The filed of quantum plasmonics [1], which combines the quantum mechanics with plasmonics, has emerged and draw much attention recently due to the shrink of plasmonic devices [2]. Here we choose the ultra-thin metal film as a platform to study the quantum behavior of electrons. More specifically, we focus on the optical properties of the nanoscale gold film.
Reflection and transmission (RT) of thin gold films with thickness varying from 2.5 nm to 30 nm are experimentally measured with different incident angles and polarization. Fig. 1 shows the experimental data. As can be seen here, the transmission curves for 7, 15, and 30 nm thick films behave quite similar and they decrease monotonically as wavelength increases. The 2.5nm thick sample, however, exhibits a distinct behavior: its transmission increases slightly with wavelength. Similar behavior is also seen on reflection curves.
Fig.1: Reflection (a) and transmission (b) for the 2.5, 7, 15, and 30 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.
The special behavior of 2.5 nm film indicates the impact of quantum confinement effect on free electrons. This effect has been investigated previously [3], but the agreement between theory and experiment is not very good and a more solid model is still needed. For this purpose, a theory based on the self-consistence solution of Schrodinger equation and Poisson equation is proposed. Calculated RT are also plotted in Fig.1 and agree well with experimental results for all films.
[1] M. S. Tame et al., Nat Phys 9, 329 (2013).
[2] M. I. Stockman, Opt Express 19, 22029 (2011).
[3] J. Dryzek and A. Czapla, Phys Rev Lett 58, 721 (1987).
zhaowei@ucsd.edu