1. Introduction

There has been considerable interest in understanding the higher-order optical nonlinearities in both organic materials [1-3] and semiconductors [4-6], which involve excited-state nonlinearities induced by two-photon absorption (2PA) [7-13]. This is so because they have potential applications in photonics and biophotonics. Furthermore, the higher-order nonlinearities strongly depend on the electronic state structures and transition properties of the material and also on the parameters (wavelength, pulse duration, and peak irradiance) of the incident laser beam. On the other hand, the proliferation of laser sources with ultrafast pulse durations offers the feasibility to observe high-order optical nonlinear effects. As such, the full understanding of the higher-order nonlinearities is crucial for both academic interest and technological applications. During the past decade, intensive efforts have been made toward this end by both theoretical and experimental approaches [14-17], although the complete understanding is still in progress.

As an interesting type of nonlinear optical materials, chalcone and its derivatives have recently received extensively attention due to their high tendency to crystallize in noncentrosymmetric structure, excellent second harmonic generation conversion efficiency, and good optical limiting behavior with nanosecond laser pulse at 532 nm wavelength [18-21]. Very recently, ultrafast optical nonlinearities in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives and their figures of merit have been studied for optical switching [22]. However, it has been demonstrated that the optical nonlinearities measured in the femtosecond regime are two-orders of magnitude smaller than that measured in nanosecond regime [21, 22], analogous to the observation reported for C₆₀ dyads [13]. To fully exploit their optical nonlinearities, it is desirable to gain a complete understanding of high-order nonlinear processes in chalcones.

In this report, we present our experimental investigation into the optical nonlinearities and nonlinear dynamics in acetone solution of 2,4,5-Trimethoxy-4′-nitrochalcone. By carrying out Z-scans with femotosecond laser pulses, it is found that the third-order nonlinearity is dominant at low laser intensity, while both third- and fifth-order nonlinearities are observable at excitation intensity exceeding a critical value. With femtosecond time-resolved degenerate pump-probe measurements, it is shown that the fifth-order effects mainly arise from 2PA-induced excited-state nonlinearities. We have unambiguously determined all the nonlinear parameters in 2,4,5-Trimethoxy-4′-nitrochalcone molecule, including the 2PA cross-section, second-order hyperpolarizability, excited-state absorption (ESA) cross-section, excited-state refraction (ESR) cross-section, lifetime of 2PA-induced excited states, and critical population of the excited states in the near infrared region.

2. Experimental details

2,4,5-Trimethoxy-4′-nitrochalcone (labeled 2,4,5TN) was synthesized by the condensation reaction of 2,4,5-trimethoxybenzaldehyde (0.01ml) with 4-nitroacetophenone (0.01ml) in ethanol (60 ml) and sodium hydroxide solution (5ml, 20%). The synthesized crude solid was purified by repeated recrystallization from acetone. The synthesis and crystal structure of 2,4,5TN have been described in Ref. [23]. The molecular structure of 2,4,5TN used in our investigation is displayed in the right top corner of Fig. 1. This chalcone derivative possesses so-called D-π-A type structure. The 2,4,5-trimethoxy acts as a donor at one end, the C=O bond acts as the electron-withdrawing group in the center, and the nitro group is an acceptor at the other end of the molecule.

 

Fig. 1. Linear absorption spectra of neat acetone (dotted line) and 2,4,5TN in acetone with a concentration of 5 × 10^-4 M (solid line). Inset is its molecular structure.

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The linear absorption spectrum of 2,4,5TN in acetone solution with a concentration of 5 × 10^-4 M, as shown in Fig. 1, has been recorded at room temperature with a Shimadzu UV-3600 spectrophotometer. We have also measured the linear absorption spectrum of a neat acetone, as shown by the dotted line in Fig. 1, confirming that the absorption of the solution in the 320-560 nm range originates from 2,4,5TN. Apparently, 2,4,5TN exhibits a strong absorption band centered at λ _abs =412 nm. It is highly transparent in the near infrared range and hence, one may expect strong 2PA effects with laser radiation at 780 nm.

The acetone solution of 2,4,5TN with a concentration of 2 × 10^-2 M was contained in 1 mm thick quartz cell for both Z-scan and transient transmission measurements. The laser source for all the experiments was a Ti:sapphire regenerative amplifier (Quantronix, Titan), operating at a wavelength of 780 nm with a pulse duration of τ _F = 350 fs (the full width at half maximum for a Gaussian pulse) and a repetition rate of 1 kHz. The spatial distribution of the pulses was nearly Gaussian, after passing through a spatial filter. Moreover, the laser pulses had near-Gaussian temporal profile, confirming by the autocorrelation signals in the transient transmission measurements. In the Z-scan experiments [24], the laser beam was focused by a lens with a 200 mm focal length, producing the beam waist at the focus ω ₀ ≃ 30.6 μm (the Rayleigh range z ₀ = 3.78 mm). To perform Z-scans, the sample was scanned across the focus along the z-axis using a computer-controlled translation stage, while the transmitted pulse energies in the presence or absence of the far-field aperture were probed by a detector (Laser Probe, PkP-465 HD), producing the closed- and open-aperture Z-scans, respectively. For the closed-aperture Z-scans, the linear transmittance of the far-field aperture was kept at 0.15. The measurement system was calibrated with carbon disulfide and the experimental uncertainty should be within ±10%. To further identify the underlying mechanism of the observed nonlinearities, a degenerate pump-probe experiment was conducted with 350 fs, 780 nm laser pulses. In the measurements, the intensity of the probe beam was less than 2% compared to that of the pump beam [22].

3. Results and discussion

To exploit the optical nonlinearities of 2,4,5TN in acetone with a concentration of 2 × 10^-2 M, we have performed the Z-scan experiments at different levels of laser intensities I ₀. As examples, typical open-aperture (filled circles) and closed-aperture (open circles) Z-scans at I ₀ = 96.5, 145, 160, and 227 GW/cm² are shown in Figs. 2, 3(a), 3(b), and 4, respectively. All the open-aperture Z-scans exhibit a decrease of transmittance with respect to the focus, typical of an induced positive nonlinear absorption effect. Previously, we have found that neat acetone possesses pure third-order refractive nonlinearity and negligible absorptive nonlinearity with I ₀ = 250 GW/cm² at 780 nm [22]. It is obvious that the observed nonlinear absorption mainly originates from 2,4,5TN. The closed-aperture Z-scans show salient features as follows: (i) a valley-to-peak configuration at lower intensities (see Figs. 2 and 3); and (ii) double valley-peak structures at higher intensity (see Fig. 4). The observations demonstrate that, at low intensities, third-order nonlinear refraction is a dominant in the overall nonlinear refractive process. Under the excitation of intense irradiances, however, both third- and higher-order nonlinear refraction effects simultaneously manifest themselves in the closed-aperture Z-scan signal [1, 9].

 

Fig. 2. Open-aperture (filled circles) and closed-aperture (open circles) Z-scans for 2,4,5TN in acetone with a concentration of 2 × 10^-2 M at I ₀ = 96.5 GW/cm². The solid lines are the theoretical curves with α ₂ = 2.25 × 10^-2 cm/GW and n ₂ = 1.36 × 10^-6 cm²/GW. Insert is Ln(1 − T) as a function of Ln(I) by converting the open-aperture Z-scan trace with the linear fit of a slope S = 1.04.

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Under the assumption that the sample only possesses third-order nonlinearities, we evaluate the nominal nonlinear absorption coefficient, α _nom, and nonlinear refraction index, n _nom, from the best fittings between the femtosecond-pulsed Z-scan theory [25] and the measured Z-scans at different levels of I ₀. It is interesting to note that, as shown in Fig. 5, the measured α _nom and n _nom values are independence of intensity in the intensity range of ~ 130 GW/cm² or less, which indicates the presence of pure third-order nonlinearities. The critical intensity I _c is estimated to 130 GW/cm² for acetone solution of 2,4,5TN with a concentration of 2 × 10^-2 M; And the third-order absorption coefficient of α ₂ = 2.25 × 10^-2 cm/GW and the third-order nonlinear refractive index of n ₂ = 1.36 × 10^-6 cm²/GW are unambiguously determined. The third-order nonlinear absorption is attributed to 2PA because (i) the excitation wavelength (λ _exc) used for the measurements fulfills the requirement (λ _abs < λ _exc < 2λ _abs) for 2PA studies at 780 nm [26], as shown in 1Fig. 1; and (ii) the normalized transmittance T(z) as a function of I(z) in log-log scale by converting the open-aperture Z-scan curves with I(z) = I ₀/(1 + z ²/z ₀ ²), shows the linear dependence with a slope of S = 1.04 (see the inset in Fig. 2), a typical characteristic for 2PA process [27].

As the intensity exceeds I _c, however, the value of α _nom (or n _nom) increases (or decreases) with increasing intensity, suggesting the simultaneous occurrence of third- and higher-order nonlinearities. Consequently, both photoinduced absorption and refraction in the solution can be described by Δα = α ₂ I + α ₃ I ² and Δn = n ₂ I + n ₄ I ², where α ₃ and n ₄ are fifth-order nonlinear absorption coefficient and refraction index, respectively, and I is the intensity inside the solution. Both α ₂ and α ₃ can be extracted by the best fittings between the measured open-aperture Z-scans and the Z-scan theory of 2PA-induced ESA [16]. As a result, we obtained α ₂ = 2.25×10^-2 cm/GW and α ₃ = 1.30×10^-4 cm³/GW². It is found that the measured α ₂ and α ₃ values are independent of I ₀ under our experimental conditions. In Figs. 2, 3 and 4, the solid lines calculated by using these nonlinear values are in good agreement with the measurements, confirming that our assumption of Δα=α ₂ I+α ₃ I ² is valid. Besides, we did not observe any significant scattering effect at the intensities ranging from 80 to 271 GW/cm². Hence, both 2PA and fifth-order nonlinear absorption effects are believed to be predominant mechanism of absorptive nonlinearities.

 

Fig. 3. Open-aperture (filled circles) and closed-aperture (open circles) Z-scans for 2,4,5TN in acetone with a concentration of 2 × 10^-2 M at the intensities of (a) 145 and (b) 160 GW/cm², respectively. The solid lines are the theoretical curves with α ² = 2.25 × 10^-2 cm/GW, n ₂ = 1.36×10^-6 cm²/GW,α ₃ = 1.30×10^-4 cm³/GW², and n ⁴ = -0.80×10^-8 cm⁴/GW²; while the dashed lines are the theoretical curves calculated by neglecting fifth-order nonlinearities (α ₃ = 0 and n ₄ = 0).

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With the obtained α ₂ and α ₃ from open-aperture Z-scans, and n ₂ = 1.36 × 10^-6 cm²/GW from the closed-aperture Z-scans at low intensities where high-order nonlinearities could be justifiably ignored, we extract n ₄ = −0.80 × 10⁻⁸ cm⁴/GW² by the best fittings between the measured closed-aperture Z-scans and the Z-scan theory [5] within the limit of I ₀ ≤ 200 GW/cm². It should be emphasized that the value of n ₄ is independent of I ₀ with laser irradiances below 200 GW/cm², which confirms that the refractive nonlinearities mainly originate from third- and fifth-order refractive effects at the intensities less than 200 GW/cm² where the other nonlinear processes are insignificant. The measured nonlinear parameters of 2,4,5TN in acetone solution at 780 nm are summarized in Table 1. We numerically simulate the Z-scans using the measured parameters (α ₂, α ₃, n ₂, and n ₄) as displayed by the solid lines in Figs. 2 and 3, which demonstrate that our assumption of Δ_n = n ₂ I +n ₄ I ² is justifiable. However, the theoretical Z-scans are not in agreement with the experimental date in the higher irradiance regime (I ₀ > 200 GW/cm²), as shown in Fig. 4. This difference is anticipated for the following reasons: (i) other nonlinear processes, such as higher-order nonlinearities and self-phase modulation, could make the experimental results deviated from the theory; and (ii) intense irradiances induce a nonlinear phase variation so large that the approximations (both slowly varying envelope approximation and the thin-sample approximation) for standard Z-scan analysis become invalid any more [24]. Consequently, the improved Z-scan theory should be adopted [28]. Nevertheless, the competition between the third- and fifth-order refractive nonlinearities is unambiguously observed from the closed-aperture Z-scan, as displayed in Fig. 4.

 

Fig. 4. Open-aperture (filled circles) and closed-aperture (open circles) Z-scans for 2,4,5TN in acetone with a concentration of 2×10^-2 M at I ₀ = 227 GW/cm². The solid lines are the Z-scan traces simulated by the same parameters as Fig. 3.

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Fig. 5. Intensity dependence of nominal nonlinear absorption coefficient α _nom (filled circles) and nominal nonlinear refraction index n _nom (open circles), respectively. The error bar is 10% and it is estimated by calibration of the Z-scan measurement system with the use of carbon disulfide as standard sample. The solid lines are for guidance to the eyes.

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Table 1. Measured linear absorption peak wavelength (λ _abs), 2PA coefficient (α ₂), fifth-order nonlinear absorption coefficient (α ₃), third-order nonlinear refraction index (n ₂), fifth-order nonlinear refraction index (n ₄), and critical intensity (I _c) for 2,4,5TN in acetone solution with a concentration of 2 × 10^-2 M at 780 nm (experimental uncertainty: ±10%).

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It is well known that several physical mechanisms might contribute to the fifth-order nonlinearity, including the intrinsic χ ⁽⁵⁾ susceptibility of the sample and other nonlinearities equivalent to the fifth-order nonlinearity, such as excited-state nonlinearities induced by 2PA in organic molecules [7, 17]. The intrinsic nonlinearities response is nearly instantaneous, whereas the typically response time of the accumulative nonlinearity in organic molecules is about picosecond time scales [8, 12, 22]. Accordingly, one way to identify whether the fifth-order nonlinearity is an intrinsic χ ⁽⁵⁾ effect or a sequential two-step χ ⁽³⁾ : χ ⁽¹⁾ effect is to measure the dynamics of the observed nonlinearities. Figure 6 presents typical degenerate pump-probe measurement with τ _F = 350 fs, 780 nm laser pulses on the acetone solution of 2,4,5TN with a concentration of 2×10^-2 M. The contribution to the signal from the solvent (acetone) has been subtracted. The normalized transient transmission signals as a function of the delay time are obtained at the pump-beam intensities of 138 and 215 GW/cm². Evidently, a fast (about 200 fs) and another longer (> 1 ps) decay components are involved in the transient signals. From these data, it is concluded that the 2PA-induced excited-state nonlinearity is dominant in the overall fifth-order nonlinear process. By using a two-exponential-component model, the best fit gives τ ₁ ~ 200 fs and τ ₂ ~ 2.5 ps for 2,4,5TN molecule. It is known that τ ₁ is the autocorrelation of the laser pulses used. The τ ₂ component is the lifetime of 2PA-induced excited states. The measured τ ₂ value is the same order of magnitude as the ones for organic dye solutions [8]. Moreover, the value of τ ₂ is independent of the pump intensity, which is consistent with the one reported previously [11]. It should be pointed out that an oscillation in the transient signals at pump intensity in excess of 200 GW/cm² is present. This oscillation may be arises from the microbubble formation in solution disturbing the experimental results.

The observed 2PA-induced excited-state nonlinearities can be understood as follows. For 2,4,5TN molecule as a polyatomic molecular system, its electronic structure can be simplified as a three-level model under the excitation of femtosecond laser pulses, as illustrated in the insert of Fig. 6. τ _e and τ _h represent the lifetime of 2PA-induced excited states and high-lying states, respectively. It has been reported that the value of τ _h in organic molecule is on tens-to-hundreds-of-femtosecond time scales [11], while τ _e is about a few picoseconds [8, 22]. At low intensity, the dominant absorption is the 2PA process caused by the transition from the ground state S ₀ to the first excited state S ₁. Moreover, the population of S ₁ is insufficient to make transitions from S ₁ to the higher-lying state S _h observable. When the population of S ₁ exceeding a critical value N _c, the electron located at S ₁ is rapidly excited into S _h by absorbing another photon before it relaxes to S ₁, leading to 2PA-induced ESA. Meanwhile, significant population redistribution produces an additional change in the refractive index caused by the 2PA-generated excited states, resulting in 2PA-induced ESR.

 

Fig. 6. Normalized transient transmission signals are obtained by dividing the experimental data for 2,4,5TN in acetone with a concentration of 2 × 10^-2 M by respective data for neat acetone. The curves are shifted vertically for clear presentation. Filled circles and open circles are the experimental results at the bump-beam intensities of 138 and 215 GW/cm², respectively; while the solid lines are the best fits using a two-exponential-component model with τ ₁ ~ 200 fs and τ ₂ ~ 2.5 ps. Insert shows a three-level diagram of 2PA-induced excited-state nonlinearities.

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As we discussed previously, the fifth-order absorptive and refractive nonlinearities caused by 2PA-induced ESA and ESR can be derived by Eqs. (1) and (2), respectively [17],

where σ _a and σ _r are the absorptive and refractive cross-sections of S ₁, respectively; ħω is the incident photon energy; and τ is the half-width at e ^-1 of the maximum for the pulse duration (τ and τ _F are related through the conversion formula $\tau ={\tau }_{\mathrm{F}}/2\sqrt{\ln 2}$. By using the measured parameters listed in Table 1, we evaluate σ _a = 1.32 × 10^-17 cm² and σ _r = −0.81 × 10^-21 cm³ for 2,4,5TN molecules. These values are on the same order of magnitude as the reports for other organic molecules [7, 10].

Table 2. Molecular intrinsic 2PA cross-section (σ _{2 PA}), second-order hyperpolarizability (γ _R), ESA cross-section (σ _a), ESR cross-section (σ _r), 2PA-induced excited-state lifetime (σ _e), and critical population of the excited states (N _c) for 2,4,5TN at 780 nm (experimental uncertainty: ±10%).

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To appreciate the contribution from one molecule to the third-order optical nonlinearity, it is convenient to define molecular nonlinear properties. The 2PA cross-section σ _2PA is calculated to be 4.78 × 10^-49 cm⁴ s photon^-1 (47.8 GM) from the 2PA coefficient by the formula σ _2PA = α ₂ ħω/N, where N is the number of molecules in cm^-3. For acetone solution of 2,4,5TN, the nonlinear refractive index of 2,4,5TN can be given as the simplified expression by n _2,solute = [n _2,solution - (1 - f)n _{2, solvent}]/f, where f is the dilute solution containing a mole fraction of solute, and n _2,solvent and n _2,solute are the nonlinear refractive indices of the solvent (acetone) and the solute (2,4,5TN), respectively [29, 30]. In our experiments, the value of f is ~ 1.5 × 10^-3, and n _2,solvent = 0.58 × 10^-6 cm²/GW [22]. We estimate n _2,solute = 5.21 × 10^-4 cm²/GW for 2,4,5TN. The real part of the third-order nonlinear susceptibility of 2,4,5TN is calculated through the relation χ _R ⁽³⁾ = 2n ₀ ² ε ₀ cn _2,solute (SI) [24], where n ₀ is the linear refractive index, ε ₀ and c are the permittivity and the light velocity in vacuum, respectively. The measured χ _R ⁽³⁾ value for 2,4,5TN is 4.45 × 10^-11 esu by using the conversion formula χ _R ⁽³⁾ (SI) = 4π × 3^-2 × 10^-8 χ _R ⁽³⁾ esu [31]. Then the molecule second-order hyperpolarizability is estimated as γ _R = 9.22 × 10^-31 esu from γ _R = χ _R ⁽³⁾/[3^-4(n ₀ ² + 2)⁴ N] [29], which is about 2 orders of magnitude greater than that of other organic molecules [7, 10, 21, 29]. Furthermore, the critical population of S ₁ is calculated to be N _c = 1.86 × 10¹⁸ cm^-3 according to N _c = α ₂ τ _e I ² _c/2ħω [17]. The molecular intrinsic photophysical parameters are summarized in Table 2.

4. Conclusion

In summary, we have experimentally investigated the optical nonlinearities of acetone solution of 2,4,5-Trimethoxy-4′-nitrochalcone in the near infrared region. By performing open- and closed-aperture Z-scan experiments, we have observed the pure third-order nonlinearities of this chalcone solution at low intensity. At the excitation intensity exceeding a critical value, we have found the concurrence of third- and fifth-order nonlinearities. Using time-resolved degenerate pump-probe measurements, we have confirmed that fifth-order effect mainly originates from 2PA-induced excited-state nonlinearities. We have determined all the nonlinear parameters in 2,4,5-Trimethoxy-4′-nitrochalcone molecular, including the 2PA cross-section, second-order hyperpolarizability, ESA cross-section, ESR cross-section, lifetime of 2PA-induced excited states, and critical population of the excited states. The excellent photophysical properties of the chalcone derivative are indicative of its feasible applications in photonic devices.