Measurements of the nonlinear refractive index in ... - OSA Publishing

Measurements of the nonlinear refractive index in scattering media using the Scattered Light Imaging Method - SLIM Kelly C. Jorge,1∗ Hans A. Garc´ıa,2 Anderson M. Amaral,1 Albert S. Reyna,1 Leonardo de S. Menezes,1 and Cid B. de Araujo ´ 1 1 Departamento

de F´ısica, Universidade Federal de Pernambuco, 50670-907 Recife, PE, Brazil 2 Departamento de F´ısica, Universidade Federal do Piau´ı, 64049-550 Terezina, PI, Brazil ∗

[email protected]

Abstract: The Scattered Light Imaging Method (SLIM) was applied to measure the nonlinear refractive index of scattering media. The measurements are based on the analysis of the side-view images of the laser beam propagating inside highly scattering liquid suspensions. Proof-of-principle experiments were performed with colloids containing silica nanoparticles that behave as light scatterers. The technique allows measurements with lasers operating with arbitrary repetition rate as well as in the single-shot regime. The new method shows advantages and complementarity with respect to the Z-scan technique which is not appropriate to characterize scattering media. © 2015 Optical Society of America OCIS codes: (190.5890) Scattering, stimulated; (160.4330) Nonlinear optical materials; (140.3295) Laser beam characterization.

References and links 1. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955-957 (1989). 2. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990). 3. H. Ma, A. S. L. Gomes, and C. B. de Araújo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666-2668 (1991). 4. D. V. Petrov, A. S. L. Gomes, and C. B. de Araújo, “Reflection Z-scan technique for measurements of optical properties of surfaces,” Appl. Phys. Lett. 65, 1067-1069 (1994). 5. D. V. Petrov, A. S. L. Gomes, and C. B. de Araújo, “Reflection of a Gaussian beam from a saturable absorber,” Opt. Commun. 123, 637-641 (1996). 6. R. A. Ganeev, G. S. Boltaev, R. I. Tugushev, and T. Usmanov, “Investigation of nonlinear optical properties of various organic materials by the Z-scan method,” Opt. Spectrosc. 112, 906-913 (2012). 7. G. Boudebs and C. B. de Araújo, “Characterization of light-induced modification of the nonlinear refractive index using a one-laser-shot nonlinear imaging technique,” Appl. Phys. Lett. 85, 3740-3742 (2004). 8. K. Fedus, G. Boudebs, C. B. de Araújo, M. Cathelinaud, F. Charpentier, and V. Nazabal, “Photoinduced effects in thin films of Te20 As30 Se50 glass with nonlinear characterization,” Appl. Phys. Lett. 94, 061122 (2009). 9. A. Marcano O., H. Maillotte, D. Gindre, and D. Métin, “Picosecond nonlinear refraction measurement in singlebeam open Z scan by charge-coupled device image processing,” Opt. Lett. 21, 101-103 (1996). 10. J. Hein, M. Helbig, and S. Rentsch, “Measurements of a nonlinear refractive index with a single laser pulse,” Appl. Opt. 36, 1173-1176 (1997).

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Received 16 Jun 2015; revised 9 Jul 2015; accepted 9 Jul 2015; published 17 Jul 2015 27 Jul 2015 | Vol. 23, No. 15 | DOI:10.1364/OE.23.019512 | OPTICS EXPRESS 19512

11. S. Cherukulappurath, G. Boudebs, and A. Monteil, “4 f coherent imager system and its application to nonlinear optical measurements,” J. Opt. Soc. Am. B 21, 273-279 (2004). 12. G. Boudebs and S. Cherukulappurath, “Nonlinear optical measurements using a 4 f coherent imaging system with phase objects,” Phys. Rev. A 69, 053812 (2004). 13. J. Jayabalan, A. Singh, and S. M. Oak, “Single-shot measurement of nonlinear absorption and nonlinear refraction,” Appl. Opt. 45, 3852-3858 (2006). 14. R. A. Ganeev, “Single-shot refraction Z-scan for measurements of the nonlinear refraction of nontransparent materials,” Appl. Phys. B 91, 273-277 (2008). 15. R. A. Ganeev and I. A. Kulagin, “Single-shot Y-scan for characterization of the nonlinear optical parameters of transparent materials,” J. Opt. A: Pure Appl. Opt. 11, 085001 (2009). 16. M. R. Ferdinandus, H. Hu, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction,” Opt. Lett. 38, 3518-3521 (2013). 17. P. Samineni, Z. Perret, W. S. Wareen, and M. C. Fischer, “Measurements of nonlinear refractive index in scattering media,” Opt. Express 18, 12727-12735 (2010). 18. M. R. Ferdinandus, M. Reichert, T. R. Ensley, H. Hu, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Dual-Arm Z-scan technique to extract dilute solute nonlinearities from solution measurements,” Opt. Mater. Express 2, 1776-1790 (2012). 19. K. C. Jorge, R. Riva, and N. A. S. Rodrigues, “Device and method for characterization of laser beams, of low and high powers, with basis on the light scattering (in Portuguese),” Patent PI 0605596-6 A, DCTA, 23 November 2006. 20. K. C. Jorge, R. Riva, J. M. S. Sakamoto, N. A. S. Rodrigues, and M. G. Destro, “Scattered light imaging method (SLIM) for characterization of arbitrary laser beam intensity profiles,” Appl. Opt. 53, 4555-4564 (2014). 21. K. C. Jorge, R. Riva, N. A. S. Rodrigues, and M. G. Destro, “M2 beam quality measurement of a single pulse of the Nd:YAG laser,” Proc. Conference on Lasers in Manufacturing, p. 323-326, Munich (2009). 22. International Organization for Standardization, ISO 11146-1/2/3. “Test methods for laser beam widths, divergence angles and beam propagation ratios. Part 1: Stigmatic and simple beams/ Part 2: General astigmatic beams/ Part 3: Intrinsic and geometrical classification, propagation and details of test methods” (ISO, Geneva, 2005). 23. A. E. Siegman, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: Applications and Issues (DLAI) (OSA, 1998), paper MQ1. 24. M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soleau, E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228-1235 (1991). 25. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008). 26. A. S. Reyna and C. B. de Araújo, “Nonlinearity management of photonic composites and observation of spatialmodulation instability due to the quintic nonlinearity,” Phys. Rev. A 89, 063803 (2014).

1.

Introduction

The Z-scan technique [1–5] has been largely used for measuring the nonlinear (NL) refractive index, n2 , and the NL absorption coefficient, α2 , of materials. The NL parameters are obtained analyzing the variation of the far-field intensity profile of a laser beam transmitted through a thin sample located at different positions with respect to the focusing lens [1–3] or reflected by the surface of a nontransparent sample [4, 5]. The technique is simple and elegant and has been used routinely to characterize optical materials. However, when the sample is a heterogeneous medium (e.g. a homogeneous solid or a liquid embedded with micro or nanoparticles (NPs), or molecule aggregates suspended in a liquid) the Z-scan technique does not distinguish if the variation of the transmitted light during the measurement is due the linear light scattering or to the effective nonlinearity of the sample. Furthermore, since it is necessary to move the sample to determine the NL parameters, the conventional Z-scan technique does not allow single-shot measurements. Indeed, this may be a serious limitation if one is dealing with fragile samples, e.g. organic and biological materials, that can be damaged by multiple laser pulses [6] or when photo-induced effects occurs in solids [7, 8]. Many attempts were made by several authors to determine n2 in single-shot experiments [9–16] but the measurement of sign and magnitude of n2 during one laser pulse remains a challenging task. On the other hand, the limitation of the Z-scan technique for the study of scattering media led to development of other techniques such as the spectral re-shaping [17] and the dual-arm Z-scan technique [18], that present good sensitivity but require laborious experimental setup.

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In the present paper we report on a new method for measurements of n2 that consists of recording with a camera the scattered light in the transverse direction to the beam propagating inside a scattering medium. The method used, labeled as Scattered Light Imaging Method (SLIM), was originally developed for laser beam characterization [19–21] using either continuous-wave or pulsed lasers. However, besides the already exploited features [19–23], one is capable of performing measurements to study the beam self-focusing (or self-defocusing)in NL experiments. In the present paper it is shown that the SLIM can be used to determine the effective NL refractive index of a composite system, ne2 f f , using lasers delivering pulses in a given repetition rate or in the single-shot regime. As a demonstration of the SLIM for measuring ef f n2 , we performed proof-of-principle experiments to characterize liquid colloids containing silica NPs. 2.

Theory

To describe the laser beam propagation inside a cell filled with a liquid colloid with NPs we followed the approach described in [24] and consider the medium as a stack of thin NL lenses that depend on the incident beam intensity, I. The refractive behavior of the composite medium is described by ne f f (I) = ne0 f f + ne2 f f I, where ne0 f f and ne2 f f are the effective linear and NL refractive indices, respectively. Both effective refractive indices contain information related to the host liquid and the NPs. Since the SLIM allows accurate measurements of the beam waist and divergence angle, the theoretical approach described in [24] was adapted to take into account the experimentally accessible parameters obtained from images collected in the perpendicular direction with respect to the beam propagation direction (z axis). Accordingly, for the theoretical interpretation of the data we that the laser considered 2 2 beam has a Gaussian profile given by I(r) = I0 w w0(z) exp − w22r(z) , where wlin (z) = lin lin r

w0

1+

z zR

2

is the beam waist for light propagating linearly for a distance z, w0 is the minin

ef f

π w2

mum beam waist, zR = 0λ M2 0 is the Rayleigh length, λ is the light wavelength, M 2 is the beam quality (or propagation) factor [22, 23], I0 is the on-axis intensity and r is the transverse distance from the optical axis. In the limit of an infinite number of thin NL lenses, and considering that the on-axis NL phase-shift, ∆Φ = 2λπ ne2 f f I0 z is small when the light propagates through the sample for a distance z such that |∆Φ| ≪ π , the propagation can be described by the ABCD matrix ! 1 z (1) −1 1 , fe f f where 1 fe f f

=

aλ M 2 4π n2 I0 ef f

J,

(2)

The nonlinearity is taken into account through the effective focal distance fe f f that depends z z

on a geometrical parameter a = 6.4 [24], and on the quantity J = 0 R du(1 + u2 )−2 ≈ π4 , where the approximation is correct within 2% for z ≥ 3zR . The a value originates from the fact that in the Z-scan technique, a = 6.4 is associated with an infinitesimal aperture positioned in the far-field, in front of the detector. In this case, the variation in the intensity transmitted by the aperture is only due to the NL change of the beam divergence angle. Since to implement the SLIM we detect the beam’s divergence angle, the measurements are equivalent to those obtained with very small aperture placed in the far-field region in the Z-scan method. R

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Using the standard way for describing the Gaussian beams propagation by an ABCD matrix and applying Eq. (1), considering that the beam at z = 0 (cell’s entry face) has the minimum waist, it is possible to obtain the beam waist, wNL (z), for arbitrary positions inside the sample including the NL effects. Then defining the NL and linear local divergence angles respectively (z) lin (z) as θNL = dwNL and θ0 (z) = dwdz , it is possible to show that for zR ≪ z ≪ fe f f we have dz

θNL (z) z +O = 1− θ0 (z) fe f f

z2 fe2f f

!

,

(3)

where the last term represents contributions of second order of (z/ fe f f ) or higher. For small ef f nonlinearities, Eq. (3) indicates that the local beam divergence angle varies linearly with n2 I0 . Therefore, by measuring θNL (z) from one side-view image of the propagating beam it is possief f ble to determine n2 using only one laser shot. In particular, for a pulsed laser with Gaussian ef f ef f √ temporal profile the light intensity must be averaged as in [2] by changing n2 by n2 / 2 in Eq. (2). 3.

Experimental details

The experiments for NL characterization of the scattering media were performed with samples having different concentrations of silica NPs suspended in a liquid. The samples were prepared by adding acetone in an ethanol solution containing spherical silica NPs with average diameter of (120 ± 21) nm. The NPs concentration is expressed through the filling fraction, f , that is the ratio between the volume of the NPs and the total volume of the sample. The ethanol solution of 1 ml corresponds to f = 4.5 × 10−4 , which provides a turbid liquid that presents strong light scattering behavior. The value of f was changed adding small quantities of acetone in the solution and the values ne2 f f were determined using the values for acetone, ethanol and silica [25] and their respective volume fractions through the expression: ne2 f f = (nacetone × Vacetone + 2 silica ×V −1 . The parameters of the samples are given nethanol ×V + n ) × (total volume) ethanol silica 2 2 in Table 1. Table 1. Characteristics of the samples.

Parameters f (×10−4 ) Vacetone ne2 f f (×10−15cm2 /W)

Sample A 0.045 99% 2.38

Sample B 2.25 50% 1.58

Sample C 2.7 40% 1.42

Sample D 4.05 10% 0.93

For the experiments it was used the second harmonic beam obtained from a linearly polarized Q-switched and mode-locked Nd:YAG laser (10 Hz, 80 ps, 532 nm). For the NL measurements the beam intensity on the samples was adjusted from 7 to 16 GW/cm2 by using a λ /2 plate followed by a Glan-Laser prism, as indicated in Fig. 1(a); the beam was focused with a 50 mm focal length lens to the center of the cell. Figure 1(b) shows the imaging optical system that was positioned in a direction perpendicular to the beam direction. It consisted of two identical cylindrical lenses with 80 mm focal length, aligned orthogonally to each other. The first lens focusses the light in the y direction (vertical plane) and second lens focusses in the z direction (horizontal plane) of the object. The overall distance (from the object to the image) was the same for both lenses. The object distance was chosen such that the magnifications on the vertical and horizontal directions were 3 and 1/3, respectively. In order to obtain an optical resolution approximately equal to the pixel size of the CCD camera (6.45 µ m×6.45µ m) it was used a 6

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mm width rectangular slit in front of each lens leading to a f -number=13. More details on the SLIM setup are given in [20]. Figure 1(c) shows the scattered light image for a laser intensity of 5 GW/cm2 propagating in a liquid scattering medium (soluble oil), corresponding to the linear regime of light propagation. NL behavior of soluble oil was no observed even for I = 16 GW/cm2 , which corresponds to the maximum laser intensity, and the evolution of the beam radius along propagation can be adequately described by wlin (z). Notice that the beam can be visualized in the entire cell. The image is processed as a matrix where each element is an image pixel. Each column represents a specific z position and the elements of the row are the measured intensity along the y direction. To determine the beam radius as a function of the z position, the laser beam profile was numerically adjusted by a Gaussian function along the columns [22, 23]. The divergence angle, θ , was determined by the slope of a linear fit adjusted in the last positions along the z axis of the beam radius curve. The intensity value is determined simultaneously with the image capture using an external beam sampler. Since the laser beam intensity presented large fluctuations, we performed a post-filtering selection and recorded only images corresponding to intensities varying at most by ±5%. For each sample four values of intensity were taken. For each of these values we recorded 50 images (corresponding to 50 pulses). The results, shown in Fig. 1(d), lead to θ0 = (10.7 ± 0.6) mrad, determined from the slope of a linear fit measured for z > 7 mm. The beam waist measured was w0 = (37 ± 7) µ m at the center of the 10 mm quartz cell that contains the colloid. For these measurements we obtained M 2 = 2.34.

1

300

(c)

2.200

250 Intensity level

1.925

y(

m)

200

w

150

2

0

100

1.650

1.375

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50 0

0

2

Beam radius ( m)

300

z

4

6

8

10

(mm)

(d)

250 200 150 7

8

z (mm)

9

10

Fig. 1. (a) Laser pulse energy control and focusing system. (b) Experimental setup of the SLIM and ray diagram for scattered light (d1 = 10.7 cm and d2 = 21.3 cm). (c) A scattered light image obtained by SLIM and the definition of the beam waist 2 w0 (vertical bar) and the divergence angle θ , between the arrow and the horizontal dashed line. (d) The beam radii (black open circles) measured for z >7 mm (it corresponds to 3 mm of the end of the cell) and the slope (red solid line) was equal to 0.0107. The linear fit determines the angle θ0 of the laser beam propagation in the linear scattering medium with I = 5 GW/cm2 .

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Z-scan measurements were also performed in order to compare the SLIM results with a wellestablished technique. The Z-scan setup used is similar to the one described in [26]. It was used a 1 mm thick sample cell mounted on a translation stage to be moved in the focus region along the z axis. The transmitted beam spatial profile was monitored using detectors placed in the farfield region. A reference channel was used to achieve a better signal-to-noise (S/N) ratio in the Z-scan measurements as in [3, 26]. The closed- and open-aperture Z-scan schemes were used. The NL absorption coefficient of the samples was smaller than the minimum value that our apparatus allows to detect (0.25 cm/GW for 10 GW/cm2 ). Hence, only closed-aperture Z-scan profiles could be obtained. 4.

Results

(a)

1.000

500

500

1

1

Figure 2 shows images obtained by SLIM of the laser beam propagation in the samples A, B, C and D with I = (9.7± 0.5) GW/cm2 . The laser beam waist was positioned in the entrance face of the cell and it is clear from Figs. 2(a)–2(d) that the scattered light increases with the concentration of scatterers. Contrarily to the images shown in Figs. 2(a)–2(c), in the Fig. 2(d) the laser beam propagation cannot be visualized with good S/N ratio along the whole sample owing to the strong light scattering. However, the θ value may be determined in a z region where the beam intensity spatial profiles were visualized with better S/N ratio, for example, in the middle of the cell. A good S/N ratio was obtained when the peak intensity is at least twice the baseline of the background (noise signal). It is important to remark that even analyzing the beam propagation along a region smaller than the entire cell, it was possible to determine ne2 f f with accuracy.

(b)

1.000

0.8750

0.6250

0.5000

0.3750

Intensity level

200

m)

m)

y(

300

400

0.7500

y(

Intensity level

0.8750

400

300

200

0.2500

0

0

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2

(c)

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8

1

6

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0

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500 0.8750

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m) 300

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0.6250

Intensity level

y(

m)

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Intensity level

0.8750

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100

0

0

0

0

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z (mm)

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4

6

z (mm)

8

10

Fig. 2. Images obtained by SLIM for I = (9.7 ± 0.5) GW/cm2 : (a) sample A; (b) sample B; (c) sample C and (d) sample D.

Figure 3 shows the divergence angle, θ , for the samples A, B, C and D with I varying from 7 #243062 © 2015 OSA


to 16 GW/cm2 . The θ value was determined as described in the section 3. Notice that θ varies linearly with the laser intensity and from the results in Fig. 3 the ne2 f f values were determined using the Eq. (3), being presented in Fig. 4 for samples A, B, C and D. It is important to observe 11.0

11.0

(a)

(b)

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(mrad)

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I (GW/cm²) 11.0

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(mrad)

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I (GW/cm²)

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8.0 6

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I (GW/cm²)

Fig. 3. Divergence angle determined from an average of 50 images (or pulses) for I varying from 7 to 16 GW/cm2 . Black squares represent the experimental data and the red solid line corresponds to the line fit for (a) sample A: θ = 10.80 − 0.15I; (b) sample B: θ = 10.91 − 0.11I; (c) sample C: θ = 10.65 − 0.08I and (d) sample D: θ = 10.71 − 0.06I. ef f

that the measured n2 values do not change as a function of laser intensity. This is an expected result since the nonlinearity of the colloid is mainly due to the third-order susceptibility. Highorder nonlinearities of the liquid and the silica NPs are negligible. The results of Fig. 3 and Fig. 4 were obtained performing an average for 50 acquired images by overlapping the data images (we refer to this procedure as Pav ). However the experiments were also analyzed for single-shot pulses (procedure referred as Pss ). Figure 5 shows the singleshot NL refractive index behavior versus I, for the sample B. The ne2 f f average values obtained by Pav (Fig. 4(b)) or by Pss are similar. However, in the case Pss , the larger standard deviation (about 20%) shows discrepancies in relation to Pav results, that are attributed to the laser fluctuations, mechanical vibrations and thermal instability of the laser cavity. These effects induce a variation of the laser beam pointing-stability and therefore it is observed when the Pss is performed. These systematic errors make evident the importance of single-shot measurements even when no degradation of the sample is observed. As the SLIM is intrinsically a single-shot method of laser beam characterization [20], whereas the Z-scan technique requires averaging of each sample position (i.e., the Z-scan is not a single-shot method), therefore, the average of the results obtained by Pav are presented here to establish a basis for comparison between the SLIM and Z-scan. In order to validate the SLIM results, we performed Z-scan measurements for all samples. The Z-scan measurements were performed averaging 10 pulses at 60 locations of the cell along the z axis, i.e.: processing 600 laser pulses; and the result for I = (9.4 ± 1.9) GW/cm2 is shown in Fig. 6. Notice that while the Z-scan profile of samples A and B, shown in Figs. 6(a) and #243062 © 2015 OSA


3.5

3.5

(a)

(b)

cm²/W)

3.0

2.5

-15

2.0

neff (10 2

neff (10 2

-15

cm²/W)

3.0

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(c)

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cm²/W)

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cm²/W)

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1.0

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8

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10

12

I (GW/cm²)

ef f

Fig. 4. Values of n2 from the θ values determined for I varying from 7 to 16 GW/cm2 . Black squares represent the experimental data and the red dotted line corresponds to the average value for (a) sample A: 2.35×10−15 cm2 /W ; (b) sample B: 1.53×10−15 cm2 /W; (c) sample C: 1.46×10−15 cm2 /W and (d) sample D: 0.94×10−15 cm2 /W.

neff (10 2

-15

cm²/W)

3.0 2.5 2.0 1.5 1.0 0.5

6

8

10

12

14

16

I (GW/cm²)

ef f

Fig. 5. Single-shot NL refractive index, n2 , obtained by SLIM for sample B. Black circles: single-shot pulses; red dotted line: average value.

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6(b), present good S/N ratio, the signal for sample C is degraded owing to the increase of the beam wavefront distortion due to the large linear light scattering. Indeed the S/N ratio becomes very poor and the Z-scan technique cannot be applied for samples with f > 3 × 10−4, as for the sample D plotted in Fig. 6(d). The solid curves in Figs. 6(a)–6(c) represent the best fit to the data. The value ne2 f f = (2.40 ± 0.36) × 10−15 cm2 /W was obtained, in agreement with the ne2 f f = 2.38 × 10−15 cm2 /W calculated for sample A. The measurements for the samples B and C also present similar agreement; for instance we obtained ne2 f f (sample B)= (2.40 ± 1.44) × ef f 10−15 cm2 /W and n2 (sample C)= (2.50 ± 1.89) × 10−15 cm2 /W . The Z-scan technique cannot be applied for the sample D because of the large light scattering. The ne2 f f values were determined from the Z-scan data following the usual procedure introduced in [1, 2] by measuring the transmittance difference peak-to-valley and determining the NL phase-shift on the beam axis. Since the NL refractive index of ethanol and acetone are positive at 532 nm, the Z-scan profiles of Fig. 6 display a positive NL refractive index for the colloids. The NL contribution of the NPs is negligible. 1.10

1.10

(a)

1.05

T (z)

T (z)

1.05

1.00

0.95

-10

-5

0

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15

z (mm)

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1.10

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z (mm)

Fig. 6. Z-scan data for I = (9.4 ± 1.9) GW/cm2 : (a) sample A; (b) sample B; (c) sample C and (d) sample D. The open circles are experimental data and the solid lines are Z-scan fits.

Figure 7 summarizes the results obtained for ne2 f f using the SLIM and the Z-scan technique as a function of f and Vacetone . It can be seen that with the Z-scan technique we could not ef f detect the changes of n2 due to the decrease of Vacetone while with the SLIM the changes become clear. The solid line was drawn considering the NL refractive indices of acetone and ethanol, and their respective volume fractions. Notice that with the Z-scan technique, it was ef f only possible to measure n2 for samples with f < 3 × 10−4 while using the SLIM we were ef f able to measure n2 for f up to 4.5×10−4, which was limited by the maximum concentration of the samples available. 5.

Summary

In summary the present experiments demonstrate the application of the Scattered Light Imaging Method (SLIM) for NL spectroscopy of scattering media. The effective NL refractive indices #243062 © 2015 OSA


neff (10 2

-15

cm²/W)

4

3

f

-4

x 10

2

1

0

4 3 2 1 0

20

40

60

Vacetone (%)

80

100

Fig. 7. Comparison of Z-scan results (filled blue circles) measured with I = (9.4 ± 1.9) ef f GW/cm2 and SLIM (filled red squares) for I = (9.7 ± 0.5) GW/cm2 with the n2 versus volume fraction of acetone and filling fraction of silica NPs. The black solid line represents the theoretical predictions of our model.

of colloids with large density of scatterers could be measured even when the Z-scan technique could not be applied. The experimental setup used has no movable parts, and the measurement ef f of n2 requires, in principle, only one laser-shot. It is also important to notice that the singleshot results are not affected by laser beam pointing-stability. In conclusion, we evaluate SLIM as a powerful tool for NL studies of heterogeneous media which may present large elastic light scattering cross-sections. Acknowledgments We acknowledge the support from the Coordenaça˜ o de Aperfeiçoamento de Pessoal de N´ıvel Superior (CAPES), the Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnológico (CNPq) through the National Institute of Photonics Project (INCT de Fotônica - INFo), and the Fundaça˜ o de Amparo a` Ciência e Tecnologia do Estado de Pernambuco (FACEPE).

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