Nonlocal effects on second harmonic generation in nanofilm plasmonic
structure
Hao Li
a
, Ning Zhu
a
, Hui Zhang
a
, Zhenshi Chen
a
, Ting Mei
b,
n
a
Laboratory of Nanophotonic Functional Materials and Devices, Institute of Optoelectronic Material and Technology, South China Normal University,
Guangzhou 510631, China
b
The Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education and Shaanxi Key Laboratory of Optical Information Technology, School of
Science, Northwestern Polytechnical University, Xi'an 710072, China
article info
Article history:
Received 18 August 2014
Received in revised form
24 October 2014
Accepted 13 November 2014
Available online 18 November 2014
Keywords:
Nonlocal effect
Harmonic generation and mixing
Plasmonic
Metal optics
Surface plasmons
abstract
We numerically studied nonlocal effects that affect enhancement of second harmonic generation (SHG)
in a metal nanofilm plasmonic structure. The hydrodynamical Drude model was implemented for metal
film in time-domain simulations that combine nonlocal effects and nonlinear effects. It is found that the
nonlocal effect on the second harmonic wave is more severe than that on the fundamental wave. The
SHG enhancement is thus weakened in the nonlocal response compared with the usual local response
described by the Drude model, and the reduction becomes appreciable for the metal film thickness down
to nanomenter scale.
& 2014 Elsevier B.V. All rights reserved.
1. Introduction
Second-harmonic generation (SHG) is an effective way to ex-
tend laser wavelengths to visible or ultraviolet [1]. However, in-
troducing strong nonlinear responses from materials to realize
efficient SHG in the subwavelength scale is still challenging. Sur-
face plasmon polaritons (SPPs) are quasi-particles with electro-
magnetic waves coupling with electron density oscillations at
metal–dielectric interface, providing a possible approach to con-
fining optical field within subwavelength scale and enhancing the
field at the interface. A number of reports on SHG enhancement in
plasmonic nanostructures have been published. Simon et al. first
reported an experimental and theoretical investigation on the
coupling of SHG light to surface plasmons in thin silver films and
observed harmonic enhancement to one and a half orders of
magnitude due to excitation of surface plasmons [2]. SHG en-
hancement with metal tips, homogeneous centrosymmetric na-
nowires, hybrid plasmonic waveguides, bowtie aperture arrays,
plasmonic slot waveguides has also been investigated [3–7].
However, as the size of plasmonic devices shrinks to an ex-
tremely small length scale, i.e. less than 10 nm approximately,
local solutions to the macroscopic Maxwell's equations can no
longer describe their electromagnetic properties accurately
whereas the nonlocal optical response of metal should be taken
into account [8]. The failure of the local picture originates from the
emergence of strong electron–electron interactions in the di-
electric response of metals. Therefore, the theoretical investigation
of plasmonic phenomena in this subnanometer regime requires
the implementation of the nonlocal (spatially dispersive) permit-
tivities to model the dielectric characteristics of plasmonic na-
nostructures, and ultimately a quantum mechanical treatment
[10]. Recently, there have been several reports on theoretical
analysis of nonlocal effects in plasmonic structures, such as pro-
pagation modes in plasmonic guides [8], optical properties of
metallic nanowires [9], nanofocusing performance of plasmonic
tips [10], etc. All these studies describe electron–electron inter-
actions through the so-called hydrodynamical model, which in-
troduces a pressure term in the Drude-like equation of motion of
the electron density [10]. Accordingly, it would also be interesting
to understand the nonlocal effects on SHG enhancement in plas-
monic structures. To the best of our knowledge, there is no ap-
plication of the nonlocal model to the direct time domain calcu-
lations of high-order harmonic fields generated in the plasmonic
structures.
In this paper, we investigate the nonlocal effects on SHG en-
hancement in a planar plasmonic guide comprising an ultra-thin
silver film. Firstly, we present a method for Finite Element Method
(FEM) nonlocal solution to the Maxwell's equations and a simu-
lation method for handling dispersive materials in time domain.
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/optcom
Optics Communications
http://dx.doi.org/10.1016/j.optcom.2014.11.055
0030-4018/& 2014 Elsevier B.V. All rights reserved.
n
Corresponding author.
E-mail address: ting.mei@ieee.org (T. Mei).
Optics Communications 339 (2015) 177–181