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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 13 — Jun. 18, 2012
  • pp: 14596–14603
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Three-photon-absorption-induced optical stabilization effects in a bifluorenylidene derivative

Junhui Liu and Yuanxu Wang  »View Author Affiliations


Optics Express, Vol. 20, Issue 13, pp. 14596-14603 (2012)
http://dx.doi.org/10.1364/OE.20.014596


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Abstract

A bifluorenylidene derivative with extended π-conjugated system has been designed and successfully synthesized. The compound displays strong three-photon absorption effect. The obtained three-photon absorption cross section is as high as 81.3 × 10−76 cm6s2. Distinguished 3PA-induced optical limiting and optical stabilization performances have been achieved. The on-axis transmitted intensity approached a constant even though the incident laser pulse fluctuation was 300%.

© 2012 OSA

1. Introduction

Novel organic compounds featuring large three-photon absorption (3PA) cross section have been of particular interest since many attractive applications are based on its high-order nonlinearity of media’s response to the exciting light. Molecules with large 3PA cross section can be widely used in the fields of ultrahigh-resolution biological imaging (three-photon confocal microscopy) [1

1. S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, “Measuring serotonin distribution in live cells with three-photon excitation,” Science 275(5299), 530–532 (1997). [CrossRef] [PubMed]

3

3. K. D. Belfield, M. V. Bondar, F. E. Hernández, O. V. Przhonska, X. Wang, and S. Yao, “A superfluorescent fluorenyl probe with efficient two-photon absorption,” Phys. Chem. Chem. Phys. 13(10), 4303–4310 (2011). [CrossRef] [PubMed]

], high-efficiency up-converted stimulated emission [4

4. G. S. He, P. P. Markowicz, T. C. Lin, and P. N. Prasad, “Observation of stimulated emission by direct three-photon excitation,” Nature 415(6873), 767–770 (2002). [CrossRef] [PubMed]

7

7. X. J. Feng, P. L. Wu, K. F. Li, M. S. Wong, and K. W. Cheah, “Highly efficient multiphoton-absorbing quadrupolar oligomers for frequency upconversion,” Chemistry 17(8), 2518–2526 (2011). [PubMed]

], optical limiting [8

8. G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett. 20(14), 1524–1526 (1995). [CrossRef] [PubMed]

,9

9. Y. Morel, A. Irimia, P. Najechalski, Y. Kervella, O. Stephan, P. L. Baldeck, and C. Andraud, “Two-photon absorption and optical power limiting of bifluorene molecule,” J. Chem. Phys. 114(12), 5391–5396 (2001). [CrossRef]

], biomedical [10

10. I. Cohanoschi, L. Echeverría, and F. E. Hernández, “Three-photon absorption measurements in hematoporphyrin IX: “Ground-breaking opportunities in deep photodynamic therapy,” Chem. Phys. Lett. 419(1-3), 33–36 (2006). [CrossRef]

], light-activated therapy field [11

11. L. Y. Zhu, Y. P. Yi, Z. G. Shuai, J. L. Brédas, D. Beljonne, and E. Zojer, “Structure-property relationships for three-photon absorption in stilbene-based dipolar and quadrupolar chromophores,” J. Chem. Phys. 125(4), 044101 (2006). [CrossRef] [PubMed]

13

13. P. Cronstrand, Y. Luo, P. Norman, and H. Àgren, “Ab initio calculations of three-photon absorption,” Chem. Phys. Lett. 375(1-2), 233–239 (2003). [CrossRef]

], three-dimensional optical data storage [14

14. P. C. Jha, Y. Luo, I. Polyzos, P. Persephonis, and H. Ågren, “Two- and three-photon absorption of organic ionic pyrylium based materials,” J. Chem. Phys. 130(17), 174312 (2009). [CrossRef] [PubMed]

], microfabrication [15

15. I. Wang, M. Bouriau, P. L. Baldeck, C. Martineau, and C. Andraud, “Three-dimensional microfabrication by two-photon-initiated polymerization with a low-cost microlaser,” Opt. Lett. 27(15), 1348–1350 (2002). [CrossRef] [PubMed]

].

In many laser-based applications, such as optical data storage and biological imaging, a random intensity fluctuation is harmful. One of the best technical approaches to reduce such laser fluctuation is to make the laser beam simply pass through a nonlinear medium. The mechanisms include reverse saturable absorption, multiphoton absorption, nonlinear refraction, and optically triggered scattering. In multiphoton-absorption-induced optical stabilization, using materials with a larger 3PA cross section value will result in a better stabilization behavior. 3PA-induced optical stabilization has some salient features: (i) instantaneous response; (ii) high linear transmittance at low incident power and rapid attenuation at high incident power, which is based on the cubic dependence. However, the relatively small 3PA cross section values of present nonlinear molecules limit their practical applications.

Here, we designed and successfully synthesized a bifluorenylidene derivative with four branches as electron donors distributed on each corner. Carbon-carbon double bond units were utilized as the connecting spacers between two fluorenylidene (by C9 and C9’) and between the central core and the peripheral groups, in order to ensure effective electronic conjugation between end groups and the core moiety, and allow large intramolecular charge transfer to take place within the chromophore. Hence, the overall molecular structure of the model compound is expected to simultaneously possess several potential 3PA-enhancing characters and cooperative enhancement including multibranched intermolecular charge transfer between core and molecular termini, increased π-electron number, elongated coplanarity of the conjugation system. The synthesized molecule with the symmetric 2D-π-2D conjugated structure, is named as 2,7,2’,7’-tetra(4-vinylanisole)-[9,9’]bifluorenylidene. D and π represent electron donor and conjugated π-electron bridge, respectively. Figure 1
Fig. 1 (a) Zn dust, AcOH, reflux; b) PBr3, 150°C; (c) DBU, acetonitrile, 60°C; (d) DMF, 4-Methoxystyrene, Palladium acetate, K2CO3, TBAB, 110°C. 1H-NMR(400MHz, CDCl3):δppm 7.87(s, 4H), 7.64(d, 4H, J = 8Hz), 7.49(d, 8H, J = 8.4Hz),7.10(d, 8H, J = 18.4Hz), 6.92(d, 8H, J = 8.8Hz),6.16(s, 4H),3.85(s, 12H). MS(ESI) m/z: 896 [M + K]+.
shows the synthetic route of the compound.

2. Experimental

The experimental setup for 3PA-induced fluorescence and nonlinear absorption effects is presented in Fig. 2
Fig. 2 Experimental setup for 3PA induced fluorescence and input-output relation measurements. Two lenses (L1, L2) and a pinhole (PH) form a spatial filter. D1 and D2 are used to obtain the incident and transmitted intensity. The fluorescence light is collected by lens L4 and coupled into the spectrometer with a photomultiplier (D3).
. In the measurement, the incident 1064 nm laser was provided by a Q-switched mode-locked Nd:YAG pulsed laser (Continuum, PY61-10) with pulse width of 38 ps, repetition rate of 10 Hz. After spatial filtering (lenses L1, L2, and the pinhole PH), the laser beam was directed to the sample, and focused inside the 10 mm cell filled with dye solution using lens L3 (focal length 25.6 cm). The focal plane is at the mid-point of the cell. The upconversion fluorescence light from the dye was collected with lens L4 perpendicular to the cell, and then coupled into the spectrometer. The laser beam was separated into two beams using a beam splitter. J3-05 probes (Molectron Co.), i.e. D1 and D2, were used to monitor the incident and transmitted laser pulse energy simultaneously, respectively. The beam waist radius at the focal plane was 26 μm (z = 0). The beam radius at the input and output plane are both 52 μm (z = −5 mm and + 5 mm, respectively). The measurement of the 3PA properties of the compound was done at 8.5 × 10−4 mol/L in CHCl3.

The linear absorption and steady fluorescence spectra of the compound were measured using a UV-VIS-NIR Cary5000 spectrophotometer and a Spex fluorescence spectrometer, respectively.

3. Result and discussion

Figure 3
Fig. 3 Linear absorption (solid line), steady-state fluorescence spectra (short dot line) and upconversion fluorescence spectra (scattered square) of the molecule in CHCl3.
shows the linear absorption and steady-state fluorescence spectra of the compound in CHCl3 at a concentration of 2.5 × 10−6 mol/L. The influences from the quartz liquid cell and the solvent have been subtracted. The molecule has strong UV absorption in the spectral ranges of 310-470 nm. One can find that an interesting feature of the absorption spectra is the absence of linear absorption in the spectra range of 470-1200 nm. This indicates that excitation in that wavelength range can only occur through nonlinear (multiphoton) absorption process. The three-photon energy of the 1064 nm radiation just falls into the strong UV absorption band, hence very large 3PA cross section value in this compound may be expected.

Excited state absorption can be discarded because of three reasons: (1) The absence of one-photon (1064 nm) and two-photon (532 nm) absorption in the absorption spectrum; (2) Quantum chemistry computations have been carried by means of the TD-HF/6-31G method and the sophisticated polarized continuum model (PCM), and the data of the first six excited states are shown in Table 1

Table 1. Electronic transition data obtained by the TD-HF/6-31G combined with PCM model

table-icon
View This Table
. The results indicate that the compound have no stepwise absorption (excited state absorption) channels such as 1 + 1 + 1, 2 + 1, or 1 + 2 photon absorption, only the one transition S0→S1 (375.35 nm) matches the 3PA rules for 1064nm wavelength laser; (3) In Fig. 4
Fig. 4 Measured upconversion fluorescence intensity as a function of the incident 1064 nm intensity. The solid lines is the best-fit curves based on the function y = axn with n = 2.92
, the upconversion fluorescence intensity exhibits a cubic dependence on incident intensity, which is characteristic of three-photon process. The shapes of the steady-state and upconversion fluorescence (in Fig. 3) are similar. The difference between the steady-state and upconversion fluorescence spectra is attributed to the reabsorption effect of the solution [8

8. G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett. 20(14), 1524–1526 (1995). [CrossRef] [PubMed]

]. Propagating within the solution sample, the different spectral components of the fluorescence emission undergo different attenuation, and the attenuation in the shorter-wavelength range is much stronger than that in the longer-wavelength range [8

8. G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett. 20(14), 1524–1526 (1995). [CrossRef] [PubMed]

]. One can be confident that the excitation process is induced by the simultaneous absorption of three photons.

Intensity-dependent transmittance measurements are utilized to obtain 3PA cross section. Neglecting the linear absorption at the pump wavelength, the beam attenuation due to three-photon absorption along the optical propagation path z is given by the following equation:
dI(z,r,t)/dz=α3I(z,r,t)3.
(1)
Here z is the propagation length inside the sample, α3is the 3PA coefficient of the sample, I(z,r,t) is the irradiance that depends on the propagation distance z, radial r, and time t. The solution for Eq. (1) is [14

14. P. C. Jha, Y. Luo, I. Polyzos, P. Persephonis, and H. Ågren, “Two- and three-photon absorption of organic ionic pyrylium based materials,” J. Chem. Phys. 130(17), 174312 (2009). [CrossRef] [PubMed]

]:
I(z=L/2,r,t)=I(z=L/2,r,t)1+2α3LI(z=L/2,r,t)2,
(2)
where Lis thickness of the sample, I(z=L/2,r,t)and I(z=L/2,r,t) is the incident intensity distribution and the transmitted intensity distribution, respectively.

As we know, the irradiance of a Gaussian beam with no absorption or beam depletion can be written as
I(z,r)=A02ω2(z)exp[2r2ω2(z)],
(3)
where ω2(z)=ω02[(1+(λz/πω02n)2], ω0 is the waist radius of the Gaussian beam, λis the laser wavelength, and A02/ω2(z)is the on-axis irradiance. In the experiments, the input plane, the beam waist and the output plane are at z = -L/2, 0 and L/2 (L = 10 mm), respectively.

Figure 5
Fig. 5 Transmitted on-axis intensity vs. incident on-axis intensity curves of the compound. The solid line represents the theoretical fitting curve. The best-fit parameter was γ = 11.9 × 10−20 cm3/W2.
shows transmitted on-axis intensity vs. incident on-axis intensity curves of the compound in CHCl3. Each data point represents an average over 10 laser pulses. The solid line represents the theoretical fitting with the best-fit parameter α3 = 11.9 × 10−20 cm3/W2. No nonlinear effect can be detected in pure solvent. One can see that the sample displays apparent optical limiting effect. The measured transmittance becomes low slowly as the incident radiance increases below 10 GW/cm2. There is a dramatic drop of the transmittance at the range 10-150 GW/cm2 of incident radiance. When the incident irradiance reaches ~150 GW/cm2, the transmittance decreases to 0.8% or so. There is no detectable decomposition even as the incident radiance reaches 200 GW/cm2.

Generally, resonant energy transfer may take place and play a major role as the dye concentration increases. It probably has an unusual concentration dependence of higher nonlinear effects [16

16. S. Delysse, P. Filloux, V. Dumarcher, C. Fiouini, and J. M. Nunzi, “Multiphoton absorption in organic dye solutions,” Opt. Mater. 9(1-4), 347–351 (1998). [CrossRef]

]. In the used solution, the transition moment μ12≈3.36 D (11 × 10−30 C﹒m), the molecular spacing r≈1.2 × 10−8 m, and the half width of the transition is Γ1/2≈0.53 eV. We may assume the excited-state lifetime τ2≈1 ps. According to the reference [16

16. S. Delysse, P. Filloux, V. Dumarcher, C. Fiouini, and J. M. Nunzi, “Multiphoton absorption in organic dye solutions,” Opt. Mater. 9(1-4), 347–351 (1998). [CrossRef]

], the multi-photon enhancement factor γR/γNR, which is from the resonant energy transfer, is estimated to be 1.4 × 10−7. Consequently, the concentration dependence of higher nonlinear effects can be ignored.

From the characteristic curve in Fig. 5, one can see when the incident intensity increased from 20 to 150 GW/cm2, the transmitted on-axis intensity approaches a constant. Even a very large fluctuation (between 20 and 150 GW/cm2) of the incident intensity can just lead to a very small fluctuation of the transmitted intensity. Therefore, this type of input-output relation can be expected to be used for optical pulse stabilization purposes.

The optical stabilization measurement results are shown in Fig. 6(a)
Fig. 6 Measured pulse energy fluctuation of incident laser pulses (a). Measured pulse energy fluctuation (b) and on-axis intensity fluctuation (c) of the corresponding transmitted laser pulses.
for the incident laser pulse energy fluctuation at the input face of the cell, in Fig. 6(b) for the corresponding transmitted laser pulse energy fluctuation at the output face of the cell and in Fig. 6(c) for the corresponding calculated on-axis transmitted laser pulse intensity fluctuation at the output face of the cell. The apparent difference between Fig. 6(b) and Fig. 6(c) is ascribed to Gaussian distribution of energy of the incident laser, since for a Gaussian beam, with the radial r increasing, the optical intensity becomes lower and the transmittance becomes higher.

From Fig. 6, one can see that the instantaneous energy fluctuation for the incident laser pulses is very severe, the maximum fluctuation can even be near 300%. However, after passing through the 3PA medium, the maximum fluctuation for the transmitted pulse energy can be reduced to less than 10%, and the on-axis transmitted intensity is almost a constant, which is an ideal optical stabilization.

Moreover, a 3PA-induced nonlinear absorptive system is one of the best technical approaches for optical stabilization and optical limiting with the advantages of (i) a fast temporal response, (ii) a higher initial transmittance for weak input signals and (iii) the threshold value of optical limiting and optical stabilization of the solution can be easily adjusted by changing its concentration.

4. Conclusions

We designed and synthesized a bifluorenylidene derivative with extended π-conjugated system. Ideal 3PA-induced optical limiting capability has been achieved. The measured 3PA cross section is as high as (81 ± 8) × 10−76 cm6s2. The optical stabilization performance of the compound is distinguished. The on-axis transmitted intensity approached a constant even though the incident laser pulse fluctuation was 300%.

Acknowledgments

This work is supported by the National Science Foundation of China (No.11004048) and the Science Foundation of The Education Department of Henan Province, China (No.2009B140002).

References and links

1.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, “Measuring serotonin distribution in live cells with three-photon excitation,” Science 275(5299), 530–532 (1997). [CrossRef] [PubMed]

2.

J. M. Leeder and D. L. Andrews, “A molecular theory for two-photon and three-photon fluorescence polarization,” J. Chem. Phys. 134(9), 094503 (2011). [CrossRef] [PubMed]

3.

K. D. Belfield, M. V. Bondar, F. E. Hernández, O. V. Przhonska, X. Wang, and S. Yao, “A superfluorescent fluorenyl probe with efficient two-photon absorption,” Phys. Chem. Chem. Phys. 13(10), 4303–4310 (2011). [CrossRef] [PubMed]

4.

G. S. He, P. P. Markowicz, T. C. Lin, and P. N. Prasad, “Observation of stimulated emission by direct three-photon excitation,” Nature 415(6873), 767–770 (2002). [CrossRef] [PubMed]

5.

K. D. Belfied, M. V. Bondar, C. O. Yanez, F. E. Hernández, and O. V. Przhonska, “Two-photon absorption and lasing properties of new fluorene derivatives,” J. Mater. Chem. 19(40), 7498–7502 (2009). [CrossRef]

6.

P. L. Wu, X. J. Feng, H. L. Tam, M. S. Wong, and K. W. Cheah, “Efficient three-photon excited deep blue photoluminescence and lasing of diphenylamino and 1,2,4-triazole endcapped oligofluorenes,” J. Am. Chem. Soc. 131(3), 886–887 (2009). [CrossRef] [PubMed]

7.

X. J. Feng, P. L. Wu, K. F. Li, M. S. Wong, and K. W. Cheah, “Highly efficient multiphoton-absorbing quadrupolar oligomers for frequency upconversion,” Chemistry 17(8), 2518–2526 (2011). [PubMed]

8.

G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett. 20(14), 1524–1526 (1995). [CrossRef] [PubMed]

9.

Y. Morel, A. Irimia, P. Najechalski, Y. Kervella, O. Stephan, P. L. Baldeck, and C. Andraud, “Two-photon absorption and optical power limiting of bifluorene molecule,” J. Chem. Phys. 114(12), 5391–5396 (2001). [CrossRef]

10.

I. Cohanoschi, L. Echeverría, and F. E. Hernández, “Three-photon absorption measurements in hematoporphyrin IX: “Ground-breaking opportunities in deep photodynamic therapy,” Chem. Phys. Lett. 419(1-3), 33–36 (2006). [CrossRef]

11.

L. Y. Zhu, Y. P. Yi, Z. G. Shuai, J. L. Brédas, D. Beljonne, and E. Zojer, “Structure-property relationships for three-photon absorption in stilbene-based dipolar and quadrupolar chromophores,” J. Chem. Phys. 125(4), 044101 (2006). [CrossRef] [PubMed]

12.

Y. P. Yi, L. Y. Zhu, and Z. G. Shuai, “The correction vector method for three-photon absorption: The effects of π conjugation in extended rylenebis(dicarboximide)s,” J. Chem. Phys. 125(16), 164505 (2006). [CrossRef] [PubMed]

13.

P. Cronstrand, Y. Luo, P. Norman, and H. Àgren, “Ab initio calculations of three-photon absorption,” Chem. Phys. Lett. 375(1-2), 233–239 (2003). [CrossRef]

14.

P. C. Jha, Y. Luo, I. Polyzos, P. Persephonis, and H. Ågren, “Two- and three-photon absorption of organic ionic pyrylium based materials,” J. Chem. Phys. 130(17), 174312 (2009). [CrossRef] [PubMed]

15.

I. Wang, M. Bouriau, P. L. Baldeck, C. Martineau, and C. Andraud, “Three-dimensional microfabrication by two-photon-initiated polymerization with a low-cost microlaser,” Opt. Lett. 27(15), 1348–1350 (2002). [CrossRef] [PubMed]

16.

S. Delysse, P. Filloux, V. Dumarcher, C. Fiouini, and J. M. Nunzi, “Multiphoton absorption in organic dye solutions,” Opt. Mater. 9(1-4), 347–351 (1998). [CrossRef]

17.

J. H. Liu, Y. L. Mao, Y. Z. Gu, M. J. Huang, W. F. Zhang, L. J. Guo, and W. B. Ma, “Large irradiance limiting induced by three-photon absorption of a symmetrical fluorene-based molecule,” Opt. Express 16(7), 4739–4746 (2008). [CrossRef] [PubMed]

OCIS Codes
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.4710) Nonlinear optics : Optical nonlinearities in organic materials

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 4, 2012
Manuscript Accepted: May 18, 2012
Published: June 15, 2012

Citation
Junhui Liu and Yuanxu Wang, "Three-photon-absorption-induced optical stabilization effects in a bifluorenylidene derivative," Opt. Express 20, 14596-14603 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-14596


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References

  1. S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, “Measuring serotonin distribution in live cells with three-photon excitation,” Science275(5299), 530–532 (1997). [CrossRef] [PubMed]
  2. J. M. Leeder and D. L. Andrews, “A molecular theory for two-photon and three-photon fluorescence polarization,” J. Chem. Phys.134(9), 094503 (2011). [CrossRef] [PubMed]
  3. K. D. Belfield, M. V. Bondar, F. E. Hernández, O. V. Przhonska, X. Wang, and S. Yao, “A superfluorescent fluorenyl probe with efficient two-photon absorption,” Phys. Chem. Chem. Phys.13(10), 4303–4310 (2011). [CrossRef] [PubMed]
  4. G. S. He, P. P. Markowicz, T. C. Lin, and P. N. Prasad, “Observation of stimulated emission by direct three-photon excitation,” Nature415(6873), 767–770 (2002). [CrossRef] [PubMed]
  5. K. D. Belfied, M. V. Bondar, C. O. Yanez, F. E. Hernández, and O. V. Przhonska, “Two-photon absorption and lasing properties of new fluorene derivatives,” J. Mater. Chem.19(40), 7498–7502 (2009). [CrossRef]
  6. P. L. Wu, X. J. Feng, H. L. Tam, M. S. Wong, and K. W. Cheah, “Efficient three-photon excited deep blue photoluminescence and lasing of diphenylamino and 1,2,4-triazole endcapped oligofluorenes,” J. Am. Chem. Soc.131(3), 886–887 (2009). [CrossRef] [PubMed]
  7. X. J. Feng, P. L. Wu, K. F. Li, M. S. Wong, and K. W. Cheah, “Highly efficient multiphoton-absorbing quadrupolar oligomers for frequency upconversion,” Chemistry17(8), 2518–2526 (2011). [PubMed]
  8. G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett.20(14), 1524–1526 (1995). [CrossRef] [PubMed]
  9. Y. Morel, A. Irimia, P. Najechalski, Y. Kervella, O. Stephan, P. L. Baldeck, and C. Andraud, “Two-photon absorption and optical power limiting of bifluorene molecule,” J. Chem. Phys.114(12), 5391–5396 (2001). [CrossRef]
  10. I. Cohanoschi, L. Echeverría, and F. E. Hernández, “Three-photon absorption measurements in hematoporphyrin IX: “Ground-breaking opportunities in deep photodynamic therapy,” Chem. Phys. Lett.419(1-3), 33–36 (2006). [CrossRef]
  11. L. Y. Zhu, Y. P. Yi, Z. G. Shuai, J. L. Brédas, D. Beljonne, and E. Zojer, “Structure-property relationships for three-photon absorption in stilbene-based dipolar and quadrupolar chromophores,” J. Chem. Phys.125(4), 044101 (2006). [CrossRef] [PubMed]
  12. Y. P. Yi, L. Y. Zhu, and Z. G. Shuai, “The correction vector method for three-photon absorption: The effects of π conjugation in extended rylenebis(dicarboximide)s,” J. Chem. Phys.125(16), 164505 (2006). [CrossRef] [PubMed]
  13. P. Cronstrand, Y. Luo, P. Norman, and H. Àgren, “Ab initio calculations of three-photon absorption,” Chem. Phys. Lett.375(1-2), 233–239 (2003). [CrossRef]
  14. P. C. Jha, Y. Luo, I. Polyzos, P. Persephonis, and H. Ågren, “Two- and three-photon absorption of organic ionic pyrylium based materials,” J. Chem. Phys.130(17), 174312 (2009). [CrossRef] [PubMed]
  15. I. Wang, M. Bouriau, P. L. Baldeck, C. Martineau, and C. Andraud, “Three-dimensional microfabrication by two-photon-initiated polymerization with a low-cost microlaser,” Opt. Lett.27(15), 1348–1350 (2002). [CrossRef] [PubMed]
  16. S. Delysse, P. Filloux, V. Dumarcher, C. Fiouini, and J. M. Nunzi, “Multiphoton absorption in organic dye solutions,” Opt. Mater.9(1-4), 347–351 (1998). [CrossRef]
  17. J. H. Liu, Y. L. Mao, Y. Z. Gu, M. J. Huang, W. F. Zhang, L. J. Guo, and W. B. Ma, “Large irradiance limiting induced by three-photon absorption of a symmetrical fluorene-based molecule,” Opt. Express16(7), 4739–4746 (2008). [CrossRef] [PubMed]

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