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Degenerate-wave mixing in new dithienylethylenes
Synthetic Metals 110 Ž2000. 229–232 www.elsevier.comrlocatersynmet
Degenerate-wave mixing in new dithienylethylenes B. Sahraoui a
b
a,)
, N. Nguyen Phu a , I.V. Kityk
a,1
, P. Frere ` b, J. Roncali
b
Laboratoire des Proprietes et Applications, CNRS EP 130, UniÕersite´ d’Angers. 2, BouleÕard LaÕoisier, ´ ´ Optiques des Materiaux ´ 49045 Angers Cedex France Laboratoire d’Ingenierie Moleculaire et Materiaux Organiques, UMR CNRS 6501, UniÕersite´ d’Angers. 2, BouleÕard LaÕoisier, ´ ´ ´ 49045 Angers Cedex France Received 26 July 1999; received in revised form 9 November 1999; accepted 10 November 1999
Abstract We report the measurement of the degenerate fourth-wave mixing ŽDFWM. of new dithienylethylenes in chloroform solutions at l s 532 nm in ps regime with different numbers of p-conjugated bonds. From these measurements, we evaluated the values of the second order hyperpolarizabilities g , which are about 10 3 larger than the g value of CS 2 . The influence of p-conjugated bonds on the third-order susceptibilities and appropriate figures of merits is discussed. The more important seems to be the possibility of a simultaneous increase of the third-order susceptibilities, together with the decrease of the absorption coefficients that open a possibility of their use as promising materials for laser wavelengths mixing. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Degenerate four wave mixing; Third-order susceptibilities; Organic nonlinear optical materials
1. Introduction Research of new materials that have great potential for use in nonlinear optical devices is currently an interesting subject of investigation. Due to their efficiency, chemical flexibility and high conjugated framework, organic compounds have received considerable attention as a possible material for non-linear optics. In particular, the organic conjugated molecules have a great potential for nonlinear optical applications w1,2x. Considerable interest has arisen during the recent years in materials possessing optical limiting and DFWM properties, to control the intensity or the pulse energy of laser beams for eye and photo-detector protection. This is a reason for seeking colorless materials, which are transparent at low energy, and slightly absorbing in the whole visible range for microjoule pulse energy w3x. In this paper, we report on a systematic study of the third order nonlinear optical properties of two new dithienylethylenes with different numbers of p-conjugated bonds. The chemical structure of the studied compounds is
)
Corresponding author. Tel.: q33-41-73-54-89; fax: q33-41-73-53-52. E-mail address: [email protected] ŽB. Sahraoui.. 1 Permanent address: Institute of Physics, WSP, Ul. Armmii Krajowej, 42 201, Czestochowa, Poland.
presented in Fig. 1 Ža: dithienylethylene, and b: dithienylbutadiene.. They were synthesized using a procedure that is described in Ref. w4x. The transconfiguration of ethylenic units was established from NMR spectra for b and from X-ray structure for a. The X-ray structure of a reveals a good planarity of the p-conjugated systems. The samples were prepared in the form of solutions of the powdered organic molecules dissolved in chloroform. The optical spectra of the molecules presented in Fig. 2 were performed with a cell thickness of about 1 cm and very weak concentration Ž4 = 10y5 molrl.. The spectra showed a well-resolved fine structure, with a maximum absorption Ž lmax . at 360 nm for molecule a and 378 nm for b. As expected, the chain extension leads to a red-shift of the lmax and an increase of the total absorption. We observe that both presented compounds have a very weak linear absorption at a wavelength of about 480 nm.
2. DFWM technique and experimental results To measure the third-order susceptibilities of studied organic compounds, we have used the DFWM technique. The experimental setup is the same as described in Ref. w5x. The excitation is provided by 30 ps laser pulses at l s 532, generated by an amplified mode locked Quantel
0379-6779r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 Ž 9 9 . 0 0 2 9 5 - 7
B. Sahraoui et al.r Synthetic Metals 110 (2000) 229–232
230
Fig. 1. Chemical structures of dithienylethylenes studied: Ža. Ž E .-1,2bis w 2- Ž 3,4-dibutylthienyl .x ethylene; Ž b . Ž E, E . -1,4-bis w 2- Ž 3,4-dihexylthienyl.buta-1,3-diene.
Nd:YAG laser operating at 1 Hz repetition rate. Two of the waves are strong counter-propagating pumps traveling in the forward and backward directions. Their intensities verify the relation I1Ž z s 0. s I2 Ž z s l .. The third input wave is a weak probe Ž I3 s 10y2 I 1 . which makes an angle of 128 with respect to the pump wave. The signal wave ²4: is radiated in backward direction of the probe beam. The theoretical interpretation of DFWM is based on the Maxwell nonlinear propagation equations. Using slowly varying envelope approximation, we obtain DFWM efficiency in the form w6x:
° p2 q
a2 4
a Rs
I ² 4 : Ž 0. I
² 3:
p Ž ctg Ž pl . . q
s~
Ž 0.
2
p q
a
p2 G 0
2
2
Ž 1.
2
4
a
p2 - 0
2
¢ q Ž ctghŽ ql . . q 2 where 2
p s
ž
48p 3 n2 c l
2
x
² 3:
/
2
I1 Ž 0 . exp Ž ya l . y
Fig. 2. Optical absorption spectra dithienylethylenes; optical density Ds logŽ1r T .. For these spectroscopic measurements, the sample thickness is l s1 cm and the concentration in chloroform is 4P10y5 molrl.
example of these results. One can observe that for concentrations larger then Copt , the intensity of the signal decreases with an increase of concentration C, which is due to the competition between the nonlinear mixing of the beams in interaction and the absorption growing with C. The transmission measurements at the small concentrations and for the range of energy intensity used Ž0–1.2 GWrcm2 . shows that all the molecules have a very weak linear absorption. The Copt values and the absorption coefficients at Copt deduced from transmission measurements are collected in Table 1.
a2 4
,
q s ip.
The parameters a , l, l, n and c are, respectively, the linear absorption coefficient, the cell length, the wavelength of the laser, the linear refractive index of the material and the velocity of light propagation in vacuum. The absolute value of x ² 3: can be obtained by adjusting the theoretical curve given by Eq. Ž1. to the experimental data of R. As all the compounds are studied in solution, an increase of the concentration leads to an increase of the absorption, so we should find a compromise between optical non-linearities and optical losses. For this purpose, we measure the influence of concentration on signal I ² 4 : for each compound. We observe that all compounds display the same behavior: a single maximum of reflected fourth beam intensity I ² 4 : that corresponds to an optimum value of concentration Copt . Fig. 3 illustrates a typical
Fig. 3. DFWM efficiency R vs. concentration for the molecule a. I ²1: s 0.7 GWrcm2 .
B. Sahraoui et al.r Synthetic Metals 110 (2000) 229–232
231
We have measured the reflectivity, R, at Copt as a function of the first pumping wave intensity for the vertical polarization of incident beams. The investigated solutions demonstrate the same behavior. Fig. 4 presents DFWM efficiency vs. first pumping beam intensity I ²1: for the compounds a and b. A good agreement between the experimental results and the theoretical curve given by Eq. Ž1. is observed. The adjustment of the theoretical curve to the experimental data allows us to deduce the susceptibility values x ² 3: for both the dithienylethylenes compounds studied. The results are collected in Table 1. In order to characterize the individual molecule, we determine the second order hyperpolarizability using the following relation w7x: ² 3: x ² 3: s F 4 Ngsolution q xsolvent
Ž 2.
where F s Ž n 2 q 2.r3 is the Lorentz field factor correction, N s NA P CrM is the number of solution molecules per the unity of volume; NA is the Avogadro number. ² 3: Since in our case, xsolvent is small Žcf. Table 1. so it can be neglected. The second order hyperpolarizabilities values are shown in Table 1. From Table 1, one can clearly see that the increasing p-conjugated bond number leads to increasing hyperpolarizabilities and output nonlinear susceptibilities. It is in agreement with the general conception of searching new organic nonlinear optical materials w7x. The more striking in these compounds is the simultaneous decrease of the absorption for the 532 nm. This leads to a drastic increase of such important technological parameters as the figure of merits Ž x ² 3:ra . Žsee Table 1. up to the fourth time. The origin of such phenomena consists in the contribution of the dominant role played by the fundamental optical Sellmeier oscillators to the output nonlinear hyperpolarizabilites g w8x. In the case of the b compounds, contribution of these higher-energy Sellmeier optical oscillators is essentially weaker. On the other hand, vibration subsystems in the case of the b compounds should be more essential and the contribution signs probably will be different from the electronic contributions. Therefore, operating by the number of the molecular fragments, we are able to achieve an increase of transparency together with the simultaneous increase of the appropriate hyperpolarizability.
Table 1 Parameters M, Copt , a , x xxxx , and g present, respectively, the molar weight, optimal concentration, linear absorption coefficient at Copt . The third order susceptibility and the value of the second order hyperpolarizabilities Molecule M wgx a b CS 2 CHCl 3
² 3: Copt a x xxxx P10 20 g P10 46 wgrlx wcmy1 x wm2 Vy2 x wm5 Vy2 x
416.2 10 570.4 8 76.1 – 119.3 –
0.3 0.1 ;0 ;0
0.9 1.2 1.94 0.18
² 3: x xxxx ra warb.un.x
1.5 3.0 3.5 12 4.71=10y3 – 3.06=10y4 –
Fig. 4. The efficiency of the degenerate four waves mixing R vs. the intensity of the wave pumps ²1: for the compounds a and b, Copt s 5 grl. The polarization state of incident wave ²1:, ²2: and ²3: is vertical Žxxx. and the continuous curve corresponds to the theoretical formula Ž1..
Comparing the measured susceptibilities with the known values for the CS 2 , one can see essentially the larger value of the output nonlinear optical susceptibilities. At the same time, the obtained nonlinear optical tensor components are smaller than for the TTF derivatives previously studied Žethylenic and bis-dithiafulvenyl substituted w5,9x.. However, the investigated dithienylethylenes compounds show very low absorption at 532 nm compared with the TTF derivatives studied previously. We observed a reduction in the linear absorption coefficient at the concentrations close to Copt compared to the spectra shown in Fig. 2, which were performed at a concentration of about three orders of magnitude smaller. It can be due to the molecular aggregations in solutions at relatively high concentrations.
3. Conclusions An experimental study of the third order nonlinear optical properties of dithienylethylenes compounds with different numbers of the p-conjugated bonds has been studied. We have revealed that the increase of the p-conjugated bonds leads not only to the increase of the third order hyperpolarizability g , but also favors an increase of ² 3: the appropriate figures of merits Ž x xxxx ra . up to fourth times. Such striking result reflects also the different sign of electronic and vibration contributions to the output nonlinear optical susceptibilities and to absorption. The merit factor x ² 3:ra is much more important for the molecule b also because of the reduction of the linear absorption coefficient, which is attributed to the formation of aggregation in the solution at high concentrations. The absolute values of the obtained susceptibilities are larger than for the CS 2 compounds, but a little lower than in the case of the tetrathiafulvalene derivatives. However,
232
B. Sahraoui et al.r Synthetic Metals 110 (2000) 229–232
in the latter case, the investigated materials have an advantage, consisting in higher transparency. The presented results unambiguously show that the presented materials could be the promising materials for the molecular engineering of the new molecule for nonlinear optics of organic materials.
References w1x F. Kajzar, J.D. Swalem, Org. Thin Films Waveguiding Nonlinear Opt. Vol. 3 Gordon & Breach, 1996.
w2x J. Zyss ŽEd.., Molecular Nonlinear Optics: Materials, Physics and Devices, Academic Press, Boston, 1994. w3x J. Perry, Opt. Lett. 22 Ž1997. 1843. w4x E.H. Elandaloussi, P. Frere, ` P. Richomme, J. Orduna, J. Garin, J. Roncali, J. Am. Chem. Soc. 119 Ž1997. 10774–10784. w5x B. Sahraoui, G. Rivoire, J. Zaremba, N. Terkia-Derdra, M. Salle, ´ J. Opt. Soc. Am. B 15 Ž2. Ž1998. 923–927. w6x Sahraoui, G. Rivoire, Opt. Commun. 138 Ž1997. 1–5. w7x J. Zyss, D.S. Chemla ŽEds.., Nonlinear Opt. Prop. Org. Mol. Cryst. Vols. 1–2 Academic, Orlando, 1987. w8x I.V. Kityk, B. Sahraoui, X. Nguyen Phu, G. Rivoire, J. Kasperczyk, Nonlinear Opt. 18 Ž1997. 13–30. w9x B. Sahraoui, M. Sylla, J.P. Bourdin, G. Rivoire, J. Zaremba, T.T. Nguyen, M. Salle, J. Mod. Opt., 42 Ž10., 2095–2107.
Degenerate-wave mixing in new dithienylethylenes B. Sahraoui a
b
a,)
, N. Nguyen Phu a , I.V. Kityk
a,1
, P. Frere ` b, J. Roncali
b
Laboratoire des Proprietes et Applications, CNRS EP 130, UniÕersite´ d’Angers. 2, BouleÕard LaÕoisier, ´ ´ Optiques des Materiaux ´ 49045 Angers Cedex France Laboratoire d’Ingenierie Moleculaire et Materiaux Organiques, UMR CNRS 6501, UniÕersite´ d’Angers. 2, BouleÕard LaÕoisier, ´ ´ ´ 49045 Angers Cedex France Received 26 July 1999; received in revised form 9 November 1999; accepted 10 November 1999
Abstract We report the measurement of the degenerate fourth-wave mixing ŽDFWM. of new dithienylethylenes in chloroform solutions at l s 532 nm in ps regime with different numbers of p-conjugated bonds. From these measurements, we evaluated the values of the second order hyperpolarizabilities g , which are about 10 3 larger than the g value of CS 2 . The influence of p-conjugated bonds on the third-order susceptibilities and appropriate figures of merits is discussed. The more important seems to be the possibility of a simultaneous increase of the third-order susceptibilities, together with the decrease of the absorption coefficients that open a possibility of their use as promising materials for laser wavelengths mixing. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Degenerate four wave mixing; Third-order susceptibilities; Organic nonlinear optical materials
1. Introduction Research of new materials that have great potential for use in nonlinear optical devices is currently an interesting subject of investigation. Due to their efficiency, chemical flexibility and high conjugated framework, organic compounds have received considerable attention as a possible material for non-linear optics. In particular, the organic conjugated molecules have a great potential for nonlinear optical applications w1,2x. Considerable interest has arisen during the recent years in materials possessing optical limiting and DFWM properties, to control the intensity or the pulse energy of laser beams for eye and photo-detector protection. This is a reason for seeking colorless materials, which are transparent at low energy, and slightly absorbing in the whole visible range for microjoule pulse energy w3x. In this paper, we report on a systematic study of the third order nonlinear optical properties of two new dithienylethylenes with different numbers of p-conjugated bonds. The chemical structure of the studied compounds is
)
Corresponding author. Tel.: q33-41-73-54-89; fax: q33-41-73-53-52. E-mail address: [email protected] ŽB. Sahraoui.. 1 Permanent address: Institute of Physics, WSP, Ul. Armmii Krajowej, 42 201, Czestochowa, Poland.
presented in Fig. 1 Ža: dithienylethylene, and b: dithienylbutadiene.. They were synthesized using a procedure that is described in Ref. w4x. The transconfiguration of ethylenic units was established from NMR spectra for b and from X-ray structure for a. The X-ray structure of a reveals a good planarity of the p-conjugated systems. The samples were prepared in the form of solutions of the powdered organic molecules dissolved in chloroform. The optical spectra of the molecules presented in Fig. 2 were performed with a cell thickness of about 1 cm and very weak concentration Ž4 = 10y5 molrl.. The spectra showed a well-resolved fine structure, with a maximum absorption Ž lmax . at 360 nm for molecule a and 378 nm for b. As expected, the chain extension leads to a red-shift of the lmax and an increase of the total absorption. We observe that both presented compounds have a very weak linear absorption at a wavelength of about 480 nm.
2. DFWM technique and experimental results To measure the third-order susceptibilities of studied organic compounds, we have used the DFWM technique. The experimental setup is the same as described in Ref. w5x. The excitation is provided by 30 ps laser pulses at l s 532, generated by an amplified mode locked Quantel
0379-6779r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 Ž 9 9 . 0 0 2 9 5 - 7
B. Sahraoui et al.r Synthetic Metals 110 (2000) 229–232
230
Fig. 1. Chemical structures of dithienylethylenes studied: Ža. Ž E .-1,2bis w 2- Ž 3,4-dibutylthienyl .x ethylene; Ž b . Ž E, E . -1,4-bis w 2- Ž 3,4-dihexylthienyl.buta-1,3-diene.
Nd:YAG laser operating at 1 Hz repetition rate. Two of the waves are strong counter-propagating pumps traveling in the forward and backward directions. Their intensities verify the relation I1Ž z s 0. s I2 Ž z s l .. The third input wave is a weak probe Ž I3 s 10y2 I 1 . which makes an angle of 128 with respect to the pump wave. The signal wave ²4: is radiated in backward direction of the probe beam. The theoretical interpretation of DFWM is based on the Maxwell nonlinear propagation equations. Using slowly varying envelope approximation, we obtain DFWM efficiency in the form w6x:
° p2 q
a2 4
a Rs
I ² 4 : Ž 0. I
² 3:
p Ž ctg Ž pl . . q
s~
Ž 0.
2
p q
a
p2 G 0
2
2
Ž 1.
2
4
a
p2 - 0
2
¢ q Ž ctghŽ ql . . q 2 where 2
p s
ž
48p 3 n2 c l
2
x
² 3:
/
2
I1 Ž 0 . exp Ž ya l . y
Fig. 2. Optical absorption spectra dithienylethylenes; optical density Ds logŽ1r T .. For these spectroscopic measurements, the sample thickness is l s1 cm and the concentration in chloroform is 4P10y5 molrl.
example of these results. One can observe that for concentrations larger then Copt , the intensity of the signal decreases with an increase of concentration C, which is due to the competition between the nonlinear mixing of the beams in interaction and the absorption growing with C. The transmission measurements at the small concentrations and for the range of energy intensity used Ž0–1.2 GWrcm2 . shows that all the molecules have a very weak linear absorption. The Copt values and the absorption coefficients at Copt deduced from transmission measurements are collected in Table 1.
a2 4
,
q s ip.
The parameters a , l, l, n and c are, respectively, the linear absorption coefficient, the cell length, the wavelength of the laser, the linear refractive index of the material and the velocity of light propagation in vacuum. The absolute value of x ² 3: can be obtained by adjusting the theoretical curve given by Eq. Ž1. to the experimental data of R. As all the compounds are studied in solution, an increase of the concentration leads to an increase of the absorption, so we should find a compromise between optical non-linearities and optical losses. For this purpose, we measure the influence of concentration on signal I ² 4 : for each compound. We observe that all compounds display the same behavior: a single maximum of reflected fourth beam intensity I ² 4 : that corresponds to an optimum value of concentration Copt . Fig. 3 illustrates a typical
Fig. 3. DFWM efficiency R vs. concentration for the molecule a. I ²1: s 0.7 GWrcm2 .
B. Sahraoui et al.r Synthetic Metals 110 (2000) 229–232
231
We have measured the reflectivity, R, at Copt as a function of the first pumping wave intensity for the vertical polarization of incident beams. The investigated solutions demonstrate the same behavior. Fig. 4 presents DFWM efficiency vs. first pumping beam intensity I ²1: for the compounds a and b. A good agreement between the experimental results and the theoretical curve given by Eq. Ž1. is observed. The adjustment of the theoretical curve to the experimental data allows us to deduce the susceptibility values x ² 3: for both the dithienylethylenes compounds studied. The results are collected in Table 1. In order to characterize the individual molecule, we determine the second order hyperpolarizability using the following relation w7x: ² 3: x ² 3: s F 4 Ngsolution q xsolvent
Ž 2.
where F s Ž n 2 q 2.r3 is the Lorentz field factor correction, N s NA P CrM is the number of solution molecules per the unity of volume; NA is the Avogadro number. ² 3: Since in our case, xsolvent is small Žcf. Table 1. so it can be neglected. The second order hyperpolarizabilities values are shown in Table 1. From Table 1, one can clearly see that the increasing p-conjugated bond number leads to increasing hyperpolarizabilities and output nonlinear susceptibilities. It is in agreement with the general conception of searching new organic nonlinear optical materials w7x. The more striking in these compounds is the simultaneous decrease of the absorption for the 532 nm. This leads to a drastic increase of such important technological parameters as the figure of merits Ž x ² 3:ra . Žsee Table 1. up to the fourth time. The origin of such phenomena consists in the contribution of the dominant role played by the fundamental optical Sellmeier oscillators to the output nonlinear hyperpolarizabilites g w8x. In the case of the b compounds, contribution of these higher-energy Sellmeier optical oscillators is essentially weaker. On the other hand, vibration subsystems in the case of the b compounds should be more essential and the contribution signs probably will be different from the electronic contributions. Therefore, operating by the number of the molecular fragments, we are able to achieve an increase of transparency together with the simultaneous increase of the appropriate hyperpolarizability.
Table 1 Parameters M, Copt , a , x xxxx , and g present, respectively, the molar weight, optimal concentration, linear absorption coefficient at Copt . The third order susceptibility and the value of the second order hyperpolarizabilities Molecule M wgx a b CS 2 CHCl 3
² 3: Copt a x xxxx P10 20 g P10 46 wgrlx wcmy1 x wm2 Vy2 x wm5 Vy2 x
416.2 10 570.4 8 76.1 – 119.3 –
0.3 0.1 ;0 ;0
0.9 1.2 1.94 0.18
² 3: x xxxx ra warb.un.x
1.5 3.0 3.5 12 4.71=10y3 – 3.06=10y4 –
Fig. 4. The efficiency of the degenerate four waves mixing R vs. the intensity of the wave pumps ²1: for the compounds a and b, Copt s 5 grl. The polarization state of incident wave ²1:, ²2: and ²3: is vertical Žxxx. and the continuous curve corresponds to the theoretical formula Ž1..
Comparing the measured susceptibilities with the known values for the CS 2 , one can see essentially the larger value of the output nonlinear optical susceptibilities. At the same time, the obtained nonlinear optical tensor components are smaller than for the TTF derivatives previously studied Žethylenic and bis-dithiafulvenyl substituted w5,9x.. However, the investigated dithienylethylenes compounds show very low absorption at 532 nm compared with the TTF derivatives studied previously. We observed a reduction in the linear absorption coefficient at the concentrations close to Copt compared to the spectra shown in Fig. 2, which were performed at a concentration of about three orders of magnitude smaller. It can be due to the molecular aggregations in solutions at relatively high concentrations.
3. Conclusions An experimental study of the third order nonlinear optical properties of dithienylethylenes compounds with different numbers of the p-conjugated bonds has been studied. We have revealed that the increase of the p-conjugated bonds leads not only to the increase of the third order hyperpolarizability g , but also favors an increase of ² 3: the appropriate figures of merits Ž x xxxx ra . up to fourth times. Such striking result reflects also the different sign of electronic and vibration contributions to the output nonlinear optical susceptibilities and to absorption. The merit factor x ² 3:ra is much more important for the molecule b also because of the reduction of the linear absorption coefficient, which is attributed to the formation of aggregation in the solution at high concentrations. The absolute values of the obtained susceptibilities are larger than for the CS 2 compounds, but a little lower than in the case of the tetrathiafulvalene derivatives. However,
232
B. Sahraoui et al.r Synthetic Metals 110 (2000) 229–232
in the latter case, the investigated materials have an advantage, consisting in higher transparency. The presented results unambiguously show that the presented materials could be the promising materials for the molecular engineering of the new molecule for nonlinear optics of organic materials.
References w1x F. Kajzar, J.D. Swalem, Org. Thin Films Waveguiding Nonlinear Opt. Vol. 3 Gordon & Breach, 1996.
w2x J. Zyss ŽEd.., Molecular Nonlinear Optics: Materials, Physics and Devices, Academic Press, Boston, 1994. w3x J. Perry, Opt. Lett. 22 Ž1997. 1843. w4x E.H. Elandaloussi, P. Frere, ` P. Richomme, J. Orduna, J. Garin, J. Roncali, J. Am. Chem. Soc. 119 Ž1997. 10774–10784. w5x B. Sahraoui, G. Rivoire, J. Zaremba, N. Terkia-Derdra, M. Salle, ´ J. Opt. Soc. Am. B 15 Ž2. Ž1998. 923–927. w6x Sahraoui, G. Rivoire, Opt. Commun. 138 Ž1997. 1–5. w7x J. Zyss, D.S. Chemla ŽEds.., Nonlinear Opt. Prop. Org. Mol. Cryst. Vols. 1–2 Academic, Orlando, 1987. w8x I.V. Kityk, B. Sahraoui, X. Nguyen Phu, G. Rivoire, J. Kasperczyk, Nonlinear Opt. 18 Ž1997. 13–30. w9x B. Sahraoui, M. Sylla, J.P. Bourdin, G. Rivoire, J. Zaremba, T.T. Nguyen, M. Salle, J. Mod. Opt., 42 Ž10., 2095–2107.