4. Results and Discussion

The nonlinear transmission of the compounds with and without aperture was measured in the far field as the sample is moved through the focal point. The scan was performed at a laser pulse energy of 20 μJ, which corresponds to a peak intensity of 0.735 GW/cm². Assuming a spatial and temporal Gaussian profile for laser pulses, the open aperture (OA) normalized energy transmittance is given by [Reference Sheik-Bahae, Said, Wei, Hagan and VanStryland17, Reference Sutherland19]

(1) $\begin{array}{}T\left(z\right)=\sum _{m=0}^{\infty }\frac{{\left(-q\left(z\right)\right)}^m}{{\left(m+1\right)}^{3/2}}\text{with}q\left(z\right)=\frac{{\beta }_{\text{eff}}{I}_0{L}_{\text{eff}}}{1+z^2/z_0^2},\end{array}$

where β _eff is the effective two photon absorption coefficient, I ₀ is the input irradiance, z is the sample position, $z_0=\pi {\omega }_0^2/\lambda$ is the Rayleigh range, ω₀ is the beam waist radius at the focal point(z = 0), and λ is the laser wavelength. For fitting the data with equation (1), we consider L _eff as the effective path lengths in the case of 2PA and is defined by $L_{\text{eff}}=1-e^{-{\alpha }_{0}L}/{\alpha }_0$ , where L is the sample length and α ₀ is the linear absorption coefficient. Similarly, for a pure nonlinear refraction curve, obtained by the division method, the normalized transmittance is given by [Reference Muruganandi, Saravanan, Vinitha, Jessie Raj and Sabari Girisun20–Reference Sabari Girisun, Saravanan and Soma22]

(2) $\begin{array}{}T=1-\frac{4\Delta {\phi }_{0}x}{\left(x^2+1\right)\left(x^2+9\right)},\end{array}$

where $\Delta {\phi }_0$ is the on-axis nonlinear phase shift at the focus and $x=z/z_0$ . The nonlinear refractive index $\gamma \left({\text{m}}^2/\text{W}\right)$ can be determined from the equation $\Delta {\phi }_0=k\gamma I_0{L}_{\text{eff}}$ , where k = 2π/λ is the wave vector and λ is the wavelength.

(3) $\begin{array}{}{I}_0=\frac{4\sqrt{\ln 2}{E}_{\text{total}}}{\sqrt[3]{\pi }{\omega }_0^2\tau },\end{array}$

where E _total is the incident energy on the sample after reflection from the front surface of the cuvette is taken into account and τ is the pulse width of the laser. The nonlinear refractive index n ₂ (esu) can be calculated from the conversion formulae:

(4) $\begin{array}{}{n}_2\left(\text{esu}\right)=\left(\frac{c{n}_0}{40\pi }\right)\gamma \left(\frac{m^2}{W}\right),\end{array}$

where n ₀ the linear refractive index and c is the velocity of light in vacuum.

The normalized OA curve for the pure compounds and the compounds with PMMA (concentration of 25% in matrix) dissolved in DMF is shown in Figure 2. The solid lines are the theoretical fit of equation (1) to the experimental data, which yields the value of effective two photon absorption coefficient β _eff.

Figure 2: Open aperture Z-scan curves for pure and PMMA-doped compounds. The open circles represent experimental data, while the solid line represents theoretical fit with β _eff = 2 cm/GW, 0.0364 cm/GW, and 0.0258 cm/GW for H1, H2, and H3, respectively, and β _eff = 2.2 cm/GW, 0.047 cm/GW, and 0.032 cm/GW for H1/PMMA, H2/PMMA, and H3/PMMA, respectively.

The pure nonlinear refraction curve obtained for pure compounds H1 and H1/PMMA is shown in Figure 3. Here, the solid lines are theoretical fit of the experimental data to equation (2).

Figure 3: Pure nonlinear curves obtained by the division method for pure compounds doped with PMMA. Solid lines are theoretical fit of the experimental data to equation (2).

The real and imaginary part of the third-order nonlinear optical susceptibility χ ⁽³⁾ can be calculated according to the following relations:

(5) $\begin{array}{c}\mathrm{Re}{\chi }^{\left(3\right)}=2n_0^2{\epsilon }_{0}c\gamma ,\mathrm{Im}{\chi }^{\left(3\right)}=\frac{n_0^2{\epsilon }_{0}c\beta \lambda }{2\pi },\end{array}$

where n ₀ is the linear refractive index, ε ₀ is the vacuum permittivity, and c is the velocity of light in vacuum.

Second-order hyperpolarizability γ _h which describes the nonlinear induced polarization per molecule, in an isotropic medium, is related to the third-order bulk susceptibility as [Reference Zhao, Singh and Prasad23–Reference Shivaraj, Parutagouda and Patila25]

(6) $\begin{array}{}{\gamma }_h=\frac{{\chi }^{\left(3\right)}}{{\left(\left(1/3\right)\left(n_0^2+2\right)\right)}^{4}N},\end{array}$

where N is the density of molecules in the unit of molecules per cm³, n ₀ is the linear refractive index of the medium, and ${\chi }^{\left(3\right)}=\sqrt{{\left(\mathrm{Re}{\chi }^{\left(3\right)}\right)}^2+{\left(\mathrm{Im}{\chi }^{\left(3\right)}\right)}^2}$ .

The values of γ_h for the pure compounds and the compounds in PMMA is of the order of 10⁻³¹ esu, which is well comparable with the value reported for silicon naphthalocyanine, SiNc $\left({\gamma }_h=1.7\times {10}^{-31}\text{esu}\right)$ , a widely known optical limiting material [Reference Guo, Sun, Wang, Zhao, Lu and Nie26]. The calculated values of n ₂, Reχ ⁽³⁾, Im χ ⁽³⁾, and γ_h for the pure compounds and compounds doped with PMMA are shown in Tables 1 and 2.

Table 1: Values of Re χ ⁽³⁾, Im χ ⁽³⁾, n ₂, and γ _h determined experimentally for pure compounds.

Table 2: Values of Re χ ⁽³⁾, Im χ ⁽³⁾, n ₂, and γ _h determined experimentally for the compounds doped with PMMA.

The dependence of the nonlinear absorption (NLA) coefficient with on-axis irradiance gives the information about the mechanism of the nonlinear absorption. Generally, nonlinear absorption can be caused by free carrier absorption, saturable absorption, and direct multiphoton absorption or excited state absorption. From our observations, it is seen that β _eff is decreasing with increasing intensity for all the compounds and intercept on the vertical axis is nonzero, as shown in Figure 4. The fall of β _eff with increasing I ₀ is a consequence of reverse saturable absorption (RSA) [Reference Guo, Xu, Wang, You and Ming27, Reference Couris, Koudoumas, Ruth and Leach28]. RSA generally arises in a molecular system where the presence of excited-state absorption to a higher lying state occurs. In particular, when the excited state absorption cross section is larger than the ground state cross section [Reference Torres-Torres, Khomenko, Tamayo-Rivera, Rangel-Rojo, Mao and Watson29]. To confirm the presence of RSA, we calculated the absorption cross-sections in the ground and excited states. The excited state cross section σ _ex can be calculated from the normalized Z-scan data as the procedure described in the literature [Reference Henari, Blau, Milgrom, Yahioglu, Phillips and Lacey30, Reference Garoni, Colombo, Kamada, Dragonetti and Roberto31].

Figure 4: Variation of β _eff with on-axis intensity I ₀ within the compound H1.

The ground state absorption cross section σ_g can be calculated from the following equation:

(7) $\begin{array}{}\alpha ={\sigma }_g{N}_{a}C,\end{array}$

where N_a is the Avogadro number, C is the concentration in moles/cm³, and α is the linear absorption coefficient.

The calculated values of σ _ex for the pure compounds H1, H2, and H3 are 1.522 × 10⁻¹⁷ cm², 1.475 × 10⁻¹⁸ cm², and 1.43 × 10⁻¹⁸ cm², respectively. For compounds H1, H2, and H3 doped with PMMA, the values of σ _ex are 1.739 × 10⁻¹⁷ cm², 1.656 × 10⁻¹⁸ cm², and 1.50 × 10⁻¹⁸ cm², respectively. The values of σ_g for the compounds H1, H2, and H3 are calculated as 2.075 × 10⁻¹⁸ cm², 8.30 × 10⁻²¹ cm², and 1.66 × 10⁻²¹ cm², respectively. It is seen that the value of σ_ex is larger than the value of σ_g for both pure compounds and compounds doped with PMMA which is in agreement with the condition for reverse saturation absorption (RSA) [Reference Tutt and Boggess32].

The dependence of β _eff on the concentration of the sample in the polymer matrix is shown in Figure 5.

Figure 5: β_eff vs. concentration of the sample H1 in the polymer matrix.

Based on the strong reverse saturated absorption, a good optical limiting of nanosecond laser pulses of the samples can be expected. Figure 6 shows the optical limiting behaviour of the compound doped with PMMA. It can be seen that the best limiting behaviour is observed with sample H1, which exhibits strongest nonlinear absorption among the samples. For incident energies less than 100 μJ/pulse, the output linearly increases with the input. But for energies more than 100 μJ/pulse, optical limiting of the pulses was observed. For input energies well below 250 μJ, there is no damage observed in the samples. But beyond 300 μJ, there is a deviation from the optical limiting behaviour. It could be due to damage of sample with laser pulses.

Figure 6: Optical limiting behavior in the compounds doped with PMMA.

These results show that the compounds exhibit larger third-order NLO properties in PMMA host as compared to the pure compounds. The π-electrons associated with the dopant molecules will form an electron cloud around the chain and can be distorted by applying an electric field, which results in variation of nonlinear effects in the samples. Even though the enhancement of NLO properties is very low, PMMA is most preferred because of its flexibility and and good resistance having a low density that aids fabrication of lightweight components, and it increases the damage threshold of the compounds.

From the results, we noticed that the nonlinear response among the three hydrazone derivatives is of the order H1 > H2 > H3. In the case of H1, the highly electron donating dimethyl amino group—N(CH₃)₂—is attached to the para position. Thus, compared to the acceptor group on the left-hand side, in which the carbon ring is attached to the highly electron accepting NO₂ at the metaposition and ester group at the ipso position, the right-hand side of the molecule acts as a donor giving away electrons easily to form a stable π-electron distributed system. Hence, there is a strong delocalization of electrons in the molecule that gives rise to the large nonlinear polarization. Consequently, the highest nonlinear response was observed with H1. In case of H2, chlorine atom is attached at the para position. Cl is an amphiprotic group, and its contribution to the molecular hyperpolarizability depends on the strength of the acceptor group attached to the phenyl ring of the molecule [Reference Honark33]. Since the acceptor group at the left-hand side is very strong, the Cl atoms acts as a donor. But in H3, a strong acceptor NO₂ group is attached at the para position. The NO₂ groups at both ends accept electrons, and hence, delocalization decreases in the molecule.

It can be noted that enhancement of PMMA nonlinear optical properties by means of a quinoid molecule was reported with χ ⁽³⁾ values of 10⁻¹⁴ esu [Reference D’Amore, Lanata, Pietralunga, Gallazzi and Zerbi13]. It is also noted that χ ⁽³⁾ value of ethyl 2-((2E)-2-(4-(dimethylamino)benzylidene)hydrazinyl)-5-nitrobenzoate is comparable with the values of the order of 10⁻¹³ esu of many varieties of azo dyes, which are well-known third-order nonlinear optical materials [Reference Ghanavatkar, Mishra and Sekar34]. Thus, the work reported here reveals that these compounds are one of the suitable classes of nonlinear optical material for photonic applications.