## Abstract

We report a systematic investigation on nonlinear optical properties of CdSe nanoparticles that are smaller as well as larger than the Bohr radius. Multiphoton absorption and nonlinear refraction properties of CdSe nanoparticles observed with 800nm wavelength and 110femtosecond Ti:Sapphire laser are presented. These nonlinear optical studies were undertaken by performing open and closed aperture Z-scan measurements. The four different sizes of CdSe nanoparticles investigated are 5nm, 10nm, 25nm and 400nm. Both the quantum dots 5nm, 10nm sizes (taking the literature value of 10.6nm as the Bohr exciton diameter) show four photon absorption (4PA), while the 25nm and 400nm show the three photon absorption (3PA) properties. All four sizes of CdSe nanoparticles show the positive nonlinear refraction (n2).

©2007 Optical Society of America

## 1. Introduction

In recent years, interest in the synthesis, characterization and application of colloidal ‘quantum dot’ semiconductor materials has grown markedly [1, 2]. Due to their direct band gap and control on the band gap over wide spectral range, semiconductor nanoparticles have many potential applications in the fields of nanophotonics and optoelectronics. Nanoparticles of CdSe are by far the most studied system among all the semiconducting nanoparticles. These colloidal quantum dots (QDs), also known as semiconductor nanoparticles, are synthesized by chemical routes and dispersed in suitable matrices to study the properties. Nanoparticles smaller than the Bohr radius of the particular semiconductor demonstrate unique optical properties due to the effects of three dimensional quantum confinement. Larger confinement potential for the smaller crystal sizes (particle in a three dimensional spherical box model) leads to broadening in the band gap, which is inversely proportional to the particle size. The bulk CdSe has a direct band gap of 1.74eV at 300K, and the typical Bohr exciton diameter of CdSe is around 10.6nm; consequently, CdSe nanoparticles of the size of <11nm show sizable quantum confinement effects with remarkably different optical properties. The changes in the properties of nanoparticles are driven mainly by two factors, namely the increase in the surface to volume ratio, and drastic changes in the electronic structure of the material due to quantum mechanical effects with decreasing crystal size.

The manifestation of quantum size effects in nonlinear optical processes depends on the electronic properties of the semiconductor, in particular, its band gap. A semiconductor nanoparticle is an example of a low-dimensional structure. The nanoparticle has a rather large number of atoms, but its size is comparable with characteristic dimensions describing the behavior of electrons and holes, thus creating an intermediate regime between molecules and bulk crystals [1]. Semiconducting materials have shown many interesting properties [3–7] because of the strong multi photon absorption observed when their band gap is more than twice the photon energy (E* _{g}*>2E

_{photon}), avoiding direct one-photon optical absorption. Three-photon absorption (3PA) and four-photon absorption (4PA) are particularly interesting as IR photons get converted to a blue or UV region. These multiphoton absorption processes play a major role in biological imaging, thereby increasing the resolution beyond the diffraction limit [8]. Multiphoton absorption in materials has also generated interest in laser direct writing [9]. Therefore there is a need for materials that show high multiphoton absorption cross-sections. There is a lack of direct measurements on the 3PA and 4PA spectra of wide-gap semiconductors, except for few reports that are available with Z-scan measurements [10–14]. In this respect femtosecond laser studies become important as the multiphoton absorption plays an important role at these time scales. Excitations at femtosecond timescales are important to overcome the contributions from free charge carrier absorption and thermal effects that accompany the nanosecond laser excitation. In this paper we report a systematic investigation into both 3PA and 4PA in CdSe nanoparticles with change in size of the particles. The 5nm and 10nm quantum sized particles show 4PA and the larger sized particles 25nm and 400nm show 3PA. We have found that the 3PA and 4PA curves fit well to a model derived by Sutherland et al. [11].

## 2. Synthesis and characterization

CdSe nanoparticles are prepared through the chemical route. The precursors, 2.35g of cadmium acetate dihydrate, 0.5g of selenium, and 1ml of Tri-n-Octylphosphine (TOP) added to 5ml of dimethylformamide (DMF), are heated at 110°C for 60 minutes under nitrogen atmosphere. This leads to formation of 5nm sized CdSe particles (zero reflux time). When it is taken over different reflux times of 30, 60 and 120 minutes, we obtained particle sizes of 10, 25 and 400nm respectively. Following this, the yellowish/red, TOP capped CdSe nanoparticles obtained are washed with acetone and ether. The size measurements and surface morphology of the CdSe nanoparticles are carried out by transmission electron microscope (TEM) studies. The TEM pictures are taken on carbon coated copper grids with JEOL (JEM 2100) system at 100KV and 58µA. The UV/VIS absorption spectrum of the nanoparticles is recorded at room temperature with spectrophotometer (Shimatzu 3101PC).

The nonlinear absorption and nonlinear refraction properties of synthesized nanoparticles are studied with 800nm wavelength, 110fs pulse width, 1KHz repetition rate Ti:Sapphire (Spectra-Physics, Mai Tai and Spitfire amplifier) laser using the standard Z-scan technique [15]. For recording the open aperture Z-scan curve and thereby obtaining the nonlinear absorption properties of the material under investigation, the laser beam with a transverse Gaussian profile is focused by a lens. The sample is moved along the axial direction of the focused beam in such a way that it moves away from the lens passing through the focal point. At the focal point the sample experiences maximum pump intensity, which decreases gradually in either direction from the focus. An f/30 configuration is used in the present studies. The thickness of the sample is chosen in such a way that it is smaller than the Raleigh range of the focusing lens, which is nearly 3.5 mm. To vary the laser intensity, calibrated neutral density filters are used. The data are recorded by scanning the cell across the focus, and the transmitted beam is focused onto the photodiode (FND-100) with a lens. A lock-in amplifier is used for signal averaging, the output of which is given to a computer with an analog-to-digital converter (ADC) card. The cell is translated along the beam propagation direction using a computer controlled stepper motor and the data are collected at steps of 0.03 mm. An aperture is introduced in front of the detector to record closed aperture Z-scan curve and obtain the nonlinear refraction coefficients.

## 3. Results and discussion

Optical absorption spectra of TOP capped CdSe nanoparticles in DMF are shown in Fig. 1. With decreasing particle size, the absorption peak of the CdSe nanoparticles shifts to shorter wavelength side. The TEM images of these four sizes of the nanoparticles are shown in Fig. 2. These nanoparticles form a clear and transparent solution in DMF and no precipitation was observed even after several days. A concentration of ~8.1×10-4 mol L^{-1} was used for nonlinear optical studies of all the sizes of the nanoparticles.

Observed data of all open aperture Z-scan experiments are theoretically fitted as shown in Fig. 3, with equations 1, 2 and 3 obtained from the derivations for multiphoton absorption coefficients by Sutherland et al. [11].

$${T}_{OA\left(nPA\right)}=\frac{1}{{\left[1+(n-1){\alpha}_{n}L{({I}_{00}\u2044\left(1+{(z\u2044{z}_{0})}^{2}\right))}^{n-1}\right]}^{\frac{1}{n-1}}}$$

$${T}_{OA\left(2PA\right)}=\frac{1}{1+{\alpha}_{2}{L}_{\mathrm{eff}}({I}_{00}\u2044\left(1+{(z\u2044{z}_{0})}^{2}\right))}$$

where I_{00} is the peak intensity, z- is the sample position, z_{0}=*πω ^{2}_{0}/λ* is Rayleigh range;

*ω*is the beam waist at the focal point (z=0), λ is the laser wavelength; effective path lengths in the sample of length L for 2PA, 3PA and 4PA is given as L

_{0}_{eff}=[1-exp (-α

_{0}L)]/α

_{0}, L′eff=[1-exp (-2α

_{0}L)]/2α0 and L″eff=[1-exp (-3α0L)]/3α

_{0}respectively.

By fitting these curves, 2PA, 3PA and 4PA coefficients were estimated. One can observe that curves of the fitted data with 2PA and 3PA deviate from the experimental data, where as 4PA fits well with a chi2 value of 0.001 for particle size of 5nm. Similar results were observed with 10nm sized particles. For the 25nm and 400nm sized particles, we observed that the 3PA (equation 2) fits better as compared to 2PA and 4PA (Fig. 3(b)). Jun He et al. [10] measured 2PA and 3PA coefficients in ZnO and ZnS bulk crystals with similar results. In order to confirm the 4PA/3PA, we have carried out the Z-scan measurements at different input intensities, and plotted intensities Vs the nonlinear absorption coefficients α as shown in Fig. 4. α_{2}, α_{3} and α_{4} represent nonlinear absorption coefficients for 2PA, 3PA and 4PA respectively. The open circles assume 2PA, the open squares assume 3PA and the filled circles assume 4PA process. Under each assumption, the curves can be seen to go as square and linearly increasing functions respectively for 2PA and 3PA for the 5nm and 10nm particles. Where as for 4PA, the absorption coefficient is constant confirming that 4PA is dominant process in the absorption for 5nm particles. An interesting behavior is seen with 10nm sized particles, where α_{4} falls off with intensity (Fig. 4(b)). This could be due to saturation of absorption of the 4PA for these sized particles. A similar behavior was observed by Henari et al. [16] with saturation in 2PA. For the other two sizes, 25nm and 400nm particles, input intensities Vs the nonlinear absorption coefficient, the 3PA coefficient is constant. This behavior for 400nm particles is shown in Fig. 4(c). All the calculated values of these nanoparticles are listed in Table. I.

Closed aperture Z-scan experiments on the CdSe nanoparticles confirm that they exhibit positive nonlinearity (Fig. 5). It may be noted that the experiments were carried out with 1KHz rep rate and if thermal nonlinearity was to play a role, then we would have observed negative nonlinearity. The results are therefore indicating the lower limit for the nonlinearity, assuming a small contribution from any thermal nonlinearity. The closed aperture data, T_{CA}, are fitted to the equation 4 [15].

where Δφ_{0} is the phase change of the laser beam due to nonlinear refraction. Δφ_{0} value is estimated for all the four sizes of the CdSe nanoparticles by fitting the experimental data.

where the dielectric constant of bulk CdSe, ε, is taken as 6.2 [17], D is the diameter of the nanoparticles in units of nm, C is the velocity of light. The nonlinear refractive index (n_{2}) and the linear refractive index (n_{0}) are estimated from equations 5 and 7 respectively. The n_{2} values shown in Table I are found to be independent of the intensities [10], over the intensity ranges from 61GWcm^{-2} to 295GWcm^{-2}. The phase change of the laser beam due to nonlinear refraction (Δφ_{0}) is less than π for all the closed aperture Z-scan curves. However at higher intensities we expect contribution from 3PA and 4PA.

## 4. Conclusions

Four sizes of the mono dispersed CdSe nanoparticles are synthesized through chemical route. Observed results indicate 4PA for the 5 and 10nm particles (quantum dots) and 3PA for the 25 and 400nm particles. Nonlinear refraction (n2) coefficients are estimated for different sized particles. All the particles show positive nonlinearity indicating the origin of nonlinearity as electronic rather than thermal even at 1KHz repetition rate for the pump.

## Acknowledgements

Authors thank Dr. Shashi Singh, CCMB, Hyderabad for the help with the TEM recording. NV thanks UGC-DAE CSR-Kolkata Center, India for the fellowship through scheme no CRS/100/UH/P/DNR/8543. Part of this work was supported by DST, Govt. of India.

## References and links

**1. **A. P. Alivisatos, “Semiconductor Clusters, Nanocrystals, and Quantum Dots,” Science , **271**, 933–937 (1996). [CrossRef]

**2. **A. P. Alivisatos, “Perspectives on the physical chemistry of semiconductor nanocrystals,” J. Phys. Chem. **100**, 13226–13239 (1996). [CrossRef]

**3. **A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. **61**, 147–149 (1992). [CrossRef]

**4. **C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, “Effects of three-photon absorption on nonlinear directional coupling,” Opt. Lett. **17**, 710–712 (1992). [CrossRef] [PubMed]

**5. **N. Venkatram, R. Sai Santosh Kumar, and D. Narayana Rao “Nonlinear absorption and scattering properties of cadmium sulphide nanocrystals with its application as a potential optical limiter,” J. Appl. Phys. **100**, 074309, 1–8, (2006). [CrossRef]

**6. **N. Venkatram, M. A. Akundi, and D. Narayana Rao, “Nonlinear absorption, scattering and optical limiting studies of CdS nanoparticles,” Opt. Express **13**, 867–872 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-867 [CrossRef] [PubMed]

**7. **R. A. Morgan, S. H. Park, S. W. Koch, and N. Peyghambarian, ‘Experimental studies of the non-linear optical properties of cadmium selenide quantum-confined microcrystallites,” Semicond. Sci. Technol. **5**, 544–548 (1990) [CrossRef]

**8. **J. W. M. Chon, M. Gu, C. Bullen, and P. Mulvaney, “Three-photon excited band edge and trap emission of CdS semiconductor nanocrystals,” Appl. Phys. Lett. **84**, 4472–4474 (2004). [CrossRef]

**9. **M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Materials , **3**, 444–447 (2004). [CrossRef] [PubMed]

**10. **Jun He, Yingli Qu, Heping Li, Jun Mi, and Wei Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express , **13**, 9235–9247 (2005). http://www.opticsexpress.org/abstract.cfm?id=86208 [CrossRef] [PubMed]

**11. **R. L. Sutherland
with contributions by
D. G. McLean and S. Kirkpatrick, *Handbook of Nonlinear Optics*, Second Edition, Revised and Expanded (New York, NY: Marcel Dekker, 2003).

**12. **K. S. Bindra and A. K. Kar, “Role of femtosecond pulses in distinguishing third- and fifth-order nonlinearity for semiconductor-doped glasses,” Appl. Phys. Lett. **79**, 3761–3763 (2001). [CrossRef]

**13. **G. S. He, Q. Zheng, A. Baev, and Paras N. Prasad, “Saturation of multiphoton absorption upon strong and ultrafast infrared laser excitation,” J. Appl. Phys. **101**, 083108-1–083108-6 (2007). [CrossRef]

**14. **V. Pacebutas, A. Krotkus, T. Suski, P. Perlin, and M. Leszczynski, “Photoconductive Z-scan measurement of multiphoton absorption in GaN,” J. Appl. Phys. **92**, 6930–6932 (2002). [CrossRef]

**15. **M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. **26**, 760–769 (1990). [CrossRef]

**16. **F. Z. Henari, W. J. Blau, L. R. Milgrom, G. Yahioglu, D. Philips, and J. A. Lacey, “Third-order Optical Nonlinearity in Zn(II) Complexes of 5, 10, 15, 10-tetraarylethynyl-substituted Porphyrins,” Chem. Phys. Lett. **267**, 229–233 (1997). [CrossRef]

**17. **S. M. Ma, J. T. Seo, Q. Yang, R. Battle, H. Brown, K. Lee, L. Creekmore, A. Jackson, T. Skyles, B. Tabibi, S. S. Jung, W. Yu, and M. Namkung, “Third-Order Nonlinear Susceptibility and Hyperpolarizability of CdSe Nanocrystals with Femtosecond Excitation,” Journal of Korean Physical Society. **48**, 1379–1384 (2006).