hv
photonics
Article
A Highly Sensitive Gold-Coated Photonic Crystal Fiber Biosensor Based on Surface Plasmon Resonance Md. Rabiul Hasan 1, *, Sanjida Akter 1 , Ahmmed A. Rifat 2 , Sohel Rana 3 and Sharafat Ali 4 1 2 3 4
*
Department of Electronics & Telecommunication Engineering, Rajshahi University of Engineering & Technology, Rajshahi 6204, Bangladesh;
[email protected] Integrated Lightwave Research Group, Department of Electrical Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia;
[email protected] Department of Electrical & Electronic Engineering, Rajshahi University of Engineering & Technology, Rajshahi 6204, Bangladesh;
[email protected] School of Computer and Communication Engineering, Center of Excellence, Advanced Communication Engineering Cluster, Pauh Putra Campus, Arau 02600, Perlis, Malaysia;
[email protected] Correspondence:
[email protected] or
[email protected]; Tel.: +88-0172-327-2314
Received: 14 February 2017; Accepted: 8 March 2017; Published: 10 March 2017
Abstract: In this paper, we numerically demonstrate a two-layer circular lattice photonic crystal fiber (PCF) biosensor based on the principle of surface plasmon resonance (SPR). The finite element method (FEM) with circular perfectly matched layer (PML) boundary condition is applied to evaluate the performance of the proposed sensor. A thin gold layer is deposited outside the PCF structure, which acts as the plasmonic material for this design. The sensing layer (analyte) is implemented in the outermost layer, which permits easy and more practical fabrication process compared to analyte is put inside the air holes. It is demonstrated that, at gold layer thickness of 40 nm, the proposed sensor shows maximum sensitivity of 2200 nm/RIU using the wavelength interrogation method in the sensing range between 1.33–1.36. Besides, using an amplitude interrogation method, a maximum sensitivity of 266 RIU−1 and a maximum sensor resolution of 3.75 × 10−5 RIU are obtained. We also discuss how phase matching points are varied with different fiber parameters. Owing to high sensitivity and simple design, the proposed sensor may find important applications in biochemical and biological analyte detection. Keywords: surface plasmon resonance; analyte detection; sensitivity; finite element method; optical fiber sensors
1. Introduction In recent years, surface plasmon resonance (SPR) phenomenon has become a hot topic because of its widespread applications in multidisciplinary fields. SPR sensors exhibit high sensitivity characteristics, which enables a new window for numerous promising applications including biological sample detection, antibody-antigen interaction, medical diagnosis, organic-chemical sensing, food quality control, bioimaging, environment monitoring, and so on [1–4]. The idea of a surface plasmon (SP) phenomenon was first theoretically demonstrated by Ritchie et al. in the 1950s [5]. In 1983, SPR sensors were first introduced by Liedberg et al., which was on the basis of prism coupling [6]. The fundamental working principle of a prism coupling SPR sensor is based on the interaction of plasmonic materials and incident transverse magnetic (TM) or p-polarized light. The incident light (photons) has a certain frequency; when this frequency resembles that of the surface electrons of the plasmonic material, the p-polarized light stimulates the free electrons of the metal surface. Due to these collective oscillations, a surface plasmon wave (SPW) is originated in the metal–dielectric interface.
Photonics 2017, 4, 18; doi:10.3390/photonics4010018
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Prism coupled-based biosensors are broadly employed because of the ease of usages. However, it is bulky and includes moving optical and mechanical parts, which limit its application in remote sensing [7]. Miniaturization of SPR-based sensors is necessary in order to reduce the sensor size and manufacturing costs. It is already known that photonic crystal fiber (PCF) exhibits unusual and appealing optical characteristics such as controllable birefringence, high confinement, and single mode propagation. [8]. Using these properties, it is possible to easily manipulate the evanescent field, which is a key parameter for controlling effective sensing performance. In contrast to prism coupling SPR sensors, PCF-based sensors provide tremendous design flexibility. Moreover, by tuning fiber structural parameters (e.g., pitch, air-hole dimension, and number of rings), sensitivity and sensing ranges can be enhanced. Fiber- or waveguide-based refractive index (RI) sensors including fiber Bragg gratings, long period fiber gratings, and micro-ring resonators are already available; however, the main limitations of these sensors are their low sensitivity and wide resonance peaks. Compared to fiber based sensors, SPR sensors provide very high sensitivity, i.e., a very small variation of an analyte’s RI can be detected from the large peak wavelength shift. Higher sensitivity results in better accuracy of the detection of an unknown analyte [9]. The selection of plasmonic material plays a key role in the performance of SPR sensors. Existing works on SPR sensors mostly use gold, silver, copper, and aluminum as the active plasmonic material [10]. Using silver material, it is possible to obtain a sharp resonance peak that increases sensing accuracy. However, silver is chemically unstable and has high susceptibility to oxidization, which reduces sensing performance [11]. Although a thin graphene layer coating can solve the oxidization issue, this additional coating increases fabrication problems and overall manufacturing cost. On the other hand, gold is chemically stable and does not easily oxidize [8]. Moreover, it also shows larger resonance peaks than other available plasmonic materials. Researchers have carried out several distinct outcomes in order to improve the performance of SPR sensors. A SPR biosensor based on polymer PCF coated with metal oxide, where alternate holes in the second layer of the hexagonal lattice were coated with indium tin oxide (ITO), has been proposed [8]. Using the same structural configuration, another PCF has been reported, where a coated graphene-Ag bimetallic layer was used as the analyte channel [12]. A single hexagonal layer-based SPR sensor has been proposed by Gao et al., where a thin gold film and titanium dioxide (TiO2 ) layer were deposited in the outer wall of the air holes [13]. Very recently, graphene-silver deposited core-based SPR sensors with selectively filled analyte channels for RI detection have been proposed [14]. These internally metal film-coated SPR sensors suffer from major drawbacks. In terms of practical sensing, it is difficult to infiltrate the analyte in the inner air holes. Moreover, making a uniform metal coating inside the selective inner air holes makes the practical fabrication process more complex and cumbersome. To overcome these challenges, externally coated metallic film SPR sensors have been introduced. A square lattice D-shaped PCF RI sensor with a nanoscale gold film in the flat outer surface has been reported by Wang et al. [15]. Another hexagonal lattice D-shaped PCF sensor, where a gold layer was deposited on the flat surface to obtain SPR phenomena, has been proposed [16]. These types of PCFs require additional care during the removal of certain portions from the PCF to obtain flat surfaces. Moreover, realizing the practical fabrication for D-shaped PCFs is not feasible due to irregular geometry. Besides, graphene-Ag-based birefringent PCF has been demonstrated by Dash and Jha for RI sensing [17]. This PCF contains an irregular arrangement of air holes that is difficult to fabricate. Another study has been performed by Akowuah et al. for the detection of multichannel sensing [18]. This PCF contains elliptical air holes, which is impractical in terms of practical fabrication. Recently, plasmonic sensors based on metallic nanowire incorporated into the PCF have been experimentally reported using a thin pair of gold nanowires and a gold nanowire array [19,20]. Based on plasmonic resonance, metal-coated tapered fiber sensors have been also explored in the literature. The tapered fiber allows a unique platform to reduce the core and cladding diameter. A tapered single-mode fiber sensor with a small fiber diameter has been fabricated [21]. Moreover, ultrathin metallic nanolayer plasmonic tapered fiber with a small diameter of 20 µm has also been experimentally reported [22].
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In this work, we propose a novel circular lattice air-hole PCF, which consists of two air-hole rings. metal we coating is deposited by a lattice thin layer of gold, whichconsists is placed outside therings. PCF In The this work, propose a novel circular air-hole PCF, which of two air-hole structure. makes the detection simpler andwhich more is straightforward analyte The metal This coating is deposited by a process thin layer of gold, placed outsidebecause the PCFthe structure. can be detected by just dropping it onto the outer surface. The proposed sensor shows a good figure This makes the detection process simpler and more straightforward because the analyte can be detected of merit in terms of amplitude sensitivity, wavelength sensitivity, linearity, and sensor resolution. by just dropping it onto the outer surface. The proposed sensor shows a good figure of merit in terms The circular sensitivity, pattern canwavelength be fabricated by usinglinearity, standard stack-and-draw, capillary stacking, and of amplitude sensitivity, and sensor resolution. The circular pattern die-cast processes [23]. Additionally, we analyze the effect of varying the thickness of gold, pitch, can be fabricated by using standard stack-and-draw, capillary stacking, and die-cast processes [23]. and air-hole dimensions thethe best sensing of performance. Additionally, we analyze in theorder effecttoofobtain varying thickness gold, pitch, and air-hole dimensions in order to obtain the best sensing performance. 2. Design Guidelines and Numerical Methods 2. Design Guidelines and Numerical Methods The cross-section view of the proposed circular lattice PCF sensor is shown in Figure 1a. It consists of two air-hole two missing air holes in the isfirst ringinin order1a.toIt create The cross-section viewrings of thewith proposed circular lattice PCF sensor shown Figure consistsa birefringence effect. For the first ring of the circular lattice PCF, air holes are arranged at a 60° of two air-hole rings with two missing air holes in the first ring in order to create a birefringence effect. ◦ anticlockwise progressive rotation. second ringare is arranged formed by 30° anticlockwise progressive progressive For the first ring of the circular latticeThe PCF, air holes at a 60 rotation of the air holes. worthby noting two air holes in the second ring withItthe rotation. The second ring It is is formed a 30◦ that anticlockwise progressive rotation of together the air holes. is centralnoting hole are relatively The reason is to accumulate the evanescent worth thatmade two air holes insmall. the second ring together with the central hole are electromagnetic made relatively field atThe thereason two opposite sides of the which can easily stimulate surface electrons.sides Here, is small. is to accumulate thePCF, evanescent electromagnetic fieldthe at the two opposite ofΛ the the center-to-center distance between two adjacent air holes, d c is the diameter of central air hole, d 1 is PCF, which can easily stimulate the surface electrons. Here, Λ is the center-to-center distance between the diameter of holes, smallerdc air holes, and d of is central the diameter ofdrest of the air holes. For theairsake of two adjacent air is the diameter air hole, diameter of smaller holes, 1 is the structural simplicity, made c = d 1. The stacked preform arrangement of the proposed PCFdsensor and d is the diameter we of rest of dthe air holes. For the sake of structural simplicity, we made = d c 1. is shown in Figure 1b. The stacked preform arrangement of the proposed PCF sensor is shown in Figure 1b.
Figure 1. (a) view of of thethe proposed circular lattice PCF PCF sensor with Λ = 2 μm, d1 = Figure (a)Cross-sectional Cross-sectional view proposed circular lattice sensor with Λ = d2c =µm, 0.2Λ, d = 0.4Λ, and t g = 40 nm. (b) Stacked preform of the proposed PCF. dc = d1 = 0.2Λ, d = 0.4Λ, and tg = 40 nm. (b) Stacked preform of the proposed PCF.
The background background material material of of the the proposed proposed sensor sensor is is fused fused silica. silica. The The refractive refractive index index of of fused fused The silica can be obtained from the Sellmeier equation [24] silica can be obtained from the Sellmeier equation [24]
B122 B2 2 2 B3 2 2 2 n ( ) 1 (1) B λ B2 λ B3 λ 1 n2 (λ) = 1 + 2 2 C1 + 22 C 2 +2 C2 3 (1) λ − C1 λ − C2 λ − C3 where n is the wavelength dependent refractive index of fused silica, and λ is the wavelength in µ m. where n is the wavelength dependent refractive index of fused silica, and λ is the wavelength in B1, B2, B3, C1, C2, and C3 are the Sellmeier constants. For fused silica, the constants are 0.69616300, µm. B1 , B2 , B3 , C1 , C2 , and C3 are the Sellmeier constants. For fused silica, the constants are 0.407942600, 0.897479400, 0.00467914826, 0.0135120631, and 97.9340025, respectively. Here, tg 0.69616300, 0.407942600, 0.897479400, 0.00467914826, 0.0135120631, and 97.9340025, respectively. Here, represents the fixed thickness of the gold layer, which is deposited on the outer surface of the PCF. tg represents the fixed thickness of the gold layer, which is deposited on the outer surface of the PCF. For this design, we kept tg = 40 nm. We used the Drude-Lorentz model to obtain the dielectric For this design, we kept tg = 40 nm. We used the Drude-Lorentz model to obtain the dielectric constant constant of the gold, and this model is characterized by the following equation [25]: of the gold, and this model is characterized by the following equation [25]:
D2 2L 2 2 ω ∆ε 2 2 ·Ω = ε ∞ − ( D j D ) −( 2 L )2 jL L
Au ε Au
ω (ω + jγD )
(ω − Ω L ) + jΓ L ω
(2) (2)
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where εAu is the permittivity of gold, ε∞ is the permittivity at high frequency with a value of 5.9673, ω is the angular frequency, which is given by ω = 2πc/λ, c is the velocity of light in vacuum, ω D is the plasma frequency, and γD is the damping frequency. Here, ω D /2π = 2113.6 THz, γD /2π = 15.92 THz, and the weighting factor ∆ε = 1.09. The spectral width and oscillator strength of the Lorentz oscillators are given by ΓL /2π = 104.86 THz and ΩL /2π = 650.07 THz, respectively. It is a challenging task to obtain a uniform thickness of the outer gold layer coated on the circular surface of the PCF. There are several methods including radio frequency (RF) sputtering, thermal evaporation, and wet-chemistry deposition that can be implemented to deposit this outer thin layer [26]. However, these normal metal coating methods suffer from extreme surface roughness. Considering this fact, chemical vapor deposition (CVD) [27] is an efficient method that offers uniform nanolayer coating with minimal surface roughness. Metal nanoparticles can also be used by maintaining their size during fabrication to obtain a thin and smooth coating surface [26]. The simulation results were carried out by using finite element method (FEM)-based COMSOL software. We imposed a circular perfectly matched layer (PML) and scattering boundary conditions in order to absorb the outgoing waves from the surface of the PCF. The thickness of the PML was selected by the convergence test, where several simulations were performed with different PML thickness. A constant liquid layer thickness of 1.6 µm was used throughout the simulation. Besides, the element size of the mesh was kept as small as possible so that smaller air holes can be mapped easily. The complete commutation domain took 45,476 triangular elements and 2136 vertex elements. 3. Simulation Results and Performance Analysis The fundamental operating mechanism of PCF-based SPR sensors depends on the mutual interaction between evanescent field and surface electrons, which occurs in the metal–dielectric interface. Due to this phenomenon, SPW that interacts with the sensing layer is generated. The performance of the SPR sensors depends on the geometrical parameters of the PCF. These parameters should be selected in such a way that offers an easy interaction of the evanescent field with the metal surface. The target property is to increase the sensitivity by making a strong coupling between core-guided mode and SPP mode. First, we select the value of dc at 0.2Λ. If we set a value of dc larger than 0.2Λ, that would reduce the effective refractive index (neff ) of the core and deteriorate the guidance along the core [17]. On the other hand, a smaller value of dc would result in strong light confinement in the core that effectively reduces the generation of SPW. The value of d1 was selected at 0.2Λ so that the evanescent field can easily pass towards a metallic layer. A larger value than 0.2Λ could prevent the efficient interaction with the sensing layer. We used d1 = dc , thereby reducing the number of degrees of freedom in the proposed PCF. Additionally, the value of d was kept as 0.4Λ. The reason for choosing comparatively larger air holes is to reduce the light confinement in the metal–dielectric interface [8]. In the entire simulation, the design parameters (Λ = 2 µm, dc = d1 = 0.2Λ, d = 0.4Λ, tg = 40 nm) are kept constant in order to obtain the best sensing performance. The mode field profiles of fundamental x-polarization and y-polarization modes and y-polarization of the SPP mode are shown in Figure 2a–c, respectively. The proposed fiber shows birefringence due to two missing air holes, which induces an effective index difference between the fundamental x-polarization and y-polarization modes. As illustrated in Figure 2b, y-polarization mode shows stronger electric field near the metal surface; therefore, the evanescent field can easily interact with the outer sensing layer compared to the fundamental x-polarization mode (shown in Figure 2a). As a result, the fundamental y-polarization mode is strongly coupled with the surface electrons of gold.
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Figure 2. Mode field distribution of fundamental (a) x-polarization core mode, (b) y-polarization core m. (d) Dispersion relation between the fundamental mode, and (c) y-polarization SPP mode at 0.652 µ µm. core-guided mode and SPP mode with naa ==1.36 1.36and and ttgg==3030nm. nm.
Figure 2d 2d shows shows the the nneff of core-guiding mode, the surface plasmon polariton (SPP) mode, and Figure eff of core-guiding mode, the surface plasmon polariton (SPP) mode, and the loss with analyte RI RI (na(n ) of) the loss spectra spectra of of the thefundamental fundamentalx-polarization x-polarizationand andy-polarization y-polarizationmodes modes with analyte a 1.36. The effective refractive index of fundamental y-polarized SPP mode was taken from the of 1.36. The effective refractive index of fundamental y-polarized SPP mode was taken from the simulation software softwarefor fordifferent different operating wavelengths. The effective refractive were simulation operating wavelengths. The effective refractive indicesindices were plotted plotted as a function of wavelength tothe obtain the dispersion curve SPP The mode. SPPiscurve is as a function of wavelength to obtain dispersion curve for SPP for mode. SPPThe curve shown shown in Figure 2d indicated by a solid black line. It can be evident that, at 0.6 μm, the real part of in Figure 2d indicated by a solid black line. It can be evident that, at 0.6 µm, the real part of the neff thethe nefffundamental of the fundamental y-polarization mode SPPcoincide mode coincide with eachThis other. This is of y-polarization mode and theand SPPthe mode with each other. is known known as the resonance or phase matching condition, andoperating the operating wavelength case μm) as the resonance or phase matching condition, and the wavelength (in (in thisthis case 0.60.6 µm) is is known as resonance wavelength. At this wavelength, a sharp peak is observed that represents the known as resonance wavelength. At this wavelength, a sharp peak is observed that represents the maximum energy energy transfer transfer from from core-guided core-guided mode mode to to the the SPP SPP mode. mode. The maximum The dispersion dispersion relation relation between between the core-guided mode and the SPP mode is shown in Figure 2d. From this figure, can be be also also the core-guided mode and the SPP mode is shown in Figure 2d. From this figure, it it can concluded that the fundamental y-polarization mode shows a higher and sharper resonance peak concluded that the fundamental y-polarization mode shows a higher and sharper resonance peak than that thatofof fundamental x-polarization to the low loss of the than thethe fundamental x-polarization mode.mode. Due toDue the very low very loss depth of thedepth fundamental fundamental x-polarization, in the rest of the study, we only considered the fundamental x-polarization, in the rest of the study, we only considered the fundamental y-polarization mode for y-polarization mode for the performance analysis. the performance analysis. Confinement loss plays a a vital vital role role in in the the evaluation evaluation of of the the sensor’s sensor’s performance, performance, and and this this Confinement loss plays parameter can be obtained by using the following equation [28]: parameter can be obtained by using the following equation [28]:
(dB/ cm) 8.686 k0 Im(neff ) 1044
α(dB/cm) = 8.686 × k0 Im(ne f f ) × 10
(3) (3)
where k0 = 2π/λ is the wave number in the free space, λ is the operating wavelength, and Im(neff) is where k0 = 2π/λ is of thethe wave number in the free space, λ is the operating wavelength, and Im(neff ) is the imaginary part effective refractive index. the imaginary part of the effective refractive index. The real part of the neff of the SPP mode is highly dependent on the small variation of analyte RI. The real part of neff ofRIthe SPP mode is highly onresponsible the small variation of analyte A slight variation of the analyte results in a change of dependent neff, which is for the shift in the RI. A slight variation of analyte RI results in a change of n , which is responsible for the shift eff phase matching point towards other resonance wavelengths. Figure 3a shows the phenomena in of the the phase matching point towards other resonance wavelengths. Figure 3a shows the phenomena of the changing phase matching points due to the variation of na from 1.33 to 1.36. As clearly demonstrated changing phase matching points due toofthe variation of na from to 1.36. clearly demonstrated from the figure, increasing the value analyte RI causes red 1.33 shifting, i.e.,Asresonance wavelength shift towards a higher wavelength. When RI of analyte is increased, it turns to shift the real part of
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Photonics 2017, 4, 18 from the figure,
11 increasing the value of analyte RI causes red shifting, i.e., resonance wavelength6 of shift towards a higher wavelength. When RI of analyte is increased, it turns to shift the real part of the neff the neff SPP of the SPPinmode 2da towards a higher As a consequence, resonanceis of the mode Figurein2dFigure towards higher value. As a value. consequence, the resonancethe wavelength wavelength is increased towards higher wavelength. Due to the change of n a from 1.33 to 1.34, from increased towards higher wavelength. Due to the change of na from 1.33 to 1.34, from 1.34 to 1.35, and 1.34 1.35, 1.35 towavelengths 1.36, resonance wavelengths are shifted to 0.6–0.61 m, 0.61–0.63 m, fromto1.35 toand 1.36,from resonance are shifted to 0.6–0.61 µm, 0.61–0.63 µm,µand 0.63–0.652µµm, and 0.63–0.652 µ m, respectively, with t g = 40 nm. It can be observed from Figure 3a that loss depth respectively, with tg = 40 nm. It can be observed from Figure 3a that loss depth can be increased by can be increased by increasing the analyte RI. of Increasing the value of nof a leads to a reduction of the increasing the analyte RI. Increasing the value na leads to a reduction the index contrast between index contrast between the core and cladding, which leads to an increase in confinement loss.loss The the core and cladding, which leads to an increase in confinement loss. The lowest confinement of lowest confinement loss of 66 dB/cm was found for an analyte RI of 1.33, where a broadening of the 66 dB/cm was found for an analyte RI of 1.33, where a broadening of the resonance spectrum was also resonance was also maximum lossµm, peakwhich was observed at 0.652 m,analyte which is observed.spectrum The maximum lossobserved. peak wasThe observed at 0.652 is 157 dB/cm for µan RI 157 dB/cm for an analyte RI of 1.36. of 1.36.
Amp. sensitivity (RIU -1)
Loss (dB/cm)
200 na=1.33 na=1.34 na=1.35 na=1.36
150 100 50
(a)
0 0.52
0.56
0.6
0.64
Wavelength (m)
0.68
0.72
100
na=1.34 na=1.35 na=1.36
0 -100 -200 -300 0.54
(b) 0.58
0.62
0.66
Wavelength (m)
0.7
0.74
Figure Figure3.3.(a) (a)Fundamental Fundamentalloss lossvariation variationfor forincreasing increasinganalyte analyteRI RIfrom from1.33 1.33toto1.36 1.36and and(b) (b)amplitude amplitude sensitivity d =d0.4Λ, andand tg =tg40= nm. sensitivityfor fordifferent differentanalyte analyteRI RIwith withΛΛ==22μm, µm,ddc c= =d1d=1 0.2Λ, = 0.2Λ, = 0.4Λ, 40 nm.
The performance of the PCF-based SPR sensor can be measured by the sensitivity. We analyzed The performance of the PCF-based SPR sensor can be measured by the sensitivity. We analyzed the sensitivity of the proposed fiber by using wavelength interrogation and amplitude interrogation. the sensitivity of the proposed fiber by using wavelength interrogation and amplitude interrogation. In wavelength interrogation, wavelength sensitivity can be computed by the following formula [14]: In wavelength interrogation, wavelength sensitivity can be computed by the following formula [14]: S (nm/ RIU) peak na (4) Sλ (nm/RIU) = ∆λ peak /∆n a (4) where Δλpeak is the difference between peak wavelength shifts and Δna is the variation of analyte RI. where ∆λpeak is the shows difference wavelength shifts andΔn ∆n the variation of analyte RI. The proposed fiber a Δλbetween peak of 10 peak nm, 20 nm, and 22 nm for a a ofis0.01, where changes in the The proposed fiber shows a ∆λpeak and of 101.35–1.36. nm, 20 nm, and the 22 nm for ∆na of 0.01, where changes inare the analyte RI are 1.33–1.34, 1.34–1.35, Thus, calculated wavelength sensitivities analyte RI and are 1.33–1.34, 1.34–1.35, and 1.35–1.36. Thus, the calculatedsensitivity, wavelength are 1000, 2000, 2200 nm/RIU, respectively. The maximum wavelength i.e.,sensitivities 2200 nm/RIU 2000, andwith 2200previously nm/RIU, respectively. The maximum sensitivity, i.e., 2200 is1000, comparable proposed results [8,12,18,28].wavelength The resolution of the sensor is nm/RIU another is comparable with previously proposed [8,12,18,28]. The resolution of the sensor is another important parameter that represents how aresults small change of analyte RI can be detected by the sensor. important parameter that represents how a small change of analyte RI can be detected by the sensor. The resolution of the proposed sensor can be obtained by the given formula [15]: The resolution of the proposed sensor can be obtained by the given formula [15]: R(RIU) na min peak (5) . R(RIU) = ∆n a × ∆λmin /∆λ peak . (5) Assuming that Δna = 0.01, Δλmin = 0.1, and Δλpeak = 22 nm, we found the resolution of the proposed sensor to bethat as ∆n high=as 4.55∆λ × 10−5=, 0.1, which comparable with [8,12,16,18,28]. Therefore, any small Assuming 0.01, andis∆λ a min peak = 22 nm, we found the resolution of the proposed −5 change RI in order can be detected with a high degree of accuracy. −510 sensor in to analyte be as high asthe 4.55 × 10of , which is comparable with [8,12,16,18,28]. Therefore, any small The wavelength interrogation method requires spectral manipulation sensitivity that − 5 change in analyte RI in the order of 10 can be detected with a high degreetoofobtain accuracy. makesThe detection process complex. On the other hand, amplitude interrogation can solve this issuethat by wavelength interrogation method requires spectral manipulation to obtain sensitivity measuring sensitivity at acomplex. specific wavelength. amplitude sensitivity can be byissue the makes detection process On the otherThe hand, amplitude interrogation canobtained solve this following equation [28]: by measuring sensitivity at a specific wavelength. The amplitude sensitivity can be obtained by the
( , na ) 1 S A (RIU 1 ) (6) 1 ) ∂α −1 ( , n n(aλ, n a ) a S A (RIU ) = − (6) α(λ, n a ) ∂n a where α(λ,na) is the overall propagation loss at RI of na, and ∂α(λ,na) is the loss difference between two loss spectra. Figure 3b depicts the amplitude sensitivity of the proposed sensor for different analyte RI values. We found a maximum amplitude sensitivity of about 266 RIU−1 at 0.655 µ m for an analyte RI of 1.35. Moreover, an amplitude sensitivity of about 185 and 241 RIU−1 was obtained for analyte RI values of 1.34 and 1.36, respectively. In this case, the designed sensor provides a following equation [28]:
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Loss (dB/cm)
200
na=1.35 na=1.36
tg=30 nm tg=40 nm tg=50 nm
150 100 50 0 0.54
(a)
0.58
0.62
0.66
Wavelength (m)
0.7
0.74
Amp. sensitivity (RIU -1)
where α(λ,na ) is the overall propagation loss at RI of na , and ∂α(λ,na ) is the loss difference between two loss spectra. Figure 3b depicts the amplitude sensitivity of the proposed sensor for different analyte RI values. We found a maximum amplitude sensitivity of about 266 RIU−1 at 0.655 µm for an analyte Photonics 2017, 4, 18 7 of 11 RI of 1.35. Moreover, an amplitude sensitivity of about 185 and 241 RIU−1 was obtained for analyte −5 by maximum resolution of 3.75 × 10In a 1% sensor changeprovides of the transmitted intensity RI values ofsensor 1.34 and 1.36, respectively. thisassuming case, the that designed a maximum sensor − 5 is detectable. resolution of 3.75 × 10 by assuming that a 1% change of the transmitted intensity is detectable. There are significant impacts of loss depth and amplitude sensitivity on the variation of gold layer thickness. thickness. In InFigure Figure4a,4a, loss spectra different thickness are shown with analyte RI loss spectra for for different goldgold thickness are shown with analyte RI values values 1.35 andrespectively. 1.36, respectively. As depicted the figure for a fixed analyte RI, increasing the of 1.35 of and 1.36, As depicted in the in figure for a fixed analyte RI, increasing the gold gold thickness reduces loss depth. The reason the higher damping losstodue the increase in layer gold thickness reduces loss depth. The reason is theishigher damping loss due thetoincrease in gold layer thickness. Moreover, increasing gold thickness a shifting theloss peak loss towards a thickness. Moreover, increasing gold thickness causescauses a shifting of the of peak towards a longer longer wavelength. Amplitude sensitivity as aoffunction of wavelength gold layer wavelength. Amplitude sensitivity as a function wavelength for different for golddifferent layer thicknesses is thicknesses is shown Figurethat 4b.the It proposed is evidentsensor that shows the proposed sensor shows of amplitude shown in Figure 4b. It isinevident amplitude sensitivities 188, 266, − 1 −1 sensitivities 188,thicknesses 266, and 241 RIU for 50 thicknesses of 30, 40, andmaximum 50 nm, respectively. Since and 241 RIU of for of 30, 40, and nm, respectively. Since sensitivity can be maximum sensitivity benm. achieved by setting tg of 40 the nm.analysis, Therefore, throughout analysis, tg = achieved by setting tgcan of 40 Therefore, throughout tg = 40 nm wasthe used to ensure 40 nm sensing was used to ensure better sensing performance. better performance. 100 tg=30 nm tg=40 nm tg=50 nm
0
-100
-200 (b) -300 0.58
0.6
0.62
0.64
0.66
0.68
Wavelength (m)
0.7
0.72
Figure 4. (a) (a) Fundamental Fundamental loss the proposed proposed sensor sensor for for different different gold gold layer layer thicknesses thicknesses Figure 4. loss variation variation of of the and forfor different gold layer thicknesses withwith Λ = 2Λ μm, c = d1 d =c0.2Λ, d = 0.4Λ and (b) (b)amplitude amplitudesensitivity sensitivity different gold layer thicknesses = 2dµm, = d1 and = 0.2Λ, and for an analyte RI of 1.35. d = 0.4Λ for an analyte RI of 1.35.
A changing pitch and diameter of the central air hole significant affects confinement loss. Loss A changing pitch and diameter of the central air hole significant affects confinement loss. Loss spectra and sensitivity of the proposed sensor for the changing pitch values are illustrated in Figure 5a,b. spectra and sensitivity of the proposed sensor for the changing pitch values are illustrated in Figure 5a,b. As the pitch values are increased from 1.8 to 2.1 µ m, loss depth reduces from 242 to 130 dB/cm for an As the pitch values are increased from 1.8 to 2.1 µm, loss depth reduces from 242 to 130 dB/cm for analyte RI of 1.36. Due to pitch change, no peak loss shift was observed for a fixed analyte RI. The an analyte RI of 1.36. Due to pitch change, no peak loss shift was observed for a fixed analyte RI. proposed sensor shows almost identical sensitivity for pitch values between 1.8 and 2.1 µ m. On the The proposed sensor shows almost identical sensitivity for pitch values between 1.8 and 2.1 µm. On the other hand, the diameter of the central air hole is varied from null to 0.3Λ for an analyte RI of 1.36, other hand, the diameter of the central air hole is varied from null to 0.3Λ for an analyte RI of 1.36, and and the results are shown in Figure 5c. When no central air hole is used, we found a loss depth of the results are shown in Figure 5c. When no central air hole is used, we found a loss depth of 68 dB/cm. 68 dB/cm. At dc = 0.3Λ, the loss depth increases to 182 dB/cm. Unlike the pitch results, an enlarging At dc = 0.3Λ, the loss depth increases to 182 dB/cm. Unlike the pitch results, an enlarging central central air-hole diameter causes an increase in loss depth. Therefore, the pitch and diameter of the air-hole diameter causes an increase in loss depth. Therefore, the pitch and diameter of the central air central air hole should be chosen in such a way that the best sensing performance is confirmed. hole should be chosen in such a way that the best sensing performance is confirmed. Considering this Considering this fact, we used Λ = 2 μm and dc = 0.2Λ in the entire analysis of the proposed sensor. fact, we used Λ = 2 µm and dc = 0.2Λ in the entire analysis of the proposed sensor. In real-world sensing applications, a sensor generally operates at a fixed wavelength. Therefore, it is necessary to discuss the dependence of the amplitude sensitivity as a function of various geometrical parameters such as pitch and air-hole diameters. Figure 6a shows the effect of a changing pitch value on amplitude sensitivity at a fixed wavelength of 0.655 µ m for an analyte RI of 1.35. As illustrated in the figure, amplitude sensitivity gradually decreases with increasing pitch. It should be noted that amplitude sensitivity is calculated by varying pitch only while other parameters are kept constant. The dependence of changing the air-hole diameter (d and d1) on amplitude sensitivity is shown in Figure 6b, with a fixed wavelength of 0.655 µ m and an analyte RI of 1.35. As seen from the figure, increasing the value of d results in no significant change in amplitude sensitivity. The variation of amplitude sensitivity with increasing d1 is also shown in the inset. It can be found that increasing d1 from 0.3 to 0.5 µ m changes amplitude sensitivity from 268 to 261 RIU−1.
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=2.0 m (b) =2.1 m (a) Figure 5. 5. (a) for increasing pitch values values from 1.8 1.8 to to 2.1 2.1 µm; µ m; (b) (b) amplitude amplitude Figure (a) Fundamental Fundamental loss loss spectrum spectrum for increasing pitch from -300 0 0.58 0.6loss 0.62 0.64 0.66 0.68 0.7central 0.72 sensitivity for different pitch values with an analyte RI of 1.35; (c) spectrum for different 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72 sensitivity for different pitch values with an analyte RI of 1.35; (c) loss spectrum for different central
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Wavelength (m) air-hole diameter diameterWavelength with dd == 0.4Λ 0.4Λ and air-hole with and tt == 40 40 nm nm with with an an analyte analyte RI RI of of 1.36. 1.36.
(m)
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Figure 6. Variation of amplitude sensitivity due to the change of (a) pitch values from 1.8 to 2.2 μm and (b) air-hole diameter, d from 0.6 to 1 μm and d1 from 0.3 to 0.5 μm at a fixed wavelength of 0.655 μm. -265 -255 -260 (RIU )
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Amp. sensitivity (RIU -1)
Amp. sensitivity (RIU -1)
-265 In real-world sensing applications, a sensor generally operates -255 -260at a fixed wavelength. Therefore, 150 dc=0.2 dc=0.3 it is necessary to discuss the dependence of the amplitude sensitivity as a function of various =0.655 m and na=1.35 -260 -266 -2656a shows the effect of a changing 100 and air-hole diameters. Figure geometrical parameters such as pitch pitch -265 value on amplitude sensitivity at a fixed wavelength of 0.655 µm for an analyte RI of 1.35. As -270 -267 50 0.3 increasing 0.35 0.4 0.45 illustrated in the figure, amplitude sensitivity gradually decreases with pitch.0.5It should be (c) d1 (m) -270 noted that amplitude sensitivity is calculated by varying pitch only while other parameters are kept 0 =0.655 m 0.58 0.6 0.62 0.64 diameter 0.66 -268 0.68 (d0.7and0.72 constant. d1 ) on amplitude sensitivity is -275 The dependence of changing the air-hole na=1.35 Wavelength ( m) (a) shown in Figure 6b, with a fixed wavelength of 0.655 µm and an analyte RI(b) of 1.35. As seen from the -269values from 1.8 to 2.1 µ m; (b) amplitude -280 Figure spectrum forsignificant increasing pitch figure, increasing the value of d results change sensitivity. The 0.6 in amplitude 0.7 0.8 0.9 variation 1 1.8 5. (a) Fundamental 1.9 2loss 2.1in no 2.2 sensitivity for different pitch values with an analyte RI of 1.35; (c) loss spectrum for different Air-hole diameter, d (increasing central m) Pitch, (m) of amplitude sensitivity withincreasing d1 is also shown in the inset. It can be found that d1 diameter with d amplitude = 0.4Λ and t sensitivity = 40 nm with an analyte 1.36.−1 . from air-hole 0.3 to 0.5 µm changes from 268 to RI 261ofRIU
-1
m should and na=1.35 A good =0.655 sensor have high linearity response. The linear fitting of the resonance -260 -266 -265 wavelength with varying analyte RI values from 1.33 to 1.36 is shown in Figure 7. The regression -265 of the linear line fitting is given by Y = 1.82X − 1.825, equation where Y indicates the resonance -270 -267 0.3 0.35 0.4 0.45 0.5 wavelength and X indicates analyte RI. The R-square value for the linear line is 0.9953, which d1 (fitting m) -270 indicates very good linearity. Due to good line fitting characteristics, the proposed =0.655 sensor m can be -268 implemented for practical RI detection. -275 na=1.35 (a) (b) In practical applications, the fluctuation of input light intensity is interrupted so that the exact -269 -280 0.8 0.9 amplitude 1 value of1.8 amplitude obtained.2.2Due to the 0.6 change in0.7 input intensity, the 1.9sensitivity 2 can be2.1 Air-hole diameter, d ( m) Pitch, ( m) sensitivity varies. The geometric parameters of the PCF determine the transmitted and reflected waves (S-parameter). In this study, we mainly focus on the transmittance of the guided mode, i.e., Figure 6. 6. Variation of amplitude amplitude sensitivity sensitivity due due to to the the change change of of (a) (a) pitch pitch values values from from 1.8 1.8 to to 2.2 2.2 µm μm and and Figure Variation of the evanescent field. The diameter of the air holes and pitch values determine how much the (b) air-hole air-hole diameter, diameter, d from from 0.6 (b) 0.6 to to 11 μm µm and and dd11from from0.3 0.3toto0.5 0.5μm µmatataafixed fixedwavelength wavelengthofof0.655 0.655μm. µm. evanescent field propagates towards the metal interface. In the case of the proposed PCF, the central air hole is required to prohibit the light wave centered in the core, could reduce the chances of A good sensor should have high linearity response. Thewhich linear fitting of the resonance reaching the with metalvarying interface. On the hand, is kept as low as possible since7. smaller air holes wavelength analyte RIother values fromd11.33 to 1.36 is shown in Figure The regression provide enough space to guide the evanescent field. Thus, the transmittance of the evanescent field equation of the linear line fitting is given by Y = 1.82X − 1.825, where Y indicates the resonance
wavelength and X indicates analyte RI. The R-square value for the linear line fitting is 0.9953, which indicates very good linearity. Due to good line fitting characteristics, the proposed sensor can be implemented for practical RI detection.
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A good sensor should have high linearity response. The linear fitting of the resonance wavelength with varying analyte RI values from 1.33 to 1.36 is shown in Figure 7. The regression equation of the linear line fitting is given by Y = 1.82X − 1.825, where Y indicates the resonance wavelength and X indicates analyte RI. The R-square value for the linear line fitting is 0.9953, which indicates very good linearity. Due to good line fitting characteristics, the proposed sensor can be implemented for practical RI detection.
Figure 7. Linear fitting of the resonance wavelength as a function of analyte RI for Λ = 2 µm, dc = d1 = 0.2Λ, d = 0.4Λ, and tg = 40 nm.
In practical applications, the fluctuation of input light intensity is interrupted so that the exact value of amplitude sensitivity can be obtained. Due to the change in input intensity, the amplitude sensitivity varies. The geometric parameters of the PCF determine the transmitted and reflected waves (S-parameter). In this study, we mainly focus on the transmittance of the guided mode, i.e., the evanescent field. The diameter of the air holes and pitch values determine how much the evanescent field propagates towards the metal interface. In the case of the proposed PCF, the central air hole is required to prohibit the light wave centered in the core, which could reduce the chances of reaching the metal interface. On the other hand, d1 is kept as low as possible since smaller air holes provide enough space to guide the evanescent field. Thus, the transmittance of the evanescent field increases. Furthermore, d is kept comparatively large, which ensures that the evanescent field is guided in the two opposite directions along the x-axis. It also increases the transmittance of the proposed sensor, which significantly increases the amplitude sensitivity. The proposed PCF can be fabricated by the standard stack-and-draw method [29]. The designed PCF has only two rings, and the pitch size is 2 µm; as a result, it has small diameter of around 10 µm. However, the standard PCF size is 125 µm. Our proposed PCF can be realized in two different ways: (1) by using external silica solid-rods and mixing them with the background material of fused silica after applying vacuum during the fabrication; and (2) jacketing the proposed PCF 2–3 times. In case of the proposed PCF, a large solid silica surface will be formed outside of the cladding. This is the similar phenomenon as illustrated in [30]. Later on, by polishing the PCF surface we can achieve the proposed PCF. Additionally, the proposed PCF size can also be achieved by following the tapering technique [31]. 4. Conclusions We propose a highly sensitive circular lattice PCF-based SPR sensor for the detection of unknown analytes. The numerical investigations were performed by using FEM with PML and scattering boundary conditions. The thin layer of gold and analyte were both placed at the outer surface of the PCF, which permitted easy fabrication and more practical detection. The proposed sensor shows a maximum sensitivity of 266 RIU−1 , which yields a maximum resolution of 3.75 × 10−5 RIU. Moreover, loss depth variations for different gold layer thicknesses, analyte RI values, pitch values, and central
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air-hole diameters are also rigorously discussed. Due to high sensitivity and high linearity, the proposed PCF SPR sensor can be considered ideal for refractive index detections. Author Contributions: M.R. Hasan and A.A. Rifat conceived the design; M.R. Hasan and S.A. Emi performed the simulations; M.R. Hasan and S. Ali analyzed the simulation data; M.R. Hasan wrote the paper; M.R. Hasan, A.A. Rifat and S. Rana made revisions and finalized the paper. Conflicts of Interest: The authors declare no conflict of interest.
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