The study on the nonlinear optical response of Sudan I

Optics Communications 281 (2008) 4121–4125

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The study on the nonlinear optical response of Sudan I Tingchao He, Changshun Wang * Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, PR China

a r t i c l e

i n f o

Article history: Received 24 October 2007 Received in revised form 10 April 2008 Accepted 10 April 2008

PACS: 42.65.An 42.65.Jx

a b s t r a c t The nonlinear optical properties of Sudan I were investigated by a single beam Z-scan technique. The Sudan I ethanol solution exhibited large nonlinear refractive indices under both CW and pulse laser excitations. The nonlinear refractive indices of Sudan I were in the order of 108 cm2/W under CW 633 nm excitation and 106 cm2/W under CW 488 nm excitation, respectively. Under the excitation of a pulse 532 nm laser, the nonlinear refractive index n2 was calculated to be 1.19  1014 cm2/W. It was discussed that the mechanism accounting for the process of nonlinear refraction was attributed to the laser heating for the CW laser excitation and the electronic effect for the pulse excitation. Moreover, the second hyperpolarizability of Sudan I was also estimated in this paper. Ó 2008 Elsevier B.V. All rights reserved.

Keywords: Sudan I Z-scan Nonlinear refractive index Second hyperpolarizability

1. Introduction Recently, there has been growing interest in the nonlinear optical properties of azo materials for their large nonlinear refraction, which are interesting for the application in optical storage, optical-limiting and optical switching application [1–3]. The nonlinear optical response of azo materials may result from electronic and/or nonelectronic process. Electronic nonlinearities occur as the result of the nonlinear response of bound electrons on an applied optical field. Electronic nonlinearity is of very importance because it is present in all dielectric materials. Moreover, recent reports have shown that a lot of organic nonlinear optical materials have large electronic optical nonlinearities due to their p delocalized electrons. The characteristic response time of electronic nonlinearity is estimated as short as 1016 s [4]. Nonelectronic responses are nonradiative interactions, such as cis–trans isomerization, the changes in density and temperature. The temporal and spatial behavior of a light beam propagating through the medium is severely affected by the nonlinear properties of optical materials. The optical nonlinearity is contributed independently by various physical mechanisms [5]. Until now, the electronic and nonelectronic nonlinearities of optical materials have been widely studied [6–8].

* Corresponding author. E-mail address: [email protected] (C. Wang). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.04.026

Z-scan technique, developed by Sheik-Bahae et al. [9], has been used widely in material characterization. It provides not only the magnitudes of the real part and the imaginary part of the nonlinear refractive index, but also the sign of the real part. In order to investigate the nonlinear optical properties of azo dyes under CW and pulse excitations, we chose Sudan I, one of the representative azo dyes, as the material used in this paper. We reported the nonlinear optical response of Sudan I under CW 633 nm, 488 nm and pulse 532 nm excitations. The nonlinear origin was discussed in terms of laser heating and resonant electronic effect, respectively. 2. Experimental Sudan I ethanol solution with the concentration of 2  104 M, 4  105 M and 2  106 M was prepared to investigate the influence of solution concentration on the nonlinear refraction. The molecular structure of Sudan I is shown in Fig. 1. Sudan I was purchased from Aldrich corporation in China and of analytical grade. The linear absorption spectra of Sudan I ethanol solution with the concentration of 2  104 M, 4  105 M, 2  106 M are shown in Fig. 2, which are recorded by the UV–VIS–NIR spectrophotometer (Type: Varian Cary 5000). The absorption of Sudan I solution is strong at 488 and 532 nm but negligible at 633 nm. The experimental setup was similar to that reported in reference [9]. In this experiment, the excitation sources were CW 633 nm He–Ne and 488 nm Ar+ lasers and pulse 532 nm Nd:YAG laser with a pulse duration of 38 picoseconds. For the CW Z-scan

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T. He, C. Wang / Optics Communications 281 (2008) 4121–4125

ness of the sample. The nonlinear refractive index n2 (m2/W) is connected with n2 (esu) by n2 ðesuÞ ¼ ðcn0 =40pÞn2 ðm2 =WÞ;

ð3Þ

2

Fig. 1. The molecular structure of Sudan I.

a

6 5

Absorption

A 4 B 3 2 1

Normalized Transmittace / a.u.

where n2 (m /W) and n2 (esu) denote the nonlinear refractive index in different units system. If there is nonlinear absorption existing in the solution, the closed transmittance is affected by the nonlinear refraction and nonlinear absorption. As a result, the determination of n2 (cm2/ W) 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 Z-scan experiment.

1.08 1.06 1.04 1.02 1.00 0.98 0.96 0.94 0.92 -15

C

-10

-5

0

400

500

600

700

b

800

Wavelength / nm Fig. 2. The absorption spectra of Sudan I with different concentration of (A) 2  104 M; (B) 4  105 M; (C) 2  106 M.

setup, a lens with 18 cm focal length was used and the spot sizes at the focal point were 37.30 lm and 24.2 lm for 633 nm and 488 nm, respectively. For the pulse Z-scan setup, repetition frequency was 10 Hz and the detector was a dual-channels energy meter (EPM2000). The focal length of the lens was 30 cm. The spot size at the focal point for 532 nm was 33.9 lm. The Sudan I ethanol solution was filled in the sample cell with a 1 mm path length.

Normalized Transmittance / a.u.

0 300

5

10

15

z / mm

1.15 1.10 1.05 1.00 0.95 0.90 0.85 -15

-10

-5

0

5

10

15

20

25

z / mm

c The nonlinear refractive index n2 (cm2/W) and the nonlinear absorption coefficient b of Sudan I ethanol solution were evaluated by the measurements of Z-scan. The difference between normalized peak and valley transmittance DTp–v denoting TP  TV can be directly measured by Z-scan technique [9]. The variation of this quantity as a function of |DU0| is given by DT p—v ¼ 0:406ð1  sÞ0:25 jDU0 j;

ð1Þ

where s ¼ 1  expð2r 20 =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 equation DU0 ¼ kLeff n2 I0 ¼ ð2p=kÞLeff n2 I0 ;

ð2Þ

where I0 is the intensity of the laser beam at focus z = 0, k = 2p/k is the wave vector, Leff = [1  exp(aL)]/a is the effective thickness of the sample, a is the linear absorption coefficient and L is the thick-

Normalized Transmittace / a.u.

3. Results and discussion

1.3 1.2 1.1 1.0 0.9 0.8 0.7 -15

-10

-5

0

5

10

15

20

z / mm Fig. 3. Z-scan curves of Sudan I ethanol solution under 633 nm excitation with three concentration: (a) 2  106 M; (b) 4  105 M; (c) 2  104 M.

4123

Tðz; DU0 Þ ¼ 1  4DU0 v=½v2 þ 9½v2 þ 1;

a

ð4Þ

kx20 =2

Normalized Transmittace / a.u.

where v = z/z0, z0 ¼ is the diffraction length of the beam, k = 2p/k is the wave vector and k is the laser wavelength, all in free space. The peak followed by a valley-normalized transmittance obtained from the closed aperture Z-scan curves indicated that the sign of nonlinear refractive indices was negative i.e. self-defocusing. The symmetrical closed aperture Z-scan curves under 633 nm and 488 nm excitations indicated that the nonlinear absorption was negligible, so the nonlinear refractive indices under 633 nm and 488 nm excitations, without division of corresponding open aperture Z-scan curves, could be obtained from Figs. 3 and 4. Under 633 nm excitation, the input power was 110 mW and the laser intensity at the focus was calculated to be 5.04  103 W/cm2 according to equation I0 ¼ 2pi =px20 , where pi was input power and x0 was the spot sizes at the focal point. For the concentration of 2  106 M and 4  105 M, the linear absorption could be neglected and the linear absorption coefficient was 0.11 cm1 for the concentration of 2  104 M. The effective thickness of the samples was Leff = 1 mm for all the three concentration. The linear transmittance of the aperture was s = 0.4. From Eqs. (1) and (2), the nonlinear refractive indices of Sudan I were calculated as 0.95  108 cm2/W (or 3.09  106 esu), 1.40  108 cm2/W (or 4.55  106 esu) and 2.80  108 cm2/W (or 9.10  106 esu), respectively. Dn0 = n2I0 with I0 being the on-axis irradiance at the focus represented the change in n2 at the focus. Dn0 was calculated as 4.79  105, 7.06  105 and 1.41  104, respectively. The input power was 9 mW under 488 nm excitation, and the laser intensity at the focus was 978.84 W/cm2. The linear absorption coefficient was a = 0.23 cm1 and the effective thickness of the sample was Leff = 0.99 mm. The linear transmittance of the aperture was s = 0.62. The nonlinear refractive index of Sudan I

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 -30

-20

-10

0

10

20

30

z / mm Fig. 4. Z-scan curves of Sudan I ethanol solution with the concentration of 2  106 M under 488 nm excitation.

1.2

1.0

0.8 -30

-20

-10

0

10

20

30

10

20

30

z / mm

b

Normalized Transmittance / a.u.

Fig. 3a–c shows the closed aperture Z-scan experimental data of Sudan I ethanol solution with the concentration of 2  106 M, 4  105 M and 2  104 M for Sudan I under 633 nm excitation. Fig. 4 shows the closed aperture Z-scan experimental data of Sudan I ethanol solution with the concentration of 2  106 M under 488 nm excitation. With the increase of the solution concentration, the transmittance of light decreased greatly. The transmittance was almost zero with the concentration 4  105 M and 2  104 M under 488 nm. All the open aperture CW Z-scan curves are nearly linear (not shown). The solid lines in Figs. 3 and 4, 5b are theoretical fit according to Eq. (4) [9]:

Normalized Transmittance / a.u.

T. He, C. Wang / Optics Communications 281 (2008) 4121–4125

1.4 1.2 1.0 0.8 0.6 -30

-20

-10

0

z / mm Fig. 5. (a) Open aperture Z-scan curve under 532 nm excitation; (b) closed aperture Z-scan curve divided by open aperture Z-scan curve under 532 nm excitation.

was calculated as 0.30  106 cm2/W (or 0.98  104 esu). Dn0 of Sudan I ethanol solution under 488 nm excitation was calculated as 2.94  104. Under 633 nm and 488 nm excitations, the nonlinear optical process of Sudan I ethanol solution could be caused by laser heating induced nonlinearity. This kind of nonlinearity denoted temporal variation of optical parameters (in particularly, refractive index) due to linear and/or nonlinear absorption in medium followed by a nonradiative relaxation down to the ground state. The laser heating led to the generation of acoustic wave that changed the medium density followed by a variation of refractive index. This process was too 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 when the heat accumulation started to play important role. Moreover, due to the increased linear absorption of the solution, the nonlinear refractive index of Sudan I under 488 nm excitation was larger than those under 633 nm excitation. Whatever the applications envisaged, fundamental investigation of laser heating induced nonlinearity will be valuable in better understanding the physics inherent of the nonlinear optical properties of azo dyes. Moreover, thermal lens effect has found valuable application in the measurement of weak absorption [10]. Though the nonlinearity of optical materials under CW laser excitation is large, it is not applicable for high-bandwidth optical signal processing due to long excitation and relaxation times (usually ls but in extreme cases as high as 1 ms and minutes, respectively, depending on the thermal properties of samples) [11]. Thus, we have investigated the nonlinear optical property of Sudan I under pulse 532 nm.

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T. He, C. Wang / Optics Communications 281 (2008) 4121–4125

The pulse Z-scan experimental system was calibrated by measuring the nonlinear refractive index of conventional CS2 solution. The nonlinear refractive index of CS2 was measured as 2.98  1014 cm2/W in our experiment and the error was below 10% compared with 3.10  1014 cm2/W reported in reference [9]. Fig. 5a shows the open aperture Z-scan experimental data of Sudan I ethanol solution under pulse 532 nm excitation while the closed aperture Z-scan experimental data divided by open aperture Z-scan experimental data is shown in Fig. 5b. The valley followed by a peak-normalized transmittance indicated that the sign of nonlinear refractive indices was positive i.e. self-focusing. The solid line in Fig. 5a is theoretical fit according to Eq. (5). The normalized transmittance for open aperture Z-scan experiment is given by X Tðz; s ¼ 1Þ ¼ ½q0 ðz; 0Þm =ðm þ 1Þ3=2 ðq0 ð0Þ < 1Þ; ð5Þ where q0 ðz; 0Þ ¼ bI0 Leff =ð1 þ z2 =z20 Þ; z0 ¼ kx20 =2 is the diffraction length of the beam and x0 is the beam waist radius at the focus point and k = 2p/k is wave vector. For the pulse Z-scan experiment, the laser intensity at the focus was 4.44  109 W/cm2. From theoretical fit result, the nonlinear absorption coefficient was obtained as 1.04 cm/GW. The linear absorption coefficient was a = 8.69 cm1 and the effective thickness of the sample was Leff = 0.67 mm. The linear transmittance of the aperture was s = 0.22. Then, the nonlinear refractive index was calculated as 1.19  1014 cm2/W (or 3.25  1012 esu). Dn0 was calculated as 5.28  105. Because the absorption at 532 nm was high, intra-pulse thermal effects could still be present even for ps pulses. Furthermore, photoinduced trans–cis transformation can happen near main absorption region even in solution [12]. However, the observed nonlinear refraction was not induced by laser heating effect or photoinduced trans-cis transformation. The sign of nonlinear refractive index due to laser heating effect and photoinduced trans-cis transformation was negative [11], but the sign of nonlinear refractive index observed in this experiment was positive. Thus, the nonlinear refraction under pulse 532 nm excitation was induced by resonant electronic nonlinear effect and was a resonant electronic nonlinearity. The electronic nonlinearity was induced by either the population redistribution or the distortion of electronic clouds. A molecule underwent a transition from the ground state to the excitation after absorbing a photon. The dipole moment of the Sudan I molecule changed during such a transition. This change would give birth to electronic nonlinearity. If the change was dramatic, it would induce large resonant electronic effect. The real part and imaginary part of the nonlinear optical susceptibility v(3) could be evaluated from the nonlinear refractive index n2 and nonlinear absorption coefficient, respectively. The relations are defined as follows [13]: Revð3Þ ðesuÞ ¼ ðcn20 =120p2 Þn2 ðm2 =WÞ and Imvð3Þ ðesuÞ ¼ ðc2 n20 =240xp2 Þb ðm=WÞ;

ð6Þ

where c is the velocity of the light in vacuum, n0 is the linear refractive index of the sample, x = 2pc/k is the angular frequency of the light field. Thus, Rev(3) (esu) and Imv(3) (esu) were calculated as 5.58  1013 esu and 2.07  1013 esu, respectively. The absolute value of was calculated from |v(3) (esu)| = [(Rev(3) (esu))2 + (Imv(3)(esu))2]1/2, and gave 5.95  1013 (esu). The nonlinear refractive index of Sudan I ethanol solution contained the contribution of ethanol. For the nonlinear refractive index of Sudan I ethanol solution, it satisfied Eq. (7) [14]: ðsolutionÞ

n2

ðsoluteÞ

¼ n2

ðsolutionÞ

ðsolventÞ

þ n2

;

ð7Þ

where n2 represents the nonlinear refractive index of Sudan I ðsoluteÞ ðsolventÞ ethanol solution, n2 and n2 represent the nonlinear refrac-

Table 1 Nonlinear refractive indices of Sudan I with different concentration under CW and pulse excitations Wavelengths

Concentration (mol/L)

a (cm1)

DTp–v

n2 (cm2/W)

CW 633 nm

2  10 M 4  105 M 2  106 M

0.11 0 0

0.50 0.25 0.17

2.80  108 1.40  108 0.95  108

CW 488 nm

2  106 M

0.23

1.20

0.30  106

8.69

0.16

Pulse 532 nm

4

2  10

4

M

1.19  1014

tive indices of solute (Sudan I) and solvent (pure ethanol). The nonlinear refractive index of ethanol was reported as 2.5  1013 esu [15], which was much smaller than that of Sudan I ethanol solution, so the contribution of solvent was negligible. We listed the nonlinear refractive indices of Sudan I ethanol solution under CW and pulse excitations as Table 1. The second hyperpolarizability of molecule in an isotropic media is related to the nonlinear optical susceptibility by the following Eq. (8) [16]: hci ¼ vð3Þ =ðL4 NÞ;

ð8Þ 3

where N is the number density of the molecules in cm and L is the local field correction factor given by [(n2 + 2)/3]. Under 532 nm excitation, the number density of the molecules of Sudan I in cm3 was N = 1.20  1017 cm3, so the corresponding second hyperpolarizability was hci = 1.83  1030 esu. This magnitude is one order smaller than that of C84 toluene solution [17] but one order larger than that of bis-naphthalocyanine viz. europium naphthalocyanines dimethyl formamide solution [18]. For practical use in ultra-fast all-optical switching devices, many considerations have been taken into to investigate the effectiveness of nonlinear materials. The figure of merit W has to be satisfied for 2p phase shift in order to evaluate its application in such devices [19]: W ¼ Dnmax =ðakÞ > 1;

ð9Þ

Under 532 nm excitation, for Sudan I ethanol solution, the figure of merit is calculated as W = 0.11 < 1, which indicates that the nonlinear optical properties of Sudan I ethanol solution are yet insufficient for application in all-optical switching technology. However, the fast response time makes Sudan I ethanol solution promising for use in nonlinear optical devices.

4. Conclusion In conclusion, we experimentally studied the nonlinear optical response of Sudan I ethanol solution by a single-beam Z-scan technique. Under CW 488 nm and 633 nm excitations, Sudan I ethanol solution showed large laser heating induced nonlinear refractive indices. Under pulse 532 nm excitation, nonlinear refractive and absorptive nonlinearities were observed in our experiment. From the analytical results, it was concluded that the observed nonlinearity was not induced by thermal effect and photoisomerization, but induced by electronic effect. Moreover, the second hyperpolarizability was estimated by utilizing the value of nonlinear optical susceptibility. The evaluation of the figure of merit W shows that the solution is insufficient for applications in all-optical switching technology but a valid candidate for nonlinear optical devices. Acknowledgement This work was supported by the National Science Foundation of China (Contract No. 10675083).

T. He, C. Wang / Optics Communications 281 (2008) 4121–4125

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