Nonlinear Optical Properties Tuning in Meso-Tetraphenylporphyrin Derivatives Substituted with Donor/Acceptor Groups in Picosecond and Nanosecond Regimes

meso-Tetraphenylporphyrin (TPP) and its two substituted derivatives (meso-tetrakis(4-cyanophenyl)porphyrin [TPP(CN)4] and meso-tetrakis(4-methoxyphenyl)porphyrin [TPP(OMe)4]) were synthesized. Their nonlinear absorption and refraction properties were studied using the Z-scan technique in the picosecond (ps) and nanosecond (ns) regimes. The open aperture Z-scan results reveal that TPP and TPP(CN)4 display an identical reverse saturable absorption (RSA) character in the ps and ns regimes. While TPP(OMe)4 exhibits a transition from saturable absorption (SA) to RSA in the ps regime and a typical RSA character in the ns regime. The closed aperture Z-scan results show that TPP(CN)4 and TPP(OMe)4 have regular enhancement of the magnitude of nonlinear refraction as compared to their parent TPP in both the ps and ns regimes. In addition, the second-order molecular hyperpolarizabilities (γ) of these three porphyrins are calculated, and the γ values of TPP(CN)4 and TPP(OMe)4 are remarkable larger than that of TPP. The introduction of the electron-withdrawing group CN and the electron-donating group OMe into TPP has enhanced its nonlinear refraction and γ value, and tuned its nonlinear absorption (TPP(OMe)4), which could be useful for porphyrin-related applications based on the desired NLO properties.

hyperpolarizabilities of these three porphyrins are calculated. The molecular structures of TPP, TPP(CN)4 and TPP(OMe)4 are shown in Figure 1.

Linear Absorption Characterization
The UV-visible spectra of TPP, TPP(CN)4, and TPP(OMe)4 in CH2Cl2 are presented in Figure 2. The Soret band of these compounds is centered around 420 nm, and the Q-bands are all located between 500 and 700 nm [12]. It can be seen from Figure 2 that the incorporation of the donor methoxy group and acceptor cyano group into TPP did not arouse obvious change in its linear absorption spectra.

Picosecond Z-Scan Measurements
To check the effect of CH2Cl2 solvent on the nonlinear absorption and refraction of the entire porphyrin/CH2Cl2 solution, the Z-scan measurements are first performed on CH2Cl2, as shown in Figure 3. The circles show the normalized transmission without an aperture (open aperture, OA), which is varying as a function of distance along the lens axis. The result reveals that no nonlinear absorption of CH2Cl2 could be observed within the limit of the intensity (1.1 GW/cm 2 ) used in the experiment. However, the closed aperture (CA) result (squares) shows an obvious valley-peak configuration, which indicates a positive nonlinear refraction. The Z-scan measurements along with the corresponding fits for TPP, TPP(CN)4, and TPP(OMe)4 in CH2Cl2 are shown in Figure 4. Figure 4a presents the OA Z-scan results. TPP and TPP(CN)4 both exhibit a notable valley at the focus, indicating a reverse saturable absorption (RSA) character with a positive nonlinear absorption coefficient. Whereas TPP(OMe)4 shows a different absorption property. It experiences a switch from saturable absorption (SA) at a low input intensity to RSA at higher intensities. The inset in Figure 4a clearly provides the SA pattern of TPP(OMe)4 at the input intensity 0.2 GW/cm 2 , and the coexistence of SA and RSA at 0.63 GW/cm 2 . It can be concluded that RSA effect will play a dominant role as the input intensity increasing largely enough. In consideration of the negligible nonlinear absorption of CH2Cl2 (in Figure 3), the nonlinear absorption effects in Figure 4a can be mainly attributed to the solutes rather than CH2Cl2 solvent. As mentioned above, the occurrence of SA heavily depends on excitation wavelength, excitation intensity, concentration and molecular structure [18][19][20], and the first three parameters for all the compounds are same in our experiment, thus we attributed the SA-to-RSA behavior in TPP(OMe)4 to its unique molecular structure. This implies that the incorporation of electron-donating groups (methoxy) into TPP can turn its nonlinear absorption property.
The OA and CA Z-scan curves are fitted based on the coupled equations involving the irradiance and the nonlinear phase shift [36]. Furthermore, the nonlinear absorption switching behavior of TPP(OMe)4 is described by a nonlinear absorption coefficient of ( ) 0 eff s α α = +β 1+ I I I I [37]. Here, α0 is the linear absorption coefficient of the sample. βeff is the effective nonlinear absorption coefficient and Is is the saturable intensity. For the RSA behavior in TPP and TPP(CN)4, the saturable intensity Is → ∞ and hence the nonlinear absorption coefficient can be simplified to α(I) = α0 + βeffI. The fittings in Figure 4a with such nonlinear absorption coefficients yield βeff values for TPP, TPP(CN)4, and TPP(OMe)4, which are 0.65, 1.0, and 4.0 cm/GW, respectively. Furthermore, the saturable intensity Is of TPP(OMe)4 can be obtained by fitting and is 1.25 ± 0.25 GW/cm 2 . The CA Z-scan curves ( Figure 4b) for the three porphyrins in CH2Cl2 exhibit primary peak-valley configurations. Since the CA Z-scan result of CH2Cl2 solvent has a valley-peak configuration ( Figure 3), it is obvious that the presence of the curves in Figure 4b is attributed to the combined effect of porphyrins solute and CH2Cl2 solvent. Furthermore, the solvent contribution has reduced the actual magnitude of nonlinear refraction in these porphyrins due to the opposite signs of their nonlinear refraction. Therefore, all the measured porphyrins have a negative nonlinear refractive index. In addition, it is clear in Figure 4b that TPP(OMe)4 has the largest difference between the normalized transmittance at peak and valley positions. This implies a larger nonlinear refraction index of TPP(OMe)4 than those of TPP and TPP(CN)4. While TPP with the smallest magnitude of normalized transmittance holds a comparative absolute value of nonlinear refraction index compared with that of CH2Cl2. The theoretical curves are obtained from the best fits with the change in refractive index expressed as 2eff n n I Δ = , where, n2eff is the effective nonlinear refractive index. The curves are reasonably well matches with the experimental data. The true n2eff values for these molecules are extracted dependent on the experimental data in Figure 3 and Figure 4b, which are −1.9, −3.2 and −9.6 (×10 −6 cm 2 /GW) for TPP, TPP(CN)4, and TPP(OMe)4, respectively. TPP(CN)4 and TPP(OMe)4 have notable nonlinear refraction compared to their parent system TPP. Moreover, the nonlinear refraction of TPP(OMe)4 has a more remarkable enhancement.

Nanosecond Z-Scan Measurements
To examine the nonlinear properties of these porphyrins in nanosecond regime, we performed the Z-scan measurements with 6 ns laser pulses. Figure 5a gives the open aperture Z-scan curves. Each of the compounds displays RSA characters under the excitation of nanosecond pulses. The CA curves of these three porphyrins are all characterized by peak-valley configurations (Figure 5b), which indicate the negative nonlinear refractions due to the coexistence of electronic effect and thermal-lensing effect [38]. The buildup time of thermal lensing can be determined by ω0/υs [39]. ω0 is the laser beam radius at focus and it is ~19 μm in our Z-scan with 6 ns laser pulses. The velocity of sound υs in CH2Cl2 is 1090 m/s [39]. Hence, the calculated buildup time of thermal nonlinearity in our experiment is ~17.4 ns. Although it is longer than the pulse duration we used, the thermal lensing effect may even come into play, which belongs to the problem of the thermally induced optical nonlinearities in liquids in the transient regime [40]. Since the nonlinear absorption and refraction of the solvent under the identical experimental conditions are extremely weak, the both of them could be neglected in the ns regime. In the thin sample and slowly varying envelope approximations, the beam propagating equations separately governing the irradiance (I) and the phase (ϕ) are: ( ) Here, z' is the propagation length in the sample. Parameters α0 and βeff denote the linear and nonlinear absorption coefficients, respectively. k is the wavevector, and n2 is the nonlinear refraction coefficient. Δnth is the transient thermal index change induced by the heating of the solution as a result of the absorption of laser pulses. It is obtained by solving the photoacoustic wave equation [38,40], and it is expressed as Equation (3) (see [38,40] Herein, dn/dT is the rate of change of the index with respect to temperature and ΔT is the temperature change in the sample induced by the absorption of laser radiation, which is described by: ( ) The related parameters in the simulations are taken from Ref. [39], which are υs = 1090 m/s, dn/dT = 5.5 × 10 −4 K −1 , Cp = 1.6 × 10 3 J/(cm 3 K), respectively. The density of CH2Cl2 is ρ0 = 1.33 × 10 3 kg/m 3 . Based on the theory and the related parameters above, the nonlinear coefficients of these molecules could be extracted, which are 100, 150 and 360 cm/GW for TPP, TPP(CN)4, and TPP(OMe)4, respectively. Meanwhile the nonlinear refractive index of TPP, TPP(CN)4, and TPP(OMe)4 are −1.3, −1.7 and −4.6 (×10 −3 cm 2 /GW), respectively. Note that the electronic effect plays a dominant role in the nonlinear refraction of these three porphyrins. It can be seen that the electron-withdrawing substituent CN and electron-donating substituent OMe both have led to the enhancement of nonlinear refraction in the ps and ns regimes, whereas their effects on the nonlinear absorption property are weak as compared with that of TPP due to the different extent of linear absorption, except that TPP(OMe)4 has a SA-to-RSA switch in the case of ps pulses.

Second-Order Molecular Hyperpolarizabilities
As controlling of the second-order molecular hyperpolarizabilities (γ) is crucial for many applications in electronic and photonic devices, we calculated the γ values of the porphyrins investigated by the formulation Equation (5) [41]: where Nc is the molecular number density per cubic centimeter, L is the local-field correction factor, which is approximately to be ( ) ( ) (3) is the nonlinear susceptibility, which can be obtained by the real (Re χ (3) ) and imaginary (lmχ (3) ) parts of it by: Here, c is the speed of light, n0 is the linear refractive index of the sample, and ω is the angular frequency of the laser pulses. Recently, the second-order molecular hyperpolarizabilities of some porphyrin-related compounds in picosecond regime have been reported. Venugopal Rao et al. [42] have reported γ values at 532 nm, 35 ps from the DFWM measurements of sixteen porphyrins with different metal ions in the ring. The highest value of 1.432 × 10 −30 esu was observed for CoTPP. The difference of nonlinear optical nonlinearities between the porphyrins is attributed to the higher electron delocalization in the molecules. Chen et al. [41] have reported the second molecular hyperpolarizabilities of a azobenzene-phthalocyanine dyad measured by a Z-scan technique at 532 nm with a pulse duration of 25 ps. which are 3.87 × 10 −30 and 4.82 × 10 −30 esu before and after illumination with 365 nm UV light, respectively. Shi et al. [30] reported the second hyperpolarizabilities of four porphyrin-heteropolyoxometalate hybrid system and TPP, which are characterized by Z-scan measurements at 532 nm with a pulse duration of 20 ps. The γ value they calculated for TPP is 0.84 × 10 −30 esu. The other four compounds possess γ values between 0.49−1.2 × 10 −30 esu. Obviously, the γ value of TPP(OMe)4 in our study is remarkable larger than those of the related compounds mentioned above in the ps regime. The obtained results imply that the introduction of the cyano or methoxy groups into TPP has obviously tuned its refraction and absorption properties, leads to the enhancements of the nonlinear refraction and the second molecular hyperpolarizabilities, which is expected to provide useful reference for exploring porphyrin derivatives with much higher second hyperpolarizabilities [43].  [44].

Experimental Section
The nonlinear absorption and nonlinear refraction of TPP, TPP(CN)4 and TPP(OMe)4 were measured by Z-scan techniques in ps and ns regime. The light source of 21 ps (FWHM) pulses is generated from a Q-switched Nd: YAG laser (PL2143A, EKSPLA, Vilnius, Lithuania) with a wavelength of 532 nm. The laser system for nanosecond Z-scan was a Surelite Q-switched Nd:YAG 532 nm laser (Continuum, Santa Clara, CA, USA) with a pulse width of 6 ns (FWHM). The spatial profiles of both ps and ns pulses have a top-hat distribution. The Z-scan techniques were arranged as that reported by Yang et al. [45]. The beam waist at the focus is ~26 μm for ps and ~19 μm for ns, respectively. The porphyrins are dissolved in dichloromethane (CH2Cl2) with the same concentration of 8.14 × 10 −5 M and placed in 2 mm-thickness quartz cells, the corresponding linear absorption coefficients are 0.8, 1.1, and 5.8 cm −1 for TPP, TPP(CN)4, and TPP(OMe)4. The incident and transmitted pulses energies were measured simultaneously by the same type energy detectors (RjP-765a, Laser Probe Inc., Utica, NY, USA). The energy meter we used is a Laser Probe Inc., Rj-7620 ENERGY RATIOMETER.

Conclusions
The nonlinear absorption and nonlinear refraction properties of TPP, TPP(CN)4, and TPP(OMe)4 are measured by the Z-scan technique at 532 nm in the ps and ns regimes. TPP and TPP(CN)4 display an identical reverse saturable absorption (RSA) character in the ps and ns regimes. While TPP(OMe)4 exhibits a transition from saturable absorption (SA) to RSA in the ps regime, and a typical RSA character in the ns regime. Furthermore, TPP(CN)4 and TPP(OMe)4 show regular enhancement of the magnitude of nonlinear refraction compared to their parent TPP in both the ps and ns regimes. The obtained results related to the three porphyrins in both the ps and ns regimes suggest that the introduction of the cyan or methoxy group into TPP has obviously tuned its NLO properties, leads to the enhancements of the nonlinear refraction and the second molecular hyperpolarizabilities, which is useful for the development of porphyrin-related applications upon desired nonlinear optical properties.