Plasmonic waveguides have attracted much attention owing
to the associated high field intensity at the metal–dielectric interface and
their ability to confine the modes at the nanometer scale. At the same time,
they suffer from relatively high propagation loss, which is due to the
presence of metal. Several alternative materials have been introduced to
replace noble metals, such as transparent conductive oxides (TCOs). A
particularly popular TCO is indium tin oxide (ITO), which is compatible with
standard microelectromechanical systems (MEMS) technology. In this work, the feasibility of ITO as an
alternative plasmonic material is investigated for infrared absorption sensing
applications: we numerically design and optimize an ITO-based
plasmonic slot waveguide for a wavelength of 4.26 µm, which is the absorption
line of CO2. Our optimization is based on a figure of merit (FOM), which
is defined as the confinement factor divided by the imaginary part of the effective mode
index (i.e., the intrinsic damping of the mode). The obtained optimal FOM is
3.2, which corresponds to 9 µm and 49 % for the propagation length
(characterizing the intrinsic damping) and the confinement factor,
respectively.
Introduction
In recent years, plasmonic effects and devices have commanded increased attention,
as they enable sub-wavelength photonics applications. The existence of
surface plasmon polaritons (SPPs), which are essentially guided
electromagnetic waves propagating along a metal–dielectric interface with
strong near-field confinement, allows for efficient light–matter
interactions (Prämassing et al., 2020; Gaur et al., 2021). For the
guided mode, the maximum intensity occurs at the metal–dielectric interface
where the field amplitudes decay exponentially in the direction
perpendicular to the interface (Dionne et al., 2006). This so-called
evanescent field represents the bound, non-radiative nature of SPPs (Barnes
et al., 2003). A plasmonic device that has attracted particular attention
is the plasmonic waveguide. A specific merit of SPP-based waveguides is that
they can break the diffraction limit related to the dielectric waveguides,
leading to strong field confinement (Sun et al., 2014). Among the
plasmonic waveguides, plasmonic slot waveguides are particularly attractive
due to the provided lateral confinement and the capability of guiding the
mode in low-index materials, which can be an asset in the fabrication of
miniaturized optical circuits. Therefore, compared with dielectric waveguides,
they allow compact integration and short coupling lengths (Osowiecki et al.,
2014). Furthermore, as plasmonic slot waveguides allow for a high-energy
fraction in low-index material, they promise high sensitivity with respect
to absorption in a gaseous sensing medium, acting as a low-index medium in such
a sensor.
Traditionally, noble metals have been widely used as plasmonic materials due to
their chemical stability, large plasma frequency and high electrical
conductivity (Paulraj et al., 2020). However, they typically suffer from
high intrinsic losses and high costs, hampering practical applications (Chen
et al., 2017). As alternatives to noble metals, transparent conductive
oxides (TCOs) can be considered. They not only show a low loss in the
infrared range but their compatibility with standard microfabrication also
makes them particularly appealing for the simple integration of plasmonic
devices (Wang et al., 2017). Another feature of TCOs is that their optical
and electrical properties can be tuned by changing the doping concentration.
In addition, TCOs are often fabricated using thin-film technology and are
utilized in optoelectronic applications, such as electrode materials in
biosensors and other sensors (Sohn et al., 2011). Among TCOs, indium tin
oxide (ITO) has attracted particular attention from many scientists and researchers due
to its surface smoothness, mechanical stability, robustness in moist air
and simple fabrication (Dao et al., 2019). Therefore, it has been used in
many studies related to optical meta-surfaces (Shrestha et al., 2018),
localized plasmonic nanoparticles (Xi et al., 2018) and active tuneable
plasmonic devices (Liu et al., 2018). Moreover, ITO is an appropriate
material for sensing applications owing to unique features such as high
electrical conductivity, substrate adhesion, and electrochemical and
physical stability (Aydin et al., 2017). However, as ITO is a
non-stoichiometric compound, its optical properties crucially depend on the
fabrication processes such as growth and deposition procedures as well as on annealing
conditions (West et al., 2010). It has already been shown that sputtering
power and annealing processes can affect the optical properties of ITO in
the mid-infrared spectrum (Wang et al., 2017). ITO thin films can be
produced using technologies such as magnetron sputtering, electron beam
evaporation and chemical vapor deposition. Among these methods, magnetron
sputtering is widely used due to the better film quality, faster deposition
rate and the associated repeatability (Zhang et al., 2020).
Although ITO has been introduced as a desirable plasmonic material to
replace noble metals, to the author's knowledge, it has neither been studied
in detail theoretically nor experimentally for application in
waveguiding systems to date. We consider ITO for waveguiding systems because
it shows a high carrier density which makes it a suitable alternative plasmonic
material in the near- and mid-infrared region. In this paper, a plasmonic
slot waveguide based on ITO has been designed and numerically analyzed for
sensing applications. Our sensor platform is designed for a wavelength of
4.26 µm, which corresponds to the absorption peak of CO2, and
serves as an example of the application of infrared absorption sensing in
gases. We used an ITO-based slot waveguide on top of 2 µm silica
as a substrate, as illustrated in Fig. 1. In practice, this substrate can be
an oxidized silicon wafer. In the simulation, the region to be occupied by
the sensing medium in the final application is associated with a
refractive index of 1, as we are studying the properties of the guided mode.
The modal properties of the proposed structure have been investigated using
the finite element method (FEM) implemented by the COMSOL Multiphysics software (COMSOL, 2022). The
refractive index of SiO2 and ITO at 4.26 µm is
nSiO2=1.38+0.00043i and
nITO=1.9213+5.65i (Wang et al., 2017),
respectively.
Cross-sectional view of an ITO-based plasmonic slot waveguide. The
blue region, which consists of the slot region and upper cladding, is considered
as the sensing medium.
(a) The real part of the effective mode index (Neff), (b) the
propagation length (LSPP) and (c) the fraction of guided electromagnetic
energy in ITO versus slot height (h) for different slot widths (w).
The confinement factor (Γ) as a function of slot height
(h) for different slot widths (w).
The preliminary results of this study were presented at the Sensors and Measurement Science International (SMSI) conference in 2021
(Saeidi et al., 2021a). In the conference paper, our sensor platform had been
optimized based on the figures of merit (FOM) as a product of the evanescent
field ratio and propagation length. In the current work, to consider the
effect of group velocity, the confinement factor including both the
evanescent field ratio and group velocity has been evaluated. Therefore, our
sensor platform is optimized based on a FOM, which is defined as the confinement
factor divided by the imaginary part of the effective mode index. Our aim is to
optimize the waveguide geometries to reach the optimal propagation length and
confinement factor simultaneously.
Results and discussionPropagation length
One of the crucial parameters for sensing applications is propagation length
(LSPP). The LSPP of an SPP mode is defined as a distance over which the
intensity of the SPP mode reduces to 1/e of its original value. The calculation of
LSPP has been discussed in Spettel et al. (2021) and Stocker et al. (2021).
In any kind of plasmonic waveguide, the presence of metal or metal-like
material causes the plasmonic waveguide to be lossy. We note that, in the
present work, potential additional losses due to the surface roughness are
not considered.
The real part of the effective mode index (Neff=KSPP/K0,
where KSPP and K0 are the wave vectors of the
SPP mode and free-space light, respectively) of the fundamental SPP mode of a plasmonic slot waveguide as a
function of slot thickness (h) is depicted in Fig. 2a. Increasing h
results in decreasing Neff. Moreover, for a given h, Neff decreases with
increasing slot width (w), which is due to less field
confinement in the slot region (Heydari et al., 2020). Furthermore, the
LSPP for a given h, shown in Fig. 2b, increases with increasing w
because the fraction of guided electromagnetic energy in the ITO rails
decreases (see Fig. 2c), which reduces the intrinsic loss associated with
the ITO. Similarly, increasing h leads to an increase in LSPP for the
same reason.
(a) The figures of merit (FOM) as a function of slot height
(h) for different slot widths (w). (b) The x component of the electric field
distribution (Ex) of the SPP mode for optimum values of the structure.
Confinement factor
Light absorption in a waveguide that is placed in a sensing medium can be
described using a generalized Beer–Lambert law (Vlk et al., 2021):
I=I0e-αcΓL,
where I and I0 indicate the measured intensity and the initial
intensity at a particular CO2 concentration c, respectively; Γ
is the confinement factor; α is the absorption coefficient; and L is
the interaction path length.
Based on this law, the confinement factor (Γ) plays a major role in
the sensitivity of the sensor. The Γ, which includes both the evanescent
field ratio (EFR) and group velocity (Vg), can describe the efficiency
of light–matter interaction. The EFR describes the amount of electromagnetic
energy present in the evanescent field which interacts with the analyte
(e.g., gas in our case). When the sensor platform is placed in a gaseous
medium to be sensed, which essentially forms the cladding, the evanescent
field interacts with the gas via absorption along the waveguide. A high EFR
indicates that the sensor interacts more efficiently with the analyte, which
eventually improves the sensitivity of the device. The EFR can be calculated
as follows:
EFR=∫∫GasεgasE⇀(x,y)2dxdy∫∫Allε(x,y)E⇀(x,y)2dxdy,
where
E⇀ indicates the electric field vector, and ε is the
permittivity of each material. The integrals extend across the cross section
of the waveguide (orthogonally with respect to the propagation direction), which is
assumed to be in the xy plane here. The integral in the numerator extends across
the area filled by the analyte, whereas the integral in the denominator
covers the entire cross section. The confinement factor (Γ) is
defined as
Γ=ngncEFR,
where ng and nc are the group index
(ng=c/Vg) and refractive index of the cladding, respectively. The
group velocity Vg corresponds to the speed of energy that flows through
the cross section of the waveguide (Robinson et al., 2008). The mixture of
both field delocalization and dispersion, which are characterized by EFR and
Vg, respectively, can cause Γ to exceed unity, which means that
the absorption per unit length in the propagation direction is larger than that
achieved by a free-space beam. The confinement factor Γ of the
fundamental mode of the plasmonic slot waveguide as a function of h for
different w is given in Fig. 3. Increasing h leads to a reduction in Γ. Moreover, for a given h, increasing w results in less field being confined in the
gap region and, correspondingly, more field penetrating the silica substrate,
which results in a decrease in Γ.
There is a trade-off between LSPP=12K0Neffim and
Γ. To quantize their trade-off, we define a dimensionless FOM as
follows:
FOM=ΓNeffimag.
This FOM acts as an indicator of the waveguide sensitivity. The FOM of the
ITO-based plasmonic slot waveguide as a function of h is illustrated in
Fig. 4a. The optimal FOM is 3.2, which is associated with w=500 nm and h=1000 nm. The obtained FOM corresponds to roughly 49 % and 9 µm
for Γ and LSPP, respectively. In comparison to the plasmonic
slot waveguides that are reported in Saeidi et al. (2021b), the proposed
structure shows a lower FOM which is mainly due to its low propagation
length. However, the Γ provided by the structure is higher than that
reported in Saeidi et al. (2021b). Further, compared with the dielectric
waveguide structures that are designed for the same purpose (Ranacher et
al., 2018a, b), the present design features a lower FOM,
but it again represents a higher Γ. We note that the optimization of the
ITO-based plasmonic slot waveguide presented in this work is performed for a
wavelength of 4.26 µm, which is the absorption line of CO2. To
consider the performance of the proposed waveguide for other gases,
different refractive indices have to be used in the model and yield different
FOMs, although the general approach remains the same.
In plasmonic slot waveguides, the x component of the electric field distribution
(Ex) is a major component that indicates lateral confinement. Figure 4b
shows the Ex of the SPP mode for the optimized parameters of the
structure, clearly illustrating that the mode is confined in the slot region,
although a part of it penetrates the silica substrate.
Conclusions
We investigated the feasibility of ITO as an alternative plasmonic material
to replace noble metals for sensing applications in the mid-infrared region.
Considering a specific example, an ITO-based plasmonic slot waveguide was
designed and numerically analyzed for a wavelength of 4.26 µm, which
is the absorption band of CO2. The plasmonic slot waveguide was
optimized based on a figure of merit (FOM) composed of the product of the
propagation length and the confinement factor, which are two crucial
quantities in sensing applications. The achieved optimal FOM is 3.2, which is
associated with 9 µm and 49 % for the propagation length and
confinement factor, respectively. As the optical properties of ITO are
highly dependent on the fabrication process such as growth and deposition
process and also on annealing conditions, based on the adopted fabrication
methods, the optical properties of ITO, such as the complex refractive index, can
vary. Thus, the obtained FOM might change if another refractive index
associated with another fabrication method is used. Nevertheless, the optimization approach introduced in this work can always be used to find the
best geometrical parameters of any plasmonic slot waveguide.
As the proposed structure shows low propagation lengths, we finally have to
conclude that ITO appears not to be an appropriate candidate for plasmonic
waveguiding systems. However, based on the achieved high confinement factor,
it could be an attractive material for applications in which a cavity or
resonator would be used.
Data availability
Research data are available upon request from the authors.
Author contributions
PS, AT, RJ and BJ conceptualized the study.
PS, RJ and GP developed the methodology. PS was responsible for the software. PS and RJ carried out the validation process.
PS prepared and wrote the original draft of the paper, and
PS, BJ, RJ, GP, AT, GS, JS and TG reviewed and edited the paper. PS was responsible for the visualizations.
BJ and RJ supervised the study. All authors have read and agreed upon the published
version of the paper.
Competing interests
At least one of the (co-)authors is a member of the editorial board of Journal of Sensors and Sensor Systems.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Special issue statement
This article is part of the special issue “Sensors and Measurement Science International SMSI 2021”. It is a result of the Sensor and Measurement Science International, 3–6 May 2021.
Financial support
This work has been funded by the COMET-K2 “Center for
Symbiotic Mechatronics” of the Linz Center of Mechatronics (LCM) within
Austrian Smart Systems Integration Research Center (ASSIC) funded by the
Austrian federal government and the federal state of Upper Austria and by the
PICASSO project funded by the BMVIT in the framework of the
“Produktion der Zukunft” program (project no. 871417).
Review statement
This paper was edited by Daniel Platz and reviewed by two anonymous referees.
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