Abstract

Based on the simplified five-level rate-equation theory, we investigate the hybrid third-order optical nonlinear processes which combine the instantaneous nonlinearity and the one-photon absorption induced excited-state nonlinearity. We obtain the analytical third-order nonlinear absorption and refraction coefficients originating from the singlet and triplet excited-state effects. We explore the photodynamic process and give the corresponding level diagram in the nanosecond, picosecond, and femtosecond regimes. We develop the pulse-duration-dependent Z-scan theory for characterizing the simultaneous instantaneous nonlinearity and cumulative effect of the excited-state nonlinearity. We also demonstrate the validity of the presented theory to analyze the experimental results.

© 2010 Optical Society of America

1. Introduction

Interaction of light with matter, which leads to abundant nonlinear optical phenomena, plays a crucial role in modern optics [1]. Optical nonlinearity may modify either the direction of propagation, phase, or spatiotemporal characteristics of an optical pulse through nonlinear medium. Alternatively, for nonlinear optical materials, the ability of transferring, processing and storing information offers the basis of photonic technology. To exploit the potential applications of the nonlinear optical material, it is imperative to accurately determine the nonlinear parameters and then to understand the photodynamic behaviors. The nonlinear optical processes may involve electronic Kerr effect, multiphoton absorption, and excited-state nonlinearity [2].

There is an extensive interest in understanding the excited-state nonlinearity of organic materials due to the academic interest and the practical applications [36]. The excited-state nonlinearity has been investigated in a variety of organic materials such as organic dyes [7, 8], conjugated molecules and polymers [913], charge transfer molecules [14], and miscellaneous molecules [1517]. In addition, the experimental observations have revealed that the optical nonlinearities depend strongly on the pulse duration of the excitation laser [1419]. The optical nonlinearities measured in nanosecond regime could be two orders of magnitude greater that in picosecond regime [1519]. To gain insight into the underlying mechanism behind the observed optical nonlinearities, some energy-level diagrams have been presented, such as three-level [20], four-level [3], and five-level models [6,17]. To understand the photodynamic process, multilevel rate-equation analysis, which requires a complex numerical computation, is usually adopted. For the experimentalists, it is highly expected to seek an analytical theory that could adequately explain and reliably predict the observed optical nonlinearities within a reasonable degree of approximation.

In the present article, based on the simplified five-level rate-equation theory, we investigate the hybrid third-order optical nonlinear processes which combine the instantaneous nonlinearity and the cumulative nonlinearity of excited-state nonlinearity induced by one-photon absorption (1PA). We give the high-accuracy approximate analytical results for the effective third-order nonlinear coefficients caused by excited-state absorption and refraction. We explore the nonlinear photodynamics process and give the corresponding level diagrams at different timescales. We develop the pulse-duration-dependent Z-scan theory under the thin sample approximation, with simultaneous instantaneous nonlinearity and cumulative nonlinearity caused by the excited-state effect. We also verify the validity of the present theory by analyzing the published experimental data.

2. Theory

As is well known, the photodynamic process for the excited-state enhancement of the third-order nonlinear absorption (NLA) process can be described by the five-level model illustrated in Fig. 1(a). This five-level model involves the excited-state absorption (ESA) from excited singlet and triplet states, as well as two-photon absorption (2PA) between singlet states. The photodynamic process in this system can be described as follows. Electrons in the singlet ground state S0 can be promoted to the singlet excited states S1 and Sh, based on 1PA and 2PA, respectively. The electrons in S1 may relax to S0 by a radiative or nonradiative transition, undergo the intersystem crossing to the lowest triplet state T1 through a spin-flip process, or be promoted to the higher-lying singlet state Sh by absorbing another photon. For an electron in T1, it may relax to S0 by a phosphorescence process or be promoted to Th by absorbing another photon. Consequently, the nonlinear absorption process in this system happens the transition processes as follows: (i) S0S1 by 1PA, (ii) S0Sh by instantaneous 2PA, (iii) S0S1Sh by a two-step 2PA, and (iv) T1Th by ESA. At the same time, 1PA populates new electronic state, which could be an excited bound state in an organic molecule. Besides the optical Kerr effect caused by the distortion of the electron cloud, the significant population redistribution also produces an additional change in the refractive index, leading to the 1PA-induced excited-state refraction (ESR).

 

Fig. 1 (a) The five-level diagram and the typical decay lifetimes of the 1PA-induced singlet and triplet ESAs as well as 2PA. Simplified level diagram for (b) 2PA, (c) 2PA and 1PA-induced singlet ESA, and (d) 1PA-induced triplet ESA.

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Under the five-level model, the rate equations for populations of states can be described by

NS0t=σ0Ih¯ωNS0βI22ħω+NS1τS1+NT1τT1,
NS1t=σ0IħωNS0σS1IħωNS1NS1τS1NS1τisc+NShτSh,
NSht=βI22ħω+σS1IħωNS1NShτSh,
NT1t=σT1IħωNT1+NS1τisc+NThτThNT1τT1,
NTht=σT1IħωNT1NThτTh,
N=NS0+NS1+NSh+NT1+NTh,
where σ0, σS1, and σT1 are the absorptive cross-sections of the ground state S0, the first excited singlet state S1, and the lowest triplet state T1, respectively. β is the 2PA coefficient from S0 to Sh. τj is the lifetime of the state j (j = S1, Sh, T1, Th) and τisc is the intersystem crossing time from S1 to T1, in particular, their typical values for the organic materials at room temperature [1417] are shown in Fig. 1(a). N and Nj are the total number density and the number density of the state j, respectively. h̄ω is the incident photon energy.

Under the thin sample approximation, the intensity and phase changes of the optical field within the sample obey the following equations

Iz=(σ0NS0+σSNS1+σTNT1+βI)I,
Δϕz=k(γI+ηSNS1+ηTNT1),
where z′ is the propagation length inside the sample, γ is the optical Kerr refraction index, ηS and ηT are the refractive cross-sections of the first excited singlet state and the lowest triplet state, respectively, and k is the wave vector in free space.

It should be noted that Eqs. (1) and (2) are sufficient for describing the characteristics of the transmitted optical field. However, for the data analysis, the complex numerical calculation is required [8]. In fact, the timescale of the pulse duration for the laser irradiation is usually tens of nanoseconds to hundreds of femtoseconds. In what follows, we neglect the populations on both Sh and Th because both τSh and τTh are much smaller than the used pulse duration. Furthermore, we assume that the S0 state is not sufficiently depleted for the incident optical intensity, i.e. NS1N and NT1N, and then we can take NS0N. Considering the laser pulses with a Gaussian temporal profile, we have I(t) = I0 exp(−t22), where τ is the half-width at e1 of the maximum for the pulse duration (τF and τ are related by τF=2ln2τ, where τF is the full width at half maximum of the pulse). The above-mentioned approximations are adopted because this condition (Z-scan measurements at relatively low irradiance) is easily satisfied. Most importantly, within the reasonable approximation, the obtained theory could adequately interpret and reliably predict the photodynamic process of the materials under the pulsed excitation of different time scales, as we demonstrate below. Under these conditions, the population densities of S1 and T1 are given by

NS1(t)=α0ħωG(t)exp(t2/τ2)I(t),
NT1(t)=α0φTI0ħωτStG(t)exp[(tt)/τT1]dt,
where
G(t)=texp(t2/τ2)exp[(tt)/τS]dt.
Here τS (with τS1=τS11+τisc1) is the effective lifetime of the first singlet state, α0 = σ0N is the linear absorption coefficient, and φT = τS/τisc is the triplet quantum yield.

Substituting Eq. (3) into Eq. (2), we obtain

I(r,z;t)z=α0I(r,z;t)[β+αS(t)+αT(t)]I2(r,z;t),
Δϕ(r,z;t)z=k[γ+nS(t)+nT(t)]I(r,z;t),
where
αS(t)=σSα0ħωexp(t2/τ2)G(t),
αT(t)=σTα0φTħωτSexp(t2/τ2)tG(t)exp[(tt)/τT]dt,
nS(t)=ηSα0ħωexp(t2/τ2)G(t),
nT(t)=ηTα0φTħωτSexp(t2/τ2)tG(t)exp[(tt)/τT]dt.
Obviously, the 1PA-induced excited-state nonlinearity can be considered to be an effective third-order process. Furthermore, this accumulative nonlinearity depends strongly on the photophysical properties, the lifetimes of excited states, and the pulse duration of laser. On the contrary, the instantaneous nonlinearity (2PA and optical Kerr effect) are independent of the photophysical properties of the excited stats and the pulse duration of laser. Accordingly, to identify and separate the competing processes of the simultaneous accumulative nonlinearity and instantaneous nonlinearity from the resultant nonlinear effect of materials, one should perform the measurements with different pulse durations.

With Eq. (5), the optical field at the exit plane of the sample is determined by

Ee(r,z;t)=E(r,z;t)exp(α0L/2)[1+q(r,z;t)]jΔϕ(r,z;t)/q(r,z;t)1/2,
where
Δϕ(r,z;t)=k[γ+nS(t)+nT(t)]I(r,z;t)Leff,
q(r,z;t)=[β+αS(t)+αT(t)]I(r,z;t)Leff.
Here Leff = [1 – exp(−α0L)]/α0 is the effective length of sample and L is the physical length of sample.

Based on the Huygens-Fresnel diffraction integral method [1], we obtain the optical field with a propagation distance d from the exit plane of the sample

Ea(ra,z;t)=kj(dz)exp[jkra22(dz)]0rEe(r,z;t)exp[jkr22(dz)]J0(krradz)dr,
where J0() is the Bessel function of zero order. If |q(0, 0;0)| < 1, one could yield the analytical expression of Ea(ra, z; t) by applying the Gaussian decomposition method [2123].

3. Discussion

To characterize the optical nonlinearities, the time-averaging technique has been extensively exploited in the Z-scan measurement due to its high sensitivity, experimental simplicity, and simultaneous determination of signs and magnitudes of the nonlinear (absorption and refraction) coefficients [22]. For the incident pulses with a Gaussian spatiotemporal profile, we obtain the normalized energy transmittance of the open-aperture (OA) Z-scan by

T(z)=1π1/2τ+ln[1+p(z,t)exp(t2/τ2)]p(z,t)exp(t2/τ2)dt,
where p(z, t) = [β + αS(t) + αT(t)]I(z)Leff and I(z)=I00/(1+z2/z02). Here I00 and z0 are the on-axis peak intensity and the Rayleigh length of the Gaussian beam, respectively. For the closed-aperture (CA) Z-scan measurements, we have
T(z,S)=exp(α0L)Sɛi+dt0Ra|Ea(ra,z;t)|22πradra.
Here ɛi=π3/2ω02I00τ/2 is the input energy within the sample, and ω0 is the waist radius of the Gaussian beam. The linear transmittance of the aperture in the far field is S=1exp(2Ra2/ωa2), where Ra is the aperture radius and ωa is the beam radius at the aperture in the linear regime.

Generally speaking, the determination of both the photophysical parameters (β, γ, σS, σT, ηS, and ηT) and the response times (τS and τT) requires the complex calculations for the best fitting of the experimental data (both OA and CA Z-scans) with Eqs. (10) and (11). In what follows, we simplify the procedure to estimate the nonlinear parameters. Using the time-average approximation as we presented previously [24], we obtain the effective nonlinear coefficients arising from the cumulative effect of 1PA-induced excited-state nonlinearity as

αS=σSα0ħω2πτ+exp(t2/τ2)G(t)dt,
αT=σTα0φTħωτS2πτ+exp(t2/τ2)[tG(t)exp[(tt)/τT]dt]dt,
nS=ηSα0ħω2πτ+exp(t2/τ2)G(t)dt,
nT=ηTα0φTħωτS2πτ+exp(t2/τ2)[tG(t)exp[(tt)/τT]dt]dt.
Here αS and αT are the effective third-order NLA coefficients originating from the singlet and triplet ESAs, whereas nS and nT are the effective third-order nonlinear refraction (NLR) indices from the singlet and triplet excited-state refractions (ESRs), respectively. To determine the effective parameters (αS, αT, nS, and nT), one should perform numerical integration. Actually, the typical values of τS and τT are about picosecond and sub-microsecond orders, respectively [1417]. In addition, the pulse duration of the laser excitation is generally tens of nanoseconds to hundreds of femtoseconds, which satisfies the condition of ττT. Accordingly, we find the analytical expressions for αS and αT at three conditions, as summarized in Table 1. Similarly, the results for nS and nT are listed in Table 2. When ττSτT, the 1PA-induced excited-state nonlinearities caused by the excited singlet and triplet states depend on the pulse duration. In this instance, the nonlinearities originate from the cumulative effect and exhibit the fluence-dependence instead of the intensity-dependence. For τSττT, however, the nonlinearities originating from the singlet and triplet states become independent and dependent of the pulse duration, respectively. In this case, the nonlinearities induced by the singlet and triplet states are treated as the instantaneous and cumulative effects, respectively.

Tables Icon

Table 1. The effective NLA coefficients caused by the excited singlet and triplet states for different laser pulses

Tables Icon

Table 2. The effective NLR indexes caused by the excited singlet and triplet states for different laser pulses

Taking the typical photophysical parameters of organic materials [1417] as listed in Table 3, we explore the effective nonlinear coefficients from the singlet and triplet states, by using numerical simulation with Eq. (12) at different pulse durations, as displayed by the symbols in Fig. 2. For comparison, the corresponding analytical results (given in Tables 1 and 2) are also shown in Fig. 2 by the solid lines. Obviously, the analytical results are in good agreement with the numerical simulations. It can also be found that the dependence of the NLA coefficient on the pulse duration is similar to that of the NLR index, as shown in Fig. 2.

 

Fig. 2 Pulse-duration dependence of (a) NLA coefficient and (b) NLR index. The used parameters are listed in Table 3. The symbols show the numerical simulation results, while the solid lines give the corresponding analytical results.

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Tables Icon

Table 3. Typical photophysical parameters used for the numerical simulations and the analytical calculations

In the subpicosecond regime, as illustrated in Fig. 2, the 1PA-induced excited-state nonlinearity becomes negligible. In this case, the instantaneous nonlinearity is the dominant mechanism in the whole nonlinear process. The NLA process can be described by 2PA in Fig. 1(b). Accordingly, the measured NLA and NLR coefficients with the subpicosecond pulses are closer to the intrinsic values. In a few to hundreds of picosecond timescales, the 1PA-induced singlet excited-state nonlinearity mainly contributes to the observed nonlinear effect as shown in Fig. 2. In this instance, the photodynamic process can be described as Fig. 1(c). The laser pulse promotes an electron from S0 to S1 by absorbing one photon. Subsequently, the electron can be excited to Sh by absorbing another photon, resulting in 1PA-induced ESA. Thus, Fig. 1(c) can adequately explain the NLA process in the picosecond regime. Under the pulsed excitation of subnanosecond to few nanoseconds, as shown in Fig. 2, the contributions of the singlet and the triplet state nonlinearities are comparable. The photodynamic process can be illustrated as Fig. 1(a) except for 2PA. The observed nonlinear effect mainly originates from the 1PA-induced excited state nonlinearities because the instantaneous nonlinear process is negligible and can be justifiably omitted in the analysis. For tens-of-nanoseconds and longer pulsed irradiance, the resultant nonlinear effect basically arises from the triplet nonlinear process, as illustrated in Fig. 2. This result is consistent with the experimental observation [14]. In the instance, NLA can be interpreted by four-level diagram as Fig. 1(d). For an electron in S1, it may relax to S0 or undergo a spin-flip process to T1. From T1, the electron may relax to S0 by a phosphorescence process or be promoted to Th by absorbing another photon. It should be noted that the above-mentioned conclusions are applicable for organic materials in general.

As we discussed previously [23], one can easily obtain the OA Z-scan trace by

T(z)=1π+ln[1+ψ(z)exp(ξ2)]ψ(z)dξ,
where ψ(z)=(β+αS+αT)I00Leff/(1+z2/z02). Similarly, the CA Z-scan trace is determined by substituting Eq. (12) into Eq. (11). To demonstrate the validity of this approach, we use the parameters listed in Table 3 and then to simulate the Z-scan traces for different pulse durations, as displayed in Fig. 3. The symbols in Fig. 3 are the numerical simulations by using Eqs. (6)(11), while the corresponding solid lines are obtained by our simplified theory. Apparently, The results indicate that the simplified theory could well describe the Z-scan measurements for the materials with the cumulative nonlinearities. In particular, the computing time of the simplified theory is much shorter than that of the rigorous numerical simulation. Therefore, the improved theory has the salient advantages of time saving and high accuracy.

 

Fig. 3 Pulse-duration dependence of (a) OA and (b) CA (S = 0.1) traces. The used parameters are listed in Table 3. Squares, circles, uptriangles, and downtriangles are the numerical simulations by using Eqs. (6)(11) for τ = 10 ps, 100 ps, 1 ns, and 10 ns, respectively, while the corresponding solid lines are obtained by our simplified theory.

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As illustrated in Fig. 3, the Z-scan signal strongly depends on the pulse duration for a given on-axis peak intensity. The valley depth of the OA Z-scan ΔTV (= 1 – TV) and the normalized peak-valley transmittance difference in the CA Z-scan ΔTPV (= TPTV, where TP and TV are the normalized transmittance at the peak and the valley, respectively) as a function of the pulse duration τ are shown in Figs. 4(a) and 4(b), respectively. Both ΔTV and ΔTPV are monotonously nonlinear increasing functions of τ.

 

Fig. 4 Pulse-duration dependence of (a) ΔTV and (b) ΔTPV (S = 0.1). The other parameters are listed in Table 3. The symbols are obtained by the numerical simulations with Eqs. (6)(11), while the corresponding solid lines are obtained by our simplified theory.

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Based on the above-mentioned discussions, the excited-state photophysical parameters can be exploited fully by performing both the OA and CA Z-scan measurements [22] under the laser excitation with the fixed photon energy in the femtosecond, picosecond, and nanosecond regimes. Under the excitation of hundreds of femtoseconds laser pulses, the instantaneous nonlinear coefficients (both β and γ) could be extracted by using the femtosecond-pulsed Z-scan theory [23]. In tens of picosecond timescales, the singlet excited-state photophysical parameters (σS and ηS) could be evaluated unambiguously by the presented Z-scan theory by ignoring the triplet state contribution. For the nanosecond pulsed excitation, the best fittings between the experimental data and the presented Z-scan theory with the known σS and ηS give the triplet state parameters of both σT and ηT. The singlet and triplet excited-state lifetimes, τS and τT, could be estimated by additional experiments such as femtosecond and nanosecond transient difference absorption [16] or pump-probe measurements [19]. In addition, the intensity-dependent Z-scan should be carried out to confirm that the observed nonlinearities are indeed a third-order process.

To check the validity of the presented theory, we have analyzed the published experimental results. Figure 5 shows the OA Z-scan traces for [(C2H5)4N]2[Cu(C3S5)2] (DCu1) in acetone solution with τF = 40 ps (squares) and 18 ns (circles), respectively [25]. Fan et al. [25] qualitatively analyzed the experimental results based on a five-level model. In this analysis, we take the typical lifetimes of τS ≃ 100 ps, τisc ≃ 2 ns, and τT ≃ 0.1 ms for organic molecules and fit the experimental data by Eq. (13) with the known parameters of L = 2 mm, I00 = 1.48 GW/cm2, h̄ω ≃ 1.18 eV, and α0 = 0.253 cm−1. The best fitting shown in Fig. 5 by the solid lines gives β = 0.1 cm/GW, σS = 2.6 × 1018 cm2, and σT = 5.4 × 1018 cm2. These values are comparable with the findings for other organic molecules [1517], which indicates that the presented theory could adequately interpret and give an insight into the physical mechanism for the observed optical nonlinearities in the nanosecond and picosecond regimes.

 

Fig. 5 The OA Z-scan traces for DCu1 under the excitation of τF = 40 ps (squares) and 18 ns (circles), respectively. The symbols are the experimental data from Ref. 25, while the solid lines are the theoretical fitting results by the use of our simplified Z-scan theory.

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Recently, He et al. [26] have reported the giant third-order optical nonlinearities of the thin films containing anionic tetracarboxylic copper phthalocyanine [CuPc(COONa)4] and cationic polydiallydimethylammonium chloride (PDDA) under the excitation of picosecond and nanosecond pulses. Figures 6(a) and 6(b) display the Z-scan traces of the 26-bilayer CuPc(COONa)4/PDDA film at τF = 21 ps and τF = 4 ns, respectively [26]. The valley-to-peak configurations shown by symbols in Fig. 6 are the results of dividing the CA Z-scan by the OA Z-scan. The experimental data indicates that the NLA coefficient and the NLR index of the film measured at τF = 4 ns are two orders larger than those at τF = 21 ps [26]. In what follows, we analyze the experimental data using our simplified theory and gain insight into the physical mechanism of the observed nonlinearities. We take the typical lifetimes of τS ≃ 100 ps, τisc ≃ 2 ns, and τT ≃ 0.1 ms for organic molecules and the known parameters of L = 285 nm, α0 ≃ 2.0 × 104 cm1, h̄ω = 2.34 eV, S = 0.13, I00 = 1.77 × 102 GW/cm2 at τF = 4 ns, and I00 = 3.65 GW/cm2 at τF = 21 ps. The best fittings shown in Fig. 6 indicate that β ≃ 0, γ ≃ 0, σS = 2.5 × 1018 cm2, σT = 9.4 × 1018 cm2, ηS = 0.41 × 1022 cm3, and ηT = 5.1 × 1022 cm3. The difference between the fitting curves and the CA Z-scan experimental data is understood as follows. In Ref. 26, the relatively rough data processing method was adopted for determining the contribution of NLR, which is the CA Z-scan trace divided by the corresponding the OA one. Consequently, the interval between the valley and the peak of the obtained nominal CA Z-scan trace becomes larger than that of the CA Z-scan trace for the pure NLR [27]. The evaluated excited-state parameters are comparable with the typical values listed in Table 3. The resultant NLA coefficients of 2.1 × 104 cm/GW at τF = 21 ps and 8.7 × 105 cm/GW at τF = 4 ns are twice larger than those reported by He et al. [26]. The total NLR indices (3.4 × 102 cm2/GW at τF = 21 ps and 4.3 cm2/GW at τF = 4 ns) are closer to the reported ones (3.7 × 102 cm2/GW at τF = 21 ps and 4.1 cm2/GW at τF = 4 ns). The observed optical nonlinearities can be understood as follows. The electronic structure of the film can be simplified as a five-level model, as illustrated in Fig. 1(a). In tens of picoseconds timescale, the singlet excited-state nonlinearity dominates the contribution to the observed nonlinear effect, whereas the triplet excited-state optical nonlinearity is the dominant mechanism under the pulsed excitation of few nanoseconds.

 

Fig. 6 The OA (squares) and CA/OA (circles) Z-scan traces of 26-bilayer CuPc(COONa)4/PDDA film under the pulsed excitation of (a) τF = 21 ps and (b) τF = 4 ns. The symbols are the experimental data from Ref. 26, while the corresponding solid lines are the theoretical fitting results by the use of our simplified Z-scan theory.

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4. Conclusion

In summary, we have investigated the enhancement of third-order optical nonlinearities by the 1PA-assisted excited state process under reasonable approximations. We have obtained the analytical results for the effective third-order nonlinearities caused by the 1PA-assisted excited-state absorption and refraction. We have studied the dominant photodynamics process of the system and discussed the corresponding level diagram in the nanosecond, picosecond, and femtosecond regimes. We have developed the pulse-duration-dependent Z-scan theory for characterizing both the instantaneous nonlinearity and the cumulative nonlinearity of excited-state nonlinear effect. We have also demonstrated that the presented theory can well describe the experimental results.

Acknowledgments

This work was supported in part by the National Science Foundation of China under 10704042 and 10934003. J. Chen also acknowledges the support from the Program for New Century Excellent Talents in University.

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21. D. Weaire, B. S. Wherrett, D. A. B. Miller, and S. D. Smith, “Effect of low-power nonlinear refraction on laser-beam propagation in InSb,” Opt. Lett. 4, 331 (1979). [CrossRef]   [PubMed]  

22. 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 (1990). [CrossRef]  

23. B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed z scans on instantaneous nonlinearity,” Appl. Opt. 47, 1187 (2008). [CrossRef]   [PubMed]  

24. B. Gu, Y. Sun, and W. Ji, “Two-photon-induced excited-state nonlinearities,” Opt. Express 16, 17745 (2008). [CrossRef]   [PubMed]  

25. H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010). [CrossRef]  

26. C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009). [CrossRef]  

27. S. L. Guo, J. Yan, L. Xu, B. Gu, X. Z. Fan, H. T. Wang, and N. B. Ming, “Second Z-scan in materials with nonlinear refraction and nonlinear absorption,” J. Opt. A, Pure Appl. Opt. 4, 504 (2002). [CrossRef]  

References

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  1. R. L. Sutherland with contributions by D. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, 2nd ed. (Dekker, New York, 2003).
    [Crossref]
  2. D. N. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photon. 2, 60 (2010).
    [Crossref]
  3. R. Lepkowicz, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Picosecond optical limiting in reverse saturable absorbers: a theoretical and experimental study,” J. Opt. Soc. Am. B 19, 94 (2002).
    [Crossref]
  4. E. Kuznetsova, R. Kolesov, and O. Kocharovskaya, “Suppression of excited-state absorption: A path to ultraviolet tunable solid-state lasers,” Phys. Rev. A 70, 043801 (2004).
    [Crossref]
  5. C. P. Singh, K. S. Bindra, and S. M. Oak, “Analysis of effect of excitation pulse characteristics on numerical simulation of reverse saturable absorption,” Opt. Commun. 269, 223 (2007).
    [Crossref]
  6. S. Scuppa, L. Orian, D. Dini, S. Santi, and M. Meneghetti, “Nonlinear absorption properties and excited state dynamics of Ferrocene,” J. Phys. Chem. A 113, 9286 (2009).
    [Crossref] [PubMed]
  7. S. V. Rao, N. K. M. N. Srinivas, and D. N. Rao, “Nonlinear absorption and excited state dynamics in Rhodamine B studied using Z-scan and degenerate four wave mixing techniques,” Chem. Phys. Lett. 361, 439 (2002).
    [Crossref]
  8. N. K. M. N. Srinivas, S. V. Rao, and D. N. Rao, “Saturable and reverse saturable absorption of Rhodamine B in methanol and water,” J. Opt. Soc. Am. B 20, 2470 (2003).
    [Crossref]
  9. A. Shukla, H. Ghosh, and S. Mazumdar, “Theory of excited-state absorption in phenylene-based π-conjugated polymers,” Phys. Rev. B 67, 245203 (2003).
    [Crossref]
  10. C. C. Byeon, M. M. Mckerns, W. Sun, T. M. Nordlund, C. M. Lawson, and G. M. Gray, “Excited state lifetime and intersystem crossing rate of asymmetric pentaazadentate porphyrin-like metal complexes,” Appl. Phys. Lett. 84, 5174 (2004).
    [Crossref]
  11. J. Yang, J. Gu, Y. Song, S. Guang, Y. Wang, W. Zhang, and J. Lang, “Excited state absorption dynamics in metal cluster polymer [WS4Cu3I(4-bpy)3]n solution,” J. Phys. Chem. B 111, 7987 (2007).
    [Crossref] [PubMed]
  12. P. Poornesh, G. Umesh, P. K. Hegde, M. G. Manjunatha, K. B. Manjunatha, and A. V. Adhikari, “Studies on third-order nonlinear optical properties and reverse saturable absorption in polythiophene/poly (methylmethacrylate) composites,” Appl. Phys. B 97, 117 (2009).
    [Crossref]
  13. S. C. Hayes and C. Silva, “Analysis of the excited-state absorption spectral bandshape of oligofluorenes,” J. Chem. Phys. 132, 214510 (2010).
    [Crossref] [PubMed]
  14. C. L. Lee, X. Yang, and N. C. Greenham, “Determination of the triplet excited-state absorption cross section in a polyfluorene by energy transfer from a phosphorescent metal complex,” Phys. Rev. B 76, 245201 (2007).
    [Crossref]
  15. T. M. Pritchett, W. F. Sun, F. Guo, B. Zhang, M. J. Ferry, J. E. Rogers-Haley, W. Shensky, and A. G. Mott, “Excited-state absorption in a terpyridyl platinum(II) pentynyl complex,” Opt. Lett. 33, 1053 (2008).
    [Crossref] [PubMed]
  16. T. M. Pritchett, W. F. Sun, B. Zhang, M. J. Ferry, Y. Li, J. E. Haley, D. M. Mackie, W. Shensky, and A. G. Mott, “Excited-state absorption of a bipyridyl platinum(II) complex with alkynyl-benzothiazolylfluorene units,” Opt. Lett. 35, 1305 (2010).
    [Crossref] [PubMed]
  17. G. Shi, C. He, Y. Li, R. Zou, X. Zhang, Y. Wang, K. Yang, Y. Song, and C. H. Wang, “Excited-state nonlinearity measurements of ZnPcBr4/DMSO,” J. Opt. Soc. Am. B 26, 754 (2009).
    [Crossref]
  18. A. Marcelli, P. Foggi, L. Moroni, C. Gellini, and P. R. Salvi, “Excited-state absorption and ultrafast relaxiation dynamics of porphyrin, diprotonated porphyrin, and tetraoxaporphyrin dication,” J. Phys. Chem. A 112, 1864 (2008).
  19. L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
    [Crossref]
  20. T. Cassano, R. Tommasi, A. P. Meacham, and M. D. Ward, “Investigation of the excited-state absorption of a Ru dioxolene complex by the Z-scan technique,” J. Chem. Phys. 122, 154507 (2005).
    [Crossref] [PubMed]
  21. D. Weaire, B. S. Wherrett, D. A. B. Miller, and S. D. Smith, “Effect of low-power nonlinear refraction on laser-beam propagation in InSb,” Opt. Lett. 4, 331 (1979).
    [Crossref] [PubMed]
  22. 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 (1990).
    [Crossref]
  23. B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed z scans on instantaneous nonlinearity,” Appl. Opt. 47, 1187 (2008).
    [Crossref] [PubMed]
  24. B. Gu, Y. Sun, and W. Ji, “Two-photon-induced excited-state nonlinearities,” Opt. Express 16, 17745 (2008).
    [Crossref] [PubMed]
  25. H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
    [Crossref]
  26. C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
    [Crossref]
  27. S. L. Guo, J. Yan, L. Xu, B. Gu, X. Z. Fan, H. T. Wang, and N. B. Ming, “Second Z-scan in materials with nonlinear refraction and nonlinear absorption,” J. Opt. A, Pure Appl. Opt. 4, 504 (2002).
    [Crossref]

2010 (4)

D. N. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photon. 2, 60 (2010).
[Crossref]

S. C. Hayes and C. Silva, “Analysis of the excited-state absorption spectral bandshape of oligofluorenes,” J. Chem. Phys. 132, 214510 (2010).
[Crossref] [PubMed]

T. M. Pritchett, W. F. Sun, B. Zhang, M. J. Ferry, Y. Li, J. E. Haley, D. M. Mackie, W. Shensky, and A. G. Mott, “Excited-state absorption of a bipyridyl platinum(II) complex with alkynyl-benzothiazolylfluorene units,” Opt. Lett. 35, 1305 (2010).
[Crossref] [PubMed]

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

2009 (4)

C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
[Crossref]

G. Shi, C. He, Y. Li, R. Zou, X. Zhang, Y. Wang, K. Yang, Y. Song, and C. H. Wang, “Excited-state nonlinearity measurements of ZnPcBr4/DMSO,” J. Opt. Soc. Am. B 26, 754 (2009).
[Crossref]

P. Poornesh, G. Umesh, P. K. Hegde, M. G. Manjunatha, K. B. Manjunatha, and A. V. Adhikari, “Studies on third-order nonlinear optical properties and reverse saturable absorption in polythiophene/poly (methylmethacrylate) composites,” Appl. Phys. B 97, 117 (2009).
[Crossref]

S. Scuppa, L. Orian, D. Dini, S. Santi, and M. Meneghetti, “Nonlinear absorption properties and excited state dynamics of Ferrocene,” J. Phys. Chem. A 113, 9286 (2009).
[Crossref] [PubMed]

2008 (4)

2007 (3)

C. L. Lee, X. Yang, and N. C. Greenham, “Determination of the triplet excited-state absorption cross section in a polyfluorene by energy transfer from a phosphorescent metal complex,” Phys. Rev. B 76, 245201 (2007).
[Crossref]

J. Yang, J. Gu, Y. Song, S. Guang, Y. Wang, W. Zhang, and J. Lang, “Excited state absorption dynamics in metal cluster polymer [WS4Cu3I(4-bpy)3]n solution,” J. Phys. Chem. B 111, 7987 (2007).
[Crossref] [PubMed]

C. P. Singh, K. S. Bindra, and S. M. Oak, “Analysis of effect of excitation pulse characteristics on numerical simulation of reverse saturable absorption,” Opt. Commun. 269, 223 (2007).
[Crossref]

2005 (1)

T. Cassano, R. Tommasi, A. P. Meacham, and M. D. Ward, “Investigation of the excited-state absorption of a Ru dioxolene complex by the Z-scan technique,” J. Chem. Phys. 122, 154507 (2005).
[Crossref] [PubMed]

2004 (2)

E. Kuznetsova, R. Kolesov, and O. Kocharovskaya, “Suppression of excited-state absorption: A path to ultraviolet tunable solid-state lasers,” Phys. Rev. A 70, 043801 (2004).
[Crossref]

C. C. Byeon, M. M. Mckerns, W. Sun, T. M. Nordlund, C. M. Lawson, and G. M. Gray, “Excited state lifetime and intersystem crossing rate of asymmetric pentaazadentate porphyrin-like metal complexes,” Appl. Phys. Lett. 84, 5174 (2004).
[Crossref]

2003 (2)

N. K. M. N. Srinivas, S. V. Rao, and D. N. Rao, “Saturable and reverse saturable absorption of Rhodamine B in methanol and water,” J. Opt. Soc. Am. B 20, 2470 (2003).
[Crossref]

A. Shukla, H. Ghosh, and S. Mazumdar, “Theory of excited-state absorption in phenylene-based π-conjugated polymers,” Phys. Rev. B 67, 245203 (2003).
[Crossref]

2002 (3)

S. V. Rao, N. K. M. N. Srinivas, and D. N. Rao, “Nonlinear absorption and excited state dynamics in Rhodamine B studied using Z-scan and degenerate four wave mixing techniques,” Chem. Phys. Lett. 361, 439 (2002).
[Crossref]

R. Lepkowicz, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Picosecond optical limiting in reverse saturable absorbers: a theoretical and experimental study,” J. Opt. Soc. Am. B 19, 94 (2002).
[Crossref]

S. L. Guo, J. Yan, L. Xu, B. Gu, X. Z. Fan, H. T. Wang, and N. B. Ming, “Second Z-scan in materials with nonlinear refraction and nonlinear absorption,” J. Opt. A, Pure Appl. Opt. 4, 504 (2002).
[Crossref]

1990 (1)

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 (1990).
[Crossref]

1979 (1)

1864 (1)

A. Marcelli, P. Foggi, L. Moroni, C. Gellini, and P. R. Salvi, “Excited-state absorption and ultrafast relaxiation dynamics of porphyrin, diprotonated porphyrin, and tetraoxaporphyrin dication,” J. Phys. Chem. A 112, 1864 (2008).

Adhikari, A. V.

P. Poornesh, G. Umesh, P. K. Hegde, M. G. Manjunatha, K. B. Manjunatha, and A. V. Adhikari, “Studies on third-order nonlinear optical properties and reverse saturable absorption in polythiophene/poly (methylmethacrylate) composites,” Appl. Phys. B 97, 117 (2009).
[Crossref]

Bindra, K. S.

C. P. Singh, K. S. Bindra, and S. M. Oak, “Analysis of effect of excitation pulse characteristics on numerical simulation of reverse saturable absorption,” Opt. Commun. 269, 223 (2007).
[Crossref]

Byeon, C. C.

C. C. Byeon, M. M. Mckerns, W. Sun, T. M. Nordlund, C. M. Lawson, and G. M. Gray, “Excited state lifetime and intersystem crossing rate of asymmetric pentaazadentate porphyrin-like metal complexes,” Appl. Phys. Lett. 84, 5174 (2004).
[Crossref]

Cassano, T.

T. Cassano, R. Tommasi, A. P. Meacham, and M. D. Ward, “Investigation of the excited-state absorption of a Ru dioxolene complex by the Z-scan technique,” J. Chem. Phys. 122, 154507 (2005).
[Crossref] [PubMed]

Chen, J. W.

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

Chen, Z.

C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
[Crossref]

Christodoulides, D. N.

Dini, D.

S. Scuppa, L. Orian, D. Dini, S. Santi, and M. Meneghetti, “Nonlinear absorption properties and excited state dynamics of Ferrocene,” J. Phys. Chem. A 113, 9286 (2009).
[Crossref] [PubMed]

Duan, W.

C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
[Crossref]

Fan, H. L.

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

Fan, X. Z.

S. L. Guo, J. Yan, L. Xu, B. Gu, X. Z. Fan, H. T. Wang, and N. B. Ming, “Second Z-scan in materials with nonlinear refraction and nonlinear absorption,” J. Opt. A, Pure Appl. Opt. 4, 504 (2002).
[Crossref]

Ferry, M. J.

Foggi, P.

A. Marcelli, P. Foggi, L. Moroni, C. Gellini, and P. R. Salvi, “Excited-state absorption and ultrafast relaxiation dynamics of porphyrin, diprotonated porphyrin, and tetraoxaporphyrin dication,” J. Phys. Chem. A 112, 1864 (2008).

Gellini, C.

A. Marcelli, P. Foggi, L. Moroni, C. Gellini, and P. R. Salvi, “Excited-state absorption and ultrafast relaxiation dynamics of porphyrin, diprotonated porphyrin, and tetraoxaporphyrin dication,” J. Phys. Chem. A 112, 1864 (2008).

Ghosh, H.

A. Shukla, H. Ghosh, and S. Mazumdar, “Theory of excited-state absorption in phenylene-based π-conjugated polymers,” Phys. Rev. B 67, 245203 (2003).
[Crossref]

Gray, G. M.

C. C. Byeon, M. M. Mckerns, W. Sun, T. M. Nordlund, C. M. Lawson, and G. M. Gray, “Excited state lifetime and intersystem crossing rate of asymmetric pentaazadentate porphyrin-like metal complexes,” Appl. Phys. Lett. 84, 5174 (2004).
[Crossref]

Greenham, N. C.

C. L. Lee, X. Yang, and N. C. Greenham, “Determination of the triplet excited-state absorption cross section in a polyfluorene by energy transfer from a phosphorescent metal complex,” Phys. Rev. B 76, 245201 (2007).
[Crossref]

Gu, B.

Gu, J.

J. Yang, J. Gu, Y. Song, S. Guang, Y. Wang, W. Zhang, and J. Lang, “Excited state absorption dynamics in metal cluster polymer [WS4Cu3I(4-bpy)3]n solution,” J. Phys. Chem. B 111, 7987 (2007).
[Crossref] [PubMed]

Guang, S.

J. Yang, J. Gu, Y. Song, S. Guang, Y. Wang, W. Zhang, and J. Lang, “Excited state absorption dynamics in metal cluster polymer [WS4Cu3I(4-bpy)3]n solution,” J. Phys. Chem. B 111, 7987 (2007).
[Crossref] [PubMed]

Guo, F.

Guo, S. L.

S. L. Guo, J. Yan, L. Xu, B. Gu, X. Z. Fan, H. T. Wang, and N. B. Ming, “Second Z-scan in materials with nonlinear refraction and nonlinear absorption,” J. Opt. A, Pure Appl. Opt. 4, 504 (2002).
[Crossref]

Hagan, D. J.

R. Lepkowicz, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Picosecond optical limiting in reverse saturable absorbers: a theoretical and experimental study,” J. Opt. Soc. Am. B 19, 94 (2002).
[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 (1990).
[Crossref]

Haley, J. E.

Hayes, S. C.

S. C. Hayes and C. Silva, “Analysis of the excited-state absorption spectral bandshape of oligofluorenes,” J. Chem. Phys. 132, 214510 (2010).
[Crossref] [PubMed]

He, C.

G. Shi, C. He, Y. Li, R. Zou, X. Zhang, Y. Wang, K. Yang, Y. Song, and C. H. Wang, “Excited-state nonlinearity measurements of ZnPcBr4/DMSO,” J. Opt. Soc. Am. B 26, 754 (2009).
[Crossref]

C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
[Crossref]

Hegde, P. K.

P. Poornesh, G. Umesh, P. K. Hegde, M. G. Manjunatha, K. B. Manjunatha, and A. V. Adhikari, “Studies on third-order nonlinear optical properties and reverse saturable absorption in polythiophene/poly (methylmethacrylate) composites,” Appl. Phys. B 97, 117 (2009).
[Crossref]

Huang, X. Q.

Ji, W.

Jiang, L.

L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
[Crossref]

Jiu, T.

L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
[Crossref]

Khoo, I. C.

Kikpatrick, S.

R. L. Sutherland with contributions by D. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, 2nd ed. (Dekker, New York, 2003).
[Crossref]

Kobyakov, A.

Kocharovskaya, O.

E. Kuznetsova, R. Kolesov, and O. Kocharovskaya, “Suppression of excited-state absorption: A path to ultraviolet tunable solid-state lasers,” Phys. Rev. A 70, 043801 (2004).
[Crossref]

Kolesov, R.

E. Kuznetsova, R. Kolesov, and O. Kocharovskaya, “Suppression of excited-state absorption: A path to ultraviolet tunable solid-state lasers,” Phys. Rev. A 70, 043801 (2004).
[Crossref]

Kuznetsova, E.

E. Kuznetsova, R. Kolesov, and O. Kocharovskaya, “Suppression of excited-state absorption: A path to ultraviolet tunable solid-state lasers,” Phys. Rev. A 70, 043801 (2004).
[Crossref]

Lang, J.

J. Yang, J. Gu, Y. Song, S. Guang, Y. Wang, W. Zhang, and J. Lang, “Excited state absorption dynamics in metal cluster polymer [WS4Cu3I(4-bpy)3]n solution,” J. Phys. Chem. B 111, 7987 (2007).
[Crossref] [PubMed]

Lawson, C. M.

C. C. Byeon, M. M. Mckerns, W. Sun, T. M. Nordlund, C. M. Lawson, and G. M. Gray, “Excited state lifetime and intersystem crossing rate of asymmetric pentaazadentate porphyrin-like metal complexes,” Appl. Phys. Lett. 84, 5174 (2004).
[Crossref]

Lee, C. L.

C. L. Lee, X. Yang, and N. C. Greenham, “Determination of the triplet excited-state absorption cross section in a polyfluorene by energy transfer from a phosphorescent metal complex,” Phys. Rev. B 76, 245201 (2007).
[Crossref]

Lepkowicz, R.

Li, C.

L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
[Crossref]

Li, J.

L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
[Crossref]

Li, Y.

T. M. Pritchett, W. F. Sun, B. Zhang, M. J. Ferry, Y. Li, J. E. Haley, D. M. Mackie, W. Shensky, and A. G. Mott, “Excited-state absorption of a bipyridyl platinum(II) complex with alkynyl-benzothiazolylfluorene units,” Opt. Lett. 35, 1305 (2010).
[Crossref] [PubMed]

G. Shi, C. He, Y. Li, R. Zou, X. Zhang, Y. Wang, K. Yang, Y. Song, and C. H. Wang, “Excited-state nonlinearity measurements of ZnPcBr4/DMSO,” J. Opt. Soc. Am. B 26, 754 (2009).
[Crossref]

L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
[Crossref]

L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
[Crossref]

Liu, H.

L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
[Crossref]

Mackie, D. M.

Manjunatha, K. B.

P. Poornesh, G. Umesh, P. K. Hegde, M. G. Manjunatha, K. B. Manjunatha, and A. V. Adhikari, “Studies on third-order nonlinear optical properties and reverse saturable absorption in polythiophene/poly (methylmethacrylate) composites,” Appl. Phys. B 97, 117 (2009).
[Crossref]

Manjunatha, M. G.

P. Poornesh, G. Umesh, P. K. Hegde, M. G. Manjunatha, K. B. Manjunatha, and A. V. Adhikari, “Studies on third-order nonlinear optical properties and reverse saturable absorption in polythiophene/poly (methylmethacrylate) composites,” Appl. Phys. B 97, 117 (2009).
[Crossref]

Marcelli, A.

A. Marcelli, P. Foggi, L. Moroni, C. Gellini, and P. R. Salvi, “Excited-state absorption and ultrafast relaxiation dynamics of porphyrin, diprotonated porphyrin, and tetraoxaporphyrin dication,” J. Phys. Chem. A 112, 1864 (2008).

Mazumdar, S.

A. Shukla, H. Ghosh, and S. Mazumdar, “Theory of excited-state absorption in phenylene-based π-conjugated polymers,” Phys. Rev. B 67, 245203 (2003).
[Crossref]

Mckerns, M. M.

C. C. Byeon, M. M. Mckerns, W. Sun, T. M. Nordlund, C. M. Lawson, and G. M. Gray, “Excited state lifetime and intersystem crossing rate of asymmetric pentaazadentate porphyrin-like metal complexes,” Appl. Phys. Lett. 84, 5174 (2004).
[Crossref]

McLean, D. G.

R. L. Sutherland with contributions by D. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, 2nd ed. (Dekker, New York, 2003).
[Crossref]

Meacham, A. P.

T. Cassano, R. Tommasi, A. P. Meacham, and M. D. Ward, “Investigation of the excited-state absorption of a Ru dioxolene complex by the Z-scan technique,” J. Chem. Phys. 122, 154507 (2005).
[Crossref] [PubMed]

Meneghetti, M.

S. Scuppa, L. Orian, D. Dini, S. Santi, and M. Meneghetti, “Nonlinear absorption properties and excited state dynamics of Ferrocene,” J. Phys. Chem. A 113, 9286 (2009).
[Crossref] [PubMed]

Miller, D. A. B.

Ming, N. B.

S. L. Guo, J. Yan, L. Xu, B. Gu, X. Z. Fan, H. T. Wang, and N. B. Ming, “Second Z-scan in materials with nonlinear refraction and nonlinear absorption,” J. Opt. A, Pure Appl. Opt. 4, 504 (2002).
[Crossref]

Moroni, L.

A. Marcelli, P. Foggi, L. Moroni, C. Gellini, and P. R. Salvi, “Excited-state absorption and ultrafast relaxiation dynamics of porphyrin, diprotonated porphyrin, and tetraoxaporphyrin dication,” J. Phys. Chem. A 112, 1864 (2008).

Mott, A. G.

Nordlund, T. M.

C. C. Byeon, M. M. Mckerns, W. Sun, T. M. Nordlund, C. M. Lawson, and G. M. Gray, “Excited state lifetime and intersystem crossing rate of asymmetric pentaazadentate porphyrin-like metal complexes,” Appl. Phys. Lett. 84, 5174 (2004).
[Crossref]

Oak, S. M.

C. P. Singh, K. S. Bindra, and S. M. Oak, “Analysis of effect of excitation pulse characteristics on numerical simulation of reverse saturable absorption,” Opt. Commun. 269, 223 (2007).
[Crossref]

Orian, L.

S. Scuppa, L. Orian, D. Dini, S. Santi, and M. Meneghetti, “Nonlinear absorption properties and excited state dynamics of Ferrocene,” J. Phys. Chem. A 113, 9286 (2009).
[Crossref] [PubMed]

Poornesh, P.

P. Poornesh, G. Umesh, P. K. Hegde, M. G. Manjunatha, K. B. Manjunatha, and A. V. Adhikari, “Studies on third-order nonlinear optical properties and reverse saturable absorption in polythiophene/poly (methylmethacrylate) composites,” Appl. Phys. B 97, 117 (2009).
[Crossref]

Pritchett, T. M.

Rao, D. N.

N. K. M. N. Srinivas, S. V. Rao, and D. N. Rao, “Saturable and reverse saturable absorption of Rhodamine B in methanol and water,” J. Opt. Soc. Am. B 20, 2470 (2003).
[Crossref]

S. V. Rao, N. K. M. N. Srinivas, and D. N. Rao, “Nonlinear absorption and excited state dynamics in Rhodamine B studied using Z-scan and degenerate four wave mixing techniques,” Chem. Phys. Lett. 361, 439 (2002).
[Crossref]

Rao, S. V.

N. K. M. N. Srinivas, S. V. Rao, and D. N. Rao, “Saturable and reverse saturable absorption of Rhodamine B in methanol and water,” J. Opt. Soc. Am. B 20, 2470 (2003).
[Crossref]

S. V. Rao, N. K. M. N. Srinivas, and D. N. Rao, “Nonlinear absorption and excited state dynamics in Rhodamine B studied using Z-scan and degenerate four wave mixing techniques,” Chem. Phys. Lett. 361, 439 (2002).
[Crossref]

Ren, Q.

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

Rogers-Haley, J. E.

Said, A. A.

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 (1990).
[Crossref]

Salamo, G. J.

Salvi, P. R.

A. Marcelli, P. Foggi, L. Moroni, C. Gellini, and P. R. Salvi, “Excited-state absorption and ultrafast relaxiation dynamics of porphyrin, diprotonated porphyrin, and tetraoxaporphyrin dication,” J. Phys. Chem. A 112, 1864 (2008).

Santi, S.

S. Scuppa, L. Orian, D. Dini, S. Santi, and M. Meneghetti, “Nonlinear absorption properties and excited state dynamics of Ferrocene,” J. Phys. Chem. A 113, 9286 (2009).
[Crossref] [PubMed]

Scuppa, S.

S. Scuppa, L. Orian, D. Dini, S. Santi, and M. Meneghetti, “Nonlinear absorption properties and excited state dynamics of Ferrocene,” J. Phys. Chem. A 113, 9286 (2009).
[Crossref] [PubMed]

Sheik-Bahae, M.

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 (1990).
[Crossref]

Shensky, W.

Shi, G.

G. Shi, C. He, Y. Li, R. Zou, X. Zhang, Y. Wang, K. Yang, Y. Song, and C. H. Wang, “Excited-state nonlinearity measurements of ZnPcBr4/DMSO,” J. Opt. Soc. Am. B 26, 754 (2009).
[Crossref]

C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
[Crossref]

Shukla, A.

A. Shukla, H. Ghosh, and S. Mazumdar, “Theory of excited-state absorption in phenylene-based π-conjugated polymers,” Phys. Rev. B 67, 245203 (2003).
[Crossref]

Silva, C.

S. C. Hayes and C. Silva, “Analysis of the excited-state absorption spectral bandshape of oligofluorenes,” J. Chem. Phys. 132, 214510 (2010).
[Crossref] [PubMed]

Singh, C. P.

C. P. Singh, K. S. Bindra, and S. M. Oak, “Analysis of effect of excitation pulse characteristics on numerical simulation of reverse saturable absorption,” Opt. Commun. 269, 223 (2007).
[Crossref]

Smith, S. D.

Song, W.

C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
[Crossref]

Song, Y.

C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
[Crossref]

G. Shi, C. He, Y. Li, R. Zou, X. Zhang, Y. Wang, K. Yang, Y. Song, and C. H. Wang, “Excited-state nonlinearity measurements of ZnPcBr4/DMSO,” J. Opt. Soc. Am. B 26, 754 (2009).
[Crossref]

L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
[Crossref]

J. Yang, J. Gu, Y. Song, S. Guang, Y. Wang, W. Zhang, and J. Lang, “Excited state absorption dynamics in metal cluster polymer [WS4Cu3I(4-bpy)3]n solution,” J. Phys. Chem. B 111, 7987 (2007).
[Crossref] [PubMed]

Srinivas, N. K. M. N.

N. K. M. N. Srinivas, S. V. Rao, and D. N. Rao, “Saturable and reverse saturable absorption of Rhodamine B in methanol and water,” J. Opt. Soc. Am. B 20, 2470 (2003).
[Crossref]

S. V. Rao, N. K. M. N. Srinivas, and D. N. Rao, “Nonlinear absorption and excited state dynamics in Rhodamine B studied using Z-scan and degenerate four wave mixing techniques,” Chem. Phys. Lett. 361, 439 (2002).
[Crossref]

Stegeman, G. I.

Sun, W.

C. C. Byeon, M. M. Mckerns, W. Sun, T. M. Nordlund, C. M. Lawson, and G. M. Gray, “Excited state lifetime and intersystem crossing rate of asymmetric pentaazadentate porphyrin-like metal complexes,” Appl. Phys. Lett. 84, 5174 (2004).
[Crossref]

Sun, W. F.

Sun, Y.

Sun, Z. H.

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

Sutherland, R. L.

R. L. Sutherland with contributions by D. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, 2nd ed. (Dekker, New York, 2003).
[Crossref]

Tommasi, R.

T. Cassano, R. Tommasi, A. P. Meacham, and M. D. Ward, “Investigation of the excited-state absorption of a Ru dioxolene complex by the Z-scan technique,” J. Chem. Phys. 122, 154507 (2005).
[Crossref] [PubMed]

Umesh, G.

P. Poornesh, G. Umesh, P. K. Hegde, M. G. Manjunatha, K. B. Manjunatha, and A. V. Adhikari, “Studies on third-order nonlinear optical properties and reverse saturable absorption in polythiophene/poly (methylmethacrylate) composites,” Appl. Phys. B 97, 117 (2009).
[Crossref]

Van Stryland, E. W.

Wang, C. H.

Wang, H. T.

S. L. Guo, J. Yan, L. Xu, B. Gu, X. Z. Fan, H. T. Wang, and N. B. Ming, “Second Z-scan in materials with nonlinear refraction and nonlinear absorption,” J. Opt. A, Pure Appl. Opt. 4, 504 (2002).
[Crossref]

Wang, X. Q.

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

Wang, Y.

G. Shi, C. He, Y. Li, R. Zou, X. Zhang, Y. Wang, K. Yang, Y. Song, and C. H. Wang, “Excited-state nonlinearity measurements of ZnPcBr4/DMSO,” J. Opt. Soc. Am. B 26, 754 (2009).
[Crossref]

J. Yang, J. Gu, Y. Song, S. Guang, Y. Wang, W. Zhang, and J. Lang, “Excited state absorption dynamics in metal cluster polymer [WS4Cu3I(4-bpy)3]n solution,” J. Phys. Chem. B 111, 7987 (2007).
[Crossref] [PubMed]

Ward, M. D.

T. Cassano, R. Tommasi, A. P. Meacham, and M. D. Ward, “Investigation of the excited-state absorption of a Ru dioxolene complex by the Z-scan technique,” J. Chem. Phys. 122, 154507 (2005).
[Crossref] [PubMed]

Weaire, D.

Wei, T. H.

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 (1990).
[Crossref]

Wherrett, B. S.

Wu, Y.

C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
[Crossref]

Xu, D.

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

Xu, L.

S. L. Guo, J. Yan, L. Xu, B. Gu, X. Z. Fan, H. T. Wang, and N. B. Ming, “Second Z-scan in materials with nonlinear refraction and nonlinear absorption,” J. Opt. A, Pure Appl. Opt. 4, 504 (2002).
[Crossref]

Yan, J.

S. L. Guo, J. Yan, L. Xu, B. Gu, X. Z. Fan, H. T. Wang, and N. B. Ming, “Second Z-scan in materials with nonlinear refraction and nonlinear absorption,” J. Opt. A, Pure Appl. Opt. 4, 504 (2002).
[Crossref]

Yang, J.

L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
[Crossref]

J. Yang, J. Gu, Y. Song, S. Guang, Y. Wang, W. Zhang, and J. Lang, “Excited state absorption dynamics in metal cluster polymer [WS4Cu3I(4-bpy)3]n solution,” J. Phys. Chem. B 111, 7987 (2007).
[Crossref] [PubMed]

Yang, K.

Yang, X.

C. L. Lee, X. Yang, and N. C. Greenham, “Determination of the triplet excited-state absorption cross section in a polyfluorene by energy transfer from a phosphorescent metal complex,” Phys. Rev. B 76, 245201 (2007).
[Crossref]

Yu, G.

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

Zhang, B.

Zhang, G. H.

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

Zhang, W.

J. Yang, J. Gu, Y. Song, S. Guang, Y. Wang, W. Zhang, and J. Lang, “Excited state absorption dynamics in metal cluster polymer [WS4Cu3I(4-bpy)3]n solution,” J. Phys. Chem. B 111, 7987 (2007).
[Crossref] [PubMed]

Zhang, X.

Zhao, X.

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

Zou, R.

C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
[Crossref]

G. Shi, C. He, Y. Li, R. Zou, X. Zhang, Y. Wang, K. Yang, Y. Song, and C. H. Wang, “Excited-state nonlinearity measurements of ZnPcBr4/DMSO,” J. Opt. Soc. Am. B 26, 754 (2009).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. B (1)

P. Poornesh, G. Umesh, P. K. Hegde, M. G. Manjunatha, K. B. Manjunatha, and A. V. Adhikari, “Studies on third-order nonlinear optical properties and reverse saturable absorption in polythiophene/poly (methylmethacrylate) composites,” Appl. Phys. B 97, 117 (2009).
[Crossref]

Appl. Phys. Lett. (1)

C. C. Byeon, M. M. Mckerns, W. Sun, T. M. Nordlund, C. M. Lawson, and G. M. Gray, “Excited state lifetime and intersystem crossing rate of asymmetric pentaazadentate porphyrin-like metal complexes,” Appl. Phys. Lett. 84, 5174 (2004).
[Crossref]

Chem. Phys. Lett. (1)

S. V. Rao, N. K. M. N. Srinivas, and D. N. Rao, “Nonlinear absorption and excited state dynamics in Rhodamine B studied using Z-scan and degenerate four wave mixing techniques,” Chem. Phys. Lett. 361, 439 (2002).
[Crossref]

IEEE J. Quantum Electron. (1)

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 (1990).
[Crossref]

J. Chem. Phys. (2)

S. C. Hayes and C. Silva, “Analysis of the excited-state absorption spectral bandshape of oligofluorenes,” J. Chem. Phys. 132, 214510 (2010).
[Crossref] [PubMed]

T. Cassano, R. Tommasi, A. P. Meacham, and M. D. Ward, “Investigation of the excited-state absorption of a Ru dioxolene complex by the Z-scan technique,” J. Chem. Phys. 122, 154507 (2005).
[Crossref] [PubMed]

J. Opt. A, Pure Appl. Opt. (1)

S. L. Guo, J. Yan, L. Xu, B. Gu, X. Z. Fan, H. T. Wang, and N. B. Ming, “Second Z-scan in materials with nonlinear refraction and nonlinear absorption,” J. Opt. A, Pure Appl. Opt. 4, 504 (2002).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. Chem. A (2)

A. Marcelli, P. Foggi, L. Moroni, C. Gellini, and P. R. Salvi, “Excited-state absorption and ultrafast relaxiation dynamics of porphyrin, diprotonated porphyrin, and tetraoxaporphyrin dication,” J. Phys. Chem. A 112, 1864 (2008).

S. Scuppa, L. Orian, D. Dini, S. Santi, and M. Meneghetti, “Nonlinear absorption properties and excited state dynamics of Ferrocene,” J. Phys. Chem. A 113, 9286 (2009).
[Crossref] [PubMed]

J. Phys. Chem. B (2)

L. Jiang, T. Jiu, Y. Li, Y. Li, J. Yang, J. Li, C. Li, H. Liu, and Y. Song, “Excited-state absorption and sign tuning of nonlinear refraction in porphyrin derivatives,” J. Phys. Chem. B 112, 756 (2008).
[Crossref]

J. Yang, J. Gu, Y. Song, S. Guang, Y. Wang, W. Zhang, and J. Lang, “Excited state absorption dynamics in metal cluster polymer [WS4Cu3I(4-bpy)3]n solution,” J. Phys. Chem. B 111, 7987 (2007).
[Crossref] [PubMed]

J. Porphyrins Phthalocyanines (1)

C. He, G. Shi, W. Duan, Y. Wu, Z. Chen, W. Song, R. Zou, and Y. Song, “Third-order nonlinear optical properties of self-assembled thin films containing tetracarboxylic copper phthalocyanine,” J. Porphyrins Phthalocyanines 13, 1243 (2009).
[Crossref]

Opt. Commun. (1)

C. P. Singh, K. S. Bindra, and S. M. Oak, “Analysis of effect of excitation pulse characteristics on numerical simulation of reverse saturable absorption,” Opt. Commun. 269, 223 (2007).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

H. L. Fan, X. Q. Wang, Q. Ren, X. Zhao, G. H. Zhang, J. W. Chen, D. Xu, G. Yu, and Z. H. Sun, “Investigation of the nonlinear absorption and optical limiting properties of two [Q]2[Cu(C3S5)2] compounds,” Opt. Laser Technol. 42, 732 (2010).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (1)

E. Kuznetsova, R. Kolesov, and O. Kocharovskaya, “Suppression of excited-state absorption: A path to ultraviolet tunable solid-state lasers,” Phys. Rev. A 70, 043801 (2004).
[Crossref]

Phys. Rev. B (2)

A. Shukla, H. Ghosh, and S. Mazumdar, “Theory of excited-state absorption in phenylene-based π-conjugated polymers,” Phys. Rev. B 67, 245203 (2003).
[Crossref]

C. L. Lee, X. Yang, and N. C. Greenham, “Determination of the triplet excited-state absorption cross section in a polyfluorene by energy transfer from a phosphorescent metal complex,” Phys. Rev. B 76, 245201 (2007).
[Crossref]

Other (1)

R. L. Sutherland with contributions by D. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, 2nd ed. (Dekker, New York, 2003).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 (a) The five-level diagram and the typical decay lifetimes of the 1PA-induced singlet and triplet ESAs as well as 2PA. Simplified level diagram for (b) 2PA, (c) 2PA and 1PA-induced singlet ESA, and (d) 1PA-induced triplet ESA.
Fig. 2
Fig. 2 Pulse-duration dependence of (a) NLA coefficient and (b) NLR index. The used parameters are listed in Table 3. The symbols show the numerical simulation results, while the solid lines give the corresponding analytical results.
Fig. 3
Fig. 3 Pulse-duration dependence of (a) OA and (b) CA (S = 0.1) traces. The used parameters are listed in Table 3. Squares, circles, uptriangles, and downtriangles are the numerical simulations by using Eqs. (6)(11) for τ = 10 ps, 100 ps, 1 ns, and 10 ns, respectively, while the corresponding solid lines are obtained by our simplified theory.
Fig. 4
Fig. 4 Pulse-duration dependence of (a) ΔTV and (b) ΔTPV (S = 0.1). The other parameters are listed in Table 3. The symbols are obtained by the numerical simulations with Eqs. (6)(11), while the corresponding solid lines are obtained by our simplified theory.
Fig. 5
Fig. 5 The OA Z-scan traces for DCu1 under the excitation of τF = 40 ps (squares) and 18 ns (circles), respectively. The symbols are the experimental data from Ref. 25, while the solid lines are the theoretical fitting results by the use of our simplified Z-scan theory.
Fig. 6
Fig. 6 The OA (squares) and CA/OA (circles) Z-scan traces of 26-bilayer CuPc(COONa)4/PDDA film under the pulsed excitation of (a) τF = 21 ps and (b) τF = 4 ns. The symbols are the experimental data from Ref. 26, while the corresponding solid lines are the theoretical fitting results by the use of our simplified Z-scan theory.

Tables (3)

Tables Icon

Table 1 The effective NLA coefficients caused by the excited singlet and triplet states for different laser pulses

Tables Icon

Table 2 The effective NLR indexes caused by the excited singlet and triplet states for different laser pulses

Tables Icon

Table 3 Typical photophysical parameters used for the numerical simulations and the analytical calculations

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

N S 0 t = σ 0 I h ¯ ω N S 0 β I 2 2 ħ ω + N S 1 τ S 1 + N T 1 τ T 1 ,
N S 1 t = σ 0 I ħ ω N S 0 σ S 1 I ħ ω N S 1 N S 1 τ S 1 N S 1 τ isc + N S h τ S h ,
N S h t = β I 2 2 ħ ω + σ S 1 I ħ ω N S 1 N S h τ S h ,
N T 1 t = σ T 1 I ħ ω N T 1 + N S 1 τ isc + N T h τ T h N T 1 τ T 1 ,
N T h t = σ T 1 I ħ ω N T 1 N T h τ T h ,
N = N S 0 + N S 1 + N S h + N T 1 + N T h ,
I z = ( σ 0 N S 0 + σ S N S 1 + σ T N T 1 + β I ) I ,
Δ ϕ z = k ( γ I + η S N S 1 + η T N T 1 ) ,
N S 1 ( t ) = α 0 ħ ω G ( t ) exp ( t 2 / τ 2 ) I ( t ) ,
N T 1 ( t ) = α 0 φ T I 0 ħ ω τ S t G ( t ) exp [ ( t t ) / τ T 1 ] d t ,
G ( t ) = t exp ( t 2 / τ 2 ) exp [ ( t t ) / τ S ] d t .
I ( r , z ; t ) z = α 0 I ( r , z ; t ) [ β + α S ( t ) + α T ( t ) ] I 2 ( r , z ; t ) ,
Δ ϕ ( r , z ; t ) z = k [ γ + n S ( t ) + n T ( t ) ] I ( r , z ; t ) ,
α S ( t ) = σ S α 0 ħ ω exp ( t 2 / τ 2 ) G ( t ) ,
α T ( t ) = σ T α 0 φ T ħ ω τ S exp ( t 2 / τ 2 ) t G ( t ) exp [ ( t t ) / τ T ] d t ,
n S ( t ) = η S α 0 ħ ω exp ( t 2 / τ 2 ) G ( t ) ,
n T ( t ) = η T α 0 φ T ħ ω τ S exp ( t 2 / τ 2 ) t G ( t ) exp [ ( t t ) / τ T ] d t .
E e ( r , z ; t ) = E ( r , z ; t ) exp ( α 0 L / 2 ) [ 1 + q ( r , z ; t ) ] j Δ ϕ ( r , z ; t ) / q ( r , z ; t ) 1 / 2 ,
Δ ϕ ( r , z ; t ) = k [ γ + n S ( t ) + n T ( t ) ] I ( r , z ; t ) L eff ,
q ( r , z ; t ) = [ β + α S ( t ) + α T ( t ) ] I ( r , z ; t ) L eff .
E a ( r a , z ; t ) = k j ( d z ) exp [ j k r a 2 2 ( d z ) ] 0 r E e ( r , z ; t ) exp [ j k r 2 2 ( d z ) ] J 0 ( k r r a d z ) d r ,
T ( z ) = 1 π 1 / 2 τ + ln [ 1 + p ( z , t ) exp ( t 2 / τ 2 ) ] p ( z , t ) exp ( t 2 / τ 2 ) d t ,
T ( z , S ) = exp ( α 0 L ) S ɛ i + d t 0 R a | E a ( r a , z ; t ) | 2 2 π r a d r a .
α S = σ S α 0 ħ ω 2 π τ + exp ( t 2 / τ 2 ) G ( t ) d t ,
α T = σ T α 0 φ T ħ ω τ S 2 π τ + exp ( t 2 / τ 2 ) [ t G ( t ) exp [ ( t t ) / τ T ] d t ] d t ,
n S = η S α 0 ħ ω 2 π τ + exp ( t 2 / τ 2 ) G ( t ) d t ,
n T = η T α 0 φ T ħ ω τ S 2 π τ + exp ( t 2 / τ 2 ) [ t G ( t ) exp [ ( t t ) / τ T ] d t ] d t .
T ( z ) = 1 π + ln [ 1 + ψ ( z ) exp ( ξ 2 ) ] ψ ( z ) d ξ ,

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