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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 17 — Aug. 23, 2004
  • pp: 3921–3927
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Z-scan measurements using femtosecond continuum generation

Leonardo De Boni, Acácio A. Andrade, Lino Misoguti, Cléber R. Mendonça, and Sérgio C. Zilio  »View Author Affiliations


Optics Express, Vol. 12, Issue 17, pp. 3921-3927 (2004)
http://dx.doi.org/10.1364/OPEX.12.003921


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Abstract

We present a single beam Z-scan technique using an intense, broadband, white-light continuum (WLC) beam for the direct measurement of nonlinear absorption spectra. In order to demonstrate the validity of our technique, we compared the results of tetraaniline and Sudan 3 solutions obtained with WLC and conventional single wavelength light sources. Both approaches lead to the same nonlinear spectrum, indicating that the association of the Z-scan technique and the WLC source results in an useful method for the measurement of nonlinear spectra of both absorbing (saturable absorption or reverse saturable absorption) and transparent (two-photon absorption) samples.

© 2004 Optical Society of America

1. Introduction

The broadband characterization of optical nonlinearities is a subject of prime importance due to the current interest in the development of new materials exhibiting high nonlinearities and for the selection of the optimum wavelength in specific applications [1

1. M. Albota, D. Beljone, J. -L. Bredas, J. E. Ehrlich, J. -Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Röckel, M. Rumi, G. Subramanian, W. W. Webb, X. L. Wu, and C. Xu, “Design of organic molecules with large two-photon absorption cross sections,” Science , 281, 1653 (1998). [CrossRef] [PubMed]

]. Usually, the nonlinear spectrum is determined by a set of measurements performed at discrete wavelengths using a tunable light source, such as an optical parametric amplifier (OPA), which is capable of a broad tunability, while keeping a good pulse quality. However, to obtain nonlinear spectra with good resolution, small wavelength increments are required, which results in a time-consuming procedure. To overcome this drawback, several groups have been developing techniques to measure the wavelength-multiplexed nonlinear spectrum, most of them using pump-probe methods with a white-light continuum (WLC) as probe. For instance, Negres et al. [2

2. R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Experiment and analysis of two-photon spectroscopy using a white-light continuum probe,” IEEE J. Quantum Electron. 38, 1205 (2002). [CrossRef]

] measured the nondegenarete two-photon absorption (2PA) spectra of ZnS and organic dyes in solution with a fixed wavelength infrared pump pulse and a weak WLC as probe. He et al. [3

3. G. S. He, T. -C. Lin, P. N. Prasad, R. Kannan, R. A. Vaia, and L. -S. Tan, “New technique for degenerate two-photon absorption spectral measurements using femtosecond continuum generation,” Opt. Express 10, 566 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-13-566 [CrossRef] [PubMed]

] recently introduced a new technique for broadband measurements of degenerate 2PA spectra also using femtosecond continuum generation. In that approach, the strong WLC is dispersed by a prism and since each color is focused at a different position onto the sample, the nondegenerate 2PA processes among different spectral components is avoided. The nonlinear 2PA spectrum is obtained by normalizing the sample transmittance at high power levels to the transmittance at a much lower power. However, this technique needs a calibration of the wavelength-channel relationship and the sample has to be fairly homogeneous because each spectral component impinges on a different position.

In the present work we report a new Z-scan technique capable of measuring the nonlinear absorption spectra with a single WLC beam. In this approach, a strong WLC beam is generated in a water cell and used in the standard open aperture Z-scan technique [8

8. M. Sheik-Bahae, A. A. Said, T. 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]

]. By performing measurements with this light source and using a spectrometer as detector, we can obtain simultaneous Z-scan signatures for each wavelength in a single scan. To demonstrate the validity of our technique, we carried out measurements in two different molecules using, for comparison sake, both WLC and conventional single wavelength Z-scan techniques. We measured solutions of aniline tetramers and Sudan 3 dissolved in C2H6OS (dimethylsulfoxide, dubbed as DMSO). Both samples present absorption bands in the visible and the nonlinear spectra obtained with the two light sources were the same in both the absorbing and transparent spectral regions. We believe that this new technique is an important tool for the characterization of saturable absorption (SA) and/or reverse saturable absorption (RSA) in the resonant regime, and also enables the measurement of degenerate two-photon absorption (2PA) spectra for nonresonant radiation.

2. Method

2.1 Experimental setup

Figure 1 schematically shows the experimental apparatus used in this work. The femtosecond pump source is a Ti:sapphire chirped pulse amplified system (CPA-2001, CLARK-MXR) delivering pulses of 150 fs duration at 775 nm, with energies up to 0.8 mJ at a 1 kHz repetition rate. Part of the beam was used to pump a tunable optical parametric amplifier (OPA), while the other part is employed for WLC generation. Our commercial OPA (TOPAS, Light Conversion) provides 120 fs pulses tunable from 460 to 2600 nm.

The WLC is produced by focusing the pump light with an f=10 cm lens into a 4 cm-thick quartz cell containing distilled water. A low-pass filter is used to remove the strong pump pulse and the infrared part of the WLC spectrum. The use of 0.3 mJ laser pulses generates about 10 µJ of WLC, whose spectrum is shown in Fig. 2. After re-collimation, the WLC beam is focused onto the sample, which is scanned along the beam propagation z-direction, as usually done in the traditional Z-scan method [8

8. M. Sheik-Bahae, A. A. Said, T. 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]

]. The WLC transmitted through the sample is completely focused into a portable spectrometer with a resolution of ~1 nm (USB 2000, Ocean Optics). The WLC is a fluctuating light source but since our portable spectrometer measures the average of about 1,000 shots (integration time of 1 second), we cannot observe the expected shot to shot fluctuation. Therefore, our results agree with the OPA results in average and the shot to shot fluctuation just increases the error bars.

The spectra are acquired for each z position as the sample is scanned along the z-direction and then normalized to the one obtained far from the focal plane. By selecting a particular wavelength from the complete set of measured spectra we obtain a Z-scan signature according to the nonlinear response at that wavelength.

Fig. 1. Schematic diagram of the experimental setup for WLC and single wavelength Z-scan measurements. The removable mirror is used to switch from discrete to WLC Z-scan, which use a photo-detector or a spectrometer, respectively.
Fig. 2. Typical spectrum of white light generated in water after passing through the low-pass filter (solid line) and chirp of the WLC measured with the OKE cross-correlation technique with a gate pulse at 700 nm (triangles).

As we mentioned earlier, we also performed conventional single wavelength Z-scan measurements using the tunable OPA light source to compare with the results obtained with the WLC. Open aperture Z-scan measurements were carried out for each selected wavelength, using a simple silicon PIN photo-detector coupled to a lock-in amplifier instead of the spectrometer.

2.2 Chirp characterization

The chirp of the WLC pulse was characterized with optical Kerr effect (OKE) measurements, using a strong pump pulse at 700 nm from the OPA and a weak WLC beam as probe. We employed a 2 mm-thick quartz cuvette filled with hexane as the fast nonlinear medium. As the OKE technique requires, two crossed calcite polarizers with transmission axes at 45° with respect to the pump beam polarization were used in the probe beam. The spectrometer was employed to measure the spectrum of the WLC passing through the gate as function of delay between pump and probe pulses. This experiment maps the frequency content of the WLC in the time domain because it allows the transmission of just a single slice of the WLC spectrum as the delayed strong pulse opens the gate. The delay of the OKE cross-correlation traces with respect to the gate pulse shown in Fig. 2, can be adjusted with a second order polynomial, which gives a rate of chirp of 18 fs/nm. This strong chirp can be attributed to the water dispersion in the long cell and also to the calcite polarizers used in the OKE setup. It is worth to say that the calcite polarizers were kept in place for the nonlinear spectra measurements to avoid any change of the chirp rate.

2.3 Samples

One of the samples studied was a solution of phenyl/-NH2 end-caped tetraaniline base (emeraldine oxidation state) dissolved in DMSO to a concentration of 5×1016 cm-3 and magnetically stirred overnight. The aniline tetramer was synthesized according to the procedure described in Ref. [9

9. C. R. Mendonça, D. S. Santos, L. De Boni, D. T. Balogh, O. N. Oliveira, and S. C. Zilio, “Dichroism induced by photoisomerization of aniline tetramers in polymeric films,” Adv. Mater. 12, 1126 (2000). [CrossRef]

]. We previously characterized its dynamic optical nonlinearity, which was shown to be dependent on the excited state population, whose relaxation time was found to be 3.4 ns [10

10. P. L. Franzen, L. De Boni, D. S. Santos, C. R. Mendonça, and S. C. Zilio, “Dynamic optical nonlinearities in aniline tetramers,” J. Phys. Chem. B (to be published).

]. Another sample used to demonstrate our technique was a solution of the di-azocompound Sudan 3/DMSO in a concentration of 6×1016 cm-3. This molecule presents a photo-induced cis-trans isomerization and strong excited state nonlinear processes [11

11. A. Andrade, S. B. Yamaki, L. Misoguti, S. C. Zilio, Tereza Z. Atvars, O. N. Oliveira, and C. R. Mendonça, “Two-photon absorption in di-azobenzene compounds,” Opt. Mater. (to be published).

]. The relaxation time of the excited trans state is on order of 3 ps. The linear spectra of both tetraaniline and Sudan 3 solutions are respectively shown in Fig. 3 (a) and (b).

3. Results and discussion

3.1 Saturable absorption

Figure 3(a) shows the normalized transmittance change obtained with WLC and single wavelength Z-scan methods for the aniline tetramer solution. The pulse energy used in the single wavelength Z-scan measurement was kept fix at 0.04 µJ (irradiance of 50 GW/cm2) over the entire wavelength region used. The nonlinear spectrum was measured in 5 nm steps around the same spectral range as for the WLC, with pulse energy of 4 µJ, resulting nearly in the same irradiance per bandwidth used in the OPA. As seen in Fig. 3, good agreement exists between the results obtained for the two light sources. The negative transmittance below 510 nm indicates a RSA process; above it, the positive normalized transmittance shows the strong SA process.

For calibration purposes, the normalized WLC Z-scan transmittance was scaled to the curve obtained with the single wavelength Z-scan. This procedure allowed characterizing the pulse intensity, beam waist (w 0) and the Rayleigh range (z 0) of each color of the WLC beam. However, from the practical point of view, we found that the energy of the WLC beam at a given wavelength can be calculated by considering the continuum as made up of a group of nearly bandwidth-limited pulses centered at various wavelengths. From the total energy and spectral distribution of the WLC pulse, the energy inside each bandwidth, which was assumed as being of the same order as those from the OPA, can be calculated. Another simplification that can be made to calculate the intensity is to consider beam waist approximately constant for all wavelengths. This procedure simplifies the analysis and gives a fairly good agreement with the traditional discrete Z-scan method.

Using the same procedure for the Sudan 3 solution, we obtained the results shown in Fig. 3(b). In this case, only the SA process was observed in the resonant absorption band. The agreement between the results obtained with the two light sources are unexpected because we are dealing with population effects and accumulative processes are likely to happen.

Fig. 3. Linear (dashed line) and nonlinear absorption spectra of (a) aniline tetramers and (b) Sudan 3 solutions. The solid line and the points were obtained with WLC and discrete Z-scan techniques, respectively.

Our explanation for the coincidence between the results of the Z-scan technique using different light sources relies on the spectral separation in time due to the chirp in the pulse. Since the positive group-velocity (GVD) forces the red side of the spectrum to propagate faster than the blue side, we should expect an accumulative nonlinear effect in the bluer part of the pulse whenever the relaxation of the nonlinear process is of the order or longer than the pulse chirp. This is the case of the samples studied here. A possible way of explaining our results is by considering that the pulse fluence is high enough to cause an appreciable saturation of the excited state population. In this case, we can assume that as soon as the WLC beam starts to be absorbed by the sample, a strong population depletion of the ground state is induced and maintained during all WLC interaction time. In other words, the leading part of the absorbed WLC beam produces the excited state population and remaining of the pulse just measures the excited state absorption (ESA). To verify this hypothesis, we considered the three-energy-level diagram shown in Fig. 4(a) and the spectral intensity distribution actually employed in the experiment (see Fig. 2) to calculate the population evolution during the pulse arrival. The numerical simulation was carried out using σ01 obtained from the linear absorption spectra and the respective concentrations, τ10 was determined previously to be 3.4 ns for tetraaniline and about 3 ps for Sudan 3, τrel was assumed to be of the order of the pulse duration and σem≈σ01. We found that as soon the molecule starts to absorb, it takes just a few bandwidths (~20 nm) to completely saturate the excited state.

Fig. 4. Three-energy-level diagram used to model the nonlinear optical processes.

3.2 Two-photon absorption

We have also used the WLC Z-scan to measure the 2PA process in Sudan 3. In this case we had to use a more concentrated solution (6×1017 cm-3) and the full WLC power (10 µJ, corresponding to an irradiance of 120 GW/cm2 in a 10 nm bandwidth) to be able to detect the weak nonlinear absorption spectrum at the transparent region. Again, a coincidence between the results obtained with the two light sources is observed, but now it is straightforward to explain it because of the chirp of the WLC pulse. As already discussed, the chirp spreads the nearly bandwidth-limited pulses in time and since the 2PA is a short-time-scale process, it takes place only within the same bandwidth. In other words, different wavelengths do not mix because they arrive at the sample in the different times and thus, we end up with a degenerate 2PA process.

As Fig. 5 shows, there is a general trend of increasing the 2PA cross-section as the wavelength approaches the resonant band. This behavior can be explained by the sum-over state model (SOS) [1

1. M. Albota, D. Beljone, J. -L. Bredas, J. E. Ehrlich, J. -Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Röckel, M. Rumi, G. Subramanian, W. W. Webb, X. L. Wu, and C. Xu, “Design of organic molecules with large two-photon absorption cross sections,” Science , 281, 1653 (1998). [CrossRef] [PubMed]

], in which the two-photon transition happens from the ground state 0 to the excited state 2, as shown in Fig. 4(b). Since the molecule also presents a one-photon allowed intermediate excited state 1, the SOS calculation predicts an enhancement of the 2PA cross-section as the light frequency comes close to resonance [12

12. M. Drobizhev, A. Karotki, M. Kruk, and A. Rebane, “Resonance enhancement of two-photon absorption in porphyrins,” Chem. Phys. Lett. , 355, 175 (2002). [CrossRef]

,13

13. K. Kamada, K. Ohta, I. Yoichiro, and K. Kondo, “Two-photon absorption properties of symmetric substituted diacetylene: drastic enhancement of the cross section near the one-photon absorption peak,” Chem. Phys. Lett. 372, 386 (2003). [CrossRef]

]. In addition, as soon as the resonant band is reached at 600 nm, the SA starts to take over the 2PA process and the normalized transmittance starts to increase, indicating the SA process already shown in Fig. 3(b).

Fig. 5. Linear (dashed line) and two-photon absorption spectra of Sudan 3 solution. The solid line and the squares were obtained with WLC and discrete Z-scan techniques, respectively.

4. Conclusions

In summary, we have introduced a new method for measuring nonlinear absorption spectra, conjugating the well-known single beam Z-scan technique and a white-light continuum source. Results obtained with this method show good agreement with those employing the traditional single wavelength source, although much faster because of the wavelength multiplexing introduced by the use of a broadband source. Moreover, since this technique is single beam, it is simpler than those using a prism or diffraction grating for dispersion. We were capable of measuring nonlinear spectra for saturable absorbers and transparent media. For 2PA processes, the degenerate results are easily interpreted as consequence of the chirp of the WLC pulse. For saturable absorbers, however, our explanation is based on the excited state saturation, a condition that is not general and depends on several parameters such as the light intensity, relaxation times, cross-sections, etc. We tried using a low intensity light but the results were not conclusive because of the bigger noise. Although the application for saturable absorbers still need some further studies, we believe that the present technique is an important tool for the measurement of nonlinear spectra.

Acknowledgments

We acknowledge the support of the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).

References and links

1.

M. Albota, D. Beljone, J. -L. Bredas, J. E. Ehrlich, J. -Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Röckel, M. Rumi, G. Subramanian, W. W. Webb, X. L. Wu, and C. Xu, “Design of organic molecules with large two-photon absorption cross sections,” Science , 281, 1653 (1998). [CrossRef] [PubMed]

2.

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Experiment and analysis of two-photon spectroscopy using a white-light continuum probe,” IEEE J. Quantum Electron. 38, 1205 (2002). [CrossRef]

3.

G. S. He, T. -C. Lin, P. N. Prasad, R. Kannan, R. A. Vaia, and L. -S. Tan, “New technique for degenerate two-photon absorption spectral measurements using femtosecond continuum generation,” Opt. Express 10, 566 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-13-566 [CrossRef] [PubMed]

4.

R. R. Alfano, ed., The supercontinuum laser source, (Springer-Verlag, New York, 1989).

5.

J. C. Wang and J. K. Wang, “Experimental and theoretical analysis of white-light seeded, collinear phase-matching, femtosecond optical parametric amplifiers,” J. Opt. Soc. Am B 21, 45 (2004). [CrossRef]

6.

M. Bellini and T. W. Hansch, “Phase-locked white-light continuum pulses: toward a universal optical frequency-comb synthesizer,” Opt. Lett. 25, 1049 (2000). [CrossRef]

7.

Y. M. Wang, Y. H. Zhao, J. S. Nelson, Z. P. Chen, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography by broadband continuum generation from a photonic crystal fiber,” Opt. Lett. 28, 182 (2003). [CrossRef] [PubMed]

8.

M. Sheik-Bahae, A. A. Said, T. 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]

9.

C. R. Mendonça, D. S. Santos, L. De Boni, D. T. Balogh, O. N. Oliveira, and S. C. Zilio, “Dichroism induced by photoisomerization of aniline tetramers in polymeric films,” Adv. Mater. 12, 1126 (2000). [CrossRef]

10.

P. L. Franzen, L. De Boni, D. S. Santos, C. R. Mendonça, and S. C. Zilio, “Dynamic optical nonlinearities in aniline tetramers,” J. Phys. Chem. B (to be published).

11.

A. Andrade, S. B. Yamaki, L. Misoguti, S. C. Zilio, Tereza Z. Atvars, O. N. Oliveira, and C. R. Mendonça, “Two-photon absorption in di-azobenzene compounds,” Opt. Mater. (to be published).

12.

M. Drobizhev, A. Karotki, M. Kruk, and A. Rebane, “Resonance enhancement of two-photon absorption in porphyrins,” Chem. Phys. Lett. , 355, 175 (2002). [CrossRef]

13.

K. Kamada, K. Ohta, I. Yoichiro, and K. Kondo, “Two-photon absorption properties of symmetric substituted diacetylene: drastic enhancement of the cross section near the one-photon absorption peak,” Chem. Phys. Lett. 372, 386 (2003). [CrossRef]

OCIS Codes
(190.4180) Nonlinear optics : Multiphoton processes
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(300.6530) Spectroscopy : Spectroscopy, ultrafast

ToC Category:
Research Papers

History
Original Manuscript: June 16, 2004
Revised Manuscript: August 5, 2004
Published: August 23, 2004

Citation
Leonardo De Boni, Acácio Andrade, Lino Misoguti, Cléber Mendonça, and Sérgio Zilio, "Z-scan measurements using femtosecond continuum generation," Opt. Express 12, 3921-3927 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-17-3921


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References

  1. M. Albota, D. Beljone, J. -L. Bredas, J. E. Ehrlich, J. -Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Röckel, M. Rumi, G. Subramanian, W. W. Webb, X. L. Wu, and C. Xu, ཿDesign of organic molecules with large two-photon absorption cross sections,ཿ Science 281, 1653 (1998). [CrossRef] [PubMed]
  2. R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, ཿExperiment and analysis of two-photon spectroscopy using a white-light continuum probe,ཿ IEEE J. Quantum Electron. 38, 1205 (2002). [CrossRef]
  3. G. S. He, T. ཿC. Lin, P. N. Prasad, R. Kannan, R. A. Vaia, and L. ཿS. Tan, ཿNew technique for degenerate two-photon absorption spectral measurements using femtosecond continuum generation,ཿ Opt. Express 10, 566 (2002) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-13-566">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-13-566</a>. [CrossRef] [PubMed]
  4. R. R. Alfano, ed., The supercontinuum laser source, (Springer-Verlag, New York, 1989).
  5. J. C. Wang and J. K. Wang, ཿExperimental and theoretical analysis of white-light seeded, collinear phasematching, femtosecond optical parametric amplifiers,ཿ J. Opt. Soc. Am B 21, 45 (2004). [CrossRef]
  6. M. Bellini and T. W. Hansch, ཿPhase-locked white-light continuum pulses: toward a universal optical frequency-comb synthesizer,ཿ Opt. Lett. 25, 1049 (2000). [CrossRef]
  7. Y. M. Wang, Y. H. Zhao, J. S. Nelson, Z. P. Chen, and R. S. Windeler, ཿUltrahigh-resolution optical coherence tomography by broadband continuum generation from a photonic crystal fiber,ཿ Opt. Lett. 28, 182 (2003). [CrossRef] [PubMed]
  8. M. Sheik-Bahae, A. A. Said, T. 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]
  9. C. R. Mendonça, D. S. Santos, L. De Boni, D. T. Balogh, O. N. Oliveira, and S. C. Zilio, ཿDichroism induced by photoisomerization of aniline tetramers in polymeric films,ཿ Adv. Mater. 12, 1126 (2000). [CrossRef]
  10. P. L. Franzen, L. De Boni, D. S. Santos, C. R. Mendonça, and S. C. Zilio, ཿDynamic optical nonlinearities in aniline tetramers,ཿ J. Phys. Chem. B (to be published).
  11. A. Andrade, S. B. Yamaki, L. Misoguti, S. C. Zilio, Tereza Z. Atvars, O. N. Oliveira, and C. R. Mendonça, ཿTwo-photon absorption in di-azobenzene compounds,ཿ Opt. Mater. (to be published).
  12. M. Drobizhev, A. Karotki, M. Kruk, and A. Rebane, ཿResonance enhancement of two-photon absorption in porphyrins,ཿ Chem. Phys. Lett. 355, 175 (2002). [CrossRef]
  13. K. Kamada, K. Ohta, I. Yoichiro, and K. Kondo, ཿTwo-photon absorption properties of symmetric substituted diacetylene: drastic enhancement of the cross section near the one-photon absorption peak,ཿ Chem. Phys. Lett. 372, 386 (2003). [CrossRef]

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