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Investigations of the Optical Properties of Nanoscale Gold Films Y. Xiao1, H. Qian1, and Z. Liu1,2,3* 1
Department of Electrical Engineering, University of California, San Diego, 9500 Gilman Dr, La Jolla, CA, USA 92093 2 Material Science and Engineering, University of California, San Diego, 9500 Gilman Dr, La Jolla, CA, USA 92093 Center for Magnetic Recording Research, University of California, San Diego, 9500 Gilman Dr, La Jolla, CA, USA 92093 *Email address:
[email protected]
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The linear and nonlinear optical properties of thin gold films with thickness varying from 2.5 nm to 15 nm are experimentally investigated and impact of quantum confinement effect is studied. 2015 Optical Society of America
OCIS codes: 310.6860, 310.6628, 190.4400
Plasmonics that utilizes the interaction of light with charged particles, such as electrons in metals, has been an area of interest for decades [1]. Both the linear and nonlinear [2] aspects of plasmonics have been explored and have led to many amazing applications. As the dimensions of the plasmonic device have been shrunk into the nanoscale [3], the quantum confinement effects need to be considered [4] to fully understand the physics within such small devices. Here we choose the ultra-thin metal film to study the quantum confinement effect on the linear and nonlinear properties. More specifically, the linear optical properties is investigated by studying the reflection and transmission of gold thin films with thickness varying from 15 nm to 2.5 nm, and z-scan measurement is performed to obtain its third order Kerr nonlinear coefficient. The optical properties of thin gold film show significant different behavior as compared to their bulk values due to the quantum confinement effect. A theory based on the self-consistence solution of Schrodinger equation and Poisson equation is proposed, and its predictions agree quite well with experimental results. Our thin gold film is grown using a sputtering technique with extreme low pressure such that it is sandwiched between the quartz substrate and air on top. Quality of the thin gold film samples is calibrated by atomic force microscopy (AFM). Figure 1(a) shows the AFM picture of our 2.5 nm sample. As can be seen here, although the film is not perfect flat, it is not broken even at 2.5 nm.
FIG. 1. (Color online) AFM picture of the 2.5 nm gold thin film edge on the substrate. The upper inset indicates that the average thickness of the film is 2.5 nm. The lower inset shows the statistics of the thickness variations
To characterize the linear optical properties of our thin films, reflection and transmission (RT) for 2.5, 7, and 15 nm films are measured using the commercial Lambda 1050 system, and RT curves are extracted to obtain the refractive index (n) and extinction coefficient (k), as shown in Fig. 2 (a) and (b) respectively. As can be seen here, the n and k for 15 nm is almost identical to the bulk values. As thickness decreases down to 7 nm, n increases slightly while k decreases slightly. For 2.5 nm film, refractive index is about 2-3 times larger, while the extinction coefficient is about 2 times smaller as compared to 15 nm case.
NM4C.1.pdf
Advanced Photonics © 2015 OSA
FIG. 2. (Color online) Refractive index (a) and extinction coefficient (b) for the 2.5, 7, and 15 nm films. The behavior for the 2.5 nm film is significantly different from thicker films. Predictions from our quantum model (QM) are also plotted, showing good agreement with experiment.
Clearly, such a distinct behavior of the optical constants is related to the change in film thickness. This effect has been studied previously [5, 6]. However, the agreement between theory and experiment is not very good, and a solid model is still needed. Here we propose a more solid model, which starts from the Schrödinger equation: (1) where m and e are the effective mass and charge of the free electrons, is the momentum operator, c is the speed of light in vacuum, and are the vector and scalar potential of the applied electromagnetic field, and is the potential determined from the quantum well structure. An iteration scheme for the coupled Schrödinger-Poisson equation is adopted [7] because the potential is modified by the free electron distribution inside the quantum well. The permittivity for the metal quantum well can be calculated using [8] ，
(2)
where the plasma frequency w p is determined by the electron density ne through w 2p = nee2 me 0 , W is the volume of the quantum well, Eij = Ei - E j is the difference in eigen energies. fi is the Fermi-Dirac occupation factor for the
ith state. We use the model from Mermin [9] to account for the relaxation process and the permittivity is corrected: (1+ i / wt )(e -1) (3) 1+ (i / wt )(e -1) / (e static -1) where e = e (w = 0). Numerical simulations based on the quantum model (QM) are preformed for our metal thin static films with different thickness. Calculated n and k are plotted in Fig. 2(a) and (b), where theoretical predictions match quite well with experimental results for all 3 different thickness samples. This clearly shows that our quantum model is valid in describing the electron dynamics inside a metal quantum well.
e corr (w ) = 1+
The application of plasmonics to nonlinear optics usually evolves the utilization of the local field enhancement effect to realize the strong “effective” nonlinearity, and this has been the major research focus [2]. The intrinsic nonlinear coefficient of metal is not small. For example gold has an intrinsic bulk third order nonlinear coefficient about 10-18 m2/V2 that comes from the interband contribution [10]. It is known that “free” electron has zero nonlinear response. However, these “free” electrons can be engineered to have nonlinear response by adding external constraint, such as quantum confinement effect [11]. To characterize the nonlinear optical properties of our nano-scale thin films, z-scan [12] experiment is performed. In our experimental setup, a laser pulse with about 100fs width from a Ti-sapphire laser is used as the laser pulse. Such short pulse duration ensure that the hot electron effect [10, 13] would not play a role in our z-scan measurement, and only the instantaneous Kerr effect is measured. Open and close aperture z-scan curves at 740nm are measured at the same time, and are shown in Fig. 3 (a) and (b) respectively. By fitting with the standard z-scan theory [12], the real and imaginary part of the Kerr coefficient n2 of the 2.5 nm gold film is calculated to be 0.65*10-
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m2/W and -2.3*10-13 m2/W, respectively. Using the experimentally measured linear refractive index n and extinction coefficient k for our 2.5 nm gold film, we finally obtain the third order susceptibility through:
c (3) =
Re{n2 }+ i Im{n2 } n(n + ik) 283
(4)
The experimentally measured third order susceptibility at 740nm is χ(3)=(3.6 + 2.6i)*10-14 m2/V2. Note that because our sample is a flat thin film, and no surface plasmon can be exited, where the local filed enhancement effect can be ruled out. This 4-order enhancement of the nonlinear susceptibility of gold is a signature of the quantum confinement effect.
FIG. 3. (Color online) Close aperture (a) and open aperture (b) z-scan curve for the 2.5 nm film. Experimental data are shown by the blue circle, and can be well fitted by the standard z-scan theory shown by the red solid line.
The third order nonlinear susceptibility of the 2.5 nm gold film is much higher than other conventional nonlinear materials. For example, the third order nonlinear susceptibility for optical fiber and Silicon are 2.5*10 -22 and 2.8*1018 m2/V2 [14], respectively. Recently, graphene has been considered to be a very good candidate for nonlinear application [15, 16] because it has a very large χ(3) of about 1*10-15 m2/V2. The third order nonlinear susceptibility of the 2.5 nm gold film is about 30 times higher than grapheme, this makes our nano-scale gold film a very promising candidate for nonlinear application. To summarize, linear and nonlinear optical properties of nano-scale gold films are experimentally investigated. The linear optical constant of 2.5 nm thin film is changed dramatically by the quantum confinement effect. A solid model is proposed and can explain the experimental results quite well. It is also found that the quantum confinement effect greatly enhances the nonlinear susceptibility of gold. References [1] J.A. Schuller, et al., Plasmonics for extreme light concentration and manipulation, Nat Mater, 9 (2010) 193-204. [2] M. Kauranen, A.V. Zayats, Nonlinear plasmonics, Nat Photonics, 6 (2012) 737-748. [3] M.I. Stockman, Nanoplasmonics: past, present, and glimpse into future, Opt Express, 19 (2011) 22029-22106. [4] M.S. Tame, et al., Quantum plasmonics, Nat Phys, 9 (2013) 329-340. [5] J. Dryzek, A. Czapla, Quantum Size Effect in Optical-Spectra of Thin Metallic-Films, Phys Rev Lett, 58 (1987) 721-724. [6] N. Trivedi, N.W. Ashcroft, Quantum Size Effects in Transport-Properties of Metallic-Films, Phys Rev B, 38 (1988) 12298-12309. [7] A. Trellakis, et al., Iteration scheme for the solution of the two-dimensional Schrodinger-Poisson equations in quantum structures, J Appl Phys, 81 (1997) 7880-7884. [8] D.M. Wood, N.W. Ashcroft, Quantum Size Effects in the Optical-Properties of Small Metallic Particles, Phys Rev B, 25 (1982) 6255-6274. [9] N.D. Mermin, Lindhard Dielectric Function in Relaxation-Time Approximation, Phys Rev B-Solid St, 1 (1970) 2362-+. [10] R.W. Boyd, et al., The third-order nonlinear optical susceptibility of gold, Opt Commun, 326 (2014) 74-79. [11] F. Hache, et al., The Optical Kerr Effect in Small Metal Particles and Metal Colloids - the Case of Gold, Appl Phys a-Mater, 47 (1988) 347357. [12] M. Sheikbahae, et al., Sensitive Measurement of Optical Nonlinearities Using a Single Beam, Ieee J Quantum Elect, 26 (1990) 760-769. [13] M. Conforti, G. Della Valle, Derivation of third-order nonlinear susceptibility of thin metal films as a delayed optical response, Phys Rev B, 85 (2012). [14] R.W. Boyd, Nonlinear Optics, 3rd Edition, Nonlinear Optics, 3rd Edition, (2008) 1-613. [15] E. Hendry, et al., Coherent Nonlinear Optical Response of Graphene, Phys Rev Lett, 105 (2010). [16] T. Gu, et al., Regenerative oscillation and four-wave mixing in graphene optoelectronics, Nat Photonics, 6 (2012) 554-559.
