A robust and ecient model for transmission of surface plasmon polaritons onto metal-insulator-metal apertures S. B. _Iplik cio gluand M. I. Aksun

2025-04-30 0 0 1.16MB 19 页 10玖币
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A robust and efficient model for transmission of surface plasmon
polaritons onto metal-insulator-metal apertures
S. B. ˙
Iplik¸cio˘glu∗and M. I. Aksun†
Department of Electrical and Electronics Engineering,
Ko¸c University, Istanbul, Turkey
Abstract
A simple yet accurate model for the transmission of surface plasmon polaritons (SPPs) in a finite
metal-insulator-metal (MIM) waveguide to the sides of the apertures is proposed and demonstrated
to be more accurate than the available models. It is as simple as using a magnetic current density
across the plane of the aperture whose value is defined by the SPPs with any number of modes in
the waveguide through the equivalence principle. Then, the generated SPPs on both sides of the
aperture are extracted from the convolution integral of the equivalent current density and Green’s
function. As a result, the model provides the transmission coefficients of the SPPs in the MIM
to the side walls of the aperture accurately and efficiently; not only for symmetric MIMs with a
single isolating layer but also for non-symmetric ones with multi-layered insulating materials. The
results are in very good agreement with those obtained by the FDTD method and better than the
other approximations available in literature for a wide range of aperture widths.
∗siplikcioglu15@ku.edu.tr
†iaksun@ku.edu.tr
1
arXiv:2210.14844v1 [physics.optics] 26 Oct 2022
I. INTRODUCTION
Surface plasmon polaritons (SPPs) have been studied extensively in the past few decades,
and deemed to have a great potential to help develop new applications/technologies in
the fields of nanotechnology, communications and life sciences [1–4]. Motivated by this
outlook and the observations of extraordinary transmission through nano-holes in metals,
there have been a flurry of studies on the transmission and reflection of SPPs at some
canonical discontinuities, like holes, ridges, abrupt terminations or transitions to different
waveguides or components [5–10]. Although mostly rigorous full-wave methods, such as
the finite-difference time-domain (FDTD) method, the Fourier-modal method, the mode
matching method or their variants, have been used to characterize the discontinuities in
these studies [6, 7, 11–13], some approximate models have also been proposed with success for
efficient and yet accurate assessment of the structures [8, 14–20]. Inevitably, the approximate
models are usually limited to either certain geometries or certain wavelength ranges. In this
work, we propose an approximate model for nanoslits in metal-dielectric interface, modeled
as metal-insulator-metal (MIM) waveguides opening up to a dielectric environment from
both ends, as shown in Fig. 1, to assess the transmission to the metal-dielectric surfaces
beyond the edges of the aperture with better accuracy and applicability than the available
models.
As it is common in integrated optics, structures that are studied in the context of plas-
monics generally involve discontinuities, either as a critical design choice or as an inevitable
byproduct of the fabrication processes. Modeling these discontinuities poses a particular
challenge due to the complexity of the problems involved, which generally have no analyti-
cal solutions. However, for plasmonics to gain importance in the design of integrated optics,
its interaction with different geometrical constructs have to be analyzed, understood and
modeled for practical use by the engineers. Towards this goal, there have been a plenty
of work to characterize discontinuities in terms of reflection and transmission coefficients
of the SPPs either on metal-insulator interface [21–24] or in metal-insulator-metal waveg-
uides [8, 14–18]. Study of reflection and transmission of SPPs on a single metal-insulator
interface goes back to the work in [21], where the upper dielectric portion of the geometry is
uniform along the interface while the lower metal portion consists of two pieces with different
real dielectric constants as the discontinuity. As a continuation, a similar study on the SPP
2
reflection for a uniform metal layer with two different dielectrics has also been reported [22].
These studies used the modal analysis and power matching at the discontinuity to extract
the reflection and transmission coefficients, and a similar approach was later used to char-
acterize the SPP reflection from a terminated lossless metallic half-plane [23]. As a natural
extension, the SPP reflectivity at step discontinuities was also studied using the method of
lines [24]. Following the discovery of extra-ordinary optical transmission [25], there have
been a flurry of activities to describe the transmission through nano-holes and nano-slits
in metal slabs [26–30], which have provided ample computational tools and good intuitive
understandings of the SPPs in the slits. Hence, these developments paved the way to model
a nanoslit in metallic slab (considered as a MIM waveguide) to predict the reflection of SPPs
in the slit and the transmission of SPPs from the slit to the SPPs on the nano-aperture sides
(metal-dielectric interface) [17, 31]. As emphasized in [17] and stated above for the modeling
of discontinuities, it is of utmost importance to have an approximate and yet accurate and
computationally efficient model for finite MIM structures, as is the main goal of the work
presented in this paper.
To put things into perspective and to delineate the contributions of this work, it would
be imperative to provide the contributions in [17], where the model for the reflection and
transmission in a finite MIM waveguide was developed in two distinct intuitive steps: i. for
the geometrical scattering part from the slit aperture, the metal layers are assumed to be
perfect conductors as their dielectrics play less significant role in diffraction, and ii. once
the near-field distribution is obtained, the transmission fields in the near vicinity of the slit
aperture are obtained by using the mode orthogonality. Although this is a brilliant approach
to get analytical expressions for the SPP generation, it is limited to a rather restricted class
of slit geometries because of the approximate nature of the model, as also stated in [17].
Restrictions stem from having to use symmetric geometries (m1=m2in Fig. 1), only
the fundamental mode in the slit (black field profile in Fig. 1) and homogeneous dielectric
region in the slit (d1=d2in Fig. 1), all of which are addressed and resolved in the proposed
approach. However, to be fair, the approximate approach presented in [17] was specifically
proposed to get analytic expressions for the transmission fields, while the main purpose of
the work presented in this paper has been to achieve a computationally efficient and accurate
model that is applicable to a rather broader spectrum of geometries, albeit at the expense
of closed-form expressions at the end.
3
In this paper, assuming the reflection from the aperture of a MIM waveguide has been
well approximated with the current vectorial mode-matching approach, an efficient, accurate
and versatile numerical model for the transmission of the SPPs from the aperture onto
the open metal-dielectric interfaces has been developed and compared with the full-wave
method (FDTD) and the approximate model proposed in [17]. The model is based on the
equivalence principle with the impedance boundary and is able to employ as many modes
in the MIM waveguide as needed with their full profiles. As a result, besides the accuracy,
the model is robust, converges fast and can easily handle MIM structures with asymmetric
metal configurations as well as planar dielectric layers as the insulating regions.
FIG. 1. A typical semi-infinite MIM waveguide with the SPP mode profiles and the effective surface
impedance model with the impressed equivalent magnetic current density. The mode profiles are
given at λ0= 900 nm for the silver-SiO2-air-copper combination (from top to bottom) with the
following material parameters: εm1=−40.6923 + 0.7733i,εm2=−37.5145 + 0.5144i,εd1= 2,
εd2= 1, w1=w2= 100 nm.
II. THEORY
For the sake of illustration, a general finite MIM configuration (or slit geometry) is shown
in Fig. 1, which captures almost all possible varieties of the geometries that have been studied
in this work. The field profiles for the first four modes (TM0,TM1,TM2,TM3) have also
been depicted on the figure as black, blue, green and red lines, respectively, as the higher
4
摘要：

Arobustandecientmodelfortransmissionofsurfaceplasmonpolaritonsontometal-insulator-metalaperturesS.B._Iplikcioglu*andM.I.Aksun„DepartmentofElectricalandElectronicsEngineering,KocUniversity,Istanbul,TurkeyAbstractAsimpleyetaccuratemodelforthetransmissionofsurfaceplasmonpolaritons(SPPs)ina nitemeta...

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