sensors Article
An Optical Fiber Refractive Index Sensor Based on the Hybrid Mode of Tamm and Surface Plasmon Polaritons Xian Zhang 1 , Xiao-Song Zhu 1,2, * and Yi-Wei Shi 1,2 1 2
*
School of Information Science and Engineering, Fudan University, 220 Handan Rd, Shanghai 200433, China;
[email protected] (X.Z.);
[email protected] (Y.-W.S.) Key Laboratory for Information Science of Electromagnetic Waves (MoE), Fudan University, 220 Handan Rd, Shanghai 200433, China Correspondence:
[email protected]; Tel.: +86-21-6564-3533
Received: 25 May 2018; Accepted: 1 July 2018; Published: 3 July 2018
Abstract: A novel high performance optical fiber refractive index (RI) sensor based on the hybrid transverse magnetic (TM) mode of Tamm plasmon polariton (TPP) and surface plasmon polariton (SPP) is proposed. The structure of the sensor is a multi-mode optical fiber with a one dimensional photonic crystal (1 DPC)/metal multi-films outer coated on its fiber core. A simulation study of the proposed sensor is carried out with the geometrical optical model to investigate the performance of the designed sensor with respect to the center wavelength, bilayer period and the thickness of silver layer. Because the lights transmitted in the fiber sensor have much larger incident angles than those in the prism based sensors, the center wavelength of the 1 DPC should shift to longer wavelength. When the coupling between TM-TPP and SPP is stronger, the sensor exhibits better performance because the electromagnetic field of the TPP-SPP hybrid mode is enhanced more in the analyte. Compared to most conventional fiber surface plasmon resonance sensors, the figure of merit of the proposed sensor is much higher while the sensitivity is comparable. The idea of utilizing TPP-SPP hybrid mode for RI sensing in the solid-core optical fiber structure presented in this paper could contribute to the study of the fiber RI sensor based on TPP. Keywords: Tamm plasmon polariton; surface plasmon polariton; one dimensional photonic crystal; refractive index; fiber sensor
1. Introduction Surface electromagnetic waves, including Bloch surface wave (BSW) excited at the interface between a homogeneous medium and a finite one-dimensional photonic crystal (1 DPC) and surface plasmon polariton (SPP) excited at the interface between metal and dielectric, have been applied to biochemical sensing in recent years [1–4]. Excitation of BSW and SPP requires phase-matching for the tangential component of the wave factor, which can be satisfied under total internal reflection condition. Tamm plasmon polariton (TPP) is another surface mode which can be excited through the interaction of light at the boundary of the Bragg mirror heterostructures or the one between metal and dielectric Bragg mirror [5,6]. TPPs exist for both transverse magnetic (TM) and transverse electric (TE) polarizations [7]. It has been studied in many applications such as the development of diodes and lasers [8], the generation of efficient third harmonic [9], the enhancement of nonlinearity for devising low threshold bistable optical switches [10,11], the realization of efficient magneto-photonic devices [12,13] and the development of monolithically-integrated photonic components and sensors [14–16]. Contrary to BSW and SPP, excitation of TPP does not require phase-matching for the tangential component of the wave factor and can be realized at any incident angle [5]. Studies have shown that TPP demonstrates itself as a narrow absorption resonance dip in the reflectance spectrum of Sensors 2018, 18, 2129; doi:10.3390/s18072129
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1 DPC/metal [17]. However, the electromagnetic field of TPP on the 1 DPC/metal2 interface Sensors 2018,system 18, x of 12 rarely extended into the surrounding analyte on the other side of the metal film like BSW and SPP. It is TPPtodemonstrates itself as for a narrow resonance dip in the reflectance spectrum of difficult directly utilize TPP sensingabsorption applications like surface plasmon resonance (SPR) sensors. 1 DPC/metal system [17]. However, the electromagnetic field of TPP on the 1 DPC/metal interface In a 1 DPC terminated by a thin plasmonic metal film, TPP and SPP can be excited simultaneously the surrounding on the Coupling other side of the metalTM-TPP film like at BSW SPP. It whenrarely total extended internal into reflection conditionanalyte is satisfied. between theand 1 DPC/metal is difficult to directly utilize TPP for sensing applications like surface plasmon resonance (SPR) interface and SPP at the metal/analyte interface might lead to the appearance of the TPP-SPP hybrid sensors. In a 1 DPC terminated by a thin plasmonic metal film, TPP and SPP can be excited mode [18,19]. The electromagnetic field of TPP localizes at the boundary of 1 DPC and metal, while that simultaneously when total internal reflection condition is satisfied. Coupling between TM-TPP at of SPP a huge enhancement theatmetal/analyte interface decays away from it. thegets 1 DPC/metal interface and at SPP the metal/analyte interfaceand might lead exponentially to the appearance of the As a result, the electromagnetic field of the hybrid mode is enhanced on the metal/analyte interface TPP-SPP hybrid mode [18,19]. The electromagnetic field of TPP localizes at the boundary of 1 DPC and extends into the that analyte medium. Therefore, the TPP-SPP hybrid modeinterface has large and metal, while of SPP gets a huge enhancement at the metal/analyte andpotential decays for exponentially away from it.[20,21]. As a result, the electromagnetic field of the hybrid mode is enhanced on refractive index (RI) sensing However, to our knowledge, there is no report on the sensing the metal/analyte interface extends analyte fiber medium. Therefore, the TPP-SPP hybrid application of TPP-SPP hybridand mode basedinto on the solid-core structure. mode largea potential for refractive index (RI) sensing [20,21].index However, to utilizing our knowledge, there In thishas paper, high performance solid-core fiber refractive sensor TPP-SPP hybrid is no report on the sensing application of TPP-SPP hybrid mode based on solid-core fiber structure. mode excited in the 1 DPC/metal structure is proposed. Theoretical analysis with a geometrical optical In this paper, a high performance solid-core fiber refractive index sensor utilizing TPP-SPP model is carried out to investigate the characteristics of the designed sensor. The interaction between hybrid mode excited in the 1 DPC/metal structure is proposed. Theoretical analysis with a TM-TPP and SPP is studied. We have optimized different parameters such as thickness of the metal geometrical optical model is carried out to investigate the characteristics of the designed sensor. The layer,interaction bilayer period and center and wavelength of theWe band gap. The results show that the RI detection between TM-TPP SPP is studied. have optimized different parameters such as rangethickness of the designed sensor with optimal parameters is extended compared with the conventional of the metal layer, bilayer period and center wavelength of the band gap. The results show solid-core fiber SPR sensors, figure of merit (FOM) is much higher.is extended compared that the RI detection rangewhile of thethe designed sensor with optimal parameters with the conventional solid-core fiber SPR sensors, while the figure of merit (FOM) is much higher.
2. Sensor Configuration and Theoretical Model 2. Sensor Configuration and Theoretical Model
Figure 1 shows the proposed solid-core fiber refractive index sensor based on 1 DPC/metal shows thethe proposed solid-core fiber refractive index sensor based 1 DPC/metal structure.Figure After 1removing cladding of a multi-mode optical fiber (MMF) forona short length that structure. After removing the cladding of a multi-mode optical fiber (MMF) for a short lengthare that can be done by chemical etching with hydrofluoric acid, periodically bilayers of TiO2 /SiO coated 2 can be done by chemical etching with hydrofluoric acid, periodically bilayers of TiO2/SiO2 are coated on the surface of the fused silica fiber core. Then the periodically bilayers are outer covered by a on the surface of the fused silica fiber core. Then the periodically bilayers are outer covered by a thin thin silver film. Atomic layer deposition (ALD) technology is the ideal method for the deposition silver film. Atomic layer deposition (ALD) technology is the ideal method for the deposition of the of the1 DPC/metal 1 DPC/metal multilayers. It has beento proven tohigh fabricate quality DPCsurface on theofouter multilayers. It has been proven fabricate qualityhigh 1 DPC on the1outer surface of solid-core fiberTo[22]. To satisfy the condition of total reflection, RI ofoutside analyte outside solid-core fiber [22]. satisfy the condition of total reflection, the RI of the analyte the fiber the fiber should shouldbe belower lower than that of the fiber TM-TPP andwould SPP would be excited simultaneously than that of the fiber core.core. TM-TPP and SPP be excited simultaneously and interact with with each light transmits in the MMF. Consequently, TPP-SPP and interact each other otherwhen whenappropriate appropriate light transmits in the MMF. Consequently, TPP-SPP hybrid demonstrate itself a narrow resonancedip diplocated located in in the the band hybrid modemode will will demonstrate itself as as a narrow resonance band gap gapofof11DPC DPCinin the the transmission spectrum. transmission spectrum.
Figure 1. Structure of of thethe solid-core sensorbased basedonon1 DPC/silver 1 DPC/silver system. Figure 1. Structure solid-corefiber fiber RI RI sensor system.
The diameter of the fiber core is 200 μm and numerical aperture (NA) is 0.2. The 1 DPC
The diameter of the fiber core is 200 µm and numerical aperture (NA) is 0.2. The 1 DPC structure structure is comprised of periodic multilayers of TiO2/SiO2, with RI n1 = 2.45 and n2 = 1.46 is comprised of periodic multilayers of TiO2 /SiO RI n1 = widely 2.45 and n = 1.46 approximately, 2 , with approximately, respectively. These two kinds of oxides have been used2 for 1 DPC in many respectively. These two kinds of oxides have been widely used for 1 DPC in many applications [10,20].
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The thickness of the two layers is denoted by d1 and d2, which is given by 3 ofthe 13 following quarter-wave film system [23]:
d1 d1 nand The thickness of the two layers is denotedn1by which (1) 2, 2 d 2 d 0 / 4 . is given by the following quarter-wave film system [23]: where λ0 is the center wavelength of then1 dDPC band gap. Silver is chosen as the metal material since (1) 1 1 = n2 d2 = λ0 /4, it is well known as a good candidate for the SPR sensor. The dielectric constant of the silver layer is where λ0 by is the wavelength of the 1 DPCmodel band gap. obtained thecenter following Drude free electron [24]: Silver is chosen as the metal material since it is well known as a good candidate for the SPR sensor. The dielectric constant of the silver layer is 2 c obtained by the following Drude free . (electron ) r model i i 1 [24]: (2) 2 p (c i )
λ2 λ c , (2) ε(λ) = ε r −5+m. iε i = 1 − 2 where λp = 1.4541 × 10−7 m, λc = 1.7614 × 10 λ p (λc + iλ) Since the diameter of fiber core is much larger than the wavelength of input light, a geometrical opticalλmodel illustrated 2 is employed to theoretically calculate the transmission spectrum where × 10−7in m,Figure λc = 1.7614 × 10−5 m. p = 1.4541 of the proposed sensor [25]. Here we only consider meridional of rays. Here wea geometrical assume the Since the diameter of fiber core is much larger than the wavelength input light, distribution the input light 2 power is close to Gaussian with the profile Pin( )spectrum expressed optical model of illustrated in Figure is employed to theoretically calculate transmission of the proposed sensor [25]. Here we only consider the meridional rays. Here we assume the distribution approximately as [26]: of the input light power is close to Gaussian with profile Pin (ϕ) expressed approximately as [26]: Pin ( ) exp( 2 / 0 ( ) 2 ) . (3) 2
2
) ∝ exp(− ϕ /ϕ0 (λ) ), (3) in ( ϕincident light, 0 depends on the input light source. The is the launching angle ofPthe relationship angle θangle and in Figure 2 follows Snell’s law ) = ncos(θ), where where ϕ is between the launching of shown the incident light, ϕ0 depends on sin( the input light source. where
n is the RI of the fiber core material. The relationship between angle θ and ϕ shown in Figure 2 follows Snell’s law sin(ϕ) = ncos(θ), where n is the RI of the fiber core material.
Figure 2. Sketch and ray model of solid-core fiber refractive index sensor based on 1 DPC/silver structure. Figure 2. Sketch and ray model of solid-core fiber refractive index sensor based on 1 DPC/silver structure.
The power of the output light of the sensor at a given wavelength is given as: The power of the output light of the sensor at a given wavelength is given as: Z π/2 /2
Pout Pout=
θ
crcr
N (θ )
PP ((θ)R) Rp (p(θ) N) ( ) ddθ.. inin
(4) (4)
Where θθcrcr denotes the critical angle of total reflection on the the interface interface between fiber core core and and Where cladding, which which is is approximately approximately 82.1 82.1◦ for NA = = 0.2. θ denotes the angle between the normal of the θ the reflection interface interface and and the the direction direction of of the the incident incident light. light. Rpp(θ) is is the the reflectance reflectance for for the the p-polarized p-polarized reflection on the the surface surface of of fiber fiber core core which which isis calculated calculated by by the the transfer transfer matrix matrix method method [27]. [27]. Reflection Reflection light on times of the light N(θ) is a function of θ, the length of the sensitive area L and core diameter which times of the light N(θ) is a function of θ, the length of the sensitive area L and core diameter D, D, which is: is: L NN (θ( ) )= L .. (5) (5) D tan θ
D tan
Therefore, the the generalized generalized expression expressionfor forthe thetransmittance transmittanceof ofthe thesensor sensorcan canbe beexpressed expressedas: as: Therefore,
R π/2 T=
θcr
Pin (θ ) R p (θ ) N (θ ) dθ . R π/2 θcr Pin ( θ ) dθ
(6)
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T
/2
cr
Pin ( ) R p ( ) N ( ) d /2
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.
(6)
P ( )d With Equation (6), the performance of the proposed sensor could be numerically evaluated. While cr
in
Withand Equation the performance of and the interact proposed sensor be numerically TM-TPP SPP are(6), excited simultaneously with each could other, the electric field evaluated. located on While TM-TPP and SPP are excited simultaneously and interact with each other, the electric field the 1 DPC/Ag interface is extended into the analyte, leading to a TPP-SPP hybrid mode. It would located on the 1 DPC/Ag interface is extended into the analyte, leading to a TPP-SPP hybrid mode. It exhibit a minimum in the transmission spectrum at a particular wavelength located in the band gap would exhibit a minimum in the transmission spectrum a particular wavelength located in the of 1 DPC, known as the resonance wavelength (RW). Theat RW will shift when the RI of the analyte band gap of 1 DPC, known as the resonance wavelength (RW). The RW will shift when the RI of the changes. Therefore, by measuring the RW from the transmission spectra of the proposed sensor, the RI analyte changes. Therefore, by measuring the RW from the transmission spectra of the proposed of the analyte can be obtained. sensor, the RI of is the can be obtained.to evaluate the performance of a SPR sensor. Usually, Sensitivity ananalyte important parameter Sensitivity is an important parameter evaluate performance the sensitivity of a wavelength-interrogatedtoSPR sensorthe is defined as: of a SPR sensor. Usually, the sensitivity of a wavelength-interrogated SPR sensor is defined as: ∆λ res res SS= , (7) (7) ∆n nss where ∆λ Δλres is is the the shift shiftin inthe theRW RWdue duetoto the change of analyte s. How accurately the value of where the RIRI change of analyte ∆nsΔn . How accurately the value of RW res RW can be determined depends on the full width at half maximum (FWHM) of resonance the resonance in can be determined depends on the full width at half maximum (FWHM) of the dip dip in the the transmission spectrum. The overall performance of a sensor is defined in terms of FOM as: transmission spectrum. The overall performance of a sensor is defined in terms of FOM as:
S . S FOM = FWHM . FOM
FW HM
(8) (8)
3. Results and Discussion 3. Results and Discussion Center wavelength λ0 is the primary parameter for designing 1 DPC. It implies where the band Center wavelength λ0 is the primary parameter for designing 1 DPC. It implies where the band gap for the normal incident light is located. However, most of the input lights transmit with large gap for the normal incident light is located. However, most of the input lights transmit with large incident angles in the optical fiber as shown in Figure 2. Therefore, the band gap of TM light with incident angles in the optical fiber as shown in Figure 2. Therefore, the band gap of TM light with large incident angles near 90 instead of small incident angles is more meaningful to the designed large incident angles near 90◦ instead of small incident angles is more meaningful to the designed fiber fiber sensor. Figure 3 shows the band gap of 1 DPC with different center wavelength, which is sensor. Figure 3 shows the band gap of 1 DPC with different center wavelength, which is calculated calculated by the methods reported in [27]. The left half and right half represents p-polarized and by the methods reported in [27]. The left half and right half represents p-polarized and s-polarized s-polarized light, i.e., TM and TE light, respectively. The shading represents wavelengths that are light, i.e., TM and TE light, respectively. The shading represents wavelengths that are forbidden to forbidden to propagate in the 1 DPC. The band gap locates around the center wavelength only in propagate in the 1 DPC. The band gap locates around the center wavelength only in small incident small incident angle ranges and it shifts towards shorter wavelength when the incident angle angle ranges and it shifts towards shorter wavelength when the incident angle increases. We firstly increases. We firstly adopt λ0 = 1000 nm to investigate the transmission spectrum of the proposed adopt λ0 = 1000 nm to investigate the transmission spectrum of the proposed sensor. As can be seen in sensor. As can be seen in Figure 3a, the band gap of the 1 DPC at incident angle larger than 82.1 Figure 3a, the band gap of the 1 DPC at incident angle larger than 82.1◦ nearly covers the wavelength nearly covers the wavelength range of 400–600 nm, which is around the SPR RW when analyte is range of 400–600 nm, which is around the SPR RW when analyte is water. Figure 3b shows the band water. Figure 3b shows the band gap of the 1 DPC with 1200 nm center wavelength. It can be observed gap of the 1 DPC with 1200 nm center wavelength. It can be observed that the band gap shifts towards that the band gap shifts towards longer wavelength with the increase of the center wavelength. longer wavelength with the increase of the center wavelength.
Figure Figure 3. 3. Band Band gap gap of of 11 DPC DPC with with different different center center wavelength. wavelength. The The left left side side represents represents p-polarized p-polarized light, while the right side represents s-polarized light. (a) λ0 = 1000 nm, (b) λ0 = 1200 nm. light, while the right side represents s-polarized light. (a) λ0 = 1000 nm, (b) λ0 = 1200 nm.
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The length of the sensitive area L affects the reflection times of the transmission light on the The length of the sensitive area L affects the reflection times of the transmission light on the sensing surface. The depth of resonance dip increases with larger L. However, when the length is too sensing surface. The depth of resonance dip increases with larger L. However, when the length is too long, the increase of the depth of resonance dip becomes negligible and the sensor becomes fragile. long, the increase of the depth of resonance dip becomes negligible and the sensor becomes fragile. Therefore, we adopt L = 5 cm in all following calculations. The thickness of silver layer dm should be Therefore, we adopt L = 5 cm in all following calculations. The thickness of silver layer dm should be small enough to excite SPP. Figure 4a shows the transmission spectra of the designed sensors with small enough to excite SPP. Figure 4a shows the transmission spectra of the designed sensors with 30 nm and 200 nm silver layer thicknesses when p-polarized light is incident. The bilayer period N 30 nm and 200 nm silver layer thicknesses when p-polarized light is incident. The bilayer period N adopted in the calculation is three. We also calculated the electric field distribution to investigate the adopted in the calculation is three. We also calculated the electric field distribution to investigate the origin of the multiple resonance dips shown in Figure 4a. The resonance dips are marked as dip 1 to origin of the multiple resonance dips shown in Figure 4a. The resonance dips are marked as dip 1 to 4 4 and dip A to C from short to long wavelength for dm = 30 nm and 200 nm, respectively. Figure 4b and dip A to C from short to long wavelength for d = 30 nm and 200 nm, respectively. Figure 4b,c and 4c show the distributions of the tangentialm electric field amplitude at these resonance show the distributions of the tangential electric field amplitude at these resonance wavelengths. wavelengths. As shown in Figure 4b, none of the three resonance dips is caused by SPR because the As shown in Figure 4b, none of the three resonance dips is caused by SPR because the 200 nm silver 200 nm silver layer is too thick. Dip A, which is located in the band gap of 1 DPC, is caused by layer is too thick. Dip A, which is located in the band gap of 1 DPC, is caused by TM-TPP. Its electric TM-TPP. Its electric field reaches maximum near the 1 DPC/Ag interface and decays in an oscillating field reaches maximum near the 1 DPC/Ag interface and decays in an oscillating form away from form away from it in the 1 DPC. The electric field distributions of dips B and C outside the band gap it in the 1 DPC. The electric field distributions of dips B and C outside the band gap indicate that indicate that these two dips are ascribed to the waveguide modes in the 1 DPC. There are almost no these two dips are ascribed to the waveguide modes in the 1 DPC. There are almost no electric field electric field distribution in the analyte for all three modes. When the silver layer is thin, the TM-TPP distribution in the analyte for all three modes. When the silver layer is thin, the TM-TPP and SPP and SPP are excited simultaneously and interact with each other. The different distributions of are excited simultaneously and interact with each other. The different distributions of electric field electric field of the four resonance dips shown in Figure 4c indicate their different origins. Dip 1 of the four resonance dips shown in Figure 4c indicate their different origins. Dip 1 located in the located in the band gap is caused by the TPP-SPP hybrid mode. Its electric field is a typical TPP band gap is caused by the TPP-SPP hybrid mode. Its electric field is a typical TPP mode in the 1 DPC, mode in the 1 DPC, while it is enhanced obviously at the Ag/analyte interface and decays while it is enhanced obviously at the Ag/analyte interface and decays exponentially away from it. exponentially away from it. Such kind of electric field indicates the coupling of the TM-TPP and SPP. Such kind of electric field indicates the coupling of the TM-TPP and SPP. The electric field in 1 DPC The electric field in 1 DPC and enhancement at the silver/analyte interface indicate that dips 2 and 3 and enhancement at the silver/analyte interface indicate that dips 2 and 3 are ascribed to the coupling are ascribed to the coupling between SPP and waveguide modes in the 1 DPC. Dip 4 is almost between SPP and waveguide modes in the 1 DPC. Dip 4 is almost caused by pure waveguide mode caused by pure waveguide mode since there is nearly no enhancement at the Ag/analyte interface. since there is nearly no enhancement at the Ag/analyte interface. Thus, the silver layer should be thin Thus, the silver layer should be thin enough to excite the TPP-SPP hybrid mode, which can extend enough to excite the TPP-SPP hybrid mode, which can extend its electric field distribution into the its electric field distribution into the analyte for RI sensing. analyte for RI sensing.
Figure 4. (a) Transmission spectra of the proposed sensor with different thickness of silver layer at Figure 4. (a) Transmission spectra of the proposed sensor with different thickness of silver layer at n = 1.37, N = 3, λ = 1000 nm. (b) Tangential electric field distribution at the resonance wavelength nss = 1.37, N = 3, λ00 = 1000 nm. (b) Tangential electric field distribution at the resonance wavelength 590 nm and the resonance angle of 87.25◦ , 864 nm and 89.54◦ , 1706 nm and 89.64◦ for dips A, B and C, 590 nm and the resonance angle of 87.25, 864 nm and 89.54, 1706 nm and 89.64 for dips A, B and C, respectively. The thickness of silver layer is 200 nm. (c) Tangential electric field distribution at 474 nm respectively. The thickness of silver layer is 200 nm. (c) Tangential electric field distribution at and 87.77◦ , 694 nm and 87.01◦ , 923 nm and 87.88◦ , 1761 nm and 89.11◦ for dips 1 to 4, respectively. 474 nm and 87.77, 694 nm and 87.01, 923 nm and 87.88, 1761 nm and 89.11 for dips 1 to 4, The thickness of silver layer is 30 nm. respectively. The thickness of silver layer is 30 nm.
The thickness TPP and SPP excited at The thickness of of silver silverlayer layeraffects affectsthe thestrength strengthofofthe theinteraction interactionbetween between TPP and SPP excited the 1 DPC/Ag interface and Ag/analyte interface, respectively. Figure 5 shows the two-dimensional at the 1 DPC/Ag interface and Ag/analyte interface, respectively. Figure 5 shows the contour maps of the normalized calculated through the proposedthrough sensor asthe a function of two-dimensional contour mapstransmittance of the normalized transmittance calculated proposed
sensor as a function of wavelength and RI of the sensed medium when p-polarized light is incident.
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wavelength and RI of the sensed medium when p-polarized light is incident. Here the bilayer period Here bilayer period Nλ=0 = 3, 1000 center wavelength 0 = 1000 nm.indicate The white lines indicate the N = 3,the center wavelength nm. The white λdashed lines the dashed photonic bandgap (PBG). photonic bandgap (PBG). The yellow regions represent the resonance dips in the transmission The yellow regions represent the resonance dips in the transmission spectra. Only TPP is excited spectra. Only TPP isstructure excited in the the 1 DPC/metal when the silveraslayer is in tooFigure thick 5a. to in the 1 DPC/metal when silver layerstructure is too thick to penetrate shown penetrate as shown Figure is 5a.150 Here layer thickness is 150 nm. The dip located near Here the silver layer in thickness nm.the Thesilver dip located near 750 nm is the waveguide mode (WG). 750 is the waveguide (WG). resonance TPP does not shift when the Figure RI of the The nm resonance dip of TPP mode does not shiftThe when the RI ofdip theofsurrounding analyte changes. 5b surrounding analyte changes. Figureof5b normalized transmittance of this the sensor without shows the normalized transmittance theshows sensorthe without the 1 DPC structure. In case, the sensor the 1 DPC structure. Insolid-core this case, fiber the sensor is just with a conventional SPR sensor a is just a conventional SPR sensor a single 30solid-core nm silverfiber layer. The SPR with dip in single 30 nm silver layer. SPRRIdip in the figure as that the sensed RI increases. be the figure red-shifts as the The sensed increases. It can red-shifts be observed the width of TPP dipItiscan much observed thatthat theofwidth of TPP dipisisbeneficial much smaller that of SPR dip, which is the beneficial to the smaller than SPR dip, which to the than measurement precision. When silver layer is measurement precision. When the silver layer is thin enough, TPP and SPP are simultaneously thin enough, TPP and SPP are simultaneously excited and interact with each other. They demonstrate excited and as interact with each other. They themselves two repulsive resonance silver dips. themselves two repulsive resonance dips.demonstrate The repulsion becomes as weaker with the increasing The becomes weaker withby thethe increasing silver layer thickness, which indicateddips by the layerrepulsion thickness, which is indicated decreasing distance between the twoisresonance as decreasing distance between the two resonance dips as shown in Figure 5c–i. shown in Figure 5c–i.
Figure 5. Two-dimensional contour maps of normalized transmittance calculated through the proposed Figure 5. Two-dimensional contour maps of normalized transmittance calculated through the sensor as a function of wavelength and RI of the sensed medium at N = 3, λ0 = 1000 nm. (a) dm = 150 nm, proposed sensor as a function of wavelength and RI of the sensed medium at N = 3, λ0 = 1000 nm. (b) without 1 DPC, dm = 30 nm, (c) dm = 30 nm, (d) dm = 40 nm, (e) dm = 50 nm, (f) dm = 60 nm, (a) dm = 150 nm, (b) without 1 DPC, dm = 30 nm, (c) dm = 30 nm, (d) dm = 40 nm, (e) dm = 50 nm, (g) d = 70 nm, (h) d = 80 nm, (i) dm = 90 nm. (f) dmm= 60 nm, (g) dm m = 70 nm, (h) dm = 80 nm, (i) dm = 90 nm.
wavelength in Figure 5 The slope of the variation of the TPP-SPP hybrid mode resonance wavelength represents the sensitivity sensitivity of the sensor. ItIt can can be be seen seen that that the sensitivity sensitivity of the sensor degrades represents rapidly when silver layer thickness is above 50 nm. 50 Thus, will further analyze the performance whenthe the silver layer thickness is above nm.weThus, we will further analyze the of the sensor with different thickness nm to obtain the50optimal 6a performance of the sensorsilver with layer different silverbelow layer 50 thickness below nm to thickness. obtain theFigure optimal shows the Figure transmission spectra the proposed sensors different silver layer thicknesses. Here thickness. 6a shows the of transmission spectra of with the proposed sensors with different silver layer thicknesses. Here the RI of the analyte ns = 1.37, the bilayer period N = 3, center wavelength λ0 = 1000 nm. As shown in the figure, the two resonance dips get closer and overlap when the thickness of the silver layer increases. This is because the repulsing coupling between the TM-TPP
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the RI of the analyte ns = 1.37, the bilayer period N = 3, center wavelength λ0 = 1000 nm. As shown in the figure, the two resonance dips get closer and overlap when the thickness of the silver layer and SPP weakens as the silver thickness increases [18]. The electric fields of the TPP-SPP hybrid increases. This is because the repulsing coupling between the TM-TPP and SPP weakens as the silver modes with different dm shown in Figure 6b also prove this. As the silver layer thickness increases, thickness increases [18]. The electric fields of the TPP-SPP hybrid modes with different dm shown in the enhancement at the Ag/analyte interface becomes weaker, which indicates the coupling between Figure 6b also prove this. As the silver layer thickness increases, the enhancement at the Ag/analyte TM-TPP and TPP weakens. However, the silver layer with a thickness less than 30 nm will cause the interface becomes weaker, which indicates the coupling between TM-TPP and TPP weakens. However, resonance dip excited by TPP-SPP hybrid state to shift towards ultraviolet range, where the fused the silver layer with a thickness less than 30 nm will cause the resonance dip excited by TPP-SPP hybrid silica fiber is not transparent. Figure 6c and d show the performance of the proposed sensor with state to shift towards ultraviolet range, where the fused silica fiber is not transparent. Figure 6c,d show various thickness of the silver layer at ns = 1.37. Results show that the FWHM increases with the the performance of the proposed sensor with various thickness of the silver layer at n = 1.37. Results thickness of silver layer, while the FOM reaches its maximum value at dm = 35 nm.s Therefore, we show that the FWHM increases with the thickness of silver layer, while the FOM reaches its maximum adopt 35 nm as the optimal thickness of the silver layer. value at dm = 35 nm. Therefore, we adopt 35 nm as the optimal thickness of the silver layer.
Figure 6. (a) Transmission spectra of the proposed sensor with different thickness of silver layer at Figure 6. (a) Transmission spectra of the proposed sensor with different thickness of silver layer at n = 1.37, N = 3, λ = 1000 nm. (b) Tangential electric field distribution of TPP-SPP dip at the resonance nss = 1.37, N = 3, λ0 0= 1000 nm. (b) Tangential electric field distribution of TPP-SPP dip at the resonance wavelength 420 nm and the resonance angle of 88.63◦ , 474 nm and 87.77◦ , 516 nm and 87.43◦ , 543 nm wavelength 420 nm and the resonance angle of 88.63, 474 nm and 87.77, 516 nm and 87.43, 543 nm and 87.24◦ for d = 20 nm, 30 nm, 40 nm, 50 nm, respectively. (c) The variations of sensitivity and and 87.24 for dmm = 20 nm, 30 nm, 40 nm, 50 nm, respectively. (c) The variations of sensitivity and FWHM of the proposed sensor versus the silver layer thickness at ns = 1.37. (d) The variation of FOM FWHM of the proposed sensor versus the silver layer thickness at ns = 1.37. versus the silver layer thickness at ns = 1.37. (d) The variation of FOM versus the silver layer thickness at ns = 1.37.
The transmission transmission spectra spectra of of the the proposed proposed sensor sensor with with different bilayer bilayer periods periods are shown in Figure 7a. ItIt can can be be observed observed that that both both width width and and depth depth of the TPP-SPP resonance dip decrease Figure As the the bilayer bilayer period period increases, increases, the the more more perfect perfect 11 DPC and the when the bilayer period increases. As stronger restriction of the band gap makes the resonance dip narrower. On the thicker restriction of the band gap makes the resonance dip narrower. Onother the hand, other the hand, the 1 DPC structure makes the excitation of the TPP-SPP mode more mode difficult, which shallows the thicker 1 DPC structure makes the excitation of thehybrid TPP-SPP hybrid more difficult, which resonance dip. As defined by Equation (8), the FOM is inversely proportional to the FWHM. Therefore, shallows the resonance dip. As defined by Equation (8), the FOM is inversely proportional to the the FOMTherefore, increases with the bilayer periods. However, the depth of resonance dip should not be dip too FWHM. the FOM increases with the bilayer periods. However, the depth of resonance small for better detecting. is a trade-off width and depththe of the resonance dip. should not be too small forHence, betterthere detecting. Hence, between there is athe trade-off between width and depth Wethe calculate the performance of the proposed sensor and the sensitivity changes of resonance dip. We calculate the performance offind the that proposed sensor and findlittle thatwith the the bilayerchanges period, which is always in theperiod, range of 1310–1420 nm/RIU. However, the FOMnm/RIU. and dip sensitivity little with the bilayer which is always in the range of 1310–1420 However, the FOM and dip depth change a lot. Figure 7b shows the depth of resonance dip and the FOM of the proposed sensor with different bilayer period at ns = 1.37. It can be seen that the FOM increases rapidly before N = 4 and much slower after that, while the depth of resonance dip decreases consistently. When the bilayer period increases from 4 to 5, the FOM increases slightly
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depth change a lot. Figure 7b shows the depth of resonance dip and the FOM of the proposed sensor 88 of period at ns = 1.37. It can be seen that the FOM increases rapidly before N 4 of=12 12 and much slower after that, while the depth of resonance dip decreases consistently. When the bilayer while depth of resonance dipFOM decreases dramatically from 0.43 to 0.15.ofTherefore, four periodthe increases from 4 to 5, the increases slightly while the depth resonancewe dipadopt decreases pairs of bilayer as the period. dramatically from 0.43optimal to 0.15. bilayer Therefore, we adopt four pairs of bilayer as the optimal bilayer period. Sensors 2018, with Sensorsdifferent 2018, 18, 18, xx bilayer
Figure 7. Transmission spectra of the proposed sensor with different bilayer periods at Figure 7. 1.37, 7. (a) (a) Transmission Transmission spectra spectra of of the the proposed proposed sensor sensor with with different different bilayer bilayer periods periods at at nnsss == 1.37, λ 0 = 1000 nm, d m = 35 nm. (b) The depth of resonance dip and FOM of the proposed sensor with λ00 = 1000 nm, dmm = 35 nm. (b) (b) The The depth depth of of resonance resonance dip and FOM of the proposed sensor with respect 1.37... respect to to various various bilayer bilayer period period at at nnsss == 1.37 1.37
Then we will analyze the performance of the proposed sensor with the optimal structure Then we will analyze the performance of the proposed sensor with the optimal structure parameters obtained above, which are bilayer period N = 4, center wavelength λ00 = 1000 nm, the parameters obtained above, which are bilayer period N = 4, center wavelength λ0 = 1000 nm, thickness of silver layer dmm = 35 nm. The RWs are obtained from the calculated transmission spectra, the thickness of silver layer dm = 35 nm. The RWs are obtained from the calculated transmission and the sensitivity of the sensor is calculated from the RWs by Equation (7). The variations of RW spectra, and the sensitivity of the sensor is calculated from the RWs by Equation (7). The variations of and sensitivity with respect to RI of the analyte are shown in Figure 8. The RI detection range of the RW and sensitivity with respect to RI of the analyte are shown in Figure 8. The RI detection range of proposed sensor is 1.33–1.45, which is much wider than conventional fiber SPR sensors since it can the proposed sensor is 1.33–1.45, which is much wider than conventional fiber SPR sensors since it can detect RI very close to the fiber core [28]. The sensitivity varies from 550 to 1380 nm/RIU in the range. detect RI very close to the fiber core [28]. The sensitivity varies from 550 to 1380 nm/RIU in the range. However, the sensitivity decreases rapidly when the RI of analyte is larger than 1.38, which make the However, the sensitivity decreases rapidly when the RI of analyte is larger than 1.38, which make the sensor’s performance degrades in the RI range of 1.38–1.45. sensor’s performance degrades in the RI range of 1.38–1.45.
Figure Theoretical results results of of resonance resonance wavelength wavelength and and sensitivity sensitivity of of the the proposed Figure 8. Figure 8. 8. Theoretical Theoretical results of resonance wavelength and sensitivity of the proposed sensor sensor at at λ = 1000 nm, N = 4, d = 35 nm. λ λ000 == 1000 1000 nm, nm, N N == 4, 4, ddmmm== 35 35 nm. nm.
In investigate the sensitivity, we we calculate calculate the the transmission transmission In order order to to investigate the cause cause of of the the decrease decrease in in sensitivity, spectra of the proposed sensor with various RI of analyte. As shown in Figure 9a, the red, spectra of the proposed sensor with various RI of analyte. As shown in Figure 9a, the red, blue blue and and purple lines are are the the transmission spectra of of the the proposed proposed 11 DPC/Ag DPC/Ag sensor purple solid solid lines transmission spectra sensor with with sensed sensed RI RI 1.36, 1.36, 1.40 and 1.45, respectively. The dashed lines are the transmission spectra of a fiber SPR sensor which has the same geometry and a 35 nm silver layer outer coating but no 1 DPC structure. It can be seen that both the SPR dips of the fiber SPR sensor and the TPP-SPP dips of the proposed sensor shift towards longer wavelength as the sensed RI increases. However, the wavelength shift of the SPR dip is much larger than the TPP-SPP dip. As a result, the distance between the two dips becomes farther
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1.40 and 1.45, respectively. The dashed lines are the transmission spectra of a fiber SPR sensor which has the same geometry and a 35 nm silver layer outer coating but no 1 DPC structure. It can be seen that both the SPR dips of the fiber SPR sensor and the TPP-SPP dips of the proposed sensor shift Sensors 2018, 18, x 9 of 12 towards longer wavelength as the sensed RI increases. However, the wavelength shift of the SPR dip is much larger than the TPP-SPP dip. As a result, the distance between the two dips becomes farther as the sensed RI increases, which leads to weaker interaction between TM-TPP and SPP. Figure 9b as the sensed RI increases, which leads to weaker interaction between TM-TPP and SPP. Figure 9b shows the amplitudes of tangential electric fields of the TPP-SPP dips at three different sensed RIs. shows the amplitudes of tangential electric fields of the TPP-SPP dips at three different sensed RIs. The gradually attenuated oscillating electric filed in 1 DPC and the enhancement at the Ag/analyte The gradually attenuated oscillating electric filed in 1 DPC and the enhancement at the Ag/analyte interface indicate that the dips located in the band gap of 1 DPC are all caused by the excitation of interface indicate that the dips located in the band gap of 1 DPC are all caused by the excitation of the TPP-SPP hybrid mode. As the sensed RI increases, the enhancement at the Ag/analyte interface the TPP-SPP hybrid mode. As the sensed RI increases, the enhancement at the Ag/analyte interface becomes weaker compared to electric field in the 1 DPC, which indicates less SPP component in the becomes weaker compared to electric field in the 1 DPC, which indicates less SPP component in the hybrid mode and weaker interaction between TM-TPP and SPP. This will make the sensor less hybrid mode and weaker interaction between TM-TPP and SPP. This will make the sensor less sensitive sensitive to the variation of the analyte RI. Therefore, the sensitivity of the proposed sensor keeps to the variation of the analyte RI. Therefore, the sensitivity of the proposed sensor keeps decreasing decreasing when RI is above 1.37 as shown in Figure 8. when RI is above 1.37 as shown in Figure 8.
Figure 9. (a) Transmission spectra of the proposed sensor with different RI of the analyte at N = 4, Figure 9. (a) Transmission spectra of the proposed sensor with different RI of the analyte at N = 4, λ0 = 1000 nm, dm = 35 nm. The transmission spectra of the sensor with a single silver layer of 35 λ0 = 1000 nm, dm = 35 nm. The transmission spectra of the sensor with a single silver layer of 35 nm is nm is also presented for comparison. (b) Tangential electric field distribution of TPP-SPP dip at the also presented for comparison. (b) Tangential electric field distribution of TPP-SPP dip at the resonance wavelength 484 nm and the resonance angle of 87.02◦ , 533 nm and 87.56◦ , 569 nm and 87.9◦ resonance wavelength 484 nm and the resonance angle of 87.02, 533 nm and 87.56, 569 nm and for ns = 1.36, 1.40, 1.45, respectively. 87.9 for ns = 1.36, 1.40, 1.45, respectively.
From From the the discussions discussions above, above, the the performance performance of of the the sensor sensor with with 1000 1000 nm nm center center wavelength wavelength degrades when RI is above 1.38. It might not be optimal for the whole RI range of 1.33–1.45. degrades when RI is above 1.38. It might not be optimal for the whole RI range of 1.33–1.45. The The proposed sensor achieve better performance thehigher higherRIRIrange rangeby by adjusting adjusting the the center proposed sensor maymay achieve better performance in in the center wavelength. wavelength. As As shown shown in in Figure Figure 9a, 9a, the the SPR SPR dip dip red red shifts shifts quickly quickly while while the the TPP-SPP TPP-SPP dip dip is is always always located located in in the the band band gap gap of of 11 DPC DPC as asthe thesensed sensedRI RIincreases. increases. The The farther farther distance distance leads leads to to weaker weaker interaction andand SPP and Therefore, to strengthen the interaction, interaction between betweenTM-TPP TM-TPP SPP lower and sensitivities. lower sensitivities. Therefore, to strengthen the the center wavelength which decides the location of band gap of 1 DPC should be adjusted according interaction, the center wavelength which decides the location of band gap of 1 DPC should be to the RI according range. Wetoadopt the center as 1200wavelength nm for theasRI1200 range and the adjusted the RI range. Wewavelength adopt the center nm1.37–1.45 for the RI range corresponding band gap of the 1 DPC is shown in Figure 3b. The transmission spectra of the fiber SPR 1.37–1.45 and the corresponding band gap of the 1 DPC is shown in Figure 3b. The transmission sensor a single 35 nm sliverwith layer and the35proposed DPC/Ag are shown in Figure 10a. spectrawith of the fiber SPR sensor a single nm sliver1 layer and sensor the proposed 1 DPC/Ag sensor Here the bilayer period N Here = 4, center wavelength nm, wavelength the thicknessλof layerthe dmthickness = 35 nm, 0= are shown in Figure 10a. the bilayer periodλN = 1200 4, center 0 =silver 1200 nm, the RI of analyte n = 1.4. As calculated by Equation (1), the thicknesses of the TiO and SiOof s nm, the RI of analyte ns = 1.4. As calculated by Equation (1), the thicknesses 2 2 of silver layer dm = 35 layers 102SiO and 171 nm, 205 nm, nm 122 for the of 1000 nm andof1200 the TiOare 2 and 2 layers are 122 102 and and 171 andcenter 205 nmwavelength for the center wavelength 1000nm, nm respectively. withCompared the blue solid Figure 9a,line the in TPP-SPP dip of the sensor and 1200 nm,Compared respectively. withline theinblue solid Figure resonance 9a, the TPP-SPP resonance with λ = 1200 nm red shifts and gets closer to the SPR dip. The tangential electric filed distributions dip of 0the sensor with λ0 = 1200 nm red shifts and gets closer to the SPR dip. The tangential electric of thedistributions TPP-SPP dipsofforthe both center wavelengths shown in Figure 10b. stronger enhancement filed TPP-SPP dips for bothare center wavelengths are The shown in Figure 10b. The at the Ag/analyte interface compared to the electric field in the 1 DPC indicates more SPP component stronger enhancement at the Ag/analyte interface compared to the electric field in the 1 DPC in the hybrid and stronger between SPP with the 1200 nm center indicates moremode SPP component in interaction the hybrid mode andTM-TPP strongerand interaction between TM-TPP and
SPP with the 1200 nm center wavelength. From this point of view, 1200 nm is more suitable than 1000 nm to be set as the center wavelength of 1 DPC in the designed fiber sensor to achieve better performance in the relatively high RI range above 1.37.
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wavelength. From this point of view, 1200 nm is more suitable than 1000 nm to be set as the center wavelength of 1 DPC in the designed fiber sensor to achieve better performance in the relatively high Sensors 2018, 18, x 10 of 12 RI range above 1.37.
Figure 35 nm, nm, 0 0== 1200 Figure 10. 10. (a) (a) Transmission Transmission spectrum spectrum of of the the proposed proposed sensor sensor at at NN==4,4,λλ 1200 nm, nm, ddmm == 35 n = 1.40. The transmission spectrum of the sensor with a single silver layer of 35 nm is also presented nss = 1.40. The transmission spectrum of the sensor with a single silver layer of 35 nm is also presented for (b) Tangential Tangential electric for comparison. comparison. (b) electric field field distribution distribution of of TPP-SPP TPP-SPP dip dip at at the the resonance resonance wavelength wavelength ◦ ◦ 533 resonance angle of 87.56 , 582 nm andnm 87.45 λ0 = 1000 1200 respectively. 533 nm nmand andthethe resonance angle of 87.56, 582 andfor 87.45 for λnm 0 =and 1000 nmnm, and 1200 nm,
respectively.
Figure 11 shows the sensitivity and FOM of the proposed sensor with different center wavelength. Figurethe11RIshows the range sensitivity FOM proposed with center Although detection of the and sensor withofλ0the = 1000 nm is sensor 1.33–1.45, thedifferent sensitivity and wavelength. Although the RI detection range of the sensor with λ 0 = 1000 nm is 1.33–1.45, the FOM decrease at larger RI due to the weaker interaction between TM-TPP and SPP. Thus, the center sensitivity and FOM nm decrease larger RI due to weaker between TM-TPP andcenter SPP. wavelength of 1000 mightatnot be suitable forthe the wholeinteraction RI range of 1.33–1.45. Larger Thus, the center 1000 nm be suitable for the whole RI range 1.33–1.45. wavelength leadswavelength to band gapoflocated at might longer not wavelength range, which strengths theofinteraction Larger center wavelength to band gap longer wavelength range, the between TM-TPP and SPPleads in the higher RIlocated range. atTherefore, the sensor with which centerstrengths wavelength interaction TM-TPP and SPPand in the higher RI RI range. theHowever, sensor with 1200 nm hasbetween much larger sensitivities FOMs in the rangeTherefore, above 1.37. the center lower wavelength 1200 nm has much larger sensitivities and FOMs in the RI range above 1.37. However, limit of its RI detection range rises to 1.37 because the resonance dip moves out of the band gap the lower limit ofwhen its RIthe detection range 1.37. rises to 1.37 because the1400 resonance dip moves out of has the band and disappears RI is below The sensor with nm center wavelength even gap and disappearsand when the RI is below 1.37. TheRIsensor withrange 1400 nm center wavelength even larger sensitivities FOMs in the even smaller detection of 1.40–1.45. From thishas point of larger sensitivities and FOMs in the even smaller RI detection range of 1.40–1.45. From this point of view, we could adopt the appropriate center wavelength for the exact required RI range to achieve view,sensor we could adopt the A appropriate center wavelength for thethe exact required RI range achieve best performance. performance comparison between proposed sensors withtodifferent best sensor performance. performance between the proposed with different center wavelengths is alsoAshown in Tablecomparison 1. The sensor with 1000 nm centersensors wavelength has a RI center wavelengths is also shown Table 1. The sensor with 1000and nm FOM centerare wavelength has than a RI detection range of 1.33–1.45. In thein range below 1.38, its sensitivity always larger − 1 detection range of 132 1.33–1.45. the range below 1.38,in itsthe sensitivity and 1.38, FOMits aresensitivity always larger than 1260 nm/RIU and RIU ,In respectively. However, range above and FOM −1, respectively. However, − 1 1260 nm/RIU and 132 RIU in the range above 1.38, its sensitivity and FOM gradually decrease to 550 nm/RIU and 63 RIU , respectively. In its RI detection range of 1.37–1.45, gradually 550center nm/RIU and 63 RIU , respectively. In and its RI detection range of 1.37–1.45, the sensor decrease with 1200tonm wavelength has−1larger sensitivity FOM than the previous sensor. thehas sensor 1200 nm center has largerwith sensitivity and FOM previous sensor. It best with performances in the wavelength RI range of 1.37–1.40 sensitivity largerthan thanthe 1840 nm/RIU and − 1 It has best performances in the RI range of 1.37–1.40 with sensitivity larger than FOM larger than 146 RIU . 1840 nm/RIU and FOM larger than 146 RIU−1.
Figure 11. Theoretical results of performance of the proposed sensor with different center wavelength. (a) Sensitivity versus ns; (b) FOM versus ns.
1260 nm/RIU and 132 RIU−1, respectively. However, in the range above 1.38, its sensitivity and FOM gradually decrease to 550 nm/RIU and 63 RIU−1, respectively. In its RI detection range of 1.37–1.45, the sensor with 1200 nm center wavelength has larger sensitivity and FOM than the previous sensor. It has best performances in the RI range of 1.37–1.40 with sensitivity larger than Sensors 2018, 18, 2129 11 of 13 1840 nm/RIU and FOM larger than 146 RIU−1.
Figure results of performance of the proposed sensor with different wavelength. Figure 11. 11.Theoretical Theoretical results of performance of the proposed sensor withcenter different center (a) Sensitivity versus n ; (b) FOM versus n . s s wavelength. (a) Sensitivity versus ns; (b) FOM versus ns. Table 1. Comparison between the proposed sensors with different center wavelengths. Configuration
Detection RI Range RIU
Sensitivity nm/RIU
FOM RIU−1
λ0 = 1000 nm, N = 4, dm = 35 nm λ0 = 1200 nm, N = 4, dm = 35 nm λ0 = 1400 nm, N = 4, dm = 35 nm
1.33–1.45 1.37–1.45 1.40–1.45
550–1380 970–1940 1480–2610
62–136 89–152 108–168
The sensor with 1400 nm center wavelength has even better performances than the previous two sensors in its RI range of 1.40–1.45. The FOMs of these sensors are much higher than that of most of the conventional fiber SPR sensors, which are usually below 50 RIU−1 , while the sensitivities are comparable [29]. It is worth noting that the proposed sensor utilizing TPP-SPP hybrid mode has a large extension in the higher limit of the RI detection range which make it able to detect RI very close to the fiber core material 4. Conclusions A novel solid-core fiber RI sensor with 1 DPC/Ag structure based on the TPP-SPP hybrid mode was proposed. Theoretical modelling was carried out to analyze the performance of the designed sensor. The influence of several parameters such as the center wavelength of 1 DPC, the bilayer period and the thickness of silver layer was investigated and the optimal parameter setting was obtained. The optimal center wavelength of 1 DPC changes with the RI detection range. The results show that the FOM of the proposed sensor is much higher than most of the conventional fiber SPR sensors while the sensitivity is comparable. The idea of utilizing TPP-SPP hybrid mode for RI sensing in the solid-core optical fiber structure presented in this paper could contribute to the study and design of the fiber RI sensor based on TPP. Author Contributions: Conceptualization, X.-S.Z.; Data curation, X.Z.; Formal analysis, X.Z.; Investigation, X.Z. and X.-S.Z.; Project administration, Y.-W.S.; Resources, X.-S.Z. and Y.-W.S.; Software, X.Z.; Supervision, Y.-W.S.; Validation, X.Z., X.-S.Z. and Y.-W.S.; Writing—original draft, X.Z.; Writing—review & editing, X.-S.Z. Funding: This research received no external funding. Acknowledgments: This work was supported by the School of Information Science and Engineering at Fudan University, and the authors thank the support of the Key Laboratory for Information Science of Electromagnetic Waves (MoE). Conflicts of Interest: The authors declare no conflict of interest.
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