1. Introduction

The study of the two-photon absorption (2PA) process in organic compounds has increased considerably in the last years because of their remarkable features that can be used in several kinds of applications [1–7]. In general, however, the 2PA of isotropic liquids is investigated using linearly polarized laser and, therefore, polarization effects on the 2PA are still not well known. Nevertheless, such effects can reveal important information about photophysical properties of biological and organic compounds. For example, 2PA circular-linear and circular dichroism effects [8,9] can provide information about the angle between dipole moments [10], symmetry of excited states [11] and, in chiral samples, allow to obtain information on magnetic-dipole and transition electric-quadrupole moment [12,13]. Moreover, from the application point of view, Lazar et. al. [14], investigating the protein structure and function, demonstrated that 2PA polarization microscopy provides higher sensibility than conventional 2PA microscopy. Therefore, one can anticipate that a deeper comprehension of the 2PA process with control of polarization will open access to understanding photophysical properties of materials that cannot be obtained using conventional 1PA and 2PA spectroscopies, as well as to the development of new applications in photonics.

Recently, 2PA spectroscopy with polarization control has drawn great attention due to the possibility of exploring optical effects beyond the electric dipole approximation and also been shown to be a powerful tool in study of complex molecular structures. For example, Olesiak-Bańska [15] and Mojzisova [16] used the polarized two-photon microscopy to investigate the organization of liquid crystalline DNA. De Boni [17] and Markowicz [18] developed extensions of the traditional Z-scan technique to study nonlinear chiroptical effects. More recently, Diaz et. al. [19] theoretically studied the effect of the π-electron delocalization curvature on the two-photon circular dichroism of molecules with axial chirality. Finally, Nag et. al. [20] and Zeng et. al. [21] showed experimentally the polarization-induced control of the fluorescence induced by 2PA of achiral and chiral organic compounds using femtosecond pulses with high repetition rate and low-repetition rate with high pulse energy (microjoule), respectively. However, high repetition rate (MHz) generates cumulative thermal and population effects and high pulse energy promotes accumulation of electrons in the excited state. Consequently, both effects may contribute to results in which there are an effective contribution of higher-energy excited states. In this context, here we investigated the polarization effect on the 2PA spectrum of a chiral compound based in azoaromatic moieties (YB3p25) using femtosecond pulses with low repetition rate (1-kHz) and low energy (nanojoule). Differently from other results, we modeled the experimental results employing the sum-over-essential states approach and the dependence on the circular/linear 2PA ratio with the intensity was not observed, given the experimental conditions employed. Moreover, we show that the interference term, between two distinct transition pathways described in the sum-over-essential states approach, is fundamental to model the 2PA circular-linear dichroism spectrum.

2. Experimental

All chemicals were of reagent grade and used as supplied (Sigma-Aldrich). The molecular structure of the chiral organic molecule (YB3p25) is presented in Fig. 1 . Details about the synthesis and purification can be found in Ref [22].

 

Fig. 1 Molecular structure of the chiral compound (YB3p25).

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We prepared YB3p25/chloroform solution with concentrations of 5x10¹⁶ and 1x10¹⁸ molecules/cm³, for linear and nonlinear optical measurements, respectively. For the optical measurements the sample was placed in a 2 mm thick quartz cuvette. The steady-state absorption spectrum was recorded using a Shimadzu UV-1800 spectrophotometer. For the nonlinear optical measurements, we employed the open aperture Z-scan technique, using 120-fs laser pulses from an optical parametric amplifier pumped by 150-fs pulses (775 nm) from a Ti:sapphire chirped pulse amplified system. The Z-scan measurements were carried out with intensities ranging from 75 to 255 GW/cm² (40 to 130 nJ/pulse) and with beam waist size at the focus varying from 17 to 19 μm. To ensure a Gaussian profile for the laser beam used in the experiments, spatial filtering is performed before the Z-scan setup. To control the laser polarization state from linear to circular, we used a broadband zero-order quarter-wave plate. To guarantee the same experimental condition for the measurements, the quarter-wave plate is kept in the setup in both experiments (linear and circular polarization), i.e., we set the angle of rotation of the λ/4 wave plate at 0° for linear polarization and at 45° for circular polarization.

In the open aperture Z-scan technique, 2PA cross-section is determined by translating the sample through the focal plane of a focused Gaussian beam, while transmittance changes in the far field intensity are monitored. For a 2PA process, the light field induces an intensity dependent absorption, α = α₀ + βI; in which I is the laser beam irradiance, α₀ is the linear absorption coefficient and β is the two-photon absorption coefficient. For excitation wavelengths far from one-photon resonances, the power transmitted through the sample due to 2PA is integrated over time (assuming a pulse with a Gaussian temporal profile), resulting in the normalized energy transmittance given by,

3. Results and discussion

The molar absorptivity spectrum of the YB3p25 compound is displayed in Fig. 2(a) . Such spectrum presents a lowest energy absorption band at 350-550 nm with molar absorptivity of c.a. 6.5 x 10⁴ mol⁻¹Lcm⁻¹.

 

Fig. 2 (a) Linear absorption spectrum of the YB3p25. (b) 2PA cross-section spectra with linearly (circles), right (squares) and left (up triangles) circularly polarized laser pulse and the solid line along it is the theoretical fitting obtained employing the sum-over-essential states approach.

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By performing theoretical calculations using Density Functional Theory (DFT), we determined that such band is associated with two strong π→π* transition from the π-conjugated backbone separated by 0.11 eV [22]. Such transitions are illustrated in Fig. 2(a) by the linewidth functions$g_e\left(\omega \right)$and$g_f\left(\omega \right)$(dashed lines). The circles, squares and triangles in the Fig. 2(b) represent, respectively, the 2PA cross-section spectra determined by performing open-aperture Z-scans with linearly (LP), right and left circularly (CP) polarized light, similar to the ones presented in Fig. 3 for distinct wavelengths (800, 880 and 930 nm).

 

Fig. 3 Open-aperture Z-scan curves for YB3p25 with linearly (circles), left (up triangles) and right (squares) circularly polarized light. The solid line represents the fitting employing the Eq. (1).

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As can be seen from Fig. 2(b), the 2PA spectra presents a well-defined 2PA allowed band located at 880 nm, with 2PA cross-section magnitude of about 225 GM for the LP and 150 GM for the CP light. Although YB3p25 has molecular chirality due to the helical structure, differences between 2PA using right and left circularly polarized light were not observed within our experimental error, as shown in Figs. 2(b) (such results can also be seen in Fig. 3). We estimate that the nonlinear circular dichroism effect, present in this sample, is very small (<1% of normalized transmittance change), limiting its observation in our experimental setup. On the other hand, there is a significant difference in the 2PA cross-section obtained using circularly (CP - right or left) and linearly (PL) polarized light. Such difference is associated with elements of the 2PA tensor [8,23], which can be correlated to the symmetry of the electronic states, as well as the angle between the dipole moments.

The 2PA circular/linear ratio, defined as ${\Omega }_{CLD}={\sigma }_{2PA}^{CP}/{\sigma }_{2PA}^{LP}$, is an important parameter for randomly oriented molecules characterization, since it can reveal information about the excited states symmetry. For example, if the molecule belongs to a well-defined symmetry point group, we can anticipate that if ${\Omega }_{CLD}<1$, the symmetry of the ground and final excited state are the same. In contrast, if ${\Omega }_{CLD}>1$, the symmetry are opposite [11]. Figure 4(a) shows the circular/linear 2PA ratio (${\Omega }_{CLD}$) as a function of the wavelength. As it can be seen, ${\Omega }_{CLD}<1$for all measurements, indicating that the excited states, responsible for the 2PA allowed band, have the same symmetry of the ground state. However, YB3p25 is a non-centrosymmetric molecule with a very complex molecular geometry and, therefore, its electronic states symmetry are not well-defined. Consequently, we cannot guarantee the symmetry of the excited states since the dipole-electric selection rules [24] are relaxed in the present case. Nevertheless, in Fig. 4(a) we can discriminate two regions where ${\Omega }_{CLD}$ tends to a constant value. The first one, between 880 and 960 nm, with $〈{\Omega }_{CLD}〉\approx 0.69$, and the other one, between 800 and 860 nm, with $〈{\Omega }_{CLD}〉\approx 0.55$. Such results indicate that these two regions are associated with two different excited electronic states (separated by c.a. 0.15 eV), which are governed by different elements of the 2PA tensor [11]. Based in this statement, we performed theoretical calculations using DFT and verified that, in fact, the 2PA band shown in Fig. 2(b) is associated with two distinct excited states strongly allowed by 2PA and separated by c.a. 0.11 eV [15]. According to the DFT calculations, the 2PA allowed states correspond to transitions to states which are also one-photon allowed, indicating the relaxation of the electric-dipole selection rules.

 

Fig. 4 (a) 2PA-CLD spectrum of the YB3p25 (diamonds). Solid and dashed lines represent the fit employing the Eq. (3) with and without the interference term, respectively. (b) Normalized transmittance change (log-log scale) as a function of laser irradiance showing the slope of approximately 1.0 for the LP and CP light beam. The inset shows the circular/linear 2PA ratio (${\Omega }_{CLD}$) as a function of irradiance.

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Figure 4(b) shows a linear dependence for the normalized transmittance change with the laser irradiance, obtained with LP and CP light at 870 nm. These results show that, for both light polarization states (linear and circular), the mechanism of absorption does not have contribution from higher-energy excited states. To emphasize such aspect, the inset of Fig. 4(b) shows that the circular/linear 2PA ratio remains constant (${\Omega }_{CLD}=0.65$) with the irradiance (75-255 GW/cm²). Such behavior indicates that the 2PA cross-sections do not present spurious effects, mainly because of three main features of our experimental setup: short pulse duration (120 fs), low repetition rate (1 KHz) and low pulse energy (nJ).

To aid the interpretation of the results and to establish a relationship between the polarization effect and the 2PA properties, we used the sum-over-essential states (SOS) approach. As YB3p25 does not present a center of inversion, the initial and intermediate electronic states have distinct permanent dipole moments. Thus, it is necessary to take into account the real intermediate energy level. Besides, non-centrosymmetric molecules do not follow the dipole-electric selection rule [24] and, therefore, one- and two-photon transitions are allowed between any electronic states. In this case, taking into account the average over all possible molecular orientations in an isotropic medium and considering the 2 + 3 energy-level diagram displayed in Fig. 5 , in which it is depicted the ground state,$|g〉$, and two excited states strongly 2PA allowed, $|e〉$and $|f〉$, the 2PA cross-section can be written as [10,25,26]:

 

Fig. 5 2 + 3 energy-level diagram with $\Delta {\overrightarrow{\mu }}_{ge}\ne 0$ used in sum-over-essential states approach in order to model the 2PA-CLD spectrum (solid lines). There are two distinct transition pathways for 2PA in this system. The first path involves the difference between permanent dipole moment of the first excited and ground states (red arrows) while the second involve a real intermediate resonance (blue arrows) due to the detuning between the photon energy and the first excited state allowed by 1PA. Hollow arrows show the transition dipole moments.

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_{$P\left(\epsilon \right)=2\left[2{\cos }^2\left(\epsilon \right)+1\right]$} and $P\left(\cos \left(\epsilon \right)\right)=2\left[2\cos \left({\epsilon }_{{}_{\Delta {\overrightarrow{\mu }}_{ge}{\overrightarrow{\mu }}_{ge}}}\right)\cos \left({\epsilon }_{{}_{{\overrightarrow{\mu }}_{ge}{\overrightarrow{\mu }}_{ef}}}\right)+\cos \left({\epsilon }_{{}_{\Delta {\overrightarrow{\mu }}_{ge}{\overrightarrow{\mu }}_{ef}}}\right)\right]$for Linear polarization;

_{$P\left(\epsilon \right)=\left[{\cos }^2\left(\epsilon \right)+3\right]$}and $P\left(\cos \left(\epsilon \right)\right)=\left[\cos \left({\epsilon }_{{}_{\Delta {\overrightarrow{\mu }}_{ge}{\overrightarrow{\mu }}_{ge}}}\right)\cos \left({\epsilon }_{{}_{{\overrightarrow{\mu }}_{ge}{\overrightarrow{\mu }}_{ef}}}\right)+3\cos \left({\epsilon }_{{}_{\Delta {\overrightarrow{\mu }}_{ge}{\overrightarrow{\mu }}_{ef}}}\right)\right]$for Circular polarization.

Where $\xi$ is the molar absorptivity, $N_A$ is the Avogrado’s number, h is the Planck’s constant, c is the speed of light, $\omega$ and ${\omega }_{g\to f}$ are the excitation laser and transition frequency respectively.$\overrightarrow{\mu }$is the transition dipole moment, and $\Delta {\overrightarrow{\mu }}_{ge}$ is the difference between the permanent dipole moments of the first excited and ground states. $g\left(2\omega \right)$ represents the normalized Lorentzian line-shape function with $\Gamma$ describing half width at half-maximum of the final state linewidth.$L=3n^2/(2n^2+1)$ is the Onsager local field factor introduced to take into account the effect of the media (chloroform) [27] with the refractive index n = 1.490 for chloroform at 20°C. $\epsilon$ is the angle between the dipole moments.

As it can be seen from Eq. (3), the 2PA cross-section is governed by three distinct contributions: the first corresponds to electronic transition induced by 2PA in a two-levels system with a change in the permanent dipole moment ($\Delta {\overrightarrow{\mu }}_{ge}\ne 0$) between the first excited and ground states (dipolar term - D); the second term corresponds to transitions in a three-levels system with one final excited state ($|f〉$) and one real intermediate excited state ($|e〉$) which is responsible for the resonance enhancement of the nonlinearity [28–30] (intermediate resonance - IR). The last contribution corresponds to a quantum interference (quantum interference - QI) between the two transition pathways previously described [25]. However, if the excitation photon energy is very close to the intermediate real state ($\omega \to {\omega }_{ge}$), the contribution of the interference term to the total 2PA cross-section is negligible. Otherwise, if the two excited states are very close and far away from the first excited state allowed by 1PA, the interference term can contribute to increase or decrease strongly the 2PA cross-section, depending on the relative phase among the dipole moments.

The solid lines showed in Fig. 2(b) and 4(a) represents the fits obtained using Eq. (3) with ${\epsilon }_{{\overrightarrow{\mu }}_{ge}{\overrightarrow{\mu }}_{ef}}={10}^{\circ }$,${\epsilon }_{\Delta {\overrightarrow{\mu }}_{ge}{\overrightarrow{\mu }}_{ge}}={50}^{\circ }$and ${\epsilon }_{\Delta {\overrightarrow{\mu }}_{ge}{\overrightarrow{\mu }}_{ef}}={90}^{\circ }$for both, linear and circular polarization. We obtained a good agreement between the experimental data and the theoretical model (Eq. (3)), changing the polarization terms from linear to circular in Fig. 2(b) and dividing both terms (${\Omega }_{CLD}={\sigma }_{2PA}^{CP}/{\sigma }_{2PA}^{LP}$) in Fig. 4(a). However, as shown in Fig. 4(a), the 2PA circular/linear ratio presents values between 0.55 and 0.7. Such values can only be modeled if we consider the interference term (QI) between the two transition pathways, since the circular/linear ratio between the polarization terms ($P\left(\epsilon \right)$) of individual transition pathways (D and IR) varies between 0.67 and 1.5 for any combination of angle between the dipole moments. In Fig. 4(a), the dashed line represent the best fit obtained employing Eq. (3) without contribution from the interference term. As it can be seen, the interference term is fundamental to model the 2PA-CLD spectrum. Furthermore, it is important to mention that although the dipoles are not pointing to the same direction (particular case of maximum 2PA cross-section), the relative phase obtained between them (angle between the dipole moments) guarantee a positive signal to the interference term, indicating constructive quantum interference between the two closely-spaced electronic levels. In this case, the quantum interference contributes to enhance the 2PA cross-section. Table 1 summarizes the spectroscopic parameters used/obtained in the SOS approach. The parameters highlighted in Table 1 were obtained from the SOS approach, while the other ones were obtained using Eq. (4) and the linewidth functions showed in Fig. 2(a).

Table 1. Spectroscopic parameters used/obtained (highlight) in/from the sum-over-essential states approach adopting a 2 + 3 energy-level diagram, with $\nu =\omega /2\pi$.

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We also performed 2PA modulation experiments by rotating the broadband zero-order quarter-wave plate (λ/4), which allows polarization changes from linear through elliptical to circular and vice-versa. If the angle of rotation (θ) of the λ/4 wave plate is 0°, the incident light keeps a linear polarization. If θ = 45°, the polarization state of the incident light changes to circular. For angles in the interval 0-45°, the polarization is elliptical with different eccentricities. In Fig. 6(a) , the squares show the experimental 2PA modulation at the wavelength corresponding to the 2PA band peak (880 nm). The solid line corresponds to the fit of the data using:

 

Fig. 6 (a) Experimental (squares) 2PA cross-section modulation for YB3p25 at 880 nm. The solid curve is the fitting of the experimental data using Eq. (5) with$\epsilon ={10}^{\circ }$. (b) Simulations from Eq. (5) assuming distinct values for the angle between dipole moments ($\epsilon$).

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5. Final remarks

In summary, we have investigated the polarization effect on the 2PA spectrum of a chiral compound based in azoaromatic moieties (YB3p25). We observed a considerable change in the 2PA circular/linear ratio within the 2PA band, which was attributed to the presence of two excited states strongly allowed by 2PA. We did not observe an intensity dependence on the circular/linear 2PA ratio, unlike published results [20,21], which was attributed to experimental conditions employed (short pulse duration (120 fs), low repetition rate (1 KHz) and low pulse energy (nJ)). In addition, we modeled the 2PA (linear and circular) and 2PA-CLD spectra using a 2 + 3 energy-level diagram within the SOS approach and correlate the symmetry of the electronic states with the angle between the dipole moments. We showed that the interference term in the SOS approach plays a fundamental role on the 2PA-CLD spectrum and that the polarized 2PA spectroscopy can be a powerful additional tool to investigate electronic structure of organic materials. As a final point, although the results and interpretation presented in this paper refers to a single molecule, we firmly believe they bring general aspects that can be used for future works in this field, and applied to different molecules.