Multiplex method for the measurement of nonlinear susceptibility spectrum applied to third-harmonic generation in a polydiacetylene

(1)

Multiplex method for the measurement of

nonlinear susceptibility spectrum applied to third-harmonic

generation in a polydiacetylene

Takayoshi Kobayashi

a,b,c,d,*

, Akihiro Mito

e

, Satoshi Kobayashi

a

,

Takashi Taneichi

a,b

, Atsuhiro Furuta

a

a_{Department of Physics, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan} b_{Department of Applied Physics and Chemistry and Institute of Laser Science, The University of Telecommunications,}

Choufu-gaoka 1-5-1, Chofu, Tokyo 182-8585, Japan

c_{Institute of Laser Engineering, Osaka University, Yamadakami 2-6, Suita, 565-0871 Osaka, Japan} d_{Department of Electrophysics, National Chiao Tung University, 1001 Ta Hsueh Rd., Hsinchu 300, Taiwan}

e_{National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 3, Tsukuba, Ibaraki 305-8563, Japan}

Received 23 May 2006; in ﬁnal form 6 November 2006 Available online 15 November 2006

Abstract

Broadband near-infrared pulse generated from NOPA (non-collinear optical parametric ampliﬁer) was used for measurement of the spectrum of susceptibility of the third harmonic generation (THG). Corrections for the eﬀects of absorption and refractive index, con-tribution of non-degenerate third-order nonlinearity, and THG by air, were properly addressed.

This multiplex method was applied to a polydiacetylene, poly[5,7-dodecadiyn-1,12-diol-bis(n-butoxylcarbonyl-methyl-urethane)] (4BCMU) in red phase resulting in a good agreement with theoretical prediction.

1. Introduction

Exact knowledge of the hyperpolarizabilities of organic molecules and polymers [1,2] is important for testing of molecular calculation, bond additivity of nonlinearity, nonlinear spectroscopy, and molecular interaction. Third-order nonlinear optical processes can be used for systems with any symmetry, in contrast to the lowest order nonlin-ear processes of the second-order, which are absent in sys-tems with inversion symmetry[3–6].

Among the many third-order processes, third-harmonic (TH) generation (THG) is a purely electronic and coherent

process, and no ambiguity in the mechanism in high con-trast to other processes such as degenerate four-wave mix-ing and optical Kerr eﬀect, in which other incoherent and coherent (like vibrational coherence) nonlinearities can contribute. Therefore, THG measurement is one of the simplest possible methods for the determination of v(3) allowing one to probe only electronic processes in a system. Hence THG v(3)spectrum is the most suitable for studying the mechanism of coherent electronic nonlinearity in a system.

Continuous spectrum of the susceptibility is desired to obtain information on the nonlinear susceptibility in the full spectral range of interest and requirement. For a con-ventional monochromatic laser, the wavelength of the laser must be tuned in a broad spectral range with a small step of wavelength. It takes very long time to get full data of the spectral response from which v(3) spectrum is calculated. In this case the results are expected to easily suﬀer from

*

Corresponding author. Address: Department of Applied Physics and Chemistry and Institute of Laser Science, The University of Telecommu-nications, Choufu-gaoka 1-5-1, Chofu, Tokyo 182-8585, Japan. Fax: +81 42 443 5825.

E-mail address:kobayashi@ils.uec.ac.jp(T. Kobayashi).

(2)

errors induced by instability of the laser during the mea-surement time, diﬀerences in mode pattern and intensity of the fundamental radiation with diﬀerent wavelengths from several lasers. It is therefore desired to study THG with a fundamental having a broad spectrum to obtain the v(3)spectrum of materials of interest.

In this paper, we propose a method for the measurement of v(3) utilizing a broadband pulse from a parametric ampliﬁer pumped with a Ti–sapphire laser fundamental seeded with a femtosecond continuum.

2. Experimental

2.1. Measurement system

Fig. 1 shows a block diagram of the optical system for measurement of multiplex nonlinear susceptibility. The output from an Er-doped fiber mode-locked laser (Clark-MXR, SerF) was amplified with a thin sapphire regenera-tive amplifier (Clark-MXR, CPA-1000) and was used as a pump source of a parametric amplifier to generate a fun-damental pulsed pump for THG. The repetition rate, cen-ter wavelength, pulse energy, and pulse duration of the output pulse were 1 kHz, 775 nm (1.6 eV), 0.5 mJ, and 160 fs, respectively. The polarization of the pulse was hor-izontal. Broadband near-infrared (IR) pulses were gener-ated in the following way. The regenerative amplified pulse was split into two, the polarization of one of the pulses was converted to be vertical with a half-wave plate and then was focused with a lens of f = 120 cm into a 10 mm cell containing CCl4 to generate white-light

continuum.

The generated continuum was directed to a beta-barium borate (BBO, b-BaB2O4) crystal for use as a seed of an

optical parametric ampliﬁer (OPA). The OPA was pumped with a major fraction of the ampliﬁed pulse with a vertical

polarization. The pump and white-light continuum were vertically and horizontally polarized and they were collin-early focused with a lens of 10 cm focal length to match the Type II phase-matching condition. This short focal length is feasible for a broad gain bandwidth of parametric ampliﬁcation in a non-collinear conﬁguration[7–9]. This is a novel type of non-collinear OPA (NOPA) aimed at gen-erating extremely short pulses using broadband pulse developed by several groups including us[10–14].

The principle of generation of broadband near-IR pulse is as follows (Fig. 2). Since the short focal length lens is used for the amplifier, the signal continuum has a broad distribution of incident angle. Signals with different wave-length components incident with different angles to the nonlinear crystal generate an idler with different wave-lengths. The idler spectrum was measured with a PtSi detector coupled to an IR polychromator. The idler had a spectrum extending from 0.46 eV (2.7 lm) to 0.78 eV (1.6 lm) corresponding to the wavelength of pump at 775 nm and that of femtosecond continuum generated in CCl4extending from 0.9 to 1.6 lm.

The output pulse from the OPA composed of a signal and an idler was used as a pump for the THG. It was focused into a polymer ﬁlm. The generated harmonic was guided to a polychromator (f = 20 cm, Ocean Optics) for a visible wavelength coupled to a CCD camera through an optical ﬁber. The spectral range of the combined system of the polychromator and detector extended from 320 to 1040 nm. The spectral resolution of the system was 3.0 nm with a slit width of 0.05 mm. The spectral sensitiv-ities of the wavelength resolving detection systems in both visible and IR were corrected using a standard tungsten lamp (Ushio Electrics).

Fig. 1. Block diagram of apparatus for measurement of broadband multiplex TH spectrum. Laser: Ti–sapphire laser with a regenerative ampliﬁer, BS: beam splitter, 1/2k: half-wave plate, delay stage: variable optical stage, CCl4cell: a cell containing CCl4for femtosecond continuum

generation, PtSi MC PD: PtSi multi-channel photodiode, and Si MC PD: Si multi-channel photodiode.

Fig. 2. Schematic figure of the broadband spectrum generation in near-IR by the OPA process. The generated white-light continuum is directed to a BBO crystal to be used as a seed of an OPA pumped with the amplified pulse with vertical polarization. The pump and white-light continuum are polarized vertically and horizontally, respectively, and the wave vectors at the beam center of both beams are collinearly focused by a lens with 10 cm focal length. This short focal length provides an angular dispersion in the femtosecond continuum resulting in a broad gain bandwidth of paramet-ric amplification in the non-collinear configuration.

(3)

As a standard of the TH susceptibility, high-refractive index glass, FDS9, was used, which has high nonlinearity under non-resonant condition and availability of reliable absolute values of THG susceptibility. A very precise mea-surement with FDS9 and another high-refractive index glass, FD2, is reported [15]. The spectral dependence of the THG was reproduced by the present method of mea-surement. Therefore, these materials can be considered to be appropriate for the standards, and the present method has been veriﬁed to be reliable.

2.2. Sample

The sample, poly(4BCMU) [16], was provided by Drs. S. Shimada and H. Matsuda, National Institute of Advanced Industrial Science and Technology.

3. Method of the determination of the susceptibility

3.1. Correction of the eﬀects of absorption and refractive index

THG takes place through the third-order nonlinear pro-cess. The nonlinear polarization is given as

PTHG ¼ vð3Þð3x; x; x; xÞExðr; tÞExðr; tÞExðr; tÞ: ð1Þ

As the wavelength of incident pulse from the OPA extends from 0.9 to 2.7 lm, the TH wave is to be generated in the range of 0.3–0.9 lm. The polydiacetylene (PDA) sample used as a third-order nonlinear material has large absorp-tion coeﬃcients below 600 nm. Therefore, the absorpabsorp-tion loss should be taken into account to obtain a correct third-order susceptibility. The position dependence of the intensity of TH, I3x, is given by the following equation as

a function of distance z from the incident plane of the non-linear material and the non-linear absorption coeﬃcient a3xat

the TH frequency: dI3x

dz ¼ BC sin 2Cz a3xI3x; ð2Þ where B and C are given as

B¼ 256p 4 c2_ðn2 x n 2 3xÞ 2ðv ð3Þ_Þ2 T2t6I3_x; ð3Þ and C¼3p kx jn3x nxj: ð4Þ

Here C is the phase mismatch determined by the diﬀerence in the refractive index between the fundamental and TH, c is the light speed, t and T are the transmittance between air and the nonlinear medium for the fundamental and TH, respectively. Eq.(2) can be analytically integrated leading to

I3x¼

B 2C2½expða3xzÞ cos 2Cz þ a3xCsin 2Cz

4C2_{þ a}2 3x

: ð5Þ

From this equation, the ratio, r, of the TH intensities of the absorptive and absorption-free samples is given by

r¼ ð4C

2_{þ a}

3x2Þ sin2Cz

2C2½expða3xzÞ cos 2Cz þ a3xCsin 2Cz

: ð6Þ

Using r together with Eq. (3), the intensity of TH output from the absorptive material is given by

I3x¼ 256p4 c2 1 ðn2 x n23xÞ 2 ðx ð3Þ_Þ2 T2_t6_I3 x 1 r sin 2 w: ð7Þ Here w = Cz0, where z0 is the thickness of the nonlinear

material, is the diﬀerence in the phase shift between the fundamental and TH brought about by the transmission through the nonlinear material. In this equation the refrac-tive indices were needed to obtain the corrected TH inten-sity, using the Kramers–Kronig relations[17].

3.2. Detector sensitivity and reference samples

The measurement of the fundamental and TH were made in the IR and visible ranges, respectively. However no detector and spectrometer are sensitive throughout these ranges. As a consequence, two detectors were used in the present measurement; CCD was used for visible, and PtSi detector was used for near-IR (Fig. 1). The spec-tral sensitivities of both detectors were calibrated with a calibrated curve of spectral luminosity sensitivity of a stan-dard lamp.

Taking into account the calibration curve, the TH inten-sity can be given by

I0_3x=P3x¼ 256p4 c2 1 ðn2 x n 2 3xÞ 2 ðx ð3Þ Þ2 T2 t6 ðI0x=QxÞ 3 1 r sin 2 w ¼ A lc kx 2 f ðnx; n3xÞ ðI0x=QxÞ 3 ðxð3Þ_Þ2 sin2w; ð8Þ fðnx; n3xÞ ¼ t6_T2 r : ð9Þ

Here I0_xand I0_3xare fundamental and TH intensity outputs of the detector, respectively, lcis the coherent length. Qx

and P3x are the wavelength-dependent sensitivity of the

detector for near-IR and visible, respectively, and A is a constant. Nonlinear susceptibility is given by

xð3Þ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k2_x I0 3x=P3x A l2c f ðnx; n3xÞ ðI0x=QxÞ 3 sin2w s ; ð10Þ

where Ix is the intensity of the fundamental output from

the absorptive material. A standard sample was used to determine the nonlinear susceptibility due to the complex-ity of determining the absolute values of Ixand I3x. In that

case, the nonlinear susceptibility is expressed as vð3Þ s ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lc;r lc;s 2 frðnx;n3xÞ sin 2 w_r fsðnx;n3xÞ sin 2 ws I 0 3x;s I0_3x;r s : ð11Þ

(4)

lc,rand lc,sare the coherent lengths of the reference and the

sample, respectively, wX, (X = r, s), is the diﬀerence in the

phase shift between fundamental and TH, and I3x,X, (X =

r, s), is the intensity of TH, for the reference (r) and the samples (s). Neither P3xand Qx, nor Ixappear in this

equa-tion. By measuring the TH spectra of the reference material and samples using the apparatus with a common conﬁgura-tion, we obtained the spectrum with a minimum error. 3.3. Reference nonlinear materials

The dependence of nonlinear susceptibility on the wave-length of the input pulse and the non-negligible absorption coeﬃcient in the reference material both lead to an error in the nonlinear susceptibility of the samples. Fundamental and TH, therefore, are required to be non-resonant to the transition in the reference materials. In this case, however, the nonlinearity of the reference material is relatively small and gives only a weak reference signal of the third har-monic. Usually fused silica is used as a reference material, but its third-order nonlinear susceptibility, vð3Þ

r , is as small

as 1.0· 1014esu. We measured the third harmonic spectra with our femtosecond continuum, but the TH signal was too weak as a reliable reference. This is because of the low peak intensity of the incident continuum, which is spectrally broadened and temporally dispersed due to the group dispersion. This chirp is crucial to obtain the TH (degenerate) generation spectrum without serious contam-ination of sum frequency generation (non-degenerate), which will be discussed in Section3.4.

Therefore, a nonlinear material with large nonlinearity and no absorption in the visible and near-IR ranges is desirable for our purpose. We found that high-refractive index glasses FDS9 and FD2 satisfy these requirements. The jv(3)j spectra of these glasses measured by a conven-tional method are shown in Fig. 3. The frequency depen-dence of jv(3)j in both glasses seem to be nearly negligible. To obtain an intense and reliable enough refer-ence signal, we applied FDS9 as a standard because its nonlinearity was higher than the other.

3.4. Contribution of non-degenerate three-wave sum frequency to the TH signal

We used white-light continuum to obtain thejv(3)j spec-tra of the samples, and contribution of the non-degenerate three-wave sum frequency (3-WSF) was carefully investi-gated. Due to the broad spectrum of the fundamental pulse, the nonlinear polarization at 3x is given, instead of Eq.(1), by PTHGðr; tÞ ¼ Z 1 1 dt1dt2dt3 Z 1 1 dx1dx2vð3Þ ð3x : x1;x2;3x x1 x2Þ Ex1 ðr; t t1Þ Ex2ðr; t t2Þ E3xx1x2ðr; t t3Þ ð12Þ Hence the output pulse with frequency 3x can be gener-ated by non-degenerate 3-WSF of three diﬀerent frequency components, when their sum is equal to 3x. To exclude the contribution from this process, we used a chirped idler pulse generated by the parametric ampliﬁcation in the BBO crystal.

In Eq. (12), t1, t2, and t3 are the arrival times of

fre-quency components of the amplified idler pulse at the posi-tion r. We measured the chirp property of the amplified pulse by the conventional cross-correlation method. The fundamental idler was mixed with the amplified Ti–sap-phire fundamental at 775 nm in the BBO crystal to gener-ate sum frequency through the second-order nonlinear process. From the cross-correlation traces, it was found that time delay between the components at 1700 and 1800 nm is220 fs, and the difference in the arrival time between 1800 and 1900 nm is250 fs. Since the white-light continuum was generated in CCl4, which was far

oﬀ-reso-nant in the range of the generated continuum, the chirp is expected to be linear. Therefore, the chirp rate can be cal-culated simply from the delay times measured above. The chirp rate is estimated to be0.42 nm/fs in average.

Since the thickness of all the samples used in the present study was less than 15 lm, the spectral component that propagates with a relative delay longer than 50 fs· 1.5 = 75 fs does not interact with each other. Therefore, the spec-tral components with specspec-tral diﬀerence more than 30 nm could not interact each other due to the chirp. The spec-trum obtained in the present study, therefore, was consid-ered to be averaged over ±15 nm or equivalently ±13 meV. Non-degenerate 3-WSF had a considerable contribution in FDS9 because the thickness of this glass plate, 0.975 mm, was substantially large. Dependence of the sus-ceptibility, however, on the wavelength was negligible, so jv(3)_{j was assumed to be constant.}

3.5. Eﬀect of TH generation by the air

The TH intensity depended on the coherence length as well asjv(3)j. Since the coherence length of the air in the range of our concern was as long as 5.0· 104lm, 104

Fig. 3. Nonlinear susceptibility of high-refractive index glasses. (1) FDS9 and (2) FD2. Data for 0.65 eV photon energy was obtained by use of the diﬀerence frequency of a YAG laser and a dye laser.

(5)

times larger than that of the reference material, it might aﬀect the TH signal from the reference and/or the sample

[18,19]. Care was taken when fused silica was used as a ref-erence, since the value ofjv(3)j in fused silica was as small as 1014esu. We measured a spectrum of the TH signal from air (Fig. 4) and found that the THG intensity of air was 100–140 times lower than that of FDS9, as one could expect from the fact thatjv(3)j of air and FDS9 was 1018and 1.3· 1013esu[15], respectively. Therefore, it is concluded that this method is feasible to measure thejv(3)j of a sample, which has nonlinearity higher than FDS9, without calibrat-ing the contribution from the air to the TH signal.

4. Spectrum of the third-order susceptibility for THG in poly(4BCMU)

Since the pioneering work of Sauteret et al. [20], PDA has received considerable attention in the ﬁeld of nonlinear optics. Recently, a low-loss single crystal waveguide with a large intensity-dependent refractive index, and directional couplers in an amorphous spin-coated ﬁlm have been fab-ricated [21,22]. Wavelength dependence of nonlinear sus-ceptibility needs to be considered for discussion of the availability of polymer materials to optical devices for communications and other applications. Studies of the mechanisms and origins of nonlinearity in polymers are crucial to develop another polymer with larger nonlinear-ity. For this purpose, ultrafast phenomena in conjugated polymers have been extensively studied[23–28].

THG measurements with PDA have been performed to study pure electronic coherent third-order nonlinearity[29– 31]. A detailed discussion on the wavelength dispersion of THG susceptibility was made by Stegeman et al. [29,30], and the spectral dependence of THG and electroabsorption were measured for PDA[31].

Using the apparatus developed in the present study, we measured jv(3)j of a ﬁlm of PDA–4BCMU, as shown in

Fig. 5, together with data taken by the point-by-point method in Ref. [29]. The peak value of jv(3)j in our mea-surement was found to be 7.7· 1011esu. Both data have a common feature: jv(3)j is larger for shorter wavelength. However, the data obtained by the point-by-point method considerably fluctuate, probably due to systematic errors in the range between 1.5 and 1.7 lm. The scattered data in this range are most probably accidental, since there is no resonance effect that might cause such a fine structure.

Calculations were performed using three-level (3L) and four-level (4L) models[30,31]. In both cases the calculated signal proﬁles have two peaks or one peak with one shoul-der in the calculated range of fundamental, from 0.9 to 1.95 lm. In the 3L model, the ratio of the two peaks at 1.37 and 1.58 lm is 1.29. For the 4L model, the peaks are at 1.34 and 1.60 lm and the intensity ratio is 1.03. It is hard to conclude which of the two models better repro-duces the observed result based on the data obtained by the point-by-point method.

The THGjv(3)j spectrum obtained in our measurement shows a considerably larger value in the shorter region than that in the longer wavelength region. This supports the result from the 3L model.

5. Conclusion

Wavelength dependence of nonlinear susceptibility of a nonlinear material was measured using a broadband near-IR pulse generated from NOPA, with less systematic error than the conventional method. It was shown that the data obtained by the present method was useful to ver-ify theoretical models.

Acknowledgements

The authors are grateful to Drs. Satoru Shimada and Hiro Matsuda for providing us with the sample of poly(4-BCMU), Prof. Hideki Hashimoto for his valuable

discus-Fig. 4. The spectrum of TH signal from the air with two diﬀerent wavelength sets (signal, idler). (1) 1.45 and 1.75 lm and (2) 1.49 and 1.65 lm.

Fig. 5. Experimentally determined jv(3)

(3x)j of poly(4BCMU) in red phase relative to FDS9 together with the data of the polymer determined using fused silica. Reproduced from Ref.[29].

(6)

sion. This research is partly supported by a Grant-in-Aid for Specially Promoted Research (#14002003) and partly supported by the program for the Promotion of Leading Researches in Special Coordination Funds for Promoting Science and Technology from the Ministry of Education, Culture, Sports, Science and Technology. This work was also supported by the ICORP program of Japan Science and Technology Agency (JST).

References

[1] D.S. Chemla, J. ZyssNonlinear Optical Properties of Organic Molecules and Crystals, vols. 1 and 2, Academic, New York, 1987. [2] T. Kobayashi (Ed.), Nonlinear Optics of Organics and

Semiconduc-tors, Springer Verlag, Berlin, 1989.

[3] N. Bloembergen, Nonlinear Optics, Benjamin, New York, 1965. [4] Y.R. Shen, The Principle of Nonlinear Optics, Wiley-Interscience,

1984.

[5] R. Boyd, Nonlinear Optics, second edn., Academic, San Diego, 2003.

[6] S. Takeuchi, T. Kobayashi, J. Appl. Phys. 75 (1994) 2757.

[7] S. Takeuchi, M. Yoshizawa, T. Masuda, T. Kobayashi, IEEE J. Quantum Electron. QE-28 (1992) 2508.

[8] S. Takeuchi, T. Masuda, T. Higashimura, T. Kobayashi, Solid State Commun. 87 (1993) 655.

[9] S. Takeuchi, T. Masuda, T. Kobayashi, Phys. Rev. B, Rapid Commun. 52 (1995) 7166.

[10] A. Shirakawa, T. Kobayashi, Appl. Phys. Lett. 72 (1998) 147. [11] E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S.

Spoerlein, W. Zinth, Appl. Phys. B 71 (2000) 457.

[12] G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, Opt. Lett. 23 (1998) 1283.

[13] A. Shirakawa, I. Sakane, T. Kobayashi, Opt. Lett. 23 (1998) 1292.

[14] A. Baltuska, T. Fuji, T. Kobayashi, Opt. Lett. 27 (2002) 306. [15] A. Mito, K. Hagimoto, C. Takahashi, Nonlinear Opt. Quantum Opt.

13 (1995) 3.

[16] T. Kobayashi, J. Lumin. 53 (1992) 159.

[17] R. Loudon, The Quantum Theory of Light, Clarendon Press, Oxford, 1973.

[18] F. Kajzar, J. Messier, Phys. Rev. A 32 (1985) 2352. [19] F. Krausz, E. Wintner, Appl. Phys. B 49 (1989) 479.

[20] C. Sauteret, J.P. Hermann, R. Frey, F. Pradere, J. Ducuing, R.H. Baugham, R.R. Chance, Phys. Rev. Lett. 36 (1976) 956.

[21] D.M. Krol, M. Thakur, Appl. Phys. Lett. 56 (1990) 1406.

[22] P.D. Townsend, J. Jackel, G.L. Baker, J.A. Shelburne III, S. Etemad, Appl. Phys. Lett. 55 (1989) 1829.

[23] T. Kobayashi, M. Yoshizawa, U. Stamm, M. Taiji, M. Hasegawa, J. Opt. Soc. Am. B 7 (1990) 1558.

[24] M. Yoshizawa, Y. Hattori, T. Kobayashi, Phys. Rev. B 47 (1993) 3882.

[25] T. Kobayashi, A. Shirakawa, H. Matsuzawa, H. Nakanishi, Chem. Phys. Lett. 321 (2000) 385.

[26] M. Yoshizawa, A. Kubo, S. Saikan, Phys. Rev. B 60 (1999) 15632. [27] Y. Yuasa, M. Ikuta, T. Kobayashi, Phys. Rev. B 72 (2005) 134302. [28] Y. Yuasa, M. Ikuta, T. Kobayashi, T. Kimura, H. Matsuda, Phys.

Rev. B 72 (2005) 134302.

[29] W.E. Torruellas, K.B. Rochford, R. Aanoni, S. Aramaki, G.I. Stegeman, Opt. Commun. 82 (1991) 94.

[30] M. Cha, W. Torruellas, G. Stegeman, H.X. Wang, A. Takahashi, S. Mukamel, Chem. Phys. Lett. 228 (1994) 73.

[31] K. Takeda, T. Hasegawa, K. Ishikawa, T. Koda, J. Photopolym. Sci. Technol. 6 (1993) 255.