Two-photon Absorption Transition Research Articles

Studying the first order hyperpolarizability spectra in chalcone-based derivatives and the relation with one- and two-photon absorption transitions.

The first-order molecular hyperpolarizability (β) dispersion was measured in seven chalcone-based molecules utilizing the tunable femtosecond hyper-Rayleigh scattering (tHRS) technique. Additionally, a theoretical model based on photophysical parameters was employed to better understand β dispersion. Due to the distinct substitution patterns of the aryl/heteroaryl rings within the chalcone structure, varying profiles of one- and two-photon absorption spectra and β dispersion were observed. The applied model highlighted two important factors contributing to achieving high β values: (i) the presence of red-shifted one-photon and two-photon absorption bands; and (ii) the number of discernible absorption bands. To contextualize these results with other molecular structures, we employed the HRS figure of merit (FOM). Remarkably, it was revealed that chemically engineered small chalcone molecules exhibit a FOM comparable to larger quadrupolar and octupolar ones. This underscores the significance of tHRS scattering measurements and their correlation with absorptive parameters in the design and characterization of nonlinear optical materials.

Theoretical and experimental study of the 6S-8S two-photon absorption cross-section in cesium atoms.

The probability of a two-photon absorption (TPA) process is quantified by means of the TPA cross-section. In this work the TPA cross-section for the 6S1/2 → 8S1/2 transition in cesium (Cs) atoms is obtained from a theoretical and experimental approach. It is calculated using second order perturbation theory including hyperfine structure and Doppler broadening for a thermal atomic vapor. The theoretical values for the TPA cross-sections of the two allowed hyperfine transitions are σ~3,3=3.10×10-24 cm4/W and σ~4,4=3.65×10-24 cm4/W. An experiment is set up to measure these cross-sections based on the quadratic dependence between the TPA transition rate and the intensity of the laser light. Values of σ~3,3=(3.6±1.1)×10-24 cm4/W and σ~4,4=(4.6±1.1)×10-24 cm4/W are obtained from the measurements. The results show an agreement between theory and experiment. To the best of our knowledge, this is the first time that these cross-sections are reported.

Tunable Non-Kasha Behaviors and Excited-State Dynamics of Quadrupolar Squaraine Aggregates.

Versatile coupling theories have been developed for rationalizing unusual aggregation phenomena of multipolar chromophores. Here, diverse excitonic couplings of a quadrupolar squaraine dye protonated by trifluoroacetic acid could be achieved and tuned unprecedentedly in different solvation media. Subtle changes of the solvent and ion pair influenced the aggregation of the donor-acceptor-donor (D-A-D)-type SQC6 and led to significant variations in optical properties. In contrast to conventional H/J aggregates, strong spectroscopic evidence of nonfluorescent and red-shifted hJ aggregation was obtained. Assumptions of the excitonic interplay with variable strength stabilized by the synergic contributions of π-π stacking and electronic interaction were addressed. Comparative excited-state dynamics in the aggregates clarified the distinctive excitonic coupling of adjacent quadrupolar molecules and the nature of the excited state beyond the dimers. Meanwhile, dominant two-photon absorption transitions could be elucidated by a resonance-enhanced mechanism. The present unusual molecular interplay provides a strategy to fine tune the optical properties of multipolar aggregates.

Photoinduced Charge Transfer in Push/Pull Systems of Two-Photon Absorption.

A series of stilbene derivatives have been constructed by modifying the stilbene systems with different H, CN, NH2, NMe2, and NO2 groups. In a vacuum, it was found that a redshift in the ultraviolet–visible spectrum occurred because of the enhancement of the donor/acceptor capabilities of this group, with the order of redshift being NO2 > NMe2 > CN > NH2 > H. For stilbene molecular systems, the peak of two-photon absorption (TPA) observed in the simulated spectra should be attributed to two transitions that are contributed by two excited states with similar energy. In the case of derivatives, such a transition is separated by energy, and two TPA peaks can be clearly observed (derivatives containing NO2 and NMe2 groups have two TPA peaks), where the magnitude of the separation is directly related to the intensity of the peripheral group. In addition, the S1 state is the intermediate state in the TPA transitions to both of the final excited states.

Photoinduced Charge Transfer in Donor-Bridge-Acceptor in One- and Two-photon Absorption: Sequential and Superexchange Mechanisms

In this work, the one- (OPA) and two-photon absorption (TPA) and transition characteristics of the porphyrin and fullerene donor–acceptor systems linked by thiophene oligomers are investigated theoretically. In the study of the transition characteristics of OPA and TPA, a combination of 2D and 3D visualization methods is used. During the OPA and TPA transitions of this D–A system, there is both superexchange charge transfer without thiophene oligomers and sequential charge transfer through thiophene oligomers. On this basis, there exist also charge recombination TPA excitations of the previous two kinds of charge transfer into an intrinsic process. The degree of polymerization of the thiophene oligomer significantly affects the efficiency of superexchange charge transfer and participates in excitation in units of quarter-thiophene. Finally, a method to enhance the charge transfer efficiency during TPA excitation is proposed, which is local excitation enhanced charge transfer excitation.

Assessment of Functionals for TDDFT Calculations of One- and Two-Photon Absorption Properties of Neutral and Anionic Fluorescent Proteins Chromophores

Performance of DFT functionals with different percentages of exact Hartree-Fock exchange energy (EX) is assessed for recovery of the CC2 reference one- (OPA) and two-photon absorption (TPA) spectra of fluorescent proteins chromophores in vacuo. The investigated DFT functionals, together with their EX contributions are BLYP (0%), B3LYP (20%), B1LYP (25%), BHandHLYP (50%), and CAM-B3LYP (19% at short range and 65% at long range). Our test set consists of anionic and neutral chromophores as naturally occurring in the fluorescent proteins. For the first time, we compare TDDFT and CC2 methods for higher excited states than the S1 state, exhibiting relatively large TPA intensity. Our TDDFT results for neutral chromophores reveal an increase in excitation energies as well as TPA and OPA intensities errors, compared to CC2-derived results, as the DFT functional contains less exact exchange. The long-range-corrected CAM-B3LYP functional performs the best, closely followed by BHandHLYP, while BLYP usually significantly underestimates all investigated spectral properties, hence being the worst in reproducing the reference CC2 results. The hybrid B3LYP and B1LYP functionals can be roughly placed in between. We propose that TDDFT may underestimate the TPA intensities for neutral chromophores of fluorescent proteins due to underestimated oscillator strengths between some excited states. In the case of anionic chromophores, we find that B3LYP and B1LYP functionals overcome others in terms of reproducing CC2 excitation energies. On the other hand, however, TPA intensity is usually significantly underestimated, and in this respect, CAM-B3LYP functional seems to be again superior. In contrast to the case of neutral chromophores, it seems that a large magnitude of excited-state dipole moments or changes in dipole moments upon excitation may be the driving force behind high TPA transition moments.

Evidence of Band-Edge Hole Levels Inversion in Spherical CuInS2 Quantum Dots.

CuInS2 (CIS) quantum dots (QDs) have emerged as one of the most promising candidates for application in a number of new technologies, mostly due to their heavy-metal-free composition and their unique optical properties. Among those, the large Stokes shift and the long-lived excited state are the most striking ones. Although these properties are important, the physical mechanism that originates them is still under debate. Here, we use two-photon absorption spectroscopy and ultrafast dynamics studies to investigate the physical origin of those phenomena. From the two-photon absorption spectroscopy, we observe yet another unique property of CIS QDs, a two-photon absorption transition below the one-photon absorption band edge, which has never been observed before for any other semiconductor nanostructure. This originates from the inversion of the 1S and 1P hole level order at the top of the valence band and results in a blue-shift of the experimentally measured one photon absorption edge by nearly 100 to 200 meV. However, this shift is not large enough to account for the Stokes shift observed, 200-500 meV. Consequently, despite the existence of the below band gap optical transition, photoluminescence in CIS QDs must originate from trap sites. These conclusions are reinforced by the multiexciton dynamics studies. From those, we demonstrate that biexciton Auger recombination behaves similarly to negative trion dynamics on these nanomaterials, which suggests that the trap state is an electron donating site.

Encryption of nonlinear optical signals in ZnO:Al thin films by ultrashort laser pulses

Described herein is the effect of optical annealing on the third-order non-linear optical properties exhibited by nanostructured Al-doped ZnO thin films. The samples were synthetized by an ultrasonic spray pyrolysis method. The optical annealing process was carried out by laser pulses at 532, 835 and 1064 nm wavelengths with, ps, fs and ps pulse duration, respectively. The optical non-linearity of the films was measured by the z-scan method with three different irradiations of excitation: 100 fs at 835 nm, 120 ps at 532 nm, and 150 ps at 1064 nm. The as-grown samples showed a saturable optical absorption that evolves into two-photon absorption transitions by a picosecond optical annealing phenomenon induced at 532 nm wavelength. Potential applications for developing optical encryption functions were considered.

Theoretical study of two-photon absorption properties of a series of platinum (II) acetylide complexes

Transition metal acetylide compounds have attracted enormous attention because of the extraordinary photophysical properties arising from the electronic interaction between the transition metal and the organic molecular fragment. In this study, the geometrical structure, electronic structure, one-photon absorption (OPA) and two-photon absorption (TPA) properties of a series of D–π′–A–π–[Pt]–π–A–π′–D type and A′–π′–A–π–[Pt]–π–A–π′–A′ type platinum(II) acetylides were studied theoretically by using density functional theory (DFT) and Zerner's intermediate neglect of differential overlap (ZINDO) methods for getting TPA materials possessing large TPA cross-section. Our analysis suggests that intramolecular charge transfer between center metal and π-conjugated organic fragment dominates in TPA transitions, in which metal center increases conjugation length in the direction of long ligand. This contribution provides detailed theoretical analysis of one- and two-photon absorption property of Platinum (II) acetylide compounds and an effective way for designing of platinum (II)/nickel (II) acetylide compounds possessing large TPA cross-section.

Dispersion dependence of two-photon absorption transition on frequency in Si PIN photodetector

The variation of two-photon absorption (TPA) coefficient \(\beta _{\mathrm{TPA}} (\omega )\) of Si excited at difference photon energy was investigated. The TPA coefficient was measured by using a picosecond pulsed laser with the wavelength could be tuned in a wide photon-energy range. An equivalent RC circuit model was adapted to derive the TPA coefficient \(\beta _{\mathrm{TPA}} (\omega )\). The results showed that \(\beta _{\mathrm{TPA}} (\omega )\) varied from \(4.2 \times 10^{-4}\) to \(1.17 \times 10^{-3 }\) cm/GW in the transparent wavelength region \(1.80<\lambda <1.36\,\upmu \)m of Si. The increasing tendency of \(\beta _{\mathrm{TPA}} (\omega )\) with the incident photon energy can be qualitatively interpreted as the photon energy increases from \(E_{\mathrm{ig}}/2\) to nearly \(E_{\mathrm{ig}}\), the electrons excited from the valance band find an increasing availability of conduction band states. Comparing with the high-energy side transitions, the TPA coefficient in low-energy side is about 10 times too small. This can be attributed that the TPA transition in low-energy side is the process of photon-assisted electron transitions from valence to conduction band occurring between different points in k-space, while is direct transition in high-energy side.

Two-Photon Circular–Linear Dichroism of Perylene in Solution: A Theoretical–Experimental Study

Herein, we report on the theoretical-experimental analysis of the two-photon absorption (TPA) and two-photon circular-linear dichroism (TPCLD) spectra of a highly conjugated, rigid, and centrosymmetric molecule in solution, that is, perylene/CH2Cl2. We show how a three-energy-level diagram, under the sum-over-essential states approach, assists in the determination of the magnitude of transition electric dipole moments and the angle between them for the main TPA transitions. We demonstrate the potential of TPCLD to reveal the symmetry of excited states and the angles between their transition electric dipole moments and that of the ground state. By means of TPCLD, we explain how the overwhelming contribution of certain TPA transitions can mask important spectral features in regions where the transition electric dipole moments are perpendicular. TPCLD is expected to enhance the understanding of the photophysical properties of materials that are not accessible using conventional linear and two-photon spectroscopy. TPA and TPCLD measurements were performed employing the open-aperture Z-scan technique using an amplified femtosecond system. Time-dependent density functional theory (TD-DFT) calculations were carried out using response theory at the B3LYP level with the aug-cc-pVDZ basis set. Solvent effects were included through the polarizable continuum model (PCM).

Solvent induced channel interference in the two-photon absorption process—a theoretical study with a generalized few-state-model in three dimensions

For the first time, we report the effect of interference between different optical channels on the two-photon absorption (TPA) process in three dimensions. We have employed response theory as well as a sum-over-states (SOS) approach involving few intermediate states to calculate the TPA parameters like transition probabilities (δ(TP)) and TPA tensor elements. In order to use the limited SOS approach, we have derived a new formula for a generalized few-state-model (GFSM) in three dimensions. Due to the presence of additional terms related to the angle between different transition moment vectors, the channel interference associated with the TPA process in 3D is significantly different and much more complicated than that in 1D and 2D cases. The entire study has been carried out on the two simplest Reichardt's dyes, namely 2- and 4-(pyridinium-1-yl)-phenolate (ortho- and para-betain) in gas phase, THF, CH(3)CN and water solvents. We have meticulously inspected the effect of the additional angle related terms on the overall TPA transition probabilities of the two 3D isomeric molecules studied and found that the interfering terms involved in the δ(TP) expression contribute both constructively and destructively as well to the overall δ(TP) value. Moreover, the interfering term has a more conspicuous role in determining the net δ(TP) associated with charge transfer transition in comparison to that of π-π* transition of the studied systems. Interestingly, our model calculations suggest that, for o- and p-betain, the quenching of destructive interference associated with a particular two-photon process can be done with high polarity solvents while the enhancement of constructive interference will be achieved in solvents having relatively small polarity. All the one- and two-photon parameters are evaluated using a range separated CAMB3LYP functional.

Theoretical study of one- and two-photon absorption spectra of azoaromatic compounds

In this study, the one- and two-photon absorption spectra of seven azoaromatic compounds (five pseudostilbenes-type and two aminoazobenzenes) were theoretically investigated using the density functional theory combined with the response functions formalism. The equilibrium molecular structure of each compound was obtained at three different levels of theory: Hartree-Fock, density functional theory (DFT), and Møller-Plesset 2. The effect of solvent on the equilibrium structure and the electronic transitions of the compounds were investigated using the polarizable continuum model. For the one-photon absorption, the allowed pi-->pi(*) transition energy showed to be dependent on the molecular structures and the effect of solvent, while the n-->pi(*) and pi-->pi(*)(n) transition energies exhibited only a slight dependence. An inversion between the bands corresponding to the pi-->pi(*) and n-->pi(*) states due to the effect of solvent was observed for the pseudostilbene-type compounds. To characterize the allowed two-photon absorption transitions for azoaromatic compounds, the response functions formalism combined with DFT using the hybrid B3LYP and PBE0 functionals and the long-range corrected CAM-B3LYP functional was employed. The theoretical results support the previous findings based on the three-state model. The model takes into account the ground and two electronic excited states and has already been used to describe and interpret the two-photon absorption spectrum of azoaromatic compounds. The highest energy two-photon allowed transition for the pseudostilbene-type compounds shows to be more effectively affected (approximately 20%) by the torsion of the molecular structure than the lowest allowed transition (approximately 10%). In order to elucidate the effect of the solvent on the two-photon absorption spectra, the lowest allowed two-photon transition (dipolar transition) for each compound was analyzed using a two-state approximation and the polarizable continuum model. The results obtained reveal that the effect of solvent increases drastically the two-photon cross-section of the dipolar transition of the pseudostilbene-type compounds. In general, the features of both one- and two-photon absorption spectra of the azoaromatic compounds are well reproduced by the theoretical calculations.

Electronic and Vibronic Contributions to Two‐Photon Absorption in Donor–Acceptor–Donor Squaraine Chromophores

Many squaraines have been observed to exhibit two-photon absorption at transition energies close to those of the lowest energy one-photon electronic transitions. Here, the electronic and vibronic contributions to these low-energy two-photon absorptions are elucidated by performing correlated quantum-chemical calculations on model chromophores that differ in their terminal donor groups (diarylaminothienyl, indolenylidenemethyl, dimethylaminopolyenyl, or 4-(dimethylamino)phenylpolyenyl). For squaraines with diarylaminothienyl and dimethylaminopolyenyl donors and for the longer examples of 4-(dimethylamino)phenylpolyenyl donors, the calculated energies of the lowest two-photon active states approach those of the lowest energy one-photon active (1B(u)) states. This is consistent with the existence of purely electronic channels for low-energy two-photon absorption (TPA) in these types of chromophores. On the other hand, for all squaraines containing indolinylidenemethyl donors, the calculations indicate that there are no low-lying electronic states of appropriate symmetry for TPA. Actually, we find that the lowest energy TPA transitions can be explained through coupling of the one-photon absorption (OPA) active 1B(u) state with b(u) vibrational modes. Through implementation of Herzberg-Teller theory, we are able to identify the vibrational modes responsible for the low-energy TPA peak and to reproduce, at least qualitatively, the experimental TPA spectra of several squaraines of this type.

Coherent control and dark pulses in second harmonic generation

We present the results of our study of the second harmonic generation (SHG) in a nonlinear crystal using phase modulated femtosecond laser pulses. We show experimentally that the SHG process is an analogue of two photon absorption (TPA), yet it provides a better way to study coherent control because it enables one easier control of some important parameters. We demonstrate that for a thick nonlinear crystal pure phase manipulation can result in nontrivial pulses maximizing the second harmonic conversion efficiency and in dark pulses which are not converted at all. With a π step phase modulation applied to the pulse we have measured conversion efficiency for a set of crystals with different thicknesses to explore the effect of a finite spectral width of the TPA transition.

Calculation of single-beam two-photon absorption transition rate of rare-earth ions using effective operator and diagrammatic representation

Effective operators needed in single-beam two-photon transition calculations have been represented with modified Goldstone diagrams similar to the type suggested by Duan et al. [C.-K. Duan, G. Ruan, M.F. Reid, J. Chem. Phys. 121 (2004) 5071]. The rules to evaluate these diagrams are different from those for effective Hamiltonian and one-photon transition operators. It is verified that the perturbation terms considered contain only connected diagrams and the evaluation rules are simplified and given explicitly.

Degenerate two-photon-absorption spectral studies of highly two-photon active organic chromophores.

Degenerate two-photon absorption (TPA) spectral properties of five AFX chromophore solutions have been studied using a single and spectrally dispersed sub-picosecond white-light continuum beam. In a specially designed optical configuration, optical pathways inside the sample solution for different spectral components of the focused continuum beam were spatially separated from each other. Thus, the nondegenerate TPA processes coming from different spectral components can be eliminated, and the direct nonlinear absorption spectrum attributed to degenerate TPA processes can be readily obtained. Using this new technique, the complete TPA spectra for these five highly two-photon-active compounds (AF-380, AF-350, AF-295, AF-270, and AF-50) were obtained in the spectral range from 600 to 950 nm on an absolute scale of TPA cross section. The relationship between the molecular structures and their TPA spectral behaviors are discussed. In general the measured TPA spectra are not identical with the linear absorption spectra on the scale of absorbed photon(s) energy. Moreover, for some sample (such as AF-380), the TPA spectrum is totally different from the linear spectrum, which implies the difference of molecular transition pathways and selection rules for one- and two-photon excitation processes. At high excitation intensity levels (>or=15 GW/cm(2)), the saturation behavior of TPA transition can be observed obviously in AF-350 and AF-380 solutions that exhibit much higher nonlinear absorptivity than the other chromophores investigated.

Two-photon absorption properties of symmetric substituted diacetylene: drastic enhancement of the cross section near the one-photon absorption peak

Two-photon absorption (TPA) spectra are presented for newly synthesized bis(pyridylstyryl)-substituted diacetylene and related methyl triflate derivatives. The TPA cross section of a derivative (MPPBT) was found to increase drastically with decreasing the incident wavelength below 650 nm and to reach (2.42±0.46)×10 −47 cm 4 s molecule −1 photon −1 at 571 nm, in addition to the weaker, lowest energy TPA peak centered at 764 nm. A four-state model was needed to account for the observed spectral shape, suggesting that the drastic enhancement is due to one-photon resonance enhancement not only of the lowest energy TPA transition but also of a higher energy two-photon transition.

INVESTIGATION OF NEAR TWO-PHOTON RESONANCE OPTICAL NONLINEARITIES IN Ni(Ac)2[N-(8-QUINOLYL) PYRIDINE-2-CARBOXAMIDE] · 4H2O BY THE Z-SCAN TECHNIQUE

We describe a modified Z-scan technique for the case when nonlinear refraction is accompanied by nonlinear absorption to separately evaluate the nonlinear refraction and the nonlinear absorption by performing straightforward measurements with the aperture removed. We divide the closed aperture (S &lt; 1) normalized Z-scan by a scan with an open aperture (S = 1). With nanosecond scale at a 532 nm wavelength, we first measured the nonlinear optical absorption and refraction coefficients of a solution of Ni(Ac)2[N-(8-quinolyl) pyridine-2-carboxamide] · 4H2O by using the modified Z-scan technique. The nonlinear absorption originates from the near resonant two-photon absorption while the mechanism of the nonlinear refraction is the near resonant two-photon absorption transition enhancement. The linear increasing dependences of the optical nonlinearities on the incident irradiance arise from the population redistribution due to the near resonant two-photon absorption.

Investigation of optical nonlinearities in Pd(po) 2 by Z-scan technique

With nanosecond scale at a 532 nm wavelength, we firstly measured the nonlinear optical absorption and refraction coefficients of Pd(po)2 complex by using Z-scan technique, here Hpo=1-hydioxy-2-pyridone. We describe an empirical expression for the case when nonlinear refraction is accompanied by nonlinear absorption to separately evaluate the nonlinear refraction and the nonlinear absorption by performing straightforward measurements with the aperture removed. The nonlinear optical response of Pd(po)2 was determined by the linear decreasing irradiance-dependence. The nonlinear absorption originates from the near resonant two-photon absorption while the mechanism of the nonlinear refraction is the near resonant two-photon absorption transition enhancement. The linear increasing dependences of the optical nonlinearities on the incident irradiance arise from the population redistribution due to the near resonant two-photon absorption.