Spatial Coherency of Light and Nonlinear Optical Properties of Colloidal Gold Studied by CW Z-Scan Technique

Roman V. Gamernyk1*, Mykola V. Periv1,2, Serhiy Z. Malynych3,4 and Oleksandr S. Zaichenko5

1Ivan Franko National university of Lviv, Kyryla and Methodiya St., 8, 79005 Lviv, Ukraine
2Ukrainian Printing Academy, Pidholosko St., 19, 79020 Lviv, Ukraine
3Hetman Petro Sahaidachny National Army Academy, Heroes of Maidan St., 32, 79012 Lviv, Ukraine
4V.E. Lashkaryov Institute of Semiconductors Physics NAS Ukraine, Nauky Ave., 41, 03028 Kyiv, Ukraine
5Lviv Polytechnic National University, 12, S. Bandery Str., Lviv 79013, Ukraine


Nonlinear refraction and absorption of a suspension of Au nanoparticles was studied by CW Z-scan at near-resonant excitation. Spatial coherency and selfinterference of the laser beam results in the emerging of ring-like interference pattern observed at the plane of the detector. The number of the interference fringes and their diameter depends on volume fraction of the nanoparticles and laser fluence at focal point. Periodical light intensity distribution across the laser beam causes modulation in the output signal that should be considered for the correct interpretation of Z-scan data.


Nanoparticles (NPs), Localized surface plasmon resonances, Z-scan technique, Photodetector


Nanophotonics based on metal nanoparticles (NPs) and their systems is a rapidly growing field of a modern technology. The main attention to metal NPs is driven by specific electronic excitations within the nanoparticles induced by impinging electromagnetic waves. Those oscillations of free electrons are known as localized surface plasmon resonances or LSPR. Especially perspective are noble metal (Au, Ag, Cu) NPs since the resonant frequency of the localized surface plasmons is observed in the visible spectral range. Any practical application of the NPs implies they are always embedded in a host medium that mainly serves as a supporting structure firmly preserving the particles’ arrangement. Optical usage of the NPs requires transparency of the host matrix in corresponding spectral range. In other words, the entire system is considered as a nanocomposite that combines properties of the host and metal NPs inclusions. Specific interactions of LSPR in metal NPs with surrounding medium give rise to the nonlinear-optical phenomena that appear at high intensities of the electromagnetic field. Therefore, studies of nanocomposite materials comprising noble metal NPs embedded in solids or suspended in liquids, are of great importance [1].

Nonlinear-optical response of a nanocomposite exhibit dual origin. First, it is associated with the nanoparticles themselves, their large surface-to-volume ratio that contributes to the second harmonic generation [2]. Photoinduced changes of the absorption coefficient also affect scattering pattern by the NPs and thus, the nonlinear refraction of the nanoparticles assembly (via Kramers-Kronig relations) [3]. Second, nonlinear optical (NLO) properties of a nanocomposite are due to modifications in the host matrix properties, namely thermal density fluctuations known as thermal lensing effect [4], and Stark effect [5]. Obviously, NLO response of a nanocomposite depends on the volume fraction of NPs, their surface properties and dielectric environment as well.

It is well established that NLO effects in noble metal NPs are greatly increased due to the enhancement of the local electric field around each nanoparticle when the frequency of incident light is close to that of LSPR [6, 7]. Since the spectral band associated with LSPR in gold NPs 20/50 nm in diameter is located at the wavelength of 520/540 nm, the resonant interaction of light with Au nanoparticles can be easily realized using second harmonic radiation of Nd:YAG laser at λ = 532 nm. Applying resonant irradiation one can achieve nonlinear-optical response of Au NPs suspension at relatively low light intensities.

In present paper we report on studies of the thirdorder refraction of Au NP aqueous suspension employing Z-scan technique. Some effects of the spatial coherency of the laser beam which occur after passing the sample are also discussed. Those effects should be taken into account for proper interpretation of experimental Z-scan data. Despite its experimental simplicity the method allows precise determining of the value of both real and imaginary parts of third-order susceptibility and their sign.


Synthesis and characterization of Au nanoparticles

Gold nanoparticles were synthesized by homogeneous nucleation technique via reduction of HAuCl4 solution in water with Аu3+ concentration of 1.3 g/l by hydrazine hydrate N2H4·0.5H2O at the presence of oligoperoxide as surfactant. The latter was prepared by radical copolymerization of N-vinyl pyrrolidone, peroxide monomer 5-(tert-Butylperoxy)-5- methylhex-1-en-3-yne, and glycidyl methacrylate as described in Inoye et al. [8]. To provide strong adhesion of oligoperoxide molecules on the nanoparticles surface the molecules were modified with thiol groups ([S] = 9.6%). Synthesis was performed at the temperature of T = 300 K in alkali environment with pH=10.6 for the molar ratio of [HAuCl4]:[N2H4] = 1:20. The reaction produces Au nanoparticles coated with thin (~1- 2 nm) polymer layer that prevents particles from aggregation.

The size of the nanoparticles was determined by transmission electron microscope (TEM) operated at acceleration voltage of 100 kV. The TEM image of Au NPs is demonstrated in Figure 1 along with the histogram nanoparticles size distribution. The TEM image was processed by freely available program ImageJ. Image analysis yields mean diameter of the nanoparticles <d> = 19.3 nm with a standard deviation σd = 8.03 nm. X-ray studies of Au NPs confirm crystal stability of nanoparticles that contain no dopants (Figure 2). The size of the NPs was also determined from FWHM of the diffraction peaks using well known Scherrer expression. The range of coherent scattering correlates with the size of NPs determined from TEM image.

Optical spectra of Au nanoparticles

The absorption spectra of Au NPs suspension was measured with diffraction monochromator with the focal length of 600 mm equipped with a stabilized halogen lamp as a light source. Quartz cell poured with the suspension was placed into the photometric sphere. The thickness of the cell is 1 mm. The signal was registered by a photomultiplier tube exploiting in the photon counting mode.

Experimentally measured absorption spectrum exhibits good agreement with one calculated by Mie theory. The calculations were performed for each fraction that represents specific size of the NPs according to the histogram in Figure 1. Total absorption spectrum of Au NPs suspension under investigation was found as a sum of partial spectra. As can be seen in Figure 3 the LSPR bandwidth for experimental spectrum exceeds that for calculated one. The discrepancy is due to inhomogeneous broadening of spectral band caused by the dispersion of the nanoparticles size and deviation of the shape of NPs from ideal sphere as well.

Absorption spectrum was used to determine the concentration of nanoparticles in the suspension. To obtain samples with lower nanoparticles concentration the initial suspension was diluted with distilled water.

Nonlinear-optical measurements

Nonlinear refraction in Au NPs suspension was determined employing standard Z-scan technique with closed aperture [9]. The experimental arrangement is shown in Figure 4. All measurements were performed at ambient temperature using second harmonic radiation from CW Nd:YAG laser at λ = 532 nm. The output power of laser beam was 45 mW. The parameters of the focused laser beam satisfied the main requirements of Z-scan method. The Rayleigh length was 1.197 mm with laser power density at focal point I0 = 1.15 × 104 W/cm2. The third order refractive index and nonlinear absorption were determined from normalized Z-scan transmission curves according to the procedure given by Sheik-Bahae et al. [9]. Corresponding values for the Au NP suspension being studied are n2 = –2.18 × 10−7 cm2/W and β = 10.75 × 10−3 cm/W.

To determine nonlinear absorption all the light passed through the sample should be registered by photodetector. So, open aperture configuration with a collecting lens was employed. Si photodetector was used for recording of the optical transmission.

Results and Discussion

An interference pattern is observed in the far field after an intense light beam travels through a medium possessing optical nonlinearities [10]. The pattern appears as a number of concentric rings that can be visualized by an opaque screen placed instead of the aperture. The ring pattern is a result of spatial phase-modulation across the Gaussian laser beam that is due to intensity dependent refractive index of the nonlinear medium. We observe the interference pattern for Au NPs suspension with a volume fraction f = 1.3 × 10–5 at laser power density I0 = 1.15 × 104 W/cm2 (Figure 5).

The number of the rings observed depends on the magnitude of nonlinear refractive index n2, i.e. it is determined by the intensity of laser beam at focal point and concentration of NPs. Decreasing of the beam intensity results in disappearing of the rings. The same effect is observed when the concentration of the nanoparticles in the suspension decreases. It should be noted here that emerging of the pattern is accompanied by changes in the shape of a typical Z-scan curve. This situation is illustrated in Figure 6 and 7. The normalized Z-scan transmission curves at a constant beam intensity of 1.15 × 104 W/cm2 for Au NP suspension with different particles concentration is presented in Figure 6, while Figure 7 depicts the curves recorded at different intensities of laser beam for the same concentration of the nanoparticles (f = 1.3 × 10–5).

Let us discuss those effects in details. Typical shape of normalized Z-scan absorption curve measured in open aperture configuration is observed for the suspensions with low NPs concentration, e.g. f = 8.03 × 10–7 (Figure 6A). The ring pattern does not appear on the screen in that case. After the concentration reaches certain value of f = 1.6 × 10–6 the additional maximum emerges on Z-scan curve (Figure 6B). We assign this maximum to the changes in spatial distribution of the laser beam intensity due to self-interference of the Gaussian beam. In other words, the intensity of the output electric signal produced by a photodetector is a function of a number of interference fringes and their distribution across the sensor.

Figure 7 depicts normalized Z-scan curves corresponding to nonlinear refraction. Unlike the previous case the measurements were performed for concentrated suspension with f = 1.3 × 10–5 at different levels of irradiation. Increasing of the laser beam power density results in the increase of peak-to-valley ratio in the curve and to the emerging of an additional weak maximum (Figure 7B). These effects make the correct determination of nonlinear refraction difficult.

The emerging of interference fringes is due to significant distortion of the wavefront that occur when light beam travels through the medium with optical nonlinearities. Single beam Z-scan technique is known to be a highly sensitive technique that allows one to register phase difference on the order of λ/300 [11]. The nonlinear optical effects in a nanocomposite containing metal NPs are enhanced in the LSPR region, so the phase difference reaches high magnitudes. We easily register phase difference up to 6π while studying Au NPs suspension within the concentration range and excitation intensities noted above. Phase difference were determined by counting the number of interference fringes projected on the opaque screen. This number increases with the increase of laser fluence. It was found experimentally that phase difference linearly depends on the laser power density at focal point. In order to measure mentioned dependence we performed Z-scan measurements simply using attenuation of the laser beam by neutral filters. The corresponding plot is shown in Figure 8. One can see that notable phase difference is observed even at low nanoparticles concentration and/or laser fluence at resonant excitation.

Obviously, the size of the interference pattern and the number of the fringes depend on laser fluence (see also Figure 5). At some point, for large laser power density, the size of the pattern exceeds that of the aperture placed in a front of a photodetector, i.e. the outer fringes do not impinge the surface of the latter. Even though the nonlinear optical effects are strong in this case, the photodetector produces weaker output signal. This weakening manifests itself as an additional maximum in Z-scan absorption curve as discussed above. Such a dependence resembles that for saturable absorption observed at high intensities of the laser beam [12] and might be wrongly attributed to the latter. Therefore, in order to determine the nonlinear-optical parameters of Au NPs suspensions correctly low particle concentration is needed.


We studied both nonlinear refraction and absorption in the aqueous suspension of gold nanoparticles at near-resonant excitation. The magnitude of nonlinear refraction confirms high optical nonlinearity of the suspension. Self-interference of the spatially coherent Gaussian beam as it travels through the medium with optical nonlinearities results in appearing of interference pattern that can be observed at the plane of the detector. The number of interference fringes and their size depends on volume fraction of the nanoparticles and laser fluence at focal point. Expanding of the interference pattern caused by the increase of the laser power density leads to the decrease in the amount of light that reaches photodetector, i.e. part of the beam goes out of the sensing area. Thus, the output signal produced by the detector become weaker for higher levels of laser fluence and the additional maximum emerges in Z-scan absorption curve. Such dependence is similar to the absorption saturation observed at high intensities of the laser excitation. The described phenomenon should be taken into account when considering nonlinear-optical properties of metal nanoparticle composite in order to interpret experimental Z-scan data correctly.


1. Pérez JLJ, Gutiérrez-Fuentes R, Ramírez JFS, Vidal OUG, Téllez-Sánchez DE, et al. 2013. Nonlinear coefficient determination of Au/Pd bimetallic nanoparticles using Z-scan. Advances in Nanoparticles 2(3): 223-228. doi: 10.4236/anp.2013.23031

2. Kauranen M, Zayats AV. 2012. Nonlinear plasmonics. Nature Photon 6: 737-748. doi: 10.1038/nphoton.2012.244

3. Lucarini V, Peiponen K-E, Saarinen JJ, Vartiainen EM. 2005. Kramers-Kronig relations in optical materials research. Springer, Heidelberg, Germany. doi: 10.1007/b138913

4. Mehendale SC, Mishra SR, Bindra KS, Laghate M, Dhami TS, et al. 1997. Nonlinear refraction in aqueous colloidal gold. Opt Commun 133(1-6): 273-276. doi: 10.1016/S0030-4018(96)00431-2

5. Christodoulides DN, Khoo IC, Salamo GJ, Stegeman GI, Van Stryland EW. 2010. Nonlinear refraction and absorption: mechanisms and magnitudes. Adv Opt Photon 2(1): 60-200. doi: 10.1364/AOP.2.000060

6. Antoine R, Brevet PF, Girault HH, Bethell D, Schiffrin DJ. 1997. Surface plasmon enhanced non-linear optical response of gold nanoparticles at the air/toluene interface. Chem Commun 1997(19): 1901-1902. doi: 10.1039/A704846G

7. Antoine R, Pellarin M, Palpant B, Broyer M, Prevel B, et al. 1998. Surface plasmon enhanced second harmonic response from gold clusters embedded in an alumina matrix. J Appl Phys 84(8): 4532-4536. doi: 10.1063/1.368679

8. Inoye H, Tanaka K, Tanahashi I, Hattori T, Nakatsuka H. 2000. Ultrafast optical switching in a silver nanoparticle system. Jpn J Appl Phys 39(9R): 5132-5133.

9. Sheik-Bahae M, Said AA, Van Stryland EW. 1989. High sensitivity, single beam n2 measurements. Opt Lett 14(17): 955-957. doi: 10.1364/OL.14.000955

10. Nadjari H, Abasi Azad Z. 2012. Determining the nonlinear coefficient of gold and silver nanocolloids using SPM and CWZ-scan. Opt Laser Technol 44(5): 1629-1632. doi: 10.1016/j.optlastec.2011.11.013

11. Sheik-Bahae M, Said AA, Wei TH, Hagan DJ, Van Stryland EW. 1990. Sensitive measurement of optical nonlinearities using a single beam. IEEE Journal of Quantum Electronics 26(4): 760-769. doi: 10.1109/3.53394

12. Kim KH, Husakou A, Herrmann J. 2010. Saturable absorption in composites doped with metal nanoparticles. Opt Express 18(21): 21918-21925. doi: 10.1364/OE.18.021918

*Correspondence to:

Roman V. Gamernyk, PhD
Department of Experimental Physics
Ivan Franko National University of Lviv, Kyryla
and Methodiya St., 8, 79005 Lviv, Ukraine

Received: January 14, 2016
Accepted: March 18, 2016
Published: March 21, 2016

Citation: Gamernyk RV, Periv MV, Malynych SZ, Zaichenko OS. 2016. Spatial Coherency of Light and Nonlinear Optical Properties of Colloidal Gold Studied by CW Z-Scan Technique. NanoWorld J 2(1): 5-9.

Copyright: © 2016 Gamernyk et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC-BY) ( which permits commercial use, including reproduction, adaptation, and distribution of the article provided the original author and source are credited.

Published by United Scientific Group
© NanoWorld Journal 2016 | United Scientific Group, #8105, Suite 112, Rasor Blvd, PLANO, TX 75024, USA | Terms and Conditions | Privacy Policy