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The nonlinear optical response of a fluorine-containing azoic dye
Optics Communications 283 (2010) 1110–1113
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
The nonlinear optical response of a fluorine-containing azoic dye Tingjian Jia a,*, Zhiguo Shang b, Yongguang Cheng c a
Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 47600, China The Graduate University for Advanced Studies, Myodaiji, Okazaki 444-8585, Japan c Department of Mathematical and Physical Science, Henan Institute of Engineering, Zhengzhou 450007, China b
a r t i c l e
i n f o
Article history: Received 2 October 2009 Received in revised form 28 October 2009 Accepted 28 October 2009
Keywords: Fluorine-containing azoic dye Electronic effect Thermal effect Intersystem crossing
a b s t r a c t The nonlinear optical nonlinearities of a fluorine-containing azoic dye in tetrahydrofuran have been investigated by using Z-scan technique with picosecond and nanosecond lasers. The experimental results reveal that the azoic dye has large optical nonlinearity under the excitations of picosecond and nanosecond 532 nm. At the picosecond 532 nm the solution presents negative nonlinear refraction due to the electronic effect, while the larger nonlinear refraction under nanosecond laser excitation is induced by thermal effect. Moreover, the different nonlinear absorption behavior under picosecond and nanosecond excitations is analyzed. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The search for nonlinear optical (NO) materials with large optical nonlinearities and fast response is essential for potential application in optical signal processing, optical limiting (OL) [1,2] and optical storage [3,4]. Though many kinds of nonlinear optical materials have been extensively studied, searching for large nonlinear optical response polymers is still in progress. Azoic dyes have many advantages over other NO materials. Photoisomerization of azoic molecules enables it easy to modify their linear and nonlinear polarizability of them as well as optical nonlinear refraction. Since the optical properties of azoic molecules can be controlled optically, it has intrigued the considerable interest of people [5,6]. The nonlinear optical phenomena of azoic dyes can result from electronic response and/or nonelectronic response. The electronic nonlinearity is induced by either population redistribution or distortion of electronic clouds. A molecule undergoes a transition from its ground state to its excitation state after absorbing a photon. The dipole moment of the molecule changes during such a transition. The change in the dipole moment will give birth to electronic nonlinearity. A nonelectronic response is a non-radiative interaction such as cis–trans isomerism, the changes in density and temperature [7–9]. It has been well known that the nonlinear optical behavior of materials can vary greatly by changing different laser duration or different laser wavelengths. Thus, studies about the mechanism of their t nonlinear optical response with different * Corresponding author. E-mail address: [email protected] (T. Jia). 0030-4018/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2009.10.110
laser duration or different laser wavelengths are expected to be more interesting and important. If the nonlinear mechanism is understood for certain laser pulses, the NLO properties optimization can be well accomplished. Z-scan technique is a simple and effective tool to determine the nonlinear properties [10]. It has been widely used in material characterization because it provides not only the magnitudes of the real part and imaginary part of the nonlinear susceptibility, but also the sign of the real part. Both nonlinear refraction and nonlinear absorption in solid and liquid samples can be measured easily by Z-scan technique, which use the change of transmittance of nonlinear materials [9]. In this work, we demonstrate the optical nonlinearities of a fluorine-containing azoic dye in tetrahydrofuran (THF) through Z-scan technique under picosecond and nanosecond lasers excitation at 532 nm in order to investigate the influence of pulse width on the nonlinear optical response of the fluorine-containing azoic dye.
2. Experimental The molecular structure of the fluorine-containing azoic dye is shown in Fig. 1. The linear absorption spectrum of the dye solution with the concentration of 4.4 105 M in THF is shown in Fig. 2, which was acquired using a UV–VISNIR spectrophotometer (Type: Cary 5000) manufactured by America Varian Company. The absorption spectrum is centered at 370 nm, corresponding to the S0 ? S1 transition of the azoic dye molecule. The absorption of the glass substrate was eliminated from the absorption spectrum.
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Z-scan. The difference between normalized peak and valley transmittance DTpv (denoting TP TV) can be directly measured by Zscan technique. The variation of this quantity as a function of |DU0| is given by
DT pv 0:406ð1 sÞ0:25 jDU0 j;
ð1Þ
where s = 1 exp(2r20 =x20 ) is the aperture linear transmittance with r0 denoting the aperture radius and x0 denoting beam radius at the aperture in the linear region. DU0 can be obtained from Eq. (2):
DU0 ¼ kLeff n2 I0 ¼ ð2p=kÞLeff n2 I0 ;
Fig. 1. The molecular structure of the fluorine-containing azoic dye.
2.0
Absorption
1.5
1.0
where I0 is the intensity of the laser beam at focus z = 0, Leff = ([1exp(aL)]/a) is the effective thickness of the sample, a is the linear absorption coefficient and L is the thickness of the sample. The nonlinear refractive index n2 (cm2/W) can be obtained from Eqs. (1) and (2). Dn0 = n2I0 with I0 being the on-axis irradiance at the focus represents the change in n2 at the focus. Fig. 3a shows the closed aperture (CA) Z-scan curve of the azoic dye solution. From the unsymmetric curve, there is obvious nonlinear absorption existing in the solution, and the closed transmittance is affected by the nonlinear refraction and absorption. As a result, the determination of n2 is less straight-forward from the closed aperture Z-scan measurement. It is necessary to separate the effect of nonlinear absorption by performing the open aperture experiment. Fig. 3b shows the open aperture (OA) Z-scan curve of the solution while the closed aperture curve divided by open aperture (CA/OA) curve of the solution is shown in Fig. 3c. The theoretical expression of the CA/OA curve can be written as:
Tðz; DU0 Þ ¼ 1 4DU0 v=ðv2 þ 9Þðv2 þ 1Þ; 0.5
ð2Þ
ð3Þ
2 0
0.0 400
600
800
Wavelength / nm Fig. 2. The absorption of azoic dye in THF with the concentration of 4.4 105 M.
In this work, picosecond and nanosecond lasers were adopted as excitation source in the Z-scan measurements [10]. For the picosecond Z-scan measurement, the radius of the beam waist (w0) are 26.03 lm, and the corresponding Rayleigh length z0 can be calculated to be 4 mm, much longer than the thickness of the quartz cell. This experiment was carried out using a mode-locked Nd:YAG laser (PY61C-10, Continuum) as the light source with a repetition rate of 10 Hz, pulse width of 38 ps and wavelength of 532 nm. The pulse Z-scan experimental system was calibrated by measuring the nonlinear refractive index of conventional CS2 solution. The mean error of the experimental data, mostly arising from the fluctuation of the laser power, is below 10%. In the nanosecond Z-scan measurement, the excitation source is a Q-switched Nd:YLF laser (LABest Sunlight-200), with 6 ns pulse duration, 10 Hz a repetition rate and wavelength of 532 nm. The radius of the beam waist and the corresponding Rayleigh length are 29.10 lm and 5 mm, respectively. The dye solution with the concentration of 1.5 103 M was placed in a quartz cell with 1 cm path length to perform Z-scan measurements. 3. Results and discussion The nonlinear refractive index n2 (cm2/W) and nonlinear absorption b (cm/W) are evaluated by carrying out the measurements of
where v = z/z0, z0 = kx is the diffraction length of the beam, k = 2p/ k is the vector and k is the laser wavelength, all in free space. In the picosecond Z-scan measurement, the effective thickness of the sample was Leff = 0.85 mm. The linear transmittance of the aperture was s = 0.5. The optical intensity at the focus point is 1.49 109 W/cm2. From the theoretical fit result, the nonlinear absorption coefficient was obtained to be 5.58 cm/GW. The value of DT pv can be obtained to be 0.39 and the third-order nonlinear index is calculated to be 7.64 1014 cm2/W (2.64 1011 esu). The nonlinear refractive index of THF was reported in order of 1013 esu [11], which was much smaller than that of azoic dye solution, so the contribution of solvent was negligible. Dn0 of solution under picosecond 532 nm excitation was calculated as 1.14 104. The value of the nonlinear optical susceptibility v(3) (esu) could be evaluated from the nonlinear refractive index n2. The relation is defined as follows [12]:
vð3Þ ðesuÞ ¼
2 2 n20 c cm cm ¼ 25:313n20 n2 107 n2 2 12p W W
ð4Þ
where n0 is the linear refractive index. For the solution sample, we use the refractive index value of the pure solvent. The values of v(3) (esu) for the solution is calculated to be 4.06 1012 esu. The second hyperpolarizability of molecule in an isotropic media is related to the nonlinear optical susceptibility by the following [13]:
< c >¼ vð3Þ =ðL4 NÞ;
ð5Þ
where N is the number density of the molecules in cm3 and L is the local field correction factor given by [(n2 + 2)/3]. Under 532 nm excitation, the number density of the molecules in the solution in cm3 was N = 9.03 1017 cm3, so the corresponding second hyperpolarizability was < c > = 1.28 1030 esu at picosecond 532 excitation.
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thermal effect increases. It is a common assumption that Z-scan measurements should be made with repetition rate of few of Hertz in order to extract a nonlinear refractive index influenced by only electronic effects. The time scale of this cumulative process is given by tc = x2/4D, where x is the beam waist and D is the thermal diffusion coefficient of the materials. Generally, the value of D ranges from 1 107 m2/s to 6 107 m2/s. The magnitude of the calculated tc is within 103 s, which is much smaller than the time interval between consecutive laser pulses 0.1 s used in this experiment [14]. The electronic nonlinearity was induced by either the population redistribution or the distortion of electronic clouds. A
1.75 1.50 1.25 1.00 0.75 0.50
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-30
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0.25 -30
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z / mm Fig. 3. Z-scan experimental data for the dye solution under picosecond 532 nm excitation: (a) CA curve; (b) OA curve; (c) CA/OA curve.
In the picosecond Z-scan measurement, the optical nonlinearity observed is induced electronic effect, but not by thermal effect. One hand, the electronic nonlinearities arise very rapidly (within the 38 ps pulse duration). Refractive index changes due to thermal nonlinearities arise due to density changes in the materials propagating with acoustic wave speed caused by heating; if we estimate it to be on the order of 3 103 m/s, the time to propagate a distance equal to the beam radius at focus is about 9 ns at 532 nm excitation, two orders longer than the pulse width, respectively. On the other hand, thermal heating induced by a single laser pulse persists over some characteristic time tc. As a result, when the time interval between consecutive laser pulses is shorter than tc, the
c Normalized Transmittance / a.u.
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a
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Fig. 4. Z-scan experimental data for the dye solution under nanosecond 532 nm excitation: (a) CA curve; (b) OA curve; (c) CA/OA curve.
T. Jia et al. / Optics Communications 283 (2010) 1110–1113
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molecule underwent a transition from the ground state to the excitation state after absorbing a photon. The dipole moment of the molecule changed during such a transition. This change would give birth to electronic nonlinearity [15,16]. Fig. 4a–c shows the CA, OA and CA/OA curves for the solution in the nanosecond Z-scan measurements, respectively. In this experiment, the optical intensity was 2.88 107 W/cm2 at the focus point. From the theoretical fit for the OA curve, the nonlinear absorption coefficient was obtained to be 7.3 107 cm/W. In the CA/OA curve, the value of DT pv can be obtained to be 0.51 and the third-order nonlinear index is calculated to be 5.11 1012 cm2/W. Dn0 was calculated to be 1.47 104. In the nanosecond Z-scan measurement, the time to propagate a distance equal to the beam radius at focus is estimated to be about 10 ns, in the same order with the pulse width. Thus, the thermal effect gave important impact on the measured optical nonlinearity. The nonlinear refraction induced by thermal effects is estimated, which results from linear absorption. The value of it can be calculated by
was dominated by singlet–singlet absorption. The larger absorption cross-section of the first singlet excited state compared to that of the ground state also leaded to a RSA under 38 ps excitation. It is always regarded as that the absorption cross-section of singlet state is much weaker than that of triplet state, so the RSA coefficient in the ps pulse excitation case (singlet–singlet absorption) was much larger than that in the nanosecond case (triplet–triplet absorption). The similar phenomena have been observed in several Refs. [17]. It is difficult to make strict comparison of the experimental data with other published data due to different pulse duration, excitation wavelength and solution concentration. However, some comparison will be useful to have general view on nonlinear optical response of this kind of structure. Under picosecond excitation, the nonlinear refractive index of this azoic dye solution is larger than those of disperse red 1 and disperse 13 solution [18].
Dn ¼ ðdn=dTÞ=DT ðdn=dTÞðIsa=qcÞ;
The optical nonlinearity of a fluorine-containing azoic dye was investigated by using single-beam Z-scan technique. Under picosecond 532 nm excitation, Z-scan measurements showed that the dye solution exhibited large electronic effect optical nonlinearity, with n2 = 7.83 1014 cm2/W and b = 5.58 cm/GW, respectively. In the nanosecond Z-scan experiment, the dye solution presented large different optical nonlinearities, with n2 = 5.11 1012 cm2/W and b = 7.7 107 cm/W. The larger nonlinear refraction at nanosecond 532 nm was shown to be of thermal origin resulting from energy transfer from dye molecules to the THF molecules while the larger nonlinear absorption was induced by triplet–triplet absorption.
ð6Þ
where s is duration of laser pulses, c is the specific heat of sample, a is coefficient of linear absorption, I is the laser intensity irradiated on the sample [10]. The calculated result shows that Dn is in the order of 104, which is in the same order with the Dn0 obtained under nanosecond 532 nm excitation. Obviously, thermal effects are, therefore, is expected to be dominant in experiments with nanosecond duration laser. However, under the picosecond excitation, Dn from thermal contribution was calculated to be in order of 103, much smaller than the Dn0 obtained from picoseconds Z-scan measurement, so the thermal effect should be negligible. The thermally induced optical nonlinearity denoted temporal variation of optical parameters (in particularly, refractive index) due to linear and/or nonlinear absorption in medium followed by a non-radiative relaxation down to the ground state. The laser heating leaded to the generation of acoustic wave that changed the medium density followed by a variation of refractive index. This process was slow (of order of a few nanosecond) and could be observed in the case of CW laser, long laser pulses, or in the case of high pulse repetition rate [14]. The different nonlinear absorption performances with nanosecond and picosecond pulses appeared to be due to the relative contributions of excited singlet–singlet and triplet–triplet absorption for different pulse durations. The laser pulse duration (38 ps), much smaller than the time of intersystem crossing (1 ns), was so small that the amount of population transfer to the triplet state was relatively small. For 6 ns laser pulse, pulse duration was much longer than the singlet excited state lifetime and the intersystem crossing rate was very fast, thus, the singlet contribution diminished, and the contribution of the triplet–triplet absorption became dominant. Due to the larger absorption cross-section of the triplet excited state compared to that of the ground state, RSA occurred. For 38 ps laser pulse, the pulse duration was much less than the singlet excited state lifetime, therefore the nonlinear absorption
4. Conclusion
References [1] J.E. Ehrlich, X.L. Wu, I.-Y.S. Lee, Z.-Y. Hu, H. Röckel, S.R. Marder, J.W. Perry, Opt. Lett. 22 (1997) 1843. [2] G.S. He, G.C. Xu, P.N. Prasad, B.A. Reinhardt, J.C. Bhatt, A.G. Dillard, Opt. Lett. 20 (1995) 435. [3] T. He, C. Wang, X. Pan, H. Yang, G. Lu, Opt. Lett. 34 (2009) 665. [4] T. Ikeda, O. Tsutsumi, Science 268 (1995) 1873. [5] P. Wang, H. Ming, J. Zhang, Z. Liang, Y. Lu, Q. Zhang, J. Xie, Y. Tian, Opt. Commun. 203 (2002) 159. [6] J.C. Liang, X.Q. Zhou, J. Opt. Soc. Am. B 22 (2005) 2468. [7] R. Rangel-Rojo, S. Yamada, H. Matsuda, D. Yankelevich, Appl. Phys. Lett. 72 (1998) 1021. [8] C. Gayathri, A. Ramalingam, Spectrochim. Acta Part A 69 (2007) 96. [9] T. He, C. Wang, J. Mod. Opt. 55 (2008) 3013. [10] M. Sheik-Bahae, A.A. Said, T.H. Wei, D.J. Hagan, E.W. Van Stryland, IEEE J. Quantum Electron. 26 (1990) 760. [11] Q.-H. Qi, J.-L. Li, T.-Q. Zhang, H. Yang, Chin. Phys. Lett. 15 (1998) 30. [12] R.W. Boyd, Nonlinear Optics, Academic Press, Amsterdam, 2003. [13] B.K. Mandal, B. Bihari, A.K. Sinha, M. Kamath, L. Chen, Appl. Phys. Lett. 66 (1995) 932. [14] A. Gnoli, L. Razzari, M. Righini, Opt. Express 13 (2005) 7976. [15] T. He, Y. Cheng, Y. Du, Y. Mo, Opt. Commun. 275 (2007) 240. [16] L. Brzozowski, E.H. Sargent, J. Mater. Sci. 12 (2001) 483. [17] W. Sun, C.C. Byeon, C.M. Lawsonb, G.M. Gray, D. Wang, Appl. Phys. Lett. 77 (2000) 1759. [18] F. Cherioux, P. Audebert, H. Maillotte, L. Grossard, F.E. Hernandez, A. Lacourt, Chem. Mater. 9 (1997) 2921.
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
The nonlinear optical response of a fluorine-containing azoic dye Tingjian Jia a,*, Zhiguo Shang b, Yongguang Cheng c a
Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 47600, China The Graduate University for Advanced Studies, Myodaiji, Okazaki 444-8585, Japan c Department of Mathematical and Physical Science, Henan Institute of Engineering, Zhengzhou 450007, China b
a r t i c l e
i n f o
Article history: Received 2 October 2009 Received in revised form 28 October 2009 Accepted 28 October 2009
Keywords: Fluorine-containing azoic dye Electronic effect Thermal effect Intersystem crossing
a b s t r a c t The nonlinear optical nonlinearities of a fluorine-containing azoic dye in tetrahydrofuran have been investigated by using Z-scan technique with picosecond and nanosecond lasers. The experimental results reveal that the azoic dye has large optical nonlinearity under the excitations of picosecond and nanosecond 532 nm. At the picosecond 532 nm the solution presents negative nonlinear refraction due to the electronic effect, while the larger nonlinear refraction under nanosecond laser excitation is induced by thermal effect. Moreover, the different nonlinear absorption behavior under picosecond and nanosecond excitations is analyzed. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The search for nonlinear optical (NO) materials with large optical nonlinearities and fast response is essential for potential application in optical signal processing, optical limiting (OL) [1,2] and optical storage [3,4]. Though many kinds of nonlinear optical materials have been extensively studied, searching for large nonlinear optical response polymers is still in progress. Azoic dyes have many advantages over other NO materials. Photoisomerization of azoic molecules enables it easy to modify their linear and nonlinear polarizability of them as well as optical nonlinear refraction. Since the optical properties of azoic molecules can be controlled optically, it has intrigued the considerable interest of people [5,6]. The nonlinear optical phenomena of azoic dyes can result from electronic response and/or nonelectronic response. The electronic nonlinearity is induced by either population redistribution or distortion of electronic clouds. A molecule undergoes a transition from its ground state to its excitation state after absorbing a photon. The dipole moment of the molecule changes during such a transition. The change in the dipole moment will give birth to electronic nonlinearity. A nonelectronic response is a non-radiative interaction such as cis–trans isomerism, the changes in density and temperature [7–9]. It has been well known that the nonlinear optical behavior of materials can vary greatly by changing different laser duration or different laser wavelengths. Thus, studies about the mechanism of their t nonlinear optical response with different * Corresponding author. E-mail address: [email protected] (T. Jia). 0030-4018/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2009.10.110
laser duration or different laser wavelengths are expected to be more interesting and important. If the nonlinear mechanism is understood for certain laser pulses, the NLO properties optimization can be well accomplished. Z-scan technique is a simple and effective tool to determine the nonlinear properties [10]. It has been widely used in material characterization because it provides not only the magnitudes of the real part and imaginary part of the nonlinear susceptibility, but also the sign of the real part. Both nonlinear refraction and nonlinear absorption in solid and liquid samples can be measured easily by Z-scan technique, which use the change of transmittance of nonlinear materials [9]. In this work, we demonstrate the optical nonlinearities of a fluorine-containing azoic dye in tetrahydrofuran (THF) through Z-scan technique under picosecond and nanosecond lasers excitation at 532 nm in order to investigate the influence of pulse width on the nonlinear optical response of the fluorine-containing azoic dye.
2. Experimental The molecular structure of the fluorine-containing azoic dye is shown in Fig. 1. The linear absorption spectrum of the dye solution with the concentration of 4.4 105 M in THF is shown in Fig. 2, which was acquired using a UV–VISNIR spectrophotometer (Type: Cary 5000) manufactured by America Varian Company. The absorption spectrum is centered at 370 nm, corresponding to the S0 ? S1 transition of the azoic dye molecule. The absorption of the glass substrate was eliminated from the absorption spectrum.
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Z-scan. The difference between normalized peak and valley transmittance DTpv (denoting TP TV) can be directly measured by Zscan technique. The variation of this quantity as a function of |DU0| is given by
DT pv 0:406ð1 sÞ0:25 jDU0 j;
ð1Þ
where s = 1 exp(2r20 =x20 ) is the aperture linear transmittance with r0 denoting the aperture radius and x0 denoting beam radius at the aperture in the linear region. DU0 can be obtained from Eq. (2):
DU0 ¼ kLeff n2 I0 ¼ ð2p=kÞLeff n2 I0 ;
Fig. 1. The molecular structure of the fluorine-containing azoic dye.
2.0
Absorption
1.5
1.0
where I0 is the intensity of the laser beam at focus z = 0, Leff = ([1exp(aL)]/a) is the effective thickness of the sample, a is the linear absorption coefficient and L is the thickness of the sample. The nonlinear refractive index n2 (cm2/W) can be obtained from Eqs. (1) and (2). Dn0 = n2I0 with I0 being the on-axis irradiance at the focus represents the change in n2 at the focus. Fig. 3a shows the closed aperture (CA) Z-scan curve of the azoic dye solution. From the unsymmetric curve, there is obvious nonlinear absorption existing in the solution, and the closed transmittance is affected by the nonlinear refraction and absorption. As a result, the determination of n2 is less straight-forward from the closed aperture Z-scan measurement. It is necessary to separate the effect of nonlinear absorption by performing the open aperture experiment. Fig. 3b shows the open aperture (OA) Z-scan curve of the solution while the closed aperture curve divided by open aperture (CA/OA) curve of the solution is shown in Fig. 3c. The theoretical expression of the CA/OA curve can be written as:
Tðz; DU0 Þ ¼ 1 4DU0 v=ðv2 þ 9Þðv2 þ 1Þ; 0.5
ð2Þ
ð3Þ
2 0
0.0 400
600
800
Wavelength / nm Fig. 2. The absorption of azoic dye in THF with the concentration of 4.4 105 M.
In this work, picosecond and nanosecond lasers were adopted as excitation source in the Z-scan measurements [10]. For the picosecond Z-scan measurement, the radius of the beam waist (w0) are 26.03 lm, and the corresponding Rayleigh length z0 can be calculated to be 4 mm, much longer than the thickness of the quartz cell. This experiment was carried out using a mode-locked Nd:YAG laser (PY61C-10, Continuum) as the light source with a repetition rate of 10 Hz, pulse width of 38 ps and wavelength of 532 nm. The pulse Z-scan experimental system was calibrated by measuring the nonlinear refractive index of conventional CS2 solution. The mean error of the experimental data, mostly arising from the fluctuation of the laser power, is below 10%. In the nanosecond Z-scan measurement, the excitation source is a Q-switched Nd:YLF laser (LABest Sunlight-200), with 6 ns pulse duration, 10 Hz a repetition rate and wavelength of 532 nm. The radius of the beam waist and the corresponding Rayleigh length are 29.10 lm and 5 mm, respectively. The dye solution with the concentration of 1.5 103 M was placed in a quartz cell with 1 cm path length to perform Z-scan measurements. 3. Results and discussion The nonlinear refractive index n2 (cm2/W) and nonlinear absorption b (cm/W) are evaluated by carrying out the measurements of
where v = z/z0, z0 = kx is the diffraction length of the beam, k = 2p/ k is the vector and k is the laser wavelength, all in free space. In the picosecond Z-scan measurement, the effective thickness of the sample was Leff = 0.85 mm. The linear transmittance of the aperture was s = 0.5. The optical intensity at the focus point is 1.49 109 W/cm2. From the theoretical fit result, the nonlinear absorption coefficient was obtained to be 5.58 cm/GW. The value of DT pv can be obtained to be 0.39 and the third-order nonlinear index is calculated to be 7.64 1014 cm2/W (2.64 1011 esu). The nonlinear refractive index of THF was reported in order of 1013 esu [11], which was much smaller than that of azoic dye solution, so the contribution of solvent was negligible. Dn0 of solution under picosecond 532 nm excitation was calculated as 1.14 104. The value of the nonlinear optical susceptibility v(3) (esu) could be evaluated from the nonlinear refractive index n2. The relation is defined as follows [12]:
vð3Þ ðesuÞ ¼
2 2 n20 c cm cm ¼ 25:313n20 n2 107 n2 2 12p W W
ð4Þ
where n0 is the linear refractive index. For the solution sample, we use the refractive index value of the pure solvent. The values of v(3) (esu) for the solution is calculated to be 4.06 1012 esu. The second hyperpolarizability of molecule in an isotropic media is related to the nonlinear optical susceptibility by the following [13]:
< c >¼ vð3Þ =ðL4 NÞ;
ð5Þ
where N is the number density of the molecules in cm3 and L is the local field correction factor given by [(n2 + 2)/3]. Under 532 nm excitation, the number density of the molecules in the solution in cm3 was N = 9.03 1017 cm3, so the corresponding second hyperpolarizability was < c > = 1.28 1030 esu at picosecond 532 excitation.
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thermal effect increases. It is a common assumption that Z-scan measurements should be made with repetition rate of few of Hertz in order to extract a nonlinear refractive index influenced by only electronic effects. The time scale of this cumulative process is given by tc = x2/4D, where x is the beam waist and D is the thermal diffusion coefficient of the materials. Generally, the value of D ranges from 1 107 m2/s to 6 107 m2/s. The magnitude of the calculated tc is within 103 s, which is much smaller than the time interval between consecutive laser pulses 0.1 s used in this experiment [14]. The electronic nonlinearity was induced by either the population redistribution or the distortion of electronic clouds. A
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z / mm Fig. 3. Z-scan experimental data for the dye solution under picosecond 532 nm excitation: (a) CA curve; (b) OA curve; (c) CA/OA curve.
In the picosecond Z-scan measurement, the optical nonlinearity observed is induced electronic effect, but not by thermal effect. One hand, the electronic nonlinearities arise very rapidly (within the 38 ps pulse duration). Refractive index changes due to thermal nonlinearities arise due to density changes in the materials propagating with acoustic wave speed caused by heating; if we estimate it to be on the order of 3 103 m/s, the time to propagate a distance equal to the beam radius at focus is about 9 ns at 532 nm excitation, two orders longer than the pulse width, respectively. On the other hand, thermal heating induced by a single laser pulse persists over some characteristic time tc. As a result, when the time interval between consecutive laser pulses is shorter than tc, the
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-10
0 z / mm
Fig. 4. Z-scan experimental data for the dye solution under nanosecond 532 nm excitation: (a) CA curve; (b) OA curve; (c) CA/OA curve.
T. Jia et al. / Optics Communications 283 (2010) 1110–1113
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molecule underwent a transition from the ground state to the excitation state after absorbing a photon. The dipole moment of the molecule changed during such a transition. This change would give birth to electronic nonlinearity [15,16]. Fig. 4a–c shows the CA, OA and CA/OA curves for the solution in the nanosecond Z-scan measurements, respectively. In this experiment, the optical intensity was 2.88 107 W/cm2 at the focus point. From the theoretical fit for the OA curve, the nonlinear absorption coefficient was obtained to be 7.3 107 cm/W. In the CA/OA curve, the value of DT pv can be obtained to be 0.51 and the third-order nonlinear index is calculated to be 5.11 1012 cm2/W. Dn0 was calculated to be 1.47 104. In the nanosecond Z-scan measurement, the time to propagate a distance equal to the beam radius at focus is estimated to be about 10 ns, in the same order with the pulse width. Thus, the thermal effect gave important impact on the measured optical nonlinearity. The nonlinear refraction induced by thermal effects is estimated, which results from linear absorption. The value of it can be calculated by
was dominated by singlet–singlet absorption. The larger absorption cross-section of the first singlet excited state compared to that of the ground state also leaded to a RSA under 38 ps excitation. It is always regarded as that the absorption cross-section of singlet state is much weaker than that of triplet state, so the RSA coefficient in the ps pulse excitation case (singlet–singlet absorption) was much larger than that in the nanosecond case (triplet–triplet absorption). The similar phenomena have been observed in several Refs. [17]. It is difficult to make strict comparison of the experimental data with other published data due to different pulse duration, excitation wavelength and solution concentration. However, some comparison will be useful to have general view on nonlinear optical response of this kind of structure. Under picosecond excitation, the nonlinear refractive index of this azoic dye solution is larger than those of disperse red 1 and disperse 13 solution [18].
Dn ¼ ðdn=dTÞ=DT ðdn=dTÞðIsa=qcÞ;
The optical nonlinearity of a fluorine-containing azoic dye was investigated by using single-beam Z-scan technique. Under picosecond 532 nm excitation, Z-scan measurements showed that the dye solution exhibited large electronic effect optical nonlinearity, with n2 = 7.83 1014 cm2/W and b = 5.58 cm/GW, respectively. In the nanosecond Z-scan experiment, the dye solution presented large different optical nonlinearities, with n2 = 5.11 1012 cm2/W and b = 7.7 107 cm/W. The larger nonlinear refraction at nanosecond 532 nm was shown to be of thermal origin resulting from energy transfer from dye molecules to the THF molecules while the larger nonlinear absorption was induced by triplet–triplet absorption.
ð6Þ
where s is duration of laser pulses, c is the specific heat of sample, a is coefficient of linear absorption, I is the laser intensity irradiated on the sample [10]. The calculated result shows that Dn is in the order of 104, which is in the same order with the Dn0 obtained under nanosecond 532 nm excitation. Obviously, thermal effects are, therefore, is expected to be dominant in experiments with nanosecond duration laser. However, under the picosecond excitation, Dn from thermal contribution was calculated to be in order of 103, much smaller than the Dn0 obtained from picoseconds Z-scan measurement, so the thermal effect should be negligible. The thermally induced optical nonlinearity denoted temporal variation of optical parameters (in particularly, refractive index) due to linear and/or nonlinear absorption in medium followed by a non-radiative relaxation down to the ground state. The laser heating leaded to the generation of acoustic wave that changed the medium density followed by a variation of refractive index. This process was slow (of order of a few nanosecond) and could be observed in the case of CW laser, long laser pulses, or in the case of high pulse repetition rate [14]. The different nonlinear absorption performances with nanosecond and picosecond pulses appeared to be due to the relative contributions of excited singlet–singlet and triplet–triplet absorption for different pulse durations. The laser pulse duration (38 ps), much smaller than the time of intersystem crossing (1 ns), was so small that the amount of population transfer to the triplet state was relatively small. For 6 ns laser pulse, pulse duration was much longer than the singlet excited state lifetime and the intersystem crossing rate was very fast, thus, the singlet contribution diminished, and the contribution of the triplet–triplet absorption became dominant. Due to the larger absorption cross-section of the triplet excited state compared to that of the ground state, RSA occurred. For 38 ps laser pulse, the pulse duration was much less than the singlet excited state lifetime, therefore the nonlinear absorption
4. Conclusion
References [1] J.E. Ehrlich, X.L. Wu, I.-Y.S. Lee, Z.-Y. Hu, H. Röckel, S.R. Marder, J.W. Perry, Opt. Lett. 22 (1997) 1843. [2] G.S. He, G.C. Xu, P.N. Prasad, B.A. Reinhardt, J.C. Bhatt, A.G. Dillard, Opt. Lett. 20 (1995) 435. [3] T. He, C. Wang, X. Pan, H. Yang, G. Lu, Opt. Lett. 34 (2009) 665. [4] T. Ikeda, O. Tsutsumi, Science 268 (1995) 1873. [5] P. Wang, H. Ming, J. Zhang, Z. Liang, Y. Lu, Q. Zhang, J. Xie, Y. Tian, Opt. Commun. 203 (2002) 159. [6] J.C. Liang, X.Q. Zhou, J. Opt. Soc. Am. B 22 (2005) 2468. [7] R. Rangel-Rojo, S. Yamada, H. Matsuda, D. Yankelevich, Appl. Phys. Lett. 72 (1998) 1021. [8] C. Gayathri, A. Ramalingam, Spectrochim. Acta Part A 69 (2007) 96. [9] T. He, C. Wang, J. Mod. Opt. 55 (2008) 3013. [10] M. Sheik-Bahae, A.A. Said, T.H. Wei, D.J. Hagan, E.W. Van Stryland, IEEE J. Quantum Electron. 26 (1990) 760. [11] Q.-H. Qi, J.-L. Li, T.-Q. Zhang, H. Yang, Chin. Phys. Lett. 15 (1998) 30. [12] R.W. Boyd, Nonlinear Optics, Academic Press, Amsterdam, 2003. [13] B.K. Mandal, B. Bihari, A.K. Sinha, M. Kamath, L. Chen, Appl. Phys. Lett. 66 (1995) 932. [14] A. Gnoli, L. Razzari, M. Righini, Opt. Express 13 (2005) 7976. [15] T. He, Y. Cheng, Y. Du, Y. Mo, Opt. Commun. 275 (2007) 240. [16] L. Brzozowski, E.H. Sargent, J. Mater. Sci. 12 (2001) 483. [17] W. Sun, C.C. Byeon, C.M. Lawsonb, G.M. Gray, D. Wang, Appl. Phys. Lett. 77 (2000) 1759. [18] F. Cherioux, P. Audebert, H. Maillotte, L. Grossard, F.E. Hernandez, A. Lacourt, Chem. Mater. 9 (1997) 2921.