merit factors, σ3/M, we show that this material is a competitive multiphoton absorber, especially in comparison to semiconductor quantum dots.

Saturation Dynamics Measures Absolute Cross Section and Generates Contrast within a Neuron

The intensity required to optically saturate a chromophore is a molecular property that is determined by its absorption cross section (σ) and the excited state lifetime. We present an analytical description of such a system and show that fluorescence around the onset of saturation is characterized by product of absorption cross section and lifetime. Using this approach we formulate a generalized method for measuring the multiphoton cross section of fluorophores and use it to obtain the absolute three-photon cross-section spectra of tryptophan. We find that the tryptophan three-photon cross section ranges from 0.28 S.I. units (m6s2photon−2) at 870 nm to 20 S.I. units at 740 nm. Further, we show that the product of molecular rate of excitation and de-excitation, denoted as β, serves as a vital contrasting agent for imaging local environment. Our contrast parameter, β, is related to fraction of the population present in the excited state and is independent of the fluorophore concentration. We show that β-imaging can be carried out in a regular two-photon microscope setup through a series of intensity scans. Using enhanced green fluorescent protein (EGFP) fluorescence from the brain slices of Thy-1 EGFP transgenic mice, we show that there is an inherent, concentration independent, variation in contrast across the soma and the dendrite.

Long-term in vivo single-cell lineage tracing of deep structures using three-photon activation.

Genetic labeling techniques allow for noninvasive lineage tracing of cells in vivo. Two-photon inducible activators provide spatial resolution for superficial cells, but labeling cells located deep within tissues is precluded by scattering of the far-red illumination required for two-photon photolysis. Three-photon illumination has been shown to overcome the limitations of two-photon microscopy for in vivo imaging of deep structures, but whether it can be used for photoactivation remains to be tested. Here we show, both theoretically and experimentally, that three-photon illumination overcomes scattering problems by combining longer wavelength excitation with high uncaging three-photon cross-section molecules. We prospectively labeled heart muscle cells in zebrafish embryos and found permanent labeling in their progeny in adult animals with negligible tissue damage. This technique allows for a noninvasive genetic manipulation in vivo with spatial, temporal and cell-type specificity, and may have wide applicability in experimental biology.

Three-photon-excited luminescence from unsymmetrical cyanostilbene aggregates: morphology tuning and targeted bioimaging.

We report an experimental observation of aggregation-induced enhanced luminescence upon three-photon excitation in aggregates formed from a class of unsymmetrical cyanostilbene derivatives. Changing side chains (-CH3, -C6H13, -C7H15O3, and folic acid) attached to the cyanostilbene core leads to instantaneous formation of aggregates with sizes ranging from micrometer to nanometer scale in aqueous conditions. The crystal structure of a derivative with a methyl side chain reveals the planarization in the unsymmetrical cyanostilbene core, causing luminescence from corresponding aggregates upon three-photon excitation. Furthermore, folic acid attached cyanostilbene forms well-dispersed spherical nanoaggregates that show a high three-photon cross-section of 6.0 × 10(-80) cm(6) s(2) photon(-2) and high luminescence quantum yield in water. In order to demonstrate the targeted bioimaging capability of the nanoaggregates, three cell lines (HEK293 healthy cell line, MCF7 cancerous cell line, and HeLa cancerous cell line) were employed for the investigations on the basis of their different folate receptor expression level. Two kinds of nanoaggregates with and without the folic acid targeting ligand were chosen for three-photon bioimaging studies. The cell viability of three types of cells incubated with high concentration of nanoaggregates still remained above 70% after 24 h. It was observed that the nanoaggregates without the folic acid unit could not undergo the endocytosis by both healthy and cancerous cell lines. No obvious endocytosis of folic acid attached nanoaggregates was observed from the HEK293 and MCF7 cell lines having a low expression of the folate receptor. Interestingly, a significant amount of endocytosis and internalization of folic acid attached nanoaggregates was observed from HeLa cells with a high expression of the folate receptor under three-photon excitation, indicating targeted bioimaging of folic acid attached nanoaggregates to the cancer cell line. This study presents a paradigm of using organic nanoaggregates for targeted three-photon bioimaging.

Direct three-photon excitation of upconversion random laser emission in a weakly scattering organic colloidal system.

We report the operation and characterization of an upconversion random laser emitting at 560 nm, when directly pumped by three photon excitation at the near IR wavelength of 1350 nm in a colloidal dye solution in the weakly scattering regime. Using a special dye with a high three-photon cross-section and TiO(2) nanoparticles (250 nm diameter), optimized upconverted emission was obtained for particle densities of ~2 x 10(9)/cm3. A strong dependence on the nanoparticle concentration and the pumping area was verified. The presence of spikes with linewidths ~0.4 nm in the emitted spectrum is the signature of coherent emission from this three-photon pumped random laser.

Determination of multiphoton absorption of silk fibroin using the Z-scan technique

The multiphoton absorption of silk fibroin at 810 nm was determined by open-aperture Z-scan. Three-photon absorption was confirmed at this wavelength and the three-photon cross section of silk fibroin was measured. Silk fibroin of varying molecular weight was tested and the cross section was found to increase exponentially with increasing molecular weight. The confirmation of a relatively large three-photon absorption cross section in silk will help lay the groundwork for future investigation of direct laser writing of three-dimensional structures within a silk matrix.

High-resolution three-photon biomedical imaging using doped ZnS nanocrystals

Three-photon excitation is a process that occurs when three photons are simultaneously absorbed within a luminophore for photo-excitation through virtual states. Although the imaging application of this process was proposed decades ago, three-photon biomedical imaging has not been realized yet owing to its intrinsic low quantum efficiency. We herein report on high-resolution in vitro and in vivo imaging by combining three-photon excitation of ZnS nanocrystals and visible emission from Mn(2+) dopants. The large three-photon cross-section of the nanocrystals enabled targeted cellular imaging under high spatial resolution, approaching the theoretical limit of three-photon excitation. Owing to the enhanced Stokes shift achieved through nanocrystal doping, the three-photon process was successfully applied to high-resolution in vivo tumour-targeted imaging. Furthermore, the biocompatibility of ZnS nanocrystals offers great potential for clinical applications of three-photon imaging.

Synthesis, tunable two and three-photon absorption properties of triazine derivatives by branches

Three novel triazine derivatives, (E)-4-(2-(4,6-dimethyl-1,3,5-triazin-2- yl)vinyl)- N,N-di-p-tolylaniline (a), 4,4′–((1E,1′E)-(6-methyl-1,3,5-triazine-2,4-diyl) bis(ethene-2,1-diyl))bis(N,N-di-p-tolylaniline) (b), and 4,4′,4′′–((1E,1′E,1′′E)-(1,3,5- triazine-2,4,6-triyl)tris(ethene-2,1-diyl))tris(N,N-di-p-tolylaniline) (c), were designed and synthesized. Their photophysical and photochemical properties were investigated systematically including single-photon absorption, nonlinear optical absorption (NOA) and up-converted fluorescence. Interestingly, the compound a with single branch showed pure three-photon absorption phenomenon, while the corresponding b and c indicated two-photon induced excited-state absorption properties, showing strong structure-dependence relationship. The results offer a method to design and synthesize organic molecules for multiphoton materials. It was noted that the three-photon cross-section value (δ3) of a was up to 1.35 × 10−76 cm6 s2. Correspondingly, the two-photon (δ2) and excited-state cross-section (δe) values of b and c also were obtained, and value of them were 485 GM and 1.03 × 10−17 cm2 for b, and 1100 GM and 1.27 × 10−18 cm2 for c, respectively.

Observation of tunable two-photon induced excited-state and three-photon absorption phenomena by structure in oligomerfluorene derivatives

The nonlinear optical properties, including two-, three-photon and excited-state absorption phenomena, were observed in three oligomerfluorene derivatives (abbreviated as OF3, OF5 and OF7) by femtosecond (450 fs) laser pulses. Their two-, three-photon and, excited-state absorption properties were studied by open Z-scan and pump-probe measurements. Interestingly, when the numbers of fluorene units increased from 3 to 5, and to 7, the corresponding absorption phenomena changed from three-photon to two-photon induced excited-state phenomena, showed strong structure dependence in these derivatives. The results offer a method to design and synthesize organic molecules for multiphoton materials. It was noted that the three-photon cross-section value (δ 3) of OF3 was up to 1.36×10−76 cm6 s2. Correspondingly, the two-photon (δ 2) and excited-state cross-section (δ e ) values of OF5 and OF7 also were obtained, and they were 1230 GM and 0.91×10−18 cm2 for OF5, and 1780 GM and 1.18×10−18 cm2 for OF7, respectively.

Multiphoton-Excited Luminescent Lanthanide Bioprobes: Two- and Three-Photon Cross Sections of Dipicolinate Derivatives and Binuclear Helicates

Multiphoton excited luminescent properties of water-soluble Eu(III) and Tb(III) complexes with derivatives of dipicolinic acid functionalized with a polyoxyethylene pendant arm and terminal groups, [Eu(L(OMe))(3)](3-), [Eu(L(NH2))(3)](3-), and [Tb(L(OH))(3)](3-), as well as of binuclear helicates with overall composition [Ln(2)(L(CX))(3)] (X = 2, 5) are investigated. Characteristic emission from the (5)D(0) and (5)D(4) excited levels of Eu(III) and Tb(III), respectively, upon approximately 800 nm excitation results from three-photon absorption (3PA) for [Eu(L(OMe))(3)](3-), [Eu(L(NH2))(3)](3-), [Tb(L(OH))(3)](3-), and [Ln(2)(L(C2))(3)], while luminescence from [Eu(2)(L(C5))(3)] is induced by two-photon absorption (2PA) owing to its 1PA spectrum extending further into the visible. The 3PA cross sections have been determined and are the first ones reported for lanthanide complexes: (i) those of Eu(III) and Tb(III) bimetallic helicates [Ln(2)(L(C2))(3)] are 20 times larger compared to the corresponding values for tris(dipicolinates); (ii) derivatization of dipicolinic acid for Tb(III) complexes has almost no influence on the 3PA cross section; however, for Eu(III) complexes a approximately 2 times decrease is observed. The feasibility of [Eu(2)(L(C5))(3)] as multiphoton luminescence bioprobe is demonstrated by two-photon scanning microscopy imaging experiments on HeLa cells incubated with this bimetallic helicate.

Upconversion luminescence and optical power limiting effect based on two- and three-photon absorption processes of ZnO crystal

Near-infrared to UV and visible upconversion luminescence was observed in single-crystalline ZnO under an 800 nm infrared femtosecond laser irradiation. The optical properties of the crystal reveal that the UV and VIS emission band are due to the exciton transition ( D 0 X) bound to neutral donors and the deep luminescent centers in ZnO, respectively. The relationship between the upconversion luminescence intensity and the pump power of the femtosecond laser reveals that the UV emission belongs to three-photon sequential band-to-band excitation and the VIS emission belongs to two-photon simultaneous defect-absorption induced luminescence. A saturation phenomenon and polarization-dependent effect are also observed in the upconversion process of ZnO. A very good optical power limiting performance at 800 nm has been demonstrated. The two- and three-photon absorption coefficients of ZnO crystal were measured to be 0.2018 cm GW −1 and 7.102 × 10 −3 cm 3 GW −2, respectively. The two- and three-photon cross sections were calculated to be 1.189 × 10 −51 cm 4 s and 1.040 × 10 −80 cm 6 s 2, respectively.

Quantum Chemical Studies of Three-Photon Absorption of Some Stilbenoid Chromophores

Three-photon absorption of a series of donor-acceptor trans-stilbene derivatives is studied by means of density functional theory applied to the third-order response function and its residues. The results obtained by using different functionals are compared with experimental data for similar systems obtained from the literature. With a Coulomb attenuated, asymptotically corrected functional, the excitation energy to the first resonance state is much improved. Comparison with experiment indicates that this is the case for the three-photon cross section as well. In particular, the overestimation of the cross sections and underestimation of excitation energies offered by the density functional theory using common density functionals is corrected for. It is argued that a reliable theory for three-photon absorption in charge transfer and other chromophore systems thereby has been obtained. Further elaboration of the theory and its experimental comparison call for explicit inclusion of solvent polarization and pulse propagation effects.

Few-states models for three-photon absorption.

Few-states models are derived for the calculation of three-photon absorption matrix elements. Together with earlier derived few-states models for two-photon absorption, the models are evaluated against results from response theory calculations that provide the full sum-over-states values. It is demonstrated that not even for systems with charge-transfer character, where few-states models for two-photon absorption are in excellent agreement with response theory, do the models provide a quantitatively correct description for three-photon absorption. The convergence behavior, merits, and shortcomings of the models are elucidated in some detail. The role of various characteristics of the electronic structure, such as symmetry, charge transfer, and conjugation--important for the formation of a large three-photon cross section--is analyzed. As for two-photon absorption cross sections, it is essential to consider generalized few-states models also for three-photon absorption, that is, to account for dipolar directions and laser beam polarization. Despite their poor quantitative performance, it is argued that few-states models at times can be useful for interpretation purposes when applied to three-photon absorption.

Three-photon induced fluorescence of the calcium probe Indo-1

We report the calcium-dependent emission spectral properties of the calcium probe Indo-1 for three-photon excitation. We found that Indo-1 could be readily excited with the femtosecond pulses from a mode-locked Ti:sapphire laser at 885 nm. This wavelength is too long for two-photon excitation, which is expected to occur for wavelengths no longer than twice the longest single-photon absorption wavelength of 400 nm. For excitation at 885 nm the emission intensity was found to depend on the cube of the laser power, as expected for simultaneous interaction with three photons. At wavelengths below 840 nm the emission intensity depends on the square of the laser power, indicating two-photon excitation at shorter wavelengths. The intensity decays of Indo-1 were found to be dependent on Ca2+ and essentially identical for one- and three-photon excitation. The emission anisotropy of Indo-1 was found to be considerably higher for three-photon excitation than for one-photon excitation, consistent with cos6 theta photoselection, as compared with cos2 theta photoselection for one-photon excitation. The high values of the anisotropy are in agreement with those expected for a three-photon process. Calcium-dependent emission spectra were observed for Indo-1 with three-photon excitation, demonstrating that three-photon excitation of Indo-1 can be used for calcium imaging by emission intensity ratio measurements. The calcium-dependent emission spectra indicate a higher three-photon cross-section for the calcium-free form of Indo-1 than for the calcium-bound form. The possible advantages of three-photon excitation include the availability of the appropriate wavelengths with solid-state lasers, enhanced spatial resolution due to a reduced size of the excited volume, absence of light quenching, and possibly high selectivity of the three-photon excitation process.

Two- and three-proton pumped exciton-induced chemistry in liquid Kr

Multi-proton pumped, exciton mediated charge transfer reactions in N 2O and F 2 doped liquid K are reported. Irradiation of F 2/Kr solutions with ≈ 300 fs pulses at 320 nm leads to three-proton induced emission from Kr 2(F(4 2Γ). Based on transmission measurements, a three-photon cross section of 2×10 −81(±1) cm 6 s 2 is extracted, and attributed to access of Kr( n=2, j= 3 2 ) exciton. Irradiation of N 2O/Kr solutions, at 320 and 225 nm leads respectively to three-proton induced and two-photon induced emission from KrO(2 1Σ). Cross calibration of these signals, and using known two-photon cross sections for reaching Kr excitons, yields a three-photon cross section of 8×10 −81 cm 6 s 2.

Green's function for delta -function potentials with a hard core: Application to multiphoton photodetachment of negative halogen ions.

We develop a simple Green's function for \ensuremath{\delta}-function potentials with a hard core, and use it to calculate polarizabilities of negative halogen ions and multiphoton-detachment cross sections for these ions. The predictions indicate an influence of a resonance for two- and three-photon cross sections, and yield approximately universal relative amplitudes as functions of a scaled electron energy.

The three-photon spectrum of the 1B2u←1A1g transition in benzene: Analysis of vibronic and rotational structure

A vibrational and rotational analysis of the three-photon fluorescence excitation spectrum of the 1B2u←1A1g transition in gas-phase benzene is presented. The group theoretically allowed origin and any associated vibrational structure are absent. In addition, there is no evidence for any rotational structure based on a rank-three transition tensor. Coherent loss mechanisms are carefully considered and then rejected as possible interferences in the three-photon fluorescence spectrum. Polarization measurements and observed vibronic structure indicate a dominant rank one (vibronic) contribution to the three-photon cross section. The lack of three-photon allowed structure in this 1B2u←1A1g transition of benzene is consistent with the pseudoparity selection rules of alternant hydrocarbon theory, yet such strict adherence to them would seem surprising. The appearance of the e2g mode ν8 in the three-photon spectrum marks the first experimental determination of its frequency in the 1B2u state.