costa2019

Plasmonics
https://doi.org/10.1007/s11468-019-00970-5
Sim-SPR: an Open-Source Surface Plasmon Resonance Simulator
for Academic and Industrial Purposes
Elton B. Costa1·Eloise P. Rodrigues2·Helder A. Pereira1
Received: 6 March 2019 / Accepted: 9 May 2019
©Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract
In this paper, an open-source simulation tool is proposed to evaluate the SPR effect considering a multilayer structure. The
open-source simulator is called Sim-SPR and it follows the principles of software engineering. Furthermore, Sim-SPR is
dedicated to analyze reflectance of prism-based SPR sensors using Otto’s configuration. It is important to emphasize that
there is no available open-source simulation tool specifically built in this context in the literature. The Sim-SPR accuracy,
efficiency, and reliability were analyzed by comparing our obtained results considering three different scenarios with two
other simulation tools available in the literature, presenting minimal relative error. The results still include a sensitivity
analysis of prism-based SPR sensors focusing on resonant angle.
Keywords Biosensor ·Open source ·Otto’s configuration ·Simulation tool ·Surface plasmon resonance
Introduction
Surface plasmon resonance (SPR) is a physical effect in
which the optical beam is reflected between a dielectric
and a thin metal layer (noble metals), exciting a surface
plasmon wave (SPW) at the other metal layer boundary
[12]. For optical applications, SPR-based sensors become a
leading technology due to diverse advantages, such as the
following [7,30]: (1) fast response; (2) small volume; and
(3) high sensitivity to variations in the medium refractive
index located close to metal thin film, for example.
Elton B. Costa
[email protected]
Eloise P. Rodrigues
[email protected]
Helder A. Pereira
helder[email protected]
1Departamento de Engenharia El´
etrica (DEE), Centro de
Engenharia El´ etrica e Inform´ atica (CEEI), Universidade
Federal de Campina Grande (UFCG), Rua Apr´ ıgio Veloso,
882, Universit´ ario, Campina Grande, Para´ ıba, 58429–900
Brazil
2Programa de P´
os-Graduac¸˜ ao em Engenharia El´ etrica
(PPgEE), Centro de Engenharia El´ etrica e Inform´ atica
(CEEI), Universidade Federal de Campina Grande (UFCG),
Rua Apr´ ıgio Veloso, 882, Universit´ ario, Campina Grande,
Para´ ıba, 58429–900 Brazil
However, SPR-based sensors and instruments comprise
a complex optical system design for practical uses. They
have expensive optical components and materials besides of
being necessary to take care in instrumental handling [23].
Therefore, simulation tools become an important apparatus
before to construct SPR-based sensors and to optimize
parameters aiming to reduce operational costs as well.
There are a few simulation tools available in the literature
that are used to analyze and to design SPR-based sensors,
such as COMSOL Multiphysics [1] and Lumerical [2], for
example, presenting themselves as robust simulation tools,
but requiring expensive license costs and their source codes
are unavailable for research improvements.
In this paper, an open-source simulation tool is proposed
to evaluate the SPR effect considering prism-based SPR
sensors using Otto’s configuration based on a multilayer
structure. The open-source simulator is called Sim-SPR1
and it is implemented in C++ language under the GNU
Lesser General Public License, following the principles of
software engineering. Furthermore, Sim-SPR is dedicated
to analyze reflectance and sensitivity of prism-based SPR
sensors, focusing on resonant angle. It is important to
emphasize that there is no available open-source simulation
tool specifically built in this context in the literature.
Therefore, Sim-SPR becomes a pioneer open-source SPR
simulator for academic and industrial purposes. Two
simulation tools already consolidated and three different
1For more information, interested readers are referred to https://github.
com/eltonbrasil/SimSPR.

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Fig. 1 Two most popular
metal-dielectric configurations
to SPR optical excitation. aOtto
[24]. bKretschmann [18]
Metal Layer
Spacer Layer
kSPW Plasmon wave
Evanescent
wave
p-polarized
light beam
Light source Position-sensitive
detector
Prism
kxMetal Layer
Analyte
kSPW Plasmon wave
Evanescent
wave
p-polarized
light beam
Light source Position-sensitive
detector
Prism
kx
(a) (b)
scenarios based on Otto’s configuration, both presented in
the literature, were used to validate our obtained results and
for comparison purpose.
This paper is organized as follows: in “Surface Plasmon
Resonance,” we discuss about the mathematical modeling
of prism-based SPR sensors with multilayer structure,
considering Fresnel equations. We present the state of
the art of simulation tools available in the literature that
consider SPR effect. Sim-SPR architecture, considered
parameters, and its respective characteristics are presented
in “Sim-SPR”. In “Simulation Scenarios,” we describe three
different scenarios [16,19,27] and two simulation tools [1,
4], both available in the literature, to validate our obtained
results and for comparison purposes. We still present the
parameters used in our simulations to analyze the sensitivity
of prism-based SPR sensors, focusing on resonant angle.
In “Results,” we discuss about the obtained results and, in
“Conclusions,” we give the conclusions.
Surface Plasmon Resonance
The plasmons excitation can be achieved through a coupler
in multilayer structures which can be built on prism, grating,
planar or cylindrical waveguide coated with a thin metal
film [10]. For prism coupling, there are two most popular
metal-dielectric configurations to SPR optical excitation:
Otto [24] and Kretschmann [18], as shown in Fig. 1. In both
metal-dielectric configurations (Otto and Kretschmann), the
p-polarized light beam2is reflected at the interface between
a prism and a very thin metal layer, being captured by
a position-sensitive detector. Consequently, the evanescent
optical wave penetrates through the metal layer and it
excites a SPW at the other metal boundary [11]. For Otto’s
configuration, as shown in Fig. 1a, it is required that
the metal surface must be separated from the prism by a
spacer layer, in which the analyte solution flows above the
metal surface. For Kretschmann’s configuration, as shown
in Fig. 1b, a thin metal film is employed onto a glass surface.
In both configurations (Otto and Kretschmann), there is
a SPW propagating at the interface between a thin metal
2The optical wave from a light source with the electric field direction
parallel to the incidence plane.
layer and a dielectric. The SPW propagation constant can be
expressed by [11]:
kSPW =k0mn2
a
m+n2
a
,(1)
in which k0=2π
λrepresents the component of the incident
light wave vector, λthe free space wavelength, mthe
metal complex dielectric constant (m=mr +jmi )that
depends on the wavelength, and nathe sample refractive
index (analyte).
The coupling condition to excite a SPW occurs when the
wave vector matches with the SPW, resulting a dip in the
angular, or wavelength, variation of the reflected light. The
coupling condition may be expressed by [11]:
kx=npk0sin(θSPR)=k0mn2
a
m+n2
a
,(2)
in which kxis the wave vector, npthe prism refractive index,
and θSPR the resonant angle that excites the surface plasmon.
AccordingtoEq.(2), the coupling condition is satisfied only
if |mr |is higher than n2
pn2 a
n2
p−n2 a
. It occurs because when the
wavelength decreases, |mr |approaches to the critical value
and a SPW can not be excited [11].
Considering a prism-based SPR sensor with Nlayers,
the reflected intensity of p-polarized light beam can be
evaluated by the matrix method using Maxwell’s equations
and Fresnel coefficients as follows [5,7]:
Mk=cos(βk)−i
qksin(βk)
−iqksin(βk)cos(βk),(3)
in which Mkis the characteristic transfer matrix and itself
represents the luminous propagation between layers, βkthe
phase factor, and qkthe transverse magnetic incident light,
given by the following equations [7]:
βk=k0dkn2
k−n2
psin2(θi), (4)
qk=n2
k−n2
psin2(θi)
n2
k
,(5)
in which dkdenotes the thickness, θithe incidence angle,
and nkthe metal layer refractive index which depends on
the wavelength. The total characteristic transfer matrix is

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evaluated by multiplication of each Mkmatrix for kth layer
index as follows [7]:
Mtotal =
N−1
k=1
Mk.(6)
The Fresnel reflection coefficient (r) of multilayers using
Mtotal matrix terms can be evaluated by [7]:
r(θi,λ) =(M11 +M12qN)q1−(M21 +M22qN)
(M11 +M12qN)q1+(M21 +M22qN),(7)
in which M11,M12,M21 and M22 are elements of the
total characteristic transfer matrix and q1and qNare the
transverse magnetic incident light for the first and the last
layers, respectively.
Consequently, the reflectance (R) of a multilayer
structure is given by [7]:
R=|r(θi,λ)|2.(8)
The reflectance can be evaluated considering two oper-
ating modes [11]: (1) angular interrogation mode (AIM)
that considers the wavelength fixed while the incidence
angle is changing and (2) wavelength interrogation mode
(WIM) that considers the incidence angle fixed while the
wavelength is changing.
The appropriate resonant angle for exciting the SPR
effect is given by [27]:
θSPR =sin−11
npn2
am
n2
a+m.(9)
Furthermore, the prism refractive index can be computed
using Sellmeier’s dispersion equation given by [8]:
np(λ) =1+A1λ2
λ2−B1+A2λ2 λ2−B2+A3λ2 λ2−B3
,(10)
in which Aiand Bi(i=1,2,3) are the Sellmeier
coefficients associated to each material [8,25].
In this paper, our analysis is focused on prism-based
SPR sensors considering Otto’s configuration. Otto’s con-
figuration is not as convenient as the Kretschmann’s
because of the strong dependence of the surface plas-
mon coupling efficiency on the thickness of the dielectric
spacer [27]. Besides that, Otto’s configuration requires
very smooth surfaces for both the metal and the dielectric
materials which are very difficult to be realized exper-
imentally [31]. However, recent advances in microfab-
rication and thin film technology makes the fabrication
of SPR biosensors based on Otto’s configuration feasi-
ble [6,21]. Among other applications, SPR biosensors
based on Otto’s configuration will be preferable in appli-
cations where direct contact with the metal surface is
undesirable [6]. The use of Otto’s configuration for prism
coupling brings some benefits to the applications in biosens-
ing, such as the following [9]: (1) high-purity metal
film can be preserved; (2) it is possible to use opaque
substrates for the metal layer; (3) the degrading effect pro-
duced by the adhesion layer applied between the substrate
and the metal film layer on the resonance curve qual-
ity factor (QF) does not occur in Otto’s configuration. As
described in details in “Angular Interrogation Mode Sensor
Sensitivity Analysis,” QF depends on the sensor sensitivity
and the spectral width of the resonance curve.
State of the Art of Simulation Tools Used
for SPR-Based Sensors Analysis and Design
Some simulation tools used for SPR-based sensors analysis
and design are described in the literature [1–4,13].
Therefore, some of these simulators do not make available
their source codes and the cost of some respective licenses
can be expensive. In this paper, we propose an open-source
simulation tool to evaluate the SPR effect considering
multilayer structures. Our proposal is dedicated to analyze
reflectance and sensor sensitivity of prism-based SPR sensors
using Otto’s configuration, focusing on resonant angle.
For SPR-based sensors analysis and design, COMSOL
Multiphysics uses the finite element method (FEM) to solve
differential equations. The wave equation is given by [1]:
∇×(∇×E)−k2
0mr E=0. (11)
Besides to solve Eq. (11) at the interface, the structure is
divided into a mesh of elements with predefined sizes and
the equation is applied element by element. The solution
is evaluated from the field variation in the structure, being
possible to generate the reflectance curves, verifying the
resonance condition considering a variation of incidence
angle. On the other hand, COMSOL Multiphysics demands
high-performance computing, expense of longer running
time, its source code is not available and its license is paid.
Jamiletal.[14] used Lumerical’s finite-difference time-
domain (FDTD) simulator [2] to optimize a SPR sensor
based on Kretschmann’s configuration. It was analyzed the
resonance curve’s full width at half maximum (FWHM)
from a graphene-based SPR sensor. Jamil et al. [14]also
monitored the performance of the SPR sensor by the FDTD
Lumerical software as well as the bio-detection sensitivity.
Lumerical also demands high-performance computing and
it does not provide its source code for future improvements.
In the field of renewable energy, solar cell, and electronic
device simulations, Wenjun et al. [15] explored the impact
of SPR effect on organic solar cell performance, considering
optical coupling at an interface with silver nanoprisms, using
Sentaurus device simulator [3]. Wenjun et al. [15]useda
conventional organic photovoltaic structure implemented as
simulation setup in the Sentaurus, with the aim to analyze
the optimization of silver nanoprism sizes, reflectivity, and
absorption. The impact of silver nanoprisms on short-circuit
current was analyzed as well. It is important to observe that
Sentaurus does not offer an open-source code.

Plasmonics
Table 1 State of the art of the simulation tools described in the literature used for SPR-based sensors analysis and design
Simulation tool COMSOL [1] Lumerical [2] Sentaurus [3]WinSpall[4]PAME[13] Sim-SPR
Reflectance analysis X X X X X X
Sensitivity analysis X X X – – X
Otto’s configuration X X X X – X
Kretschmann’s configuration X X X X – –
AIM X X X X X X
WIM X X X – X –
C++ language – – – X – X
Python language – – – – X –
Nlayers X X X X X X
Free license – – – X X X
Source code – – – – X X
Optical fiber–based coupling X X X – X –
Prism-based coupling X X X X – X
Adam et al. [13] proposed the plasmonic assay modeling
environment (PAME). It is an open-source application
for modeling plasmonic systems of bulk and metallic
films, also used for modeling plasmonic biosensors. It is
implemented in Python programming language, there is a
graphical interface that provides results in terms of graphs
and its functional architecture is designed with integrated
subprograms along with data analysis framework. PAME
is presented as only one open-source application close to
our purpose in this paper. While PAME uses optical fibers
as a coupling method to design plasmonic biosensors, our
proposal considers prism-based SPR sensors.
WinSpall [4] is another software described in the
literature used for simulations of SPR-based sensors. It is
based on Fresnel equations considering multilayer structure.
It is free and easy to use for thin film analysis using
evanescent waves. It is developed by RES-TEC Solutions
and it has been used as a good alternative to simulate
resonance curves, operating with AIM mode. Therefore,
WinSpall does not offer sensitivity analysis and does not
provide its source code for future improvements [4].
SPR effect modeling implemented in MATLAB and
Mathcad was presented in the literature as useful to
determine parameters for designing optical sensors. Fontana
[8] used Mathcad to determine the wavelength dependence
of the optimum thickness for the maximum sensitivity of the
SPR effect. In addition, Huang et al. [30] used MATLAB to
design a prism-based SPR sensor based on Kretschmann’s
configuration, considering AIM and WIM modes. However,
all of these softwares require high-cost licenses to be used.
Table 1summarizes the main features of the simulation tools
described in this section and brings a comparison with our
proposal, evidencing the main features of the Sim-SPR.
Sim-SPR
Figure 2shows the Sim-SPR sequence diagram. The SPR
effect is evaluated based on the characteristic transfer
matrix, as evaluated by Eq. (6), considering a multilayer
structure of prism-based sensor using Otto’s configuration.
Sim-SPR considers the general case of plane wave
interaction with a stack of Nlayers (N−1 interfaces). It uses
features from the most recent C++ standards, benefiting
from their well-developed C++ libraries, as Armadillo for
linear algebra and a direct programming interface (DPI)3
to GNU Octave templates was developed to evaluate
parameters using complex numbers. Interfaces are used to
enable users to enter the required input parameters and
to obtain the reflectance results. The numerical results of
reflectance and resonance angle are saved in a structured
data file.
Algorithm 1 describes the Sim-SPR pseudocode. Sim-
SPR initializes parameters, such as the following (lines 3
and 4): (1) incidence angle and (2) step-scale (for AIM
mode). Between lines 6 and 8, the user selects the prism-
based coupling configuration (in this paper, Otto’s con-
figuration). Within lines 9 to 17, Sim-SPR reads param-
eters as refractive indexes and layers thickness for the
metal and analyte layers, number of layers and wave-
length. Then, reflectance class is instantiated to evaluate the
reflectance. Subsequently (by using Eq. (8)), it is returned
the reflectance value for each incidence angle, considering
AIM mode (lines 18 to 24). Sim-SPR is structured on a
verification environment. It assumes an unlimited number
of layers and it imposes a limit to the incidence angle, as
described in Algorithm 1, in which reflectance and sensitiv-
ity methods are instantiated (lines 18 to 27). Both methods
provide an well-regulated algorithm, in which allows possi-
ble expansions.
3DPI is an interface which can be used to interface C++ with foreign
languages. These foreign languages can be Octave, MATLAB, and
Python as well as others.

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loop
READ
PARAMETERS
AIM
AIM Evaluation data.txt
USER
Minimum Reflectance
Sensor Sensitivity
Resonant Angle
Fig. 2 Sim-SPR sequence diagram
Algorithm 2 describes the pseudocode to evaluate the
reflectance. The reflectance is obtained from the evaluated
reflection coefficients (line 6), as described by Eq. (7). Once
the reflectance curve as a function of the incident angle is
generated, the point with the lowest reflectance level will be
associated with an angle.
Algorithm 3 describes the angular sensitivity evaluation
pseudocode. The sensitivity method is governed only by
three initialized parameters, such as the following: (1)
na;(2)np; and (3) refractive index of the metal layer
(nmetal). Consequently, the output evaluated by Eq. (12)
(line 3) is returned in degree per refractive index unit
(◦/RIU) (line 4). For improvement of the angular sensitivity
results, Sim-SPR uses some features implemented by
a multiprocessing programming in C++ using OpenMP
library (line 2), in which is possible to run simulations
in parallel for each refractive index of sensing medium
shifts (na).