| Journal of Biomedical Systems and Engineering
Received: 07 August 2026; Revised: 11 September 2026; Accepted: 16 September 2026; Published Online: 21 September 2026.
J. Biomed. Syst. Eng., 2026, 1(1), 26802 | Volume 1 Issue 1 (September 2026) | DOI: https://doi.org/10.64189/bse.26802
© The Author(s) 2026
This article is licensed under Creative Commons Attribution NonCommercial 4.0 International (CC-BY-NC 4.0)
Enhanced Surface Plasmon Resonance Sensor
Employing Blue Phosphorus and Franckeite for Urine
Glucose Detection
Rajeev Kumar,
1
Lalit Garia,
2
Biswajit Brahma
3
and Akash Kumar Bhoi
4
1
Department of Electronics and Communication Engineering, Graphic Era (Deemed to be University), Dehradun, Uttarakhand,
248001, India
2
Department of Electronics and Communication Engineering, Bipin Tripathi Kumaon Institute of Technology, Dwarahat, Uttarakhand,
263653, India
3
McKesson Corporation, 32559 Lake Bridgeport St, Fremont, CA 94555, USA
4
Department of Electronics and Telecommunication Engineering, Symbiosis Institute of Technology, Pune Campus, Symbiosis
International (Deemed University), Pune, Maharashtra, 412115, India
*Email: rajeevkrc@gmail.com (Rajeev Kumar)
Abstract
A multilayer surface plasmon resonance (SPR) sensor for glucose detection in urine samples based on the CaF
2
prism/Cu/SiO
2
/Blue Phosphorus (BlueP)/Franckeite/Glucose configuration is presented in this work. The
suggested design enhances the interaction of the evanescent field with the glucose-containing sensing medium
(SM) by combining a Cu plasmonic layer with SiO
2
, BP, and Franckeite layers. To achieve a strong SPR response
and better sensing properties, the Cu and SiO
2
layer thicknesses are optimized. The sensor exhibits a maximum
angular sensitivity of 385.55°/RIU at the optimized structure with a remarkable Rmin value. For various layer
thickness combinations, the corresponding minimum reflectance (R
min
), full width at half maximum (FWHM),
detection accuracy (DA), and figure of merit (FoM) are methodically assessed. To detect glucose, the analyte's
refractive index (RI) is changed over the range under consideration, and the resulting resonance-angle shift is
examined. The optimized sensor shows a sensitivity of 381.11°/RIU at an analyte RI of 1.347, with R
min
=
0.11866, FWHM = 4.63°, DA = 0.215/°, and FoM = 82.31/RIU. Additionally, the PD is obtained of 208.16 (at RI
=1.335) and 210.16 (at RI=1.347). The findings show that the suggested multilayer architecture offers a viable
platform for sensitive, label-free, and real-time urine glucose concentration monitoring. Experimental
fabrication and validation using manufactured sensor prototypes and actual urine samples have not been
carried out because the current study is limited to numerical analysis. In order to verify the anticipated sensing
performance and evaluate the usefulness of the suggested sensor, experimental research will be taken into
consideration in subsequent work.
Keywords: Surface plasmon resonance; Sensor; Blue Phosphorus; Sensitivity; Detection accuracy.
1. Introduction
Glucose is a basic biomolecule that plays an essential role in maintaining the energy balance of the body and is
mainly regulated by insulin. Diabetes mellitus, which is primarily classified as Type I and Type II diabetes, can
be caused by abnormal glucose regulation. If the condition is not identified and treated in its early stages, it can
lead to serious complications like kidney failure, cardiovascular problems, liver dysfunction, blindness, and
other organ damage.
[1–3]
The importance of precise, quick, and frequent glucose monitoring is highlighted by
the rising incidence of diabetes globally. The development of non-invasive sensing techniques was prompted
by the invasiveness of conventional finger-prick techniques, which can result in pain, discomfort, and even
infection.
[4]
Urine is a particularly appealing alternative sampling medium because it is simple and painless to
collect and may offer valuable insights into glucose metabolism. However, there are a number of drawbacks to
traditional colorimetric and electrochemical techniques, including interference from other metabolites,
temperature and pH dependence, frequent calibration requirements, electrode instability, and limited long-
term reliability.
[5]
For accurate glucose monitoring, it is therefore very desirable to develop a sensitive, label-
free, and non-invasive sensing platform. SPR sensors present a viable solution in this regard since variations in
the SPR response can be used to track changes in the RI of the SM.
[6]
At the interface between a metal and a
dielectric medium, incident polarized light interacts with free electrons to cause SPR, an optical sensing
phenomenon. Light is coupled through a high-RI prism onto a thin metallic layer, usually made of gold (Au),
silver (Ag), or copper (Cu), at the proper incident angle in a conventional Kretschmann configuration.
[7]
There
is a noticeable drop in reflected intensity when the momentum of the incident photons and the surface plasmon
polaritons match at a certain resonance condition. SPR is a promising method for the real-time, label-free
detection of a variety of chemical and biological analytes because the resonance condition is extremely sensitive
to changes in the RI of the SM. The optical properties and thickness of the metallic layer, along with the
characteristics of the nearby dielectric or sensing layers, have a significant impact on the sensing performance
of an SPR sensor.
[8]
The RI close to the metal surface is changed by variations in the analyte concentration, which
results in a discernible change in the resonance angle or wavelength. Because of their high sensitivity, quick
response time, small size, and potential for use in chemical, environmental, and biomedical sensing, SPR sensors
have garnered a lot of interest.
Applying appropriate dielectric and two-dimensional (2D) material layers over the plasmonic metal can greatly
enhance the performance of an SPR sensor because these layers have a significant impact on analyte interaction,
electromagnetic-field confinement, SPP propagation, and overall resonance properties.
[9–11]
Because of its
chemical stability, appropriate RI, optical transparency, and compatibility with multilayer SPR configurations,
silicon dioxide (SiO
2
) is widely regarded as a helpful intermediate or protective layer among various dielectric
materials. The SiO
2
layer's thickness and presence can change the metal–dielectric interface's effective optical
environment, which in turn can change the resonance angle, resonance wavelength, R
min
, and resonance
linewidth. Effective coupling of the evanescent field with the analyte can be maintained while a controlled
separation between the metallic layer and the functional sensing layers is provided by an appropriately
optimized SiO
2
layer.
[12]
An appealing method for improving the interaction of the SPR-generated
electromagnetic field with the sensing medium, in addition to SiO
2
, is the integration of 2D materials like Blue
Phosphorus (BlueP).
[13,14]
BlueP's layered structure, large exposed surface area, and thickness-dependent
optical and electronic properties can boost the interaction between the evanescent field and target molecules
and offer more active sites for analyte adsorption.
[15]
The presence of an appropriately optimized BlueP layer
can increase the effective sensing region and alter the local RI environment, which can lead to an observable
shift in the SPR response because a significant portion of the SPR field is confined near the metal surface.
Additionally, another material that shows promise for building high-performance plasmonic sensing platforms
is Franckeite, a naturally occurring layered van der Waals material made of alternating sublayers.
[16]
Its layered
design and anisotropic optical properties can offer more control over the distribution of electromagnetic fields
and light-matter interaction within the multilayer structure. Therefore, the combination of Franckeite and
BlueP can produce a synergistic functional interface where each 2D material's unique optical and surface
properties enhance analyte interaction and improve SPR response modulation.
The investigation of alternative two-dimensional (2D) materials is still crucial for increasing the flexibility of
plasmonic sensor design, even though graphene and MoS
2
have been thoroughly studied for SPR sensing due to
their advantageous optical and electronic properties. BlueP is a promising surface-modifying material for
improving the interaction between the evanescent field and the sensing medium because of its distinct layered
structure and advantageous optical response. Franckeite, a naturally occurring layered van der Waals material,
offers complementary optical properties that can further alter the multilayer structure's electromagnetic
response. In order to take advantage of their complementary contributions to light-matter interaction, BlueP
and Franckeite are combined in this work instead of depending solely on one traditional 2D material. In order
to achieve improved resonance-angle sensitivity and good sensing performance, the suggested
Cu/SiO
2
/BlueP/Franckeite configuration thus offers an alternative material platform to frequently studied
graphene- and MoS
2
-based SPR sensors. The sensitivity, FWHM, DA, and FoM derived from the numerical
analysis are used to further assess the choice quantitatively.
Moreover, the combined SiO
2
/BlueP/Franckeite arrangement can offer greater flexibility in optimizing the
electric-field distribution across the metal–dielectric–analyte region and in engineering the effective refractive-
index profile of the sensing structure. Because overly thick functional layers can decrease the effective
interaction of the evanescent field with the analyte and broaden or weaken the resonance, while properly
chosen thicknesses can improve field confinement and preserve a sharp resonance profile, the thickness, order,
and optical properties of these layers must be carefully optimized. As a result, adding SiO₂, BlueP, and
Franckeite as complementary dielectric and 2D functional layers is a viable method for modifying the optical
response of SPR sensors and obtaining better resonance characteristics, increased refractive-index sensitivity,
and improved overall sensing performance for chemical and biological detection applications. In order to
improve the interaction of the evanescent field with the glucose-containing SM and enable sensitive detection
over the RI range of 1.33–1.347, the suggested structure makes use of the synergistic optical properties of the
constituent layers.
2. Proposed structure, refractive index, modeling and performance parameters
In the Kretschmann configuration, the optical coupling medium is the CaF₂ prism. At the CaF
2
/Cu interface,
incident p-polarized light is internally reflected after entering the CaF
2
prism as shown in Fig.1. CaF
2
is chosen
because the surface plasmon mode supported by the metal layer and the incident light have appropriate
momentum matching thanks to its refractive index. The in-plane component of the incident wavevector can be
adjusted until the SPR condition is met by changing the incident angle θ. The principal plasmonic metal layer
is the Cu layer. Energy is transferred from the incident optical wave to collective oscillations of free electrons
in Cu when the momentum of the incident p-polarized light matches the surface plasmon wavevector at the
metal/dielectric interface. The SPR resonance dip, a noticeable minimum in the reflected intensity, is the result
of this. Thus, a crucial optimization parameter is the Cu thickness. Strong plasmon excitation and a sharp
resonance can be achieved in the studied structure by optimizing a Cu thickness in the roughly 30–50 nm range.
The SiO
2
layer is positioned as a dielectric spacer between Cu and BlueP. It adjusts the metal interface's effective
optical environment and regulates the evanescent electric field's penetration and distribution in the direction
of the sensing area. The linewidth, sensitivity, minimum reflectance, and resonance angle are all significantly
impacted by its thickness. The best combination with the Cu thickness can be found by investigating SiO
2
thicknesses of roughly 5–15 nm based on the optimization previously demonstrated. An appropriately chosen
SiO
2
thickness can enhance the plasmonic field's coupling with the two-dimensional materials on top. Above
SiO
2
is a 2D, atomically thin layer called BlueP (blue phosphorus). BlueP increases the interaction of the
evanescent plasmonic field with the analyte and alters the optical response of the multilayer structure due to
its large interfacial surface area and strong light–matter interaction. The electromagnetic field produced at the
Cu/SiO
2
interface can interact with the 2D-material region and eventually the glucose layer because of its
location directly below Franckeite. Another 2D substance that was deposited above BlueP is the Franckeite
layer. It also changes the sensing interface's optical dispersion and effective RI. Cu/SiO
2
/BlueP/Franckeite
produces a multilayer electromagnetic environment where the analyte can be reached by the evanescent field.
When compared to a basic Cu-based SPR structure, the presence of these 2D layers can increase the refractive-
index sensitivity because the sensing response is highly dependent on the electric-field interaction near the
analyte interface. The sensing/analyte medium is the glucose layer that is at the top. The corresponding RI
values in the numerical model are used to represent the glucose concentration. About n
s
=1.335 for the lower
concentration condition and n
s
=1.347 for the higher concentration condition, which correspond to the
examined glucose range, are the two conditions taken into consideration. Its effective RI varies in response to
changes in glucose concentration. The Franckeite layer's dielectric environment is altered as a result, which
alters the surface-plasmon resonance condition.
1.8nm
0.123nm
0-15nm
25-60nm
Glucose (Analyte)
0-10g/dl
1.335-1.347
Incident light
Reflected light
CaF
2
prism
Franckiete
(2D material)
BlueP
(2D material)
SiO
2
(Dielectric layer)
Cu
(Metal layer)
(Coupling prism)
Fig. 1: Proposed Structure
2.2 Refractive index of constituent layers
The RI of each layer has a major impact on the recommended SPR excitation condition and sensing performance.
The ability of a material to interact with incident electromagnetic waves and slow their propagation is
represented by the RI. An SPR sensor reaches resonance when the wave vectors of the incident p-polarized light
and the SP wave vector at the metal–dielectric interface coincide. The SPR resonance angle shifts as a result of
the momentum matching condition being altered by any change in the analyte medium's RI. CaF
2
is used as the
coupling prism in the proposed structure, providing efficient light coupling for plasmon excitation, with an RI
of 1.4329 at a wavelength of 633 nm. The plasmonics layer of Cu (thickness = 25 to 60 nm) is usually described
using RIs of 0.0369 + 4.5393*I because of its metallic nature and optical losses. The third layer is used as a SiO
2
layer (thickness 0-15nm) and has an RI of 1.4570. The BlueP layer has a complex RI of 2.1666 + 0.1005i with a
thickness of 0.123 nm due to strong light-matter interaction, which improves electromagnetic field confinement
at the sensing interface.
[14]
The next Franckeite layer is used as a biorecognition element layer for the detection
of glucose in a urine sample. The RI of glucose with concentration is given in Table 1. The RI of urine varies with
the concentration of dissolved substances, particularly glucose, making it a suitable parameter for SPR-based
glucose sensing. Because there are more glucose molecules in the sensing medium when the glucose
concentration rises, the RI of the urine sample typically rises as well. Therefore, corresponding RI values within
the chosen physiological range can be used to represent different glucose concentrations for SPR analysis. The
resonance condition is altered by the RI variation, which also results in a discernible shift in the SPR curve.
Thus, it is possible to identify and measure the amount of glucose in urine samples by keeping an eye on the
resonance-angle or resonance-wavelength shift. Using SPR sensors, this RI-based method offers a
straightforward, label-free way to detect glucose.
Table 1: Refractive index of Glucose concentration (g/dl)
[17]
Urine glucose concentration
Refractive index
0–15 mg/dl (normal range)
1.335
0.625 g/dl
1.336
1.25 g/dl
1.337
2.5 g/dl
1.338
5 g/dl
1.341
10 g/dl
1.347
2.3 Mathematical modeling used in SPR sensor
The optical response of the suggested SPR structure is examined using the transfer matrix method (TMM) under
the Kretschmann configuration. Surface plasmon polaritons (SPPs) at the metal–dielectric interface is excited
in this configuration by coupling p-polarized incident light through the CaF
2
prism. The thicknesses, refractive
indices, and dielectric characteristics of each layer have a significant impact on the occurrence of SPR. The TMM
makes it possible to calculate the multilayer structure's overall optical response by relating the tangential
components of the electric and magnetic fields across each interface. The reflection coefficient and associated
reflectivity are obtained by multiplying the characteristic matrices of all constituent layers using the Fresnel
equations. The expression for reflectivity (R) is as follows (Eq. 1).
[18]
(1)
Where,
(2)
where rp represents the reflection coefficient. The TMM used to simulate light propagation and determine the
reflectivity of a multilayer SPR structure, as indicated by Eq. 2, is described by the provided formulas. For p-
polarized light, the reflection coefficient is r
p
. The optical response of every intermediate layer between the
prism and SM is represented by the characteristic matrix elements m
11
, m
12
, m
21
, and m
22
, respectively.
Where
is defined as in Eq. 3:
(3)
The characteristic matrix (m
k
) of the SPR structure is obtained by multiplying the TMM of each intermediate
layer. The symbols m
11
, m
12
, m
21
, and m
22
stand for the components of the overall transfer matrix. The
characteristic matrices of each layer in an N-layer SPR configuration are multiplied to form the total matrix. Eq.
4 illustrates how each layer's phase constant (β
k
) and optical admittance (q
k
) are determined by its RI,
thickness, wavelength, and incident angle. This matrix formulation enables the calculation of the reflectivity
and reflection coefficient of the proposed sensor by taking into account the contributions of each layer.
(4)
(5)
2.4 Performance parameters of the proposed sensor
The performance of the proposed SPR sensor is evaluated using a number of important metrics, including
sensitivity (S), FWHM, DA, and FoM. These parameters determine the sensor's ability to detect minute changes
in the RI caused by different cancer cells. Changes in the cancerous cell RI are what cause the shift in resonance
angle. Sensitivity is the most important consideration when evaluating the performance of SPR sensors. Eq. 6
illustrates how the resonance angle (Δθ
res
) varies with a unit change in the analyte medium's RI (Δn
s
), which is
known as sensitivity.
[19]
(6)
The sensor's ability to precisely determine the resonance angle is indicated by DA, which represents the
sharpness of the SPR reflectance curve. Eq. 7 defines it.
(1/º) (7)
Higher DA is obtained with a narrow resonance dip. FWHM is the SPR resonance curve's angular width
calculated at half of the R
min
value. A smaller FWHM indicates improved sensing resolution, less energy loss,
and a sharper resonance response. The Eq. 8 uses the FoM, which combines resonance sharpness and
sensitivity, to assess the overall sensing capability.
(8)
3. Results and discussion
The optimization of the proposed SPR sensor is illustrated in Fig. 2 by examining the impact of Cu and SiO
2
thicknesses on the sensing response. Fig. 2(a) shows the angular sensitivity as a function of the optimized Cu
thickness for the SiO
2
thicknesses (0, 1, 5, 10, 12, and 15 nm), showing that the SiO
2
layer has a significant effect
on the optimum Cu thickness and sensitivity. As Cu thickness reaches its optimal value, the sensitivity increases,
followed by a decrease or saturation. This indicates that an appropriate Cu thickness is crucial for effective
excitation of the surface plasmon mode. The Cu/SiO
2
combination is optimized to achieve a maximum
sensitivity of approximately 380–400 °/RIU. Fig. 2(a) shows that the ideal Cu thickness and maximum
sensitivity are both significantly influenced by the SiO
2
thickness. In the absence of SiO
2
, the sensitivity rises
steadily with Cu thickness and approaches the upper Cu-thickness range at about 191.08–341.57 °/RIU. The
sensitivity increases significantly with 1 nm SiO
2
, approaching 191.98–352.27 °/RIU. The sensitivity increases
significantly with 5 nm SiO
2
, ranging from 196.33– 397.44 °/RIU. The sensitivity variation for 10 nm SiO
2
is
203.73– 387.127°/RIU (from 44nm) and then decreases to 313.93 (60nm) at a Cu thickness of 25–60 nm. At
SiO
2
= 12nm, the sensitivity variation is 207.45– 381.11 °/RIU (from 41nm) and then decreases to 229.23°/RIU
(60nm). And at SiO
2
= 15nm, the sensitivity varies from 214.19– 373.37 °/RIU (from 37nm) and then decreases
to 81.88 °/RIU (60nm). As a result, the SiO
2
layer alters the electromagnetic field distribution at the sensing
interface and adds an extra dielectric/plasmonic coupling region. The two investigated glucose conditions are
represented by the minimum reflectance (R
min
) for glucose RIs of 1.335 (0-0.015g/dl) and 1.347 (10g/dl),
respectively, in Figs. 2(b) and 2(c). The SPR resonance condition is represented by the deep minimum in each
curve in Fig. 2(b). Stronger coupling between the incident p-polarized light and the surface plasmon mode is
indicated by a lower R
min
. The R
min
value for SiO
2
= 0 and 1 nm occurs at roughly 42–47nm Cu thickness. The
minimum gradually moves toward lower Cu thickness (45 nm), as the SiO
2
thickness increases to 5, 10, 12, and
15 nm. This shift demonstrates that the dielectric SiO
2
layer alters the Cu layer's effective optical environment,
which in turn alters the SPR coupling condition. Stronger plasmon excitation and a sharper resonance are
indicated by curves with deeper minima, which are ideal for precise glucose detection. In Fig. 2 (c), the increased
glucose RI alters the optical boundary condition at the sensing interface, which significantly modifies the R
min
value when compared to Fig. 2(b). Depending on the SiO₂ thickness, the R
min
value occurs between 36 and 40
nm Cu thickness. The R
min
value is near 37–38 nm for SiO
2
= 0 and 1 nm, while the resonance position is
systematically altered when 5–15 nm SiO
2
is added. Specifically, the reflectance response is significantly shifted
and broadened by the 12-15 nm SiO
2
layers. The suggested glucose sensor is based on this behavior, which
shows that the glucose-induced RI variation can be converted into a quantifiable SPR response. As Cu and SiO
2
thicknesses increase, the distinct SPR dips shift as well. This is due to the alteration of the effective optical
environment and electromagnetic-field distribution at the Cu/BlueP/Franckeite/analyte interface caused by
the dielectric SiO
2
layer. The alterations in resonance condition between n
s
=1.335 and n
s
=1.347 confirm that
the proposed multilayer structure is responsive to fluctuations in the RI caused by glucose. CaF
2
functions as
the optical coupling prism, Cu plays a role in the surface plasmon excitation, SiO
2
acts as a dielectric spacer and
adjusts the plasmonic coupling, while BlueP and Franckeite enhance the light-matter interaction at the sensing
interface. Therefore, it is crucial to increase the thicknesses of Cu and SiO
2
to achieve a robust, well-defined SPR
response and improve the glucose-sensing sensitivity of the proposed structure.
Fig. 2: (a)Sensitivity vs optimized Cu thickness, Min. reflectance: (b) n
s
= 1.335 (c) n
s
= 1.347
The angular reflectance curve of the suggested SPR sensor for various combinations of Cu and SiO
2
thicknesses
is shown in Fig. 3. When the phase-matching condition between the incident light and surface plasmon
polaritons (SPPs) is met, the R
min
value seen in the curves corresponds to the excitation of SPW at the metal–
dielectric interface. The incident optical energy is effectively transferred from the CaF
2
prism to the plasmon
mode at the resonance angle, causing a dramatic drop in reflected intensity. This resonance dip's location is
extremely sensitive to changes in the glucose analyte's RI, which serves as the foundation for the sensing
mechanism. In Fig. 3(a), the SiO
2
layer thickness varies while the Cu thickness is kept at 45 nm. The resonance
dip gradually moves toward higher incident angles as the SiO
2
thickness increases, indicating a change in the
multilayer structure's effective refractive index. The SiO
2
layer controls the evanescent field's penetration from
the Cu surface toward the BlueP/Franckeite sensing region by acting as a dielectric spacer. A deeper resonance
dip and increased sensitivity result from improved plasmon-analyte interaction and field confinement brought
about by an appropriate SiO
2
thickness. Excessive dielectric thickness, however, can widen the resonance curve
and lower coupling efficiency. The thicknesses of Cu and SiO
2
are changed simultaneously in Fig. 3(b). The Cu
layer is a key factor in plasmon excitation strength. Strong plasmon resonance may not be supported by an
excessively thin Cu layer, while excessive absorption of incident light occurs before it reaches the sensing
interface when the Cu thickness is too large. To achieve effective plasmon excitation and maximum optical
energy transfer to the surface plasmon mode, an ideal Cu thickness is therefore necessary. The observed
variations in dip depth and resonance angle show that SPR performance is highly dependent on metal thickness.
By raising the local electromagnetic field intensity at the sensing interface, the addition of BlueP and Franckeite
layers improves the sensor's performance even more. These 2D materials allow for better adsorption of glucose
molecules and stronger perturbation of the plasmon field due to their high carrier mobility, large surface area,
and strong light-matter interaction. As a result, even a slight variation in the glucose RI results in a discernible
shift in the resonance angle. Better DA, a lower FWHM, and a higher FoM are all indicated by the deeper and
sharper reflectance curves. Therefore, Fig. 3 shows that the suggested glucose SPR sensor's plasmonic coupling
efficiency, field enhancement, and overall sensing performance can be greatly enhanced by carefully optimizing
the Cu and SiO
2
layers in combination with BlueP and Franckeite. The SPR performance for various Cu and SiO
2
thickness combinations is summarized in Table 1. The sensitivity improves from 302.33 to 385.55°/RIU as the
SiO
2
thickness increases from 0 to 10 nm, suggesting a stronger interaction between the glucose analyte and
the evanescent field. Cu = 43 nm and SiO
2
= 10 nm yield the highest sensitivity of 385.55°/RIU. Nevertheless,
the sensitivity decreases to 381.11 and 373.37°/RIU, respectively, when the SiO
2
thickness is increased to 12
and 15 nm. As SiO
2
thickness increases, the FWHM typically rises while the DA falls. For Cu = 45 nm and SiO
2
=
5 nm, the FoM reaches a maximum value of 103.67 /RIU, indicating the best overall balance between sensitivity
and resonance sharpness. Accordingly, 43 nm Cu/10 nm SiO₂ offers the highest angular sensitivity, while 45
nm Cu/5 nm SiO
2
can be regarded as the ideal combination based on FoM.
Fig. 3: Reflectance curve at various Cu & SiO
2
thicknesses (a) Cu (45nm) & SiO
2
(0nm, 5nm & 10nm); (b) Cu (43nm,
40nm & 37nm) & SiO
2
(10nm, 5nm & 10nm)
The SPR response of the proposed sensor is influenced by Cu thickness and glucose concentration, as illustrated
in Fig. 4. Angular sensitivity with optimized Cu thickness varies for different glucose refractive indices, ranging
from 1.335 to 1.347, as shown in Fig. 4(a). Initially, the sensitivity increases with the thickness of Cu, reaching
a peak value of approximately 385°/RIU at a depth of 42 to 43 nm Cu thickness. Subsequently, it gradually
diminishes. The dependence of plasmonic coupling and electromagnetic-field penetration on the Cu thickness
is the reason for this behavior; an excessively thick layer increases optical absorption and reduces coupling
efficiency, whereas a very thin layer provides insufficient plasmon excitation. The corresponding variation of
minimum reflectance (R
min
) is shown in Fig. 4(b), where a prominent minimum is seen close to the optimized
Cu thickness, indicating effective energy transfer from the incident light to the surface plasmon mode. The
reflectance curves for various glucose refractive indices are displayed in Fig. 4(c), where clear resonance dips
are seen, and their locations systematically change as the glucose refractive index changes. Changes in glucose
concentration alter the sensing medium's refractive index, which alters the SPR phase-matching condition and
causes this resonance-angle shift. Strong plasmonic coupling is indicated by the deep and sharp resonance dips
found close to the optimized Cu thickness, which also make it possible to detect minute changes in RI. Overall,
the findings show that the structure is appropriate for glucose sensing because an ideal Cu thickness of roughly
42–43 nm offers a good balance between high sensitivity, low Rmin, and a sharp SPR resonance. The SPR
performance of the suggested sensor for urine glucose detection at various glucose concentrations and analyte
refractive indices is shown in Table 2. When the refractive index shifts from 1.335 to 1.338 for the 42 nm Cu
and 12 nm SiO
2
configuration, the resonance-angle shift increases, and Δθ
res
increases from 0.315° to 0.987°. As
a result, the sensitivity rises from 315.69 to 329.25°/RIU, indicating that the sensor is capable of accurately
identifying minute variations in the RI brought on by glucose. Strong coupling between the incident light and
the surface plasmon mode is indicated by the Rmin values, which stay extremely low and reach 2.7×10
−6
a.u. at
n
s
=1.337. While the DA drops from 0.233 to 0.219 /°, the FWHM slightly increases from 4.29° to 4.55°. Good
sensing performance is indicated by the FoM staying around 72 /RIU. With R
min
= 0.118 (a.u.), FWHM = 4.63°,
DA = 0.215 /°, and FoM = 82.31 /RIU, the sensitivity for the 40 nm Cu and 12 nm SiO
2
configuration is reported
as 381.11°/RIU. Table 3 thus shows that the sensor exhibits a quantifiable and systematic response to changes
in glucose-induced RI, and that the optimized Cu/SiO
2
thickness and corresponding resonance response offer
good sensitivity and FoM for urine glucose detection.
Table 2: Measured performance parameters for Urine Glucose Detection
Conc. of
glucose
(g/dl)
RI of
analyte
Cu
Thick.
(nm)
SiO
2
Thick.
(nm)
Δθ
res
(°)
S
(°/RIU)
R
min.
(a.u.)
FWHM
(°)
DA
(1/°)
FoM
(/RIU)
0-15
1.335
42
12
-
-
-
4.29
0.233
-
0.625
1.336
0.315
315.69
4.3×10
-4
4.37
0.228
72.24
1.25
1.337
0.644
322
2.7×10
-6
4.45
0.224
72.36
2.5
1.338
0.987
329.25
4×10
-4
4.55
0.219
72.36
5.25
1.341
2.125
354.16
4.3×10
-4
4.79
0.208
65.90
0-15
1.335
40
4.5733
381.11
2×10
-2
4.46
0.224
85.45
10
1.347
0.11866
4.63
0.215
82.31
Table 3: Measured performance parameters at remarkable R
min
value
Cu
thick.
(nm)
SiO
2
thick.
(nm)
S
(°/RIU)
At n
s
=1.335
At n
s
=1.347
R
min.
(a.u.)
FWHM
(°)
DA
(1/°)
FoM
(/RIU)
R
min.
(a.u.)
FWHM
(°)
DA
(1/°)
FoM
(/RIU)
45
0
302.33
1.5×10
-4
2.99
0.334
101.11
1.9×10
-2
3.78
0.264
79.98
45
1
309.68
2.5×10
-5
3.06
0.326
101.20
2.5×10
-2
3.86
0.259
80.22
45
5
347.30
8.8×10
-4
3.35
0.298
103.67
7.7×10
-2
4.25
0.235
81.71
43
10
385.55
2×10
-4
4.05
0.246
95.19
0.188
4.21
0.237
91.58
40
12
381.11
2.1×10
-2
4.46
0.224
85.45
0.118
4.63
0.215
82.31
37
15
373.37
7.1×10
-4
4.84
0.206
77.14
9×10
-2
4.81
0.207
77.62
Fig. 4: (a) Sensitivity; (b) Rmin; (c) reflectance curve at various glucose concentrations
3.1 Electric field analysis
The electromagnetic response derived from the analytical/TMM model is validated through numerical
investigation of the suggested SPR sensor using COMSOL Multiphysics, which is based on the finite element
method (FEM). The sensor geometry is built in accordance with the multilayer configuration, and the electric-
field distribution and reflectance characteristics are calculated using Electromagnetic Waves, Frequency
Domain (ewfd) physics. The prism boundary introduces the incident optical wave, and the proper
port/scattering boundary conditions are applied to ensure that the reflected field is properly excited and
detected. Perfectly Matched Layers (PMLs) are used to terminate the computational domain's outer boundaries
in order to accurately represent an open optical environment by absorbing outgoing electromagnetic waves
and suppressing artificial reflections from the computational boundaries. In COMSOL Multiphysics, a mesh-
convergence analysis was carried out to ensure the accuracy and repeatability of the FEM results. The mesh
was gradually improved, and following each improvement, the electric-field distribution and computed
resonance characteristics were tracked. When additional refinement produced a negligible variation in the
computed resonance response (less than 1%), mesh convergence was deemed accomplished. For all of the FEM
simulations shown in this work, the converged mesh was subsequently used. This process reduces numerical
discretization errors at a manageable computational cost. At the Cu/SiO₂/BlueP/Franckeite/analyte interfaces,
where the electric field varies quickly due to the excitation of surface plasmon polaritons, a fine and non-
uniform mesh is used with strong mesh refinement. In areas where the electromagnetic field varies slowly,
relatively coarser elements can be utilized to lower computational costs without sacrificing accuracy. To
conduct a mesh-convergence analysis, the mesh should undergo a gradual refinement until the resonance angle
and minimum reflectance exhibit minimal variation. The COMSOL results are then used to determine the
electric-field intensity, resonance condition, and reflectance response, which can be used to examine the
influence of the glucose refractive index and the enhancement of the evanescent field near the sensing interface.
The metal-dielectric sensing interface exhibits a robust localized electric field, indicating efficient excitation of
the SPR mode. Conversely, the systematic alteration in resonance condition with analyte RI demonstrates the
feasibility of the proposed sensor for glucose detection. The penetration depth (PD) of the evanescent
electromagnetic field in an SPR sensor is frequently calculated using the 1/e factor, or roughly 37%. The electric
field intensity drops exponentially as it moves from the sensing surface into the analyte when surface plasmon
resonance is excited at the metal–dielectric interface. The distance from the metal–analyte interface at which
the electric field intensity drops to 1/e, or roughly 37% of its maximum value at the interface, is known as the
PD. Mathematically, the intensity distribution can be expressed as I(z)=I
0
e
−z/PD
, where I
0
is the maximum field
intensity at the sensing interface and z is the distance from the interface. At z=PD, I(z)=I
0
/e ≈ 0.368I
0
.
Consequently, the penetration depth of the evanescent field in COMSOL Multiphysics is calculated using the
37% intensity level as a reference.
[20]
A greater penetration depth means that the electromagnetic field
penetrates the glucose/analyte medium more deeply, increasing the volume of interaction between the analyte
molecules and the evanescent field. However, because the field becomes less localized at the sensing interface,
an overly deep penetration depth is not always ideal. Therefore, the 1/e criterion offers a consistent and
physically significant way to measure the effective sensing depth and assess the performance of the suggested
SPR sensor. The electric-field-normalized distribution and SPP mode of the suggested SPR sensor, as
determined by COMSOL Multiphysics, is shown in Fig. 5. The normalized electric-field intensity is plotted
against the distance from the CaF
2
prism to the SM in Fig. 5(a). The excitation of the SPR mode is confirmed by
a strong enhancement of the electric field near the Cu/SiO
2
/BlueP/Franckeite sensing interface. The SPP field's
evanescent nature is demonstrated by the field's gradual decrease with increasing distance from the metal
interface. The penetration depth of the evanescent field into the sensing medium is determined using the
horizontal reference associated with the 1/e (≈37%) criterion; the marked PDs are roughly 205–210 nm for
the analyte conditions under consideration. An enlarged view of the field enhancement surrounding the
multilayer sensing region is shown in the inset of Fig. 5(a), which amply illustrates the strong localization of the
electromagnetic field close to the Cu and nearby 2D-material layers. Effective confinement of the plasmonic
field is confirmed by the 2D electric-field distribution shown in Fig. 5(b), where the field is strongly
concentrated at the metal–dielectric/sensing interface and gradually decays away from the interface. The
corresponding 3D SPP-mode distribution is displayed in Fig. 5(c), which offers a more accurate depiction of the
electric field's strong localization and spatial variation surrounding the sensing region. Comparably, another
2D field-distribution view of the multilayer structure is shown in Fig. 5(d). Its corresponding 3D representation
is shown in Fig. 5(e). These distributions' alternating the high- and low-field regions show the electromagnetic-
field variation connected to the excited plasmon mode. Overall, effective SPP excitation is confirmed by the
strong electric-field enhancement at the Cu/SiO₂/BlueP/Franckeite/glucose interface, which also shows that
the evanescent field interacts with the glucose sensing medium sufficiently to achieve high refractive-index
sensitivity.
Fig. 5: (a) Electric field normalized (Norm.); electric field distribution (b) 2D (c) 3D; SPP mode (d) 2D (e)3D
Using proven thin-film deposition and 2D material integration techniques, the suggested SPR sensor is
fabrication feasible process as shown in Fig. 6. The CaF
2
prism surface can be gently cleaned with acetone and
isopropyl alcohol (IPA) to get rid of organic residues and contaminants before fabrication.
[7]
After a quick rinse
with deionized water, it is dried with either clean air or filtered nitrogen. The CaF
2
surface may be harmed by
prolonged exposure to harsh chemicals and abrasive wiping. The Cu, SiO
2
, BlueP, and Franckeite layers can then
be sequentially deposited using the cleaned prism. An optimized Cu layer of about 30–50 nm can be deposited
using DC magnetron sputtering or thermal/electron-beam evaporation after a polished CaF
2
prism has been
cleaned and used as the optical coupling substrate.
[21]
Sputtering, evaporation, or other controlled thin-layer
techniques can then be used to deposit a thin SiO
2
dielectric spacer of about 5–15 nm over the Cu layer.
[22]
After
mechanical exfoliation and controlled dry or wet transfer, atomically thin layers of BlueP (0.123 nm) and
Franckeite (1.8 nm) can be integrated onto the SiO
2
surface.
[23,24]
Because BlueP might be susceptible to
environmental deterioration, its structural and optical qualities can be maintained through careful processing
and appropriate encapsulation. After that, the created multilayer can be combined with a microfluidic chamber
to add glucose solutions at precise concentrations. Changes in glucose concentration alter the analyte layer's
effective RI, resulting in a discernible change in the SPR resonance angle. Deviations from the optimal numerical
model may be caused by practical factors like surface roughness, transfer-induced defects, layer-thickness
variations, interface contamination, and environmental stability, but these are fabrication and optimization
considerations rather than fundamental limitations. Therefore, the suggested multilayer architecture offers a
feasible route for glucose RI sensing and fabrication feasibility.
or Thermal
Sputtering
evaporation
RF sputtering
or E-beam
evaporation
CVD growth
Dry
transfer
Silanization
Microfluidic flow
cell
CaF
2
prism
Cu layer
deposition
deposition
SiO
2
layer
BlueP layer
transfer
Franckeite layer
transfer
Surface
functionalizationGlucose (analyte)
Fig. 6: Fabrication feasibility
Because the numerical model for the proposed SPR sensor assumes ideal and time-invariant material
properties, stability and repeatability are crucial practical considerations. Maintaining a steady SPR response
over a predetermined amount of time when the sensor is exposed to the analyte is referred to as stability. While
the BlueP/Franckeite layers alter the optical response and sensing interface, the SiO
2
layer offers the underlying
Cu layer a helpful protective and dielectric barrier. However, Cu oxidation, environmental degradation of BlueP,
moisture or contamination at the 2D-material interfaces, temperature fluctuations, and changes in the optical
constants of the ultrathin layers could all have an impact on the long-term stability of the suggested structure.
To reduce degradation, BlueP may specifically need appropriate encapsulation or regulated environmental
conditions. Repeatability is the process of measuring the same glucose concentration repeatedly under identical
experimental conditions, resulting in nearly identical resonance angles and sensitivity values. For good
repeatability, the Cu and SiO
2
thicknesses must be uniform, the transfer and coverage of BlueP and Franckeite
must be consistent, the concentration of the analytes must be stable, the temperature must be controlled, and
microfluidic delivery must be reproducible. However, because the current numerical analysis does not include
material aging, oxidation, fabrication imperfections, surface roughness, temperature effects, or repeated
measurement cycles, it cannot independently establish experimental repeatability or long-term stability. Thus,
to quantitatively establish stability, repeatability, and sensor-to-sensor reproducibility, experimental
measurements involving multiple independently fabricated sensors and repeated glucose exposure–washing
cycles are required, while the predicted performance should be regarded as an ideal numerical assessment.
When discussing the practical applicability of the proposed sensor, it is important to acknowledge these
limitations.
For the suggested SPR sensor to be implemented practically, the fabrication tolerance of the ultrathin BlueP
and Franckeite layers is crucial. Small variations from the ideal layer thickness can alter the multilayer
structure's effective optical response, which in turn affects the resonance angle, R
min
value, FWHM, and sensing
performance. Such variations may result from surface roughness, layer uniformity, thickness-control accuracy,
and the deposition process in practical fabrication. Therefore, to replicate the optimal numerical performance,
the ultrathin material thickness must be precisely controlled. While suitable deposition and thickness-
characterization methods would be needed for experimental implementation, the thickness values taken into
consideration in this study should be viewed as nominal optimized parameters. Future work will take into
account a systematic tolerance analysis, experimental validation and testing with real urine samples to evaluate
the sensor. The sensitivity and FoM of the suggested sensor are contrasted with those of previously published
SPR sensors in Table 4. The suggested structure shows enhanced RI detection capability with a much higher
sensitivity of 381.11°/RIU. Despite this, its FoM (82.31/RIU) is marginally lower than Ref. 27, it provides a good
overall sensing performance and is still competitive with the reported structures.
Table 4: Comparison with proposed and existing work
References
Structure
Wavelength(nm)
S (°/RIU)
FoM(/RIU)
[17]
Prism/Ag/MXene/Ag/ZnO/Graphene
633
184
27.23
[25]
BK7/Au/MoS2/h-BN/Graphene
633
194.12
16.04
[26]
BK7/Au/PtSe
2
/Graphene
633
200
-
[27]
BK7/MgO/Ag/BP
633
234
38.18
[28]
Prism/Ag/Graphene/WS
2
633
288.86
88.89
Proposed work
CaF
2
/Cu/SiO
2
/BlueP/Franckeite
633
381.11
82.31
4. Conclusion
The proposed structure was used in this work to numerically investigate a multilayer SPR sensor for urine
glucose detection. Cu and SiO
2
thickness optimization showed that the thickness of the constituent layers has a
significant impact on sensor performance. The optimized structures attained the remarkable DA and FoM,
narrow reflectance curve, and higher sensitivity among the configurations examined. The optimization study
yielded a maximum sensitivity of 385.55°/RIU, indicating the robust response of the suggested structure to
variations in the analyte RI for glucose detection. The sensor's sensitivity for the urine-glucose sensing range
was 381.11°/RIU at RI = 1.347, along with R
min
= 0.11866, FWHM = 4.63°, DA = 0.215/°, and FoM = 82.31/RIU.
The suggested structure's suitability for glucose sensing is suitable by the systematic resonance-angle variation
with rising glucose-related RI. More options for regulating the optical field and improving light-matter
interaction at the sensing interface are made possible by the addition of BlueP and Franckeite layer. Moreover,
the PD of 208.16 (at RI =1.335) and 210.16 (at RI=1.347) is achieved. As a result, the suggested sensor may be
a viable platform for urine-based glucose monitoring that is non-invasive or minimally invasive. However, to
determine its practical applicability, experimental fabrication, material-thickness tolerance analysis,
temperature and environmental stability assessment, and validation using real urine samples are needed.
Acknowledgement
Not applicable.
CRediT Author Contribution Statement
Rejeev Kumar: Conceptualization, Methodology, Supervision, Writing—original draft preparation , Writing—
review and editing. Lalit Garia: Formal analysis, Writing—original draft preparation. Biswajit Brahma:
Methodology, Writing—original draft preparation. Akash Kumar Bhoi: Conceptualization, Formal analysis,
Resources, Writing—review and editing. All authors have read and approved the final version of the manuscript
for publication and agree to be accountable for all aspects of the work, ensuring that questions related to the
accuracy or integrity of any part of the work are appropriately investigated and resolved.
Funding Declaration
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-
profit sectors.
Data Availability Statement
All data generated or analysed during this study are included in this published article.
Conflict of Interest
Akash Kumar Bhoi serves as the Editor-in-Chief, Rajeev Kumar as the Managing Editor, and Biswajit Brahma as
an Editorial Board Member. To ensure a rigorous and unbiased peer-review process, they were not involved in
any stage start from editorial evaluation, peer review process and final publication decision. The handling of
this manuscript was managed independently by another editorial board member. The other author declare no
competing interests.
Artificial Intelligence (AI) Use Disclosure
The authors declare that artificial intelligence (AI)-assisted tools were used only for language refinement,
grammar improvement, and manuscript structuring purposes during the preparation of this work. All technical
content, experimental implementation, results, and interpretations were independently developed and verified
by the authors.
Supporting Information
Not applicable.
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