## Z-scan study of thermal nonlinearities in silicon naphthalocyanine-toluene solution with the excitations of the picosecond pulse train and nanosecond pulse

Optics Express, Vol. 15, Issue 4, pp. 1718-1731 (2007)

http://dx.doi.org/10.1364/OE.15.001718

Acrobat PDF (304 KB)

### Abstract

Using the Z-scan technique, we studied the nonlinear absorption and refraction behaviors of a dilute toluene solution of a silicon naphthalocyanine (Si(OSi(*n*-hexyl)_{3})_{2}, SiNc) at 532 nanometer with both a 2.8-nanosecond pulse and a 21-nanosecond (HW1/eM) pulse train containing 11 18-picosecond pulses 7 nanosecond apart. A thermal acoustic model and its steady-state approximation account for the heat generated by the nonradiative relaxations subsequent to the absorption. We found that when the steady-state approximation satisfactorily explained the results obtained with a 21-nanosecond pulse train, only the thermal-acoustic model fit the 2.8-nanosecond experimental results, which supports the approximation criterion established by Kovsh et al.

© 2007 Optical Society of America

## 1. Introduction

2. J. S. Shirk, J. R. Lindle, F. J. Bartoli, C. A. Hoffman, A. H. Kafafi, and A. W. Snow, “Off-resonat third-order optical nonlinearities of meta-substituted phthalocyanines,” Appl. Phys. Lett **55**,1287–1288 (1989). [CrossRef]

3. T. H. Wei, D. J. Hagan, M. J. Sence, E. W. V. Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B **54**,46–51 (1992). [CrossRef]

7. T. Tomiyama, I. Watanabe, A. Kuwano, M. Habiro, N. Takane, and M. Yamada, “Rewritable optical-disk fabrication with an optical recording material made of naphthalocyanine and polythiophene,” Appl. Opt **34**,8201–8208 (1995). [CrossRef] [PubMed]

8. J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, “Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics,” Pure and Appl. Chem **68**,1429–1434 (1996). [CrossRef]

*Z*-scan technique, we characterized the nonlinear absorption and refraction properties of a silicon naphthalocyanine (Si(OSi(

*n*-hexyl)

_{3})

_{2}, dubbed SiNc)-toluene solution at 532 nanometer (nm). Using a laser pulse with a width of τ= 2.8 nanoseconds (ns) (HW1/eM) and a Gaussian distributed train, composed of 11 18-picosecond (ps) pulses 7 ns apart, with an envelope width of τ

_{env}= 21 ns, nonradiative relaxations induced a thermal lensing effect (∆

*n*), in addition to internal nonlinearities, is expected to contribute to the nonlinearities. ∆

_{therm}*n*results from a temperature rise (∆θ), caused by nonradiative relaxation subsequent to optical excitation, and the solvent density change (∆ρ) induced by a ∆θ-driven thermal acoustic wave. Strictly speaking, ∆ρ needs to be derived by solving the thermal acoustic wave; however, a steady-state approximation of the wave equation can be made to simplify the calculation of ∆ρ provided that the pulse duration is more than 1.5 times longer than the thermal transit time τ

_{therm}_{ac}(time for the acoustic wave to propagate across the beam cross section) [9

9. D. I. Kovsh, S. Yang, D. J. Hagan, and E. W.Van Stryland, “Nonlinear optical beam propagation for optical limiting,” Appl. Opt **38**,5168–5180 (1999). [CrossRef]

*ν*= 1170 m/s for the solvent (toluene)[10

_{s}10. P. Brochard and V. Grolier-Mazza, “Thermal nonlinear refraction in dye solution: a study of the transient regime,” J. Opt. Soc. Am. B **14**,405–414 (1997). [CrossRef]

*w*

_{0}= 14.1 μm and 18.9 μm (HW1/e

^{2}M for both) in this study. This resulted in τ

_{ac}=

*w*

_{0}/

*ν*= 12.0 ns for the 2.8-ns pulse and τ

_{s}_{ac}=

*w*

_{0}/

*ν*= 16.2 ns for the pulse train. The steady state approximation was relatively appropriate for a 21-ns pulse train (τ

_{s}_{env}/τ

_{ac}= 1.3) compared with a 2.8-ns pulse (t/tac = 0.2). In this paper, we respectively derive ∆ρ by strictly solving the thermal acoustic wave equation and from the steady state approximation for both a 2.8-ns pulse and a 21-ns pulse train. As a result, ∆ρ obtained using both approaches yields close Δ

*n*’s for a 21-ns pulse train but causes significantly different ∆

_{therm}*n*’s for a 2.8-ns pulse (

_{therm}*νide infra*).

## 2. Experiments

*Z*-scan technique (Fig. 1) is a simple yet sensitive technique for measuring the nonlinear absorption and refraction of materials. Its operation has been described in detail by Sheik-Bahae

*et al*. [11

11. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W.Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron **26**,760–769 (1990). [CrossRef]

_{1}splits and directs a small portion of the incident pulse to the detector D

_{4}, which monitors the fluctuation of the incident pulse energy. The rest of the pulse is tightly focused by a lens and transmitted through the sample at various positions (

*z*) relative to the beam waist at

*z*= 0. The beam splitter BS2 divides the transmitted pulse into two and directs them to detectors D

_{6}and D

_{5}. When D

_{6}monitors the total transmitted pulse energy, D

_{5}, which has an aperture in front, measures the energy of the axial portion of a transmitted pulse. With the sample in the linear regime, we carefully adjusted the aperture radius to allow 40% of the transmitted energy to reach D

_{5}. We devided D

_{6}and D

_{5}by D

_{4}and then normalized the values with the corresponding values obtained in the linear regime (at the starting

*z*), which yielded the normalized transmittance (NT) and the normalized axial transmittance (NT

_{a}) as a function of sample position

*z*. Because D

_{6}(which has no aperture) collected all the transmitted energy, NT involves nonlinear absorption alone. The partially obstructed D

_{5}reflects beam broadening or narrowing at the aperture, a result of nonlinear refraction, in addition to nonlinear absorption. NT

_{a}reveals, therefore, not only the nonlinear absorption, but also the nonlinear refraction. If we divide NT

_{a}by NT, the resultant ratio (NT

_{d}) retains only the information of nonlinear refraction.

_{00}mode at 10 Hz. The incident intensity (Fig. 2) and phase of the

*n*th pulse in a train are, respectively,

*w*(

*z*) =

*w*

_{0}[1+(

*z*/

*z*

_{0})

^{2}]

^{1/2}is the laser beam radius (HW1/e

^{2}M) at

*z*.

*w*

_{0}denotes

*w*(0) and equals 21 μm.

*I*

_{00}

^{(n)}is the on-axis peak intensity at

*z*= 0. τ is the pulse width (HW1/eM) and equals 18 ps.

*t*and

*r*refer to the temporal distribution of the intensity relative to the peak of the 0th pulse and the lateral distribution of the laser beam, respectively.

*k*= 2π/λ (λ = 532 nm) is the wave propagation number.

*R*(

*z*) =

*z*[1+(

*z*

_{0}/

*z*)

^{2}] is the curvature radius of the wave front at

*z*.

*z*

_{0}= π

*w*

^{2}

_{0}/λ is the diffraction length. All the above-introduced parameters pertain to free space. Integration of Eq. (1) over the pulse width (from -∞ to ∞) and the beam cross section relates

*I*

_{00}

^{(n)}to the pulse energy ε

_{(n)}as

_{env}= 21 ns, the energy of the

*n*th pulse is

*n*= -5 to 5, we obtain the full pulse train energy ε

_{t}, with which ε

^{(n)}is expressed as

*I*

_{00}

^{(n)}needed in our theoretical analysis is derived from ε

_{t}, experimentally measured by D

_{4}, via Eqs. (3)–(5).

_{t}= 0.8 μJ and 1.4 μJ, and a 2.8-ns pulse with a pulse energy of ε = 1.4 μJ and 2.5 μJ, we performed, at room temperature

*θ*= 25 °C,

_{e}*Z*-scan measurements on a SiN c-toluene solution with a concentration of 6.1 × 10

^{17}cm

^{-3}and contained in a 1-mm-thick quartz cell.

## 3. Theoretical model

12. D. G. Mclean, R. L. Sutherland, M. C. Brant, D. M. Brandelik, P. A. Fleitz, and T. Pottenger. “Nonlinear absorption study of a C60-toluene solution,” Opt. Lett **18**,858–860 (1993). [CrossRef] [PubMed]

*ν*0) and vibronic level

*ν*≠ 0), is conventionally named

*S*for the singlet manifold and

_{i}*T*for the triplet manifold (Fig. 3). The subscript

_{i}*i*refers to the ordering of the electronic states. At thermodynamic equilibrium, all SiNc molecules reside in S

_{0}and the solution has an equilibrium temperature of θ

_{e}= 25 °C and a solvent density of ρ

*= 0.79 g.cm*

_{e}^{-3}throughout the solution. The equations governing the intensity attenuation and phase change with the penetration depth

*z*’ into the sample can be written as[14

14. T. H. Wei and T. H. Huang, “A study of photophysics using the Z-scan technique: lifetime determination for high-lying excited states,” Opt. and Quantum Electron **28**1495–1508 (1996). [CrossRef]

*I*and ϕ are the intensity and phase, respectively, of a 2.8-ns pulse or an individual 18-ps pulse within each train. α is the absorption coefficient and ∆

*n*denotes the refractive index change. In Eqs. (7) and (8),

*I*and ϕ changes are contributed to the one-photon excitations

*S*

_{0}→

*ν*)S

_{1},

*S*

_{1}→∣

*ν*)

*S*

_{2}, and

*T*

_{1}→∣

*ν*)

*T*

_{2}represented by their first three terms. σ

*a*in Eq. (7) denotes the absorption cross section of the states specified by the subscripts. The

*σr*, the refractive cross section, of a band can be derived from

*σa*associated with the same band according to the Kramers-Krönig relation. The 4th terms in Eqs. (7) and (8) pertain to the two-photon excitation

*S*

_{0}→∣

*ν*)

*S*

_{2}. The 5th term in Eq. (8) denotes the Kerr effect of the solvent (toluene),

*n*

_{2}= 5.5 × 10

^{-15}cm

^{2}/W, and the 6th term of Eq. (8) represents the thermal effect where Δ

*n*will be respectively estimated via Eq. (18) in combination with Eq. (16) or via Eq. (19) alone in this study (

_{therm}*νide infra*). Combining optical excitation with a 532-nm pulse and the subsequent relaxation, the population redistributes in various states with time rates of [13]

*N*and τ are respectively the population density and relaxation time

*S*

_{0}-∣

*ν*)

*S*

_{1}and two-photon-absorption

*S*

_{0}∣

*ν*)

*S*

_{2}induced population-density redistributions between

*S*

_{0}and ∣

*ν*)

*S*

_{1}are denoted by the first two terms of Eqs. (9) and (10). Nonradiative relaxations ∣

*ν*)

*S*

_{1}⇝∣ 0)

*S*

_{1}and ∣

*ν*)

*S*

_{2}⇝∣ 0)

*S*

_{1}are assumed to follow the above mentioned excitations well within the pulse width (18 ps or 2.8 ns) [14

14. T. H. Wei and T. H. Huang, “A study of photophysics using the Z-scan technique: lifetime determination for high-lying excited states,” Opt. and Quantum Electron **28**1495–1508 (1996). [CrossRef]

*S*

_{1}⇝

*S*

_{0}induced population redistributions between ∣ 0)

*S*

_{1}and

*S*

_{0}, τ

_{f}being the lifetime and equal to 3.1 ns [1]. Population redistribution between ∣ 0)

*S*

_{1}and ∣ 0)

*T*

_{1}via intersystem crossing (ISC) ∣ 0)

*S*

_{1}⇝∣

*ν*)

*T*

_{1}⇝∣ 0)

*T*

_{1}is expressed by the 4th term of Eq. (10) and the 1 st term of Eq. (11), respectively, τ

_{ISC}being the lifetime and equal to 16 ns [16

16. J. H. Brannon and D. Madge, “Picosecond laser Photophysics. group 3A phthalocyanines,” J. Am. Chem. Soc **102**,62–65 (1980). [CrossRef]

*T*

_{1}and

*S*

_{0}as a result of intersystem crossing (ISC) ∣ 0)

*T*

_{1}⇝

*S*

_{1}, is expressed by the 4th term of Eq. (9) and the 2nd term of Eq. (11), respectively, τ

_{T1}being the lifetime and falling in the μs regime [17]. Since ∣ 0)

*T*

_{1}→∣

*ν*)

*T*

_{2}absorption is verified in this paper (

*νide infra*), we neglect the population redistributions between ∣0)

*T*

_{1}and ∣

*ν*)

*T*

_{2}because the ∣

*ν*)

*T*

_{2}⇝∣ 0)

*T*

_{2}⇝∣

*ν*)

*T*

_{1}⇝∣ 0)

*T*

_{1}relaxation subsequent to the excitation is believed to be much shorter than the pulse widths (18 ps or 2.8 ns) [14

14. T. H. Wei and T. H. Huang, “A study of photophysics using the Z-scan technique: lifetime determination for high-lying excited states,” Opt. and Quantum Electron **28**1495–1508 (1996). [CrossRef]

18. C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines,” Phys. Rev. A **49**,1149–1157 (1994). [CrossRef] [PubMed]

*ν*)

*S*

_{1}⇝∣ 0)

*S*

_{1}, ∣

*ν*)

*S*

_{2}⇝∣ 0)

*S*

_{1}, and ∣

*ν*)

*T*

_{1}⇝∣ 0)

*T*

_{1}[18

18. C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines,” Phys. Rev. A **49**,1149–1157 (1994). [CrossRef] [PubMed]

*Q*denotes the thermal energy accumulated within the solute molecules per unit volume. The first term on the right-hand side represents the heat generated via ∣

*ν*)

*S*

_{1}⇝ ∣ 0)

*S*

_{1}relaxation subsequent to the

*S*

_{0}→ ∣

*ν*)

*S*

_{1}excitation. ω

_{S1}(λ

_{S1}= 780 nm) corresponds to the energy of ∣ 0)

_{S1}relative to

*S*

_{0}. The second and third terms describe the contributions of the sequential ∣

*ν*)

*S*

_{2}⇝∣ 0)

*S*

_{2}⇝∣

*ν*)

*S*

_{1}⇝∣ 0)

*S*

_{1}relaxations following the one-photon ∣ 0)

*S*

_{1}→∣

*ν*)

*S*

_{2}excitation and the two-photon

*S*

_{0}→∣

*ν*)

*S*

_{2}excitation, respectively. The last term describes the contribution of the sequential relaxations, ∣

*ν*)

*T*

_{2}⇝∣ 0)

*T*

_{2}⇝∣

*ν*)

*T*

_{1}⇝∣ 0)

*T*

_{1}, following the one-photon excitation ∣ 0)

*T*

_{1}→∣

*ν*)

*T*

_{2}.

*Q*) dissipates throughout the surrounding solvent molecules in a local thermal equilibrium time τ

_{therm}. For the concentration (6.1 × 10

^{17}cm

^{-3}) of present interest, τ

_{therm}is estimated to be 65 ps [19

19. T. H. Wei, T. H. Huang, and M. S. Lin, “Signs of nonlinear refraction in chloroaluminum phthalocyanine solution,” Appl. Phys. Lett **72**,2505–2507 (1998). [CrossRef]

_{therm}is significantly shorter than its pulse width, ∆θ is considered to increase simultaneously with

*Q*when the sample is interacting with a 2.8-ns pulse. As a result, ∆θ at time

*t*can be obtained as

*t*= -∞) encounters the sample, ∆θ = 0. In Eq. (13)

*C*denotes the isobaric specific heat and equals 1.71 J/g°C for toluene [20]. On the other hand, because τ

_{p}_{therm}is considerably longer than its width, an individual 18-ps pulse, say the

*n*th, in a 21-ns train does not experience the thermal lensing effect induced by itself, but yields a temperature rise of

*n*is introduced to single out ∆θ and

*Q*caused by the

*n*th pulse. Denoting the leading pulse in a train as the -5th one, the

*n*th pulse in a train encounters the sample with a temperature rise of

_{ISC}=16 ns) and μs order for τ

_{T1}are greatly longer than the relaxation time constants

*S*1 ⇝∣

*ν*)

*T*

_{1}⇝∣ 0)

*T*

_{1}and ∣ 0)

*T*

_{1}⇝

*S*

_{0}relaxations are ignored.

*ν*is the velocity of the acoustic wave and equals 1170 m/s,

_{s}*b*= -ρ(∂ρ/∂θ)

_{p}, with the subscript

*p*denoting the pressure, is the volume expansivity and equals 1.25 × 10

^{-3}(°C

^{-1})[20], and γ

_{e}= ρ(∂

*n*

^{2}/∂ρ)

_{θ}is the electrostrictive coupling constant. All the parameters pertain to the solvent (toluene). According to the Lorenz-Lorenz law, γ

_{e}can be expressed as (

*n*

^{2}- 1){

*n*

^{2}+ 2)/3 with

*n*denoting the refractive index [21

21. D. I. Kovsh, D. J. Hagan, and E. W. Stryland, “Numerical modeling of thermal refraction in liquids in the transient regime,” Opt. Express **4**,315–327 (1999). [CrossRef] [PubMed]

*n*

_{0}= 1.49 for toluene [20], γ

_{e}is estimated to be 1.71. As will be shown later, the second term on the right-hand side of Eq. (16) (the electrostrictive effect) does not play a significant role compared with the first term (thermal effect) for our absorptive solution [21

21. D. I. Kovsh, D. J. Hagan, and E. W. Stryland, “Numerical modeling of thermal refraction in liquids in the transient regime,” Opt. Express **4**,315–327 (1999). [CrossRef] [PubMed]

*I*, into Eq. (16) to solve for ∆ρ with the initial condition of ∆ρ = 0 and ∂(∆ρ)/∂

*t*= 0 at

*t*= - ∞. Regarding the interaction of the

*n*th 18-ps pulse in a train with the solution, we substitute ∆θ derived from Eq. (15), in combination with

*I*, into Eq. (16) to derive ∆ρ for the

*n*th pulse to experience. Time integrations of ∂

^{2}(∆ρ)/∂

*t*

^{2}and ∂(∆ρ)/∂

*t*over the pulse separation of 7 ns are involved in solving the differential Eq. (16). Accompanying these integrations, ∆ρ and ∂(∆ρ)/∂

*t*experienced by the (

*n*- 1)th pulse are used as the initial conditions. Given ∆ρ = ∂(∆ρ)/∂

*t*= 0 for the leading (-5th) pulse, ∆ρ and ∂(∆ρ)/∂

*t*for each later pulse in a train can be obtained one by one. Once after ∆θ and ∆ρ are obtained for a 2.8-ns pulse or a 21-ns pulse train, thermally induced refractive index change can be deduced as

21. D. I. Kovsh, D. J. Hagan, and E. W. Stryland, “Numerical modeling of thermal refraction in liquids in the transient regime,” Opt. Express **4**,315–327 (1999). [CrossRef] [PubMed]

*n*/∂ρ)

_{θ}= γ

_{e}/2

*n*ρ, as derived from γ

_{e}= ρ(∂

*n*

^{2}/∂ρ)

_{θ}, Eq. (17) can be approximated as

_{env}is considerably longer than τ

_{ac}, the second-order time derivative of ∆ρ, i.e., the 1st term on the left-hand side of Eq. (16), can be ignored. This simplifies Eq. (16) as ∆ρ = -

*b*ρ∆θ + γ

_{e}

*I*/2

*ncv*

^{2}

_{s}, which in turn approximates Eq. (18

18. C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines,” Phys. Rev. A **49**,1149–1157 (1994). [CrossRef] [PubMed]

*Z*-scan experiments are numerically fitted by calculating the normalized transmittance (NT) and the normalized axial transmittance (NT

_{a}). Via Eqs. (7) and (8), we integrate through the thickness of the sample to obtain the intensity and the phase at the exit surface of the sample considering the initial input intensities given by Eqs. (1) to (5) and by Eq. (6) for ps pulse trains and ns pulses, respectively. Huygens-Fresnel formalism is thus applied to calculate the intensity distribution at the aperture. (σ

*a*)

_{S0}= 2.8 × 10

^{-18}cm

^{2}, (σ

*a*)

_{S1}= 5.0 × 10

^{-17}cm

^{2}, (σ

*r*)

_{S0}≅ 0, β = 0, (σ

*r*)

_{S1}= 1.2 × 10

^{-18}cm

^{2}, γ=0, and

*n*

_{2}= 5.5 × 10

^{-15}cm

^{2}/W were previously determined in the study with single 18-ps pulses switched out of the pulse trains using a Pockels cell [24]. The triplet contributions and thermal effect were ignored in the fitting because the pulse duration is much shorter than both the intersystem crossing time and the thermal lensing formation time. The population densities required in Eqs. (7) and (8) are functions of both space and time. The dynamic behaviors can be obtained by calculating the rate equations (9) to (11).

## 4. Results and discussion

*Z*-scan data below, NT and NT

_{a}are marked with triangles and squares, respectively. NT

_{d}is marked with dots. Solid lines and dash lines represent the theoretical fitting with Δ

*n*from Eq. (18) in combination with Eq. (16) and that with Eq. (19) alone. We will discuss the results of the two different input excitations separately.

_{therm}### 4.1. Pulse train results

_{t}=0.8 μJ and 1.4 μJ. There are two parameters, (σ

*a*)

_{T1}and (σ

*r*)

_{T1}, undetermined by the single 18-ps pulse

*Z*-scan experiments. Using (σ

*a*)

_{T1}= 6.0 × 10

^{-17}cm

^{2}and (σ

*r*)

_{T1}= -5.5 × 10

^{-17}cm

^{2}, we best fit the results with ∆

*n*

_{therm}, determined using Eq. (18) in combination with Eq. (16). However, only a small deviation is generated when ∆

*n*

_{therm}is determined using Eq. (19) alone given

*dn*/

*dθ*≈ (

*∂n*/

*∂ρ*)

_{θ}(∂ρ/∂θ)

_{p}= -

*bγe*/(2

*n*), estimated to be -6.0× 10

^{-4}(°C

^{-1}) using

*n*= 1.49. Therefore, we claim that the ratio of τ

_{env},τ

_{ac}=1.3 can be considered large enough to satisfy the steady-state assumption.

_{d}is greater than 1 before, and less than 1 after, the beam waist in the

*Z*-scan data (Figs. 4(c) and 5(c)). This type of

*Z*-scan data indicates that the solution possesses negative nonlinear refraction, which we would expect from an absorptive liquid solution [11

11. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W.Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron **26**,760–769 (1990). [CrossRef]

*I*. Although the induced index refraction change is linearly proportional to the incident energy, the distortion of the refracted laser pulse in the far field (where the aperture is located) does not possess the proportionality when the induced thermal lens is strong. Therefore, the discrepancies (or errors) between the approximated simulation curve and the acquired

*Z*-scan data are not expected to follow the variation of the incident pulse energies. We must also realize that

*Z*-scan experimental data is obtained using an energy meter which neglects the fine spatial dependence even in a closed-aperture setup. Actually, the result obtained from the averaged steady-state equation, Eq. (19), can occasionally even out-fit the one obtained from the thermal-acoustic equation, Eq. (18), in combination with Eq. (16), because Eq. (16) is an approximation as well.

### 4.2. 2.8-ns pulse results

*Z*-scan results. While the steady state equation, Eq. (19), could not be applied to the

*Z*-scan data, the thermal acoustic equation, Eq. (18), in combination with Eq. (16), still produced an excellent fit. Observed from a larger variation of the steady-state prediction than the experimental data in Figs. 6 and 7, it is clear that the thermal-induced negative-lensing effect is still building up within the duration of a 2.8-ns laser pulse, as the thermal acoustic equation successfully predicted.

## 5. Conclusion

*Z*-scan technique to the SiNc-toluene solution and quantitatively accounted for the energy transfer between the energy bands in the solute molecules and the heat generated from the non-radiative relaxations. The thermal-lensing effect due primarily to the density change in the solvent toluene was presented, and the resultant thermal-acoustic model was verified using two excitations: 2.8-ns pulses and 18-ps pulse trains. The validity of the simplified steady-state model was also examined. By introducing the thermal models, the internal nonlinearities of metallo-phthalocyanine molecules can be better characterized using the

*Z*-scan technique, and the energy transfer from the molecules to the surrounding solvent can also be more accurately modeled.

## Acknowledgments

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6. | S. R. Mishra, H. S. Rawat, M. P. Joshi, and S. C. Mehendale, “The role of non-linear scattering in optical limiting in C60 solution,” J. Phys. B:At. Mol. Phys. |

7. | T. Tomiyama, I. Watanabe, A. Kuwano, M. Habiro, N. Takane, and M. Yamada, “Rewritable optical-disk fabrication with an optical recording material made of naphthalocyanine and polythiophene,” Appl. Opt |

8. | J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, “Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics,” Pure and Appl. Chem |

9. | D. I. Kovsh, S. Yang, D. J. Hagan, and E. W.Van Stryland, “Nonlinear optical beam propagation for optical limiting,” Appl. Opt |

10. | P. Brochard and V. Grolier-Mazza, “Thermal nonlinear refraction in dye solution: a study of the transient regime,” J. Opt. Soc. Am. B |

11. | M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W.Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron |

12. | D. G. Mclean, R. L. Sutherland, M. C. Brant, D. M. Brandelik, P. A. Fleitz, and T. Pottenger. “Nonlinear absorption study of a C60-toluene solution,” Opt. Lett |

13. | T. H. Wei, T. H. Huang, S. Yang, D. Liu, J. K. Hu, and C. W. Chen, “Z-scan study of optical nonlinearity in C60-toluene solution,” Mol. Phys |

14. | T. H. Wei and T. H. Huang, “A study of photophysics using the Z-scan technique: lifetime determination for high-lying excited states,” Opt. and Quantum Electron |

15. | A. Seilmeier and W. Kaiser, in |

16. | J. H. Brannon and D. Madge, “Picosecond laser Photophysics. group 3A phthalocyanines,” J. Am. Chem. Soc |

17. | C. Jensen |

18. | C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines,” Phys. Rev. A |

19. | T. H. Wei, T. H. Huang, and M. S. Lin, “Signs of nonlinear refraction in chloroaluminum phthalocyanine solution,” Appl. Phys. Lett |

20. | D. R. Lide. in |

21. | D. I. Kovsh, D. J. Hagan, and E. W. Stryland, “Numerical modeling of thermal refraction in liquids in the transient regime,” Opt. Express |

22. | D. Landau and E. M. Lifshitz, in |

23. | J. -M. Heritier, “Electrostrictive limit and focusing effects in pulsed photoacoustic detection,” Opt. Comm |

24. | C. W. Chang and M. S. thesis, National Chung Cheng University, pp. 28, (1999). |

**OCIS Codes**

(000.6850) General : Thermodynamics

(190.4710) Nonlinear optics : Optical nonlinearities in organic materials

(190.4870) Nonlinear optics : Photothermal effects

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: November 21, 2006

Revised Manuscript: January 26, 2007

Manuscript Accepted: January 29, 2007

Published: February 19, 2007

**Citation**

Sidney S. Yang, Tai-Huei Wei, Tzer-Hsiang Huang, and Yun-Ching Chang, "Z-scan study of thermal nonlinearities in silicon naphthalocyanine-toluene solution with the excitations of the picosecond pulse train and nanosecond pulse," Opt. Express **15**, 1718-1731 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-4-1718

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### References

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- T. Tomiyama, I. Watanabe, A. Kuwano,M. Habiro, N. Takane, andM. Yamada, "Rewritable optical-disk fabrication with an optical recording material made of naphthalocyanine and polythiophene," Appl. Opt. 34, 8201-8208 (1995). [CrossRef] [PubMed]
- J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, "Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics," Pure and Appl. Chem. 68, 1429-1434 (1996). [CrossRef]
- D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, "Nonlinear optical beam propagation for optical limiting," Appl. Opt. 38, 5168-5180 (1999). [CrossRef]
- P. Brochard and V. Grolier-Mazza, "Thermal nonlinear refraction in dye solution: a study of the transient regime," J. Opt. Soc. Am. B 14, 405-414 (1997). [CrossRef]
- M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990). [CrossRef]
- D. G. Mclean, R. L. Sutherland, M. C. Brant, D. M. Brandelik, P. A. Fleitz, T. Pottenger. "Nonlinear absorption study of a C60-toluene solution," Opt. Lett. 18, 858-860 (1993). [CrossRef] [PubMed]
- T. H. Wei, T. H. Huang, S. Yang, D. Liu, J. K. Hu and C. W. Chen, "Z-scan study of optical nonlinearity in C60-toluene solution," Mol. Phys. 103, 1847-1857 (2005).
- T. H. Wei and T. H. Huang, "A study of photophysics using the Z-scan technique: lifetime determination for high-lying excited states," Opt. and Quantum Electron. 28, 1495-1508 (1996). [CrossRef]
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- J. H. Brannon and D. Madge, "Picosecond laser Photophysics. group 3A phthalocyanines," J. Am. Chem. Soc. 102, 62-65 (1980). [CrossRef]
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- T. H. Wei, T. H. Huang, and M. S. Lin, "Signs of nonlinear refraction in chloroaluminum phthalocyanine solution," Appl. Phys. Lett. 72, 2505-2507 (1998). [CrossRef]
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- D. I. Kovsh, D. J. Hagan, and E.W. Stryland, "Numerical modeling of thermal refraction in liquids in the transient regime," Opt. Express 4, 315-327 (1999). [CrossRef] [PubMed]
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- J. -M. Heritier, "Electrostrictive limit and focusing effects in pulsed photoacoustic detection," Opt. Comm. 44, 267-272 (1983). [CrossRef]
- C. W. Chang, M. S. thesis, National Chung Cheng University, pp. 28, (1999).

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