Two-photon Absorption Probability Research Articles

Manipulating Two-Photon Absorption of Molecules through Efficient Optimization of Entangled Light.

We report how the unique temporal and spectral features of pulsed entangled photons from a parametric downconversion source can be utilized for manipulating electronic excitations through the optimization of their spectral phase. A new comprehensive optimization protocol based on Bayesian optimization has been developed in this work to selectively excite electronic states accessible by two-photon absorption. Using our optimization method, the entangled two-photon absorption probability for a thiophene dendrimer can be enhanced by up to a factor of 20, while classical light turns out to be nonoptimizable. Moreover, the optimization involving photon entanglement enables selective excitation that would not be possible otherwise. In addition to optimization, we have explored entangled two-photon absorption in the small entanglement time limit showing that entangled light can excite molecular electronic states that are vanishingly small for classical light. We demonstrate these opportunities with an application to a thiophene dendrimer.

Entangled two-photon absorption spectroscopy with varying pump wavelengths

In entangled two-photon absorption (eTPA) spectroscopy, information about the energy-level structure of an arbitrary sample is retrieved by Fourier transforming sets of measured two-photon absorption probabilities of entangled photon pairs where the degree of entanglement and the delay time between the photons are varied. This works well for simple systems but quickly becomes rather difficult when many intermediate states are involved. We propose and discuss an extension of eTPA spectroscopy that solves this problem by means of repeated measurements at different pump wavelengths, thus reducing the experimental complexity of eTPA spectroscopy by removing the need to control the correlations of the entangled photons. Specifically, we demonstrate that our extension works well for a variety of realistic experimental setups.

Enhanced two-photon absorption of frequency-entangled N00N states in type-I SPDC

We study the two-photon absorption properties of frequency-entangled N00N states produced in a Hong-Ou-Mandel interferometer using type-I degenerate photon pairs, generated via spontaneous parametric down-conversion. By comparing our results with N00N states with no frequency entanglement, we demonstrate enhanced two-photon absorption due to frequency entanglement. We also derive an analytic expression for the enhancement factor which is found to be greater than one for all finite values of the ratio of the bandwidth of the pump to the bandwidth of the detected photons. We have also found suppression and enhancement in the two-photon absorption probabilities for specific time delays applied to the N00N states.

Synthesis and Photoswitching Properties of Bioinspired Dissymmetric γ-Pyrone, an Analogue of Cyclocurcumin.

Cyclocurcumin (CC), a turmeric curcuminoid with potential therapeutic properties, is also a natural photoswitch that may undergo E/Z photoisomerization under UV light. To be further exploited in relevant biological applications, photoactivation under near-infrared (NIR) irradiation is required. Such requirement can be met through opportune chemical modifications, by favoring two-photon absorption (TPA) probability. Herein, a general and efficient synthesis of a biomimetic 2,6-disubstituted-γ-pyrone analogue of CC is described, motivated by the fact that molecular modeling previews an order of magnitude increase of its NIR TPA compared to CC. Three retrosynthetic pathways have been identified (i) via an aryl-oxazole intermediate or via aryl-diynone through (ii) a bottom-up or (iii) a top-down approach. While avoiding the passage through unstable synthons or low-yield intermediate reactions, only the latest approach could conveniently afford the 2,6-disubstituted-γ-pyrone analogue of CC, in ten steps and with an overall yield of 18%. The photophysical properties of our biomimetic analogue have also been characterized showing an improved photoisomerization yield over the parent natural compound. The potentially improved nonlinear optical properties, as well as enhanced stability, may be correlated to the enforcement of the planarity of the pyrone moiety leading to a quadrupolar D-π-A-π-D system.

A Theoretical Study of One- and Two-Photon Activity of D-Luciferin

In the present work, we have theoretically studied the one and two-photon absorption (OPA and TPA) probabilities of the native D-luciferin molecule and attempted to find the origin of its larger TPA cross-sections in polar solvents than in non-polar ones. The calculations using state-of-the-art linear and quadratic response theory in the framework of time-dependent density functional theory using hybrid B3LYP functional and cc-pVDZ basis set suggests that two-photon transition probability of this molecule increases with increasing solvent polarity. In order to explicate our present findings, we employed the generalized few-state-model and inspected the role of different optical channels related to the TPA process. We have found that the two-photon transition probability is always guided by a destructive interference term, the magnitude of which decreases with increasing solvent polarity. Furthermore, we have evaluated OPA parameters of D-luciferin and noticed that the the excitation energy is in very good agreement with the available experimental results.

Relation between Nonlinear Optical Properties of Push-Pull Molecules and Metric of Charge Transfer Excitations.

We establish the relationships between the metric of charge transfer excitation (Δr) for the bright ππ* state and the two-photon absorption probability as well as the first hyperpolarizability for two families of push-pull π-conjugated systems. As previously demonstrated by Guido et al. (J. Chem. Theory Comput. 2013, 9, 3118-3126), Δr is a measure for the average hole-electron distance upon excitation and can be used to discriminate between short- and long-range electronic excitations. We indicate two new benefits from using this metric for the analyses of nonlinear optical properties of push-pull systems. First, the two-photon absorption probability and the first hyperpolarizability are found to be interrelated through Δr; if β ∼ (Δr)(k), then roughly, δ(TPA) ∼ (Δr)(k+1). Second, a simple power relation between Δr and the molecular hyperpolarizabilities of push-pull systems offers the possibility of estimating properties for longer molecular chains without performing calculations of high-order response functions explicitly. We further demonstrate how to link the hyperpolarizabilities with the chain length of the push-pull π-conjugated systems through the metric of charge transfer.

Entanglement-enhanced two-photon absorption in spectral phase-modulated type-I parametric down-conversion

We demonstrate control of the two-photon absorption probability for a simple three-level atom using type-I nondegenerate down-converted photons that have been phase-modulated using a spectral phase filter of variable modulation frequency and modulation depth. We find enhancement of two-photon absorption for entangled photons, as compared with that for unentangled photons. We also find that, for certain pairs of modulation frequency and depth values, we can either further enhance or suppress the absorption process relative to that for zero phase modulation.

Polarised two-photon excitation of quantum well excitons for manipulation of optically pumped terahertz lasers

Optical pumping of excited exciton states in a semiconductor quantum well embedded in a microcavity is a tool for realisation of ultra-compact terahertz (THz) lasers based on stimulated optical transition between excited (2p) and ground (1s) exciton state. We show that the probability of two-photon absorption by a 2p-exciton is strongly dependent on the polarisation of both pumping photons. Five-fold variation of the threshold power for terahertz lasing by switching from circular to co-linear pumping is predicted. We identify photon polarisation configurations for achieving maximum THz photon generation quantum efficiency.

Polarization selection rules in exciton-based terahertz lasers

Optical pumping of excited exciton states in semiconductor quantum wells is a tool for the realization of ultracompact terahertz (THz) lasers based on stimulated optical transition between excited ($2p$) and ground ($1s$) exciton states. We show that the probability of two-photon absorption by a $2p$ exciton is strongly dependent on the polarization of both photons. Variation of the threshold power for THz lasing by a factor of 5 is predicted by switching from linear to circular pumping. We calculate the polarization dependence of the THz emission and identify photon polarization configurations for achieving maximum THz photon generation quantum efficiency.

Polarization Control of Optically Pumped Terahertz Lasers

ABSTRACTTwo-photon pumping of excited exciton states in semiconductor quantum wells is a tool for realization of ultra-compact terahertz (THz) lasers based on stimulated optical transition between excited 2p and ground 1s exciton state. We show that the probability of two-photon absorption by a 2p-exciton is strongly dependent on the polarization of both photons. Variation of the threshold power for THz lasing by a factor of 5 is predicted by switching from linear to circular pumping. We calculate the polarization dependence of the THz emission and identify photon polarization configurations for achieving maximum THz photon generation quantum efficiency.

Coherent control of two-photon absorption of Pr3+ ion by shaped ultrashort laser pulses

Enhancing the photoluminescence and depressing the background emission are important problems in rare earth ion-doped materials. In this letter, the two-photon absorption (TPA) probability in a Pr3+ ion system is enhanced by a factor of 12.3 by a π-phase step scanning of ultrashort laser pulses. This level is significantly higher than that achieved by a transform-limit pulse. However, the laser intensity of shaped pulse is reduced to 37% of the initial transform-limited pulse. In this method, the TPA probability can also be reduced to 58%. Furthermore, the effect of the shift of the intermediate energy level and the bandwidth of final states on TPA probability is discussed.

Two-electron dynamics in nonlinear double excitation of helium by intense ultrashort extreme-ultraviolet pulses

We present a theoretical study for multiphoton double excitation of He atoms exposed to an intense ultrashort extreme-ultraviolet (EUV) pulse, where the photon energy coincides with the transition energy from the ground state to a Rydberg state, by solving the time-dependent Schr\odinger equation in the hyperspherical coordinates. Photoelectron spectra under the conditions comparable with a recent experiment [Hishikawa et al., Phys. Rev. Lett. 107, 243003 (2011)] are calculated and analyzed. We identify the mechanism of the enhanced three-photon absorption probability which is more than one order of magnitude larger than that for the two-photon process in accordance with the experiment. The enhancement is attributed to a propensity rule for double excitation in a two-step mechanism, in which a one-photon absorption by one electron to a Rydberg state is followed by a two-photon absorption by the other electron to an excited orbital, while the first electron remains at nearly the same principle quantum number. Based on the time-dependent perturbation theory, the three-photon absorption probability exhibits peculiar cubic dependence on the pulse duration due to the propensity rule, in contrast to the linear dependence of the two-photon absorption probability. Thus a crossover between the two- and three-photon absorption probabilities takes place for sufficiently intense and long pulses. We also study the time evolution of a doubly excited two-electron wave packet created by an intense ultrashort EUV pulse efficiently using the same enhancement scheme, opening up the possibility of visualizing the correlated motion of two electrons in the time domain.

The features of nonlinear absorption of two-photon excited excitons in CdSe/ZnS quantum dots

The nonlinear absorption features have been discovered in the case of two-photon resonant excitation of excitons in colloidal CdSe/ZnS quantum dots by powerful picosecond laser pulses. Two utilized methods — measurement of the traces of luminescence (the dependence of luminescence intensity upon distance) and nonlinear transmission measurement — have allowed us to determine the coefficients of two-photon absorption and to reveal the deviation from two-photon absorption and from the dependence of two-photon excited photoluminescence intensity upon distance at high excitation. The decreasing of two-photon absorption at high excitation was explained by accompanying processes of state-filling and Stark shift of exciton transition. The extinction of luminescence at high excitation was attributed to dominating nonradiative Auger recombination and to state-filling and Stark shift of exciton transition provoking the decreasing of two-photon absorption probability.

Nonlinear spectrum effect on the coherent control of molecular systems

This work demonstrates that the detuning of the fs-laser spectrum from the two-photon absorption band of organic materials can be used to reach further control of the two-photon absorption by pulse spectral phase manipulation. We investigate the coherent control of the two-photon absorption in imidazole–thiophene core compounds presenting distinct two-photon absorption spectra. The coherent control, performed using pulse phase shaping and genetic algorithm, exhibited different growth rates for each sample. Such distinct trends were explained by calculating the two-photon absorption probability considering the intrapulse interference mechanism, taking into account the two-photon absorption spectrum of the samples. Our results indicate that tuning the relative position between the nonlinear absorption and the pulse spectrum can be used as a novel strategy to optimize the two-photon absorption in broadband molecular systems.

Origin and effect of high-order dispersion in ultrashort pulse multiphoton microscopy in the 10 fs regime

Short pulses can induce high nonlinear excitation, and thus they should be favorable for use in multiphoton microscopy. However, the large spectral dispersion can easily destroy the advantages of the ultrashort pulse if there is no compensation. The group delay dispersion (GDD), third-order dispersion, and their effects on the intensity and bandwidth of second-harmonic generation (SHG) signal were analyzed. We found that the prism pair used for compensating the GDD of the two-photon microscope actually introduces significant negative high-order dispersion (HOD), which dramatically narrowed down the two-photon absorption probability for ultrashort pulses. We also investigated the SHG signal after GDD and HOD compensation for different pulse durations. Without HOD compensation, the SHG efficiency dropped significantly for a pulse duration below 20 fs. We experimentally compared the SHG and two-photon excited fluorescence (TPEF) signal intensity for 11 fs versus 50 fs pulses, a pulse duration close to that commonly used in conventional multiphoton microscopy. The result suggested that after adaptive phase compensation, the 11fs pulse can yield a 3.2- to 6.0-fold TPEF intensity and a 5.1-fold SHG intensity, compared to 50 fs pulses.

DFT study of linear and nonlinear optical properties of donor-acceptor substituted stilbenes, azobenzenes and benzilideneanilines

A theoretical analysis of the linear and nonlinear optical properties of six push-pull pi-conjugated molecules with stilbene, azobenzene and benzilideneaniline as a backbone is presented. The photophysical properties of the investigated systems were determined by using response functions combined with density functional theory (DFT). Several different exchange-correlation potentials were applied in order to determine parameters describing the one- and two-photon spectra of the studied molecules. In particular, the recently proposed Coulomb-attenuated model (CAM-B3LYP) was used to describe charge-transfer (CT) excited states. In order to compare theoretical predictions with available experimental data, calculations with inclusion of solvent effects were performed. The BLYP and the CAM-B3LYP functionals were found to yield values of two-photon absorption (TPA) probabilities closer to experimental values than the B3LYP functional or the HF wavefunction. Moreover, molecular static hyperpolarisabilities were determined using both DFT and second-order Møller-Plesset perturbation (MP2) theory. Likewise, the CAM-B3LYP functional was found to outperform other applied exchange-correlation potentials in determining first hyperpolarisability (beta). Moreover, it was confirmed on a purely theoretical basis that the presence of a -C=C- bridge between the phenyl rings leads to a much larger nonlinear optical response in comparison with a -N=N- bridge.

Peculiarities of two-photon impurity absorption spectra in a quantum molecule with a tunnel-transparent potential barrier

The effect of dissipative tunneling parameters on the spectral dependence of the probability of two-photon impurity absorption in a quantum molecule is theoretically investigated. The effect of the tunnel barrier transparency on two-photon impurity absorption in a quantum molecule is shown to manifest itself as a change in the width of energy levels of the virtual and final states due to variations in such parameters of dissipative tunneling as temperature, photon-mode frequency, and the constant of interaction with a heat bath.

Linear and nonlinear optical properties of azobenzene derivatives

The results of computations of spectroscopic parameters of lowest-lying electronic excited states of azobenezene derivatives are presented. The analysis of experimentally recorded spectra was supported by quantum chemical calculations using density functional theory. The theoretically determined resonant (two-photon absorption probabilities) and non-resonant (first-order hyperpolarisability) nonlinear optical properties are also discussed, with an eye towards the performance of recently proposed long-range corrected (LRC) schemes (LC-BLYP and CAM-B3LYP functionals).

Pulse shapes for optimized two-photon laser scanning microscopy

A numerical model describing the effect of different pulse shapes on the probability of two-photon absorption for two-photon laser scanning microscopy (2PLSM) is reported. Despite the commercial preference for sech2 pulses, this pulse shape does not provide the best performance. The presented model reveals that a square or parabolic pulse shape is preferable and shows that applications of such pulse shapes can improve the probability of two-photon absorption by up to 50% to facilitate improved 2PLSM.

General Method for Reducing Adaptive Laser Pulse-Shaping Experiments to a Single Control Variable

Adaptive laser pulse shaping has proven to be expeditious for discovering laser pulse shapes capable of manipulating complex systems. However, if adaptive control is to be a valuable interrogative technique that informs physical and chemical research, methods that make it possible to infer mechanistic information from experimental results must be developed. Here, we demonstrate multivariate statistical analysis to extract a single control variable from results of a 137-parameter adaptive laser pulse-shaping optimization of multiphoton electronic excitation in a ruthenium(II) coordination complex in solution. We show that this single variable can be used to linearly manipulate the observed fitness, which is determined by the ratio of molecular emission to second harmonic generation of the laser pulse, over the range explored during the adaptive optimization. Further, manipulation of this variable reveals the latent control mechanism. For this system, that mechanism entails focusing the second harmonic power spectrum of the laser field in a spectral region where the probability of two-photon absorption by the molecule is also large. The statistical tools developed are general and will help elucidate control mechanisms in future adaptive pulse-shaping experiments.