Figure of merit enhancement of surface plasmon resonance biosensor based on Talbot effect

Abstract

This paper reports the numerical investigation of the Talbot effect for biomaterial detection at optical frequencies. Cytop polymer grating Plasmonics structure with periodicity comparable to the incident wavelength are applied to evaluate of the plasmonics Talbot biosensor. Significant sensitivity from the proposed Talbot biosensor is obtained. For this purpose, the effect of the different biomaterials including Ether, Ethyleneglycol, Chlorobenzene and Quinoline on plasmonics Talbot effects at wavelength range of 550-650 nm are then inspected to improve the structural parameters of the biosensor. Also, the sensitivity and figure-of-merit are calculated. Our numerical results show that the proposed biosensor are able to operate as a high sensitivity with maximum FOM of 20.99, and sensitivity of 324 nm/refractive index unit for small change of \(\Delta n\)= 0.4, in the refractive index of biomaterials. We believe that the proposed biosensor can be applied as a label free on-chip biosensor.

Full text

Vol.:(0123456789)
Optical and Quantum Electronics (2021) 53:518
https://doi.org/10.1007/s11082-021-03168-4
1 3
Figure ofmerit enhancement ofsurface plasmon resonance
biosensor based onTalbot effect
ShahryarFarhadi1· AliFarmani1 · AbdolsamadHamidi1
Received: 18 January 2021 / Accepted: 15 July 2021 / Published online: 14 August 2021
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
Abstract
This paper reports the numerical investigation of the Talbot effect for biomaterial detec-
tion at optical frequencies. Cytop polymer grating Plasmonics structure with periodicity
comparable to the incident wavelength are applied to evaluate of the plasmonics Talbot
biosensor. Significant sensitivity from the proposed Talbot biosensor is obtained. For this
purpose, the effect of the different biomaterials including Ether, Ethyleneglycol, Chlo-
robenzene and Quinoline on plasmonics Talbot effects at wavelength range of 550-650 nm
are then inspected to improve the structural parameters of the biosensor. Also, the sensitiv-
ity and figure-of-merit are calculated. Our numerical results show that the proposed bio-
sensor are able to operate as a high sensitivity with maximum FOM of 20.99, and sensitiv-
ity of 324 nm/refractive index unit for small change of
Δn
= 0.4, in the refractive index of
biomaterials. We believe that the proposed biosensor can be applied as a label free on-chip
biosensor.
Keywords Surface Plasmon Resonance· Biosensor· Talbot effect
1 Introduction
When a monochromatic beam is propagated through a periodic structure such as grat-
ing platforms, the pattern of that configuration is provided to repeat itself occasionally
with increasing distance of the pattern from the platform which known as Fresnel regime
(Salama etal. 1999; Siegel etal. 2001; Wang etal. 2009). This distance is known as the Tal-
bot distance, and fantastic effects may also be defined at this distances, where the multiple
frequency self-imaging pattern can occur. This phenomena as a self-imaging pattern of the
grating structure was introduced by H.F. Talbot in 1836, and has been the received remark-
able attention from research groups in the field of atom optics and plasmonics (Podan-
chuk etal. 2014; Kovalenko etal. 2013; Zhang etal. 2009; Dennis etal. 2007). Therefore,
various research groups have used talbot effect form practical applications in gratings and
diffractive structure. Also, several optimized algorithms are proposed (Chen etal. 2020;
Wang and Chen 2020; Xu etal. 2019; Zhao etal. 2019). As an example Li etal proposed
* Ali Farmani
farmani.a@lu.ac.ir
1 School ofElectrical andComputer Engineering, Lorestan University, Khoramabad, Iran
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intelligence platform (Li et al. 2018). Wang etal proposed machine learning algorithm
(Wang etal. 2017). And several related works are presented recently (Xia etal. 2017; Chen
etal. 2016; Shen etal. 2016; Hu etal. 2015). This optimized algorithms have advanced
applications (Xu and Chen 2014; Zhang etal. 2020, 2021; Zhao etal. 2021). Chen group
work on bio-science with optimized algorithm (Tu etal. 2021; Shan etal. 2021; Yu etal.
2021; Hu etal. 2021; Zhao etal. 2014; Yu etal. 2020). The interest in this phenomena is
not only theoretical aspect (Koriakovskii and Marchenko 1981; Liu etal. 2015). The Tal-
bot effects as a remarkable phenomena of periodic structure have a advanced applications,
such as switch, sensor, optical metrology, laser array illumination, detector and so on Feng
etal. 2020; Fu and Yang 2020; Jiang etal. 2020,?. For example protein is a main compo-
nents which is considered by research groups (Zhang and Liu 2019; Xu etal. 2020). Alz-
heimer detection is also so important (Zhu etal. 2020) and several sensing platforms (Zhu
etal. 2020; Hu etal. 2020; Qu etal. 2019; Jiang etal. 2013; Wang etal. 2020; Zou etal.
2019). However, the self-imaging pattern is seen as the period of the structure is highly
larger than the incident light beam, for the condition of resonant diffraction periodic struc-
ture whose period is relatively comparable to the incident frequency, the electric field pro-
file at the repeated distance of the periodic structure will also revive periodically, called as
the quasi-Talbot phenomena (Podanchuk etal. 2013, 2011, 2013, 2015; Iwata etal. 2011).
In the year 2012, Hua research group developed Talbot effect beyond the paraxial limit at
optical frequencies (Hua et al. 2012). In the year 2018, JINWOO group experimentally
demonstrate a new design for passive Talbot amplification of repetitive optical waveforms
(Jeon etal. 2018). In the year 2020, Aviad and co-worker focused on use of talbot effect in
label free biosensors for therapeutic purpose. They proposed a label-free sensor on a chip,
operating in near-infrared for monitoring of absorption line signatures based on molecu-
lar vibrations (Katiyi and Karabchevsky 2020). In the same year, X-ray measurements is
introduced by Talbot effect by Brazhnikov research group. These proposed sensors able to
detect a very small quantity of molecules (Brazhnikov etal. 2020).
In several practical applications, long grating structures are applied because of its good
behavior, with periods ranging from several centimeter to higher than hundred of centime-
tres (Lin etal. 2020; Zuo etal. 2015, 2017; Zhang etal. 2020). However, there exist some
advanced nano-applications in which small footprint displacements and exact contrast need
to be calculated (Li etal. 2018, 2017; Wang etal. 2017; Xia etal. 2017). In typical, several
applications based on the Talbot effect, cannot be used to nano-scale configuration with
grating platforms comparable to the incident beam wavelength. Some numerical researches
have focused on the self-image patterns in one-dimenssional structure the paraxial limit,
and many of them differences in the self-image patterns were predicted. Also, these numer-
ical results, always, have not been validated by experimental ones owing to their restriction
in fabrication process.
Fortunately, in this years, by introducing the plasmonics fields, the Talbot effect was
seen in naoscale structure (Wang etal. 2010; Li et al. 2011; Shi etal. 2015; Kim et al.
2020). However, the fast damping of surface waves in nobel metals restricted the investi-
gate to only the first Talbot distance. Therefore, the new material such as polymers with
high mobility features is needed (Kim etal. 2020). Despite remarkable practical investiga-
tions on biosensors based on talbot, there is still much researches to improve the overall
performance of such biosensors.
In this work, we have analyzed the Talbot effect of polymer grating in the self-imaging
pattern of Cytop polymer for biomaterial detections. We have numerically modeled the
periodic structure with finite-difference time-domain (FDTD) as an Ether, Ethyleneglycol,
Chlorobenzene and Quinoline biosensor. As expected, the Talbot effect appears. We have
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numerically found that the contrast of the self-images pattern changes as we harness the
biomaterials. Also, a comparison of the previous results with the proposed model provided
and shows that a changes of the contrast of the self-images pattern is due to the change of
refractive index of biomaterial. Therefore, the proposed structure can be used as a highly
sensitive biosensor.
The rest of this paper is organized as follows. In Sect.2, the numerical structure of the
Talbot biosensor is presented. Then, pivotal parameters of sensors are introduced. In the
same Section, the main operation mechanism of proposed model is provided. In Sect.3,
by utilizing the different biomaterials, the Talbot effect for monitoring of the materials is
applied. Moreover, obtained result compared with some previous works. Finally, the main
conclusions in Sect.4 is presented.
2 Proposed Talbot bioensor
2.1 Structure oftheTalbot bioensor
Figure1 presented the 3D-view of the proposed biosensor. As can be seen, the proposed
plasmonics talbot biosensor is composed of a Cytop polymer grating layer for generating
of talbot wave and air medium. The talbot structure is assumed to be illuminated by a tun-
able semiconductor laser in the range of 550 nm to 650 nm, and incident angle of
𝜃
is
injected from left edge side. As a talbot biosensor, several biomaterials including Ether,
Ethyleneglycol, Chlorobenzene and Quinoline are inspected. Schematic configuration of
proposed sensor is depicted in Fig.1. It consists of Cytop as substrate with grating period
of
Λ
and duty cycle of 50 percent. The refractive index of polymer Cytop in range of 0.2
μm to 1.2 μm is shown in Fig.2. The grooves are etched to depth of 0.5 μm. Other struc-
tural parameters of the device are tabulated in Table1.
The main reason for choosing the talbot biosensor is that its simple and practical
configuration with relatively compact footprint. The total footprint of the biosensor is
3.9 μm
×
2.4 μm
×
1.9 μm which is a very good candidate for portable platforms. It is
worth to mentioning that the surface of injected biomaterial in the talbot biosensor has a
grating configuration; therefore, it can be used for simultaneous biomaterials detection.
Fig. 1 The 3D-schematic of the
talbot biosensor
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S.Farhadi et al.
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For selecting the appropriate parameters such as previous works, optimized algorithm is
considered (Zhang etal. 2019, 2020a, b, c, d, 2021). For example Yang group used clas-
sification for optimization of the structures (Yang etal. 2019; Zhang etal. 2021; Gong
etal. 2019).
Incident light of plane wave has been applied along the z axis. The pattern of electric
field interference of the structure with air background is shown in Fig.3. For a diffrac-
tion grating the self-imaging pattern is repeated at a distance known Talbot plane, c:
Where
𝜆
and n
r
are the free space wavelength and background refractive index, respec-
tively. To examine sensing operation of device, grooves were filled with different material
as listed in Table2. From Table2 it can been seen that for different wavelength, refractive
(1)
c=(
𝜆
∕nr)(
1
−√
1
−(
𝜆
∕nrΛ)2)
Table 1 The layers feature of the
proposed Talbot biosensor Parameter Size
Λ
g
1.2 μm
W
g
0.6 μm
h
g
0.5 μm
L
g
1.9 μm
h
s
2 μm
Fig. 2 The calculated of refrac-
tive index of polymer Cytop
Table 2 The refractive index of
tested biomaterial as a function
of wavelength
Parameters
𝜆=550nm
𝜆=650nm
Ether n = 1.3 n = 1.31 n = 1.33 n = 1.34
Ethyleneglycol n = 1.4 n = 1.42 n = 1.44 n = 1.45
Chlorobenzene n = 1.5 n = 1.51 n = 1.52 n = 1.53
Quin0line n = 1.6 n = 1.63 n = 1.64 n = 1.65
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index of biomaterials change, and the self-imaging intensity pattern changes but the Talbot
distance remains the same.
In next section, firstly, the crucial parameters of the biosensor is reviewed. Then, to gain
a deep point of view about the mechanism of the structure several parameters are adjusted
to find the appropriate results.
2.2 Talbot biosensor characteristics
To obtain deep point of view about talbot biosensor, potential results should be considered
to detection of biomaterials including FoM, and sensitivity. In this regard, the sensitivity is
expressed as:
where
Δ𝜆
and
Δn
are respectively, reflection red-blue shifts and the biomaterial refractive
index changes.
Also, figure of merit (FoM), as another main feature of the talbot biosensor, is calcu-
lated from:
where FWHM refers to the full width at half of the maximum parameter at the central
wavelength.
In next section, firstly, it assume air condition for talbot biosensor with room tempera-
ture condition
T=300◦K
, and the incident wavelength of laser is tuned from
𝜆0
= 550 nm
to
𝜆0
=650 nm, and calculation is done by using FDTD package. Then, the effect of the dif-
ferent biomaterials including Ether, Ethyleneglycol, Chlorobenzene and Quinoline on the
talbot reuslts are considered. Finally, to improve the calculated result, by considering best
geometry of the talbot biosensor, highest sensitivity is calculated.
3 Result anddiscussion
To deep study the performance of the talbot biosensor, the FDTD method for detection
of air is used. The electric field profile in this case is obtained in Fig.3. In this case the
temperature is 300 K. Here, the geometrical parameters are set as L
g
= 1200 nm, w
g
=
(2)
S
=
Δ𝜆
Δn
(3)
FoM
=[
S
FWHM
(1∕RIU
)]
Fig. 3 The calculated of self-
imaging pattern as the biomate-
rial is air
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S.Farhadi et al.
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500 nm, and n
air
= 1 so that the talbot resonance wavelength is occurred around 550 nm.
As can be seen, the self-imaging pattern is repeated with highly sensitivity and high
contrast.
To further study the results of the proposed configuration, we have also investigated
the effect of the
Λs
on the transmittance curve. As can be seen in Fig.4, at resonance
wavelength, the transmission variation by
Λs
is less than 0.1 and the throughput is
greater than 0.9.
As D.C (Wg/
Λg
) is the another important parameter for evaluating the structure,
this parameters is provided in Fig.5. To discuss how the strong light-matter interaction
between incident light and layer of Cytop and its effects on the sensing characteristics,
we used different D.C of 30%, 40%, 50%, 60%, and 70% for transmission spectra, while
keeping other parameters fixed. Figure5 shows the transmission versus the resonance
wavelength for different D.C. As can be seen, the variation of D.C leads to red and blue-
shift of the transmission spectrum which is used for sensing mechanism.
To investigate how the length Lg affects the sensing properties, we tuned the Lg from
1.8 to 2 μm in steps of 0.05 μm, while keeping the other parameters fixed. Figure6 illus-
trates the relationship between the transmission spectrum and the wavelength for different
Lg. Figure6 shows the red shift of the transmission can be used for sensing mechanism.
To exact study the effect of different biomaterials on the electric field profile, bio-
materials are changed, whereas the other parameters are fixed. As illustrated in Fig.7,
different self-imaging pattern are produced for various biomaterials. In this case, easily
several biomaterials can be detected.
Fig. 4 The transmission spectra of structure for different
Λs
Fig. 5 The transmission spectra of structure for different D.Cs
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The transmission spectra of sensor for different sensing materials is depicted in Fig.8.
The dip resonance frequency of device for air is about 525.2 nm. As it seen, by increasing
the
Δ
n the resonance frequency is red shifted.
Finally, we analyze the performance of parameters for different biomaterials including
Ether, Ethyleneglycol, Chlorobenzene and Quinoline. The resonance frequency and rela-
tive sensitivity of talbot biosensor for each material is listed in Table3.
As can be observed in Table4, highest sensitivity of 324 nm/RIU by considering Chlo-
robenzene can be provided. Also, the highest FoM of 20.99 for Quinoline is obtained. The
results are highly improved compared with previous works Farmani etal. 2018; Farmani
2019; Farmani and Mir 2019; Farmani etal. 2020; Hamzavi-Zarghani etal. 2019; Amoo-
soltani etal. 2019; Mozaffari and Farmani 2019; Farmani etal. 2020. Finally, by consid-
ering FDTD algorithm and the excitation of talbot waves, the performance of the talbot
biosensor remarkably enhanced compared to the obtained results of the previous works
provided in Table4. As a result, the obtained results can be used in recent advanced appli-
cations Wang etal. 2017; Zhang etal. 2020, 2019; Sun etal. 2019.
4 Conclusion
Here, we have reported the model for a high sensitivity surface plasmon resonance biosen-
sor for biomaterials detection, based on plasmonics Talbot effects. The performance of the
biosensor was numerically studied with FDTD method. To evaluate of the biosensor differ-
ent biomaterials including Ether, Ethyleneglycol, Chlorobenzene and Quinoline were also
studied. It was observed that, for small variation of
Δn
= 0.4, in the biomaterials refractive
index, FoM and sensitivity as high as 20.99 and 324nm/RIU are achievable in the bio-
sensor, respectively. We envision that the proposed biosensor based on plasmonics Talbot
effect can be used as a potential platform for on-chip biosensors.
Fig. 6 The transmission spectra of structure for different Lg
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S.Farhadi et al.
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Fig. 7 The calculated of self-
imaging pattern as the biomateri-
als are Ether, Ethyleneglycol,
Chlorobenzene and Quinoline
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Funding Information This research did not receive any specific grant from funding agencies.
Data Availability Statement All data included in this paper are available upon request by contact with the
contact corresponding author.
Declaration
Fig. 8 The calculated of self-imaging pattern as the biomaterials are Ether, Ethyleneglycol, Chlorobenzene
and Quinoline
Table 3 The calculated sensing
parameters of the proposed
structure
Material
𝜆r
FWHM (nm) S (nm/RIU) FOM(RIU
−1
)
Air 525.2 17.3 – –
Ether 537.8.2 18.7 42 2.24
Ethyleneglycol 556.2 17.3 184 9.15
Chlorobenzene 588.6 20.1 324 16.12
Quin0line 618.2 14.1 296 20.99
Table 4 Comparison of the sensing parameters of the present and previous works
References FoM S Structure
Golfazani etal. (2020) 9.8 693.8 Metal-dielectric-metal Waveguide
Amoosoltani etal. (2020) 9 1500 Plasmonics Disk Resonators
Moradiani etal. (2020) 10 1271 PIT-like resonator
This Work 20.99 324 Plasmonics Cytop Polymer grating
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S.Farhadi et al.
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Conflict of interests The authors declare that they have no conflict of interest.
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