Highly sensitive double D-shaped channel photonic crystal fiber based plasmonic refractive index sensor

M. Ifaz Ahmad Isti; M. Hussayeen Khan Anik; Samiha Nuzhat; Rubel Chandra Talukder; Sadia Sultana; Shovasis Kumar Biswas; Shovasis Kumar Biswas; Hriteshwar Talukder; Hriteshwar Talukder

doi:10.1364/OPTCON.452020

1. Introduction

The diverse contributions of the scientific communities in technological advancement have led us to the efficacious detection of sample analytes. Amidst all, in the world of optical physics, the SPR technology has been a carrier of success in bio-sensing and imaging, medical diagnostics, detection of gas, glucose level monitoring, disease detection, monitoring of the environment, temperature sensing and many more [1–3]. The application of this technology made its way to photonic metamaterials, light-harvesting and transformation optics [4 6]. In 1907, with the contribution of Zenneck, the theoretical introduction to SPR first came in [7]. The physical presence of the surface plasmon waves (SPW) was demonstrated at the metal-dielectric interface in 1957 [8]. Conventional SPR sensors based on prism coupling can be put under two classifications: Kretschmann [9] and Otto configurations [10]. In 1983, SPR sensors were first introduced based on prism coupling [11]. The conventional prism coupling SPR system is being replaced by PCF SPR sensors in the present days due to its bulky nature and hindrance in remote sensing applications. These sensors are now more favored for their miniaturized features, and simple design flexibility. PCF SPR sensors can be figuratively distinguished into two classes: internally and externally coated sensors. Internally coated sensors have selectively filled analyte channels, which decreases the fabrication feasibility. As the sensing performance is a function of the selection of plasmonic metal, gold and silver are generally the topmost choices. Usage of silver portrays a steeper peak point at resonance, with respect to the alternative plasmonic metals. Yet it forms brittle oxide layers in an aqueous environment, which impedes its extensive applications in plasmonic sensors [12]. Gold is more chemically inert and stable for a longer period, has easier structural formation and most importantly, oxidation of the metal film is highly unlikely [13]. Moreover, it displays greater resonance peak shifts in comparison to the usage of other plasmonic metals. However, the sensing accuracy can get decreased due to its large absorption coefficient, which results in depicting a broader resonance band. But, with a better spatial design structure, this blemish can be resolved. Numerous contributions came from different scientific communities in sensor designing. A sensor with silver and graphene layered selective analyte channels having a sensing range from 1.46–1.49 of the analyte index has shown a wavelength sensitivity (S_λ) and a sensor resolution (R) of 3000 nm/RIU and 3.33×10⁻⁵ RIU, respectively along with an amplitude sensitivity (S_A) of 418 RIU⁻¹ [14]. A PCF with a polymer layer and a conductive metal-oxide has portrayed an S_λ, R and S_A of 2000 nm/RIU, 5×10⁻⁵ RIU and 80 RIU⁻¹, respectively [15]. Another H-shaped deep groove fiber portrayed better results. But the deep grooves make the fiber more fragile [16]. Besides, a geometrical design with diamond ring PCF portrays an S_λ and S_A of 6000 nm/RIU and 508 RIU⁻¹, respectively [17]. An S_λ, S_A and R of 4000 nm/RIU, 320 RIU⁻¹ and 2.5×10⁻⁵ RIU has been portrayed by a gold layered SPR sensor with an external sensing mechanism, respectively [18]. All these sensors have been implemented with the incorporation of different designs with different metal layers. But in terms of sensitivity with respect to analyte changes, the results are not highly satisfactory. A D-shaped sensor with gold and TiO₂ metal film has shown S_λ and S_A of 46,000 nm/RIU and 1086 RIU⁻¹, having a sensing range of 1.33–1.43 [19]. The majority of these works do not focus on lower refractive index analyte detections, particularly, less than 1.30. A D-shape design has been proposed for low refractive index detection, particularly, 1.27–1.32 [20].

The work in this paper comes forward with a dual slotted D-shape microchannel design structure, based on an external sensing mechanism along with the presence of circular air holes. Usage of gold as the plasmonic metal layer enhances the resonance peak shifts. Airholes are arranged in a square lattice arrangement, with three different diameters. The design structure attains the highest wavelength sensitivity of 34,000 nm/RIU and the highest amplitude sensitivity of 331 RIU⁻¹ with a wide sensing range of 1.16–1.37RI. The sensor has a wavelength resolution of 2.94×10⁻⁶ RIU, all of which make it a worthy candidate for efficacious analyte detection. Usage of the plasmonic metal, gold with thickness scaled down below 10 nm is regarded non-viable as it leads to discontinuous film [21]. Our offered structure has a metal thickness of 80 nm, which is well above the threshold thickness. Extensive analysis has also been conducted to investigate the fabrication tolerance in terms of the metal breadth, the air hole area, and the pitch.

2. Theoretical considerations

Surface plasmons are free electron oscillations occurring in a metal conductor. A gathering of these electrons is considered as plasma excitations. The application of an external field causes longitudinal oscillations to take place in the conductor to create surface plasmons due to electronic transportations [1]. The generation of surface plasmon polaritons requires a metal-dielectric interface which can support the occurrence of resonance, where surface plasmon waves (SPW) get formed, which propagate through the interface. The SPW has a propagation constant of β [22] :

(1)$$\beta = \frac{\omega }{c}\sqrt {\frac{{{\epsilon _M}{\epsilon _D}}}{{{\epsilon _M} + {\epsilon _D}}}}. $$

Here, ${\boldsymbol \omega }$ is the angular frequency, the velocity of light is c. ${\mathrm{\epsilon }_{\boldsymbol M}}$ and ${\mathrm{\epsilon }_{\boldsymbol D}}$ are the dielectric permittivity of the metal and the dielectric medium, respectively. When the propagation constants are matched, the phase-matching condition is established where the phases of SPW and externally applied electromagnetic (EM) field of light, coincide with each other. In PCF based SPR sensors, the propagation of light occurs by modified total internal reflection (TIR) or by optical confinement of light through the photonic bandgap. At the phase-matching condition, the frequency and momentum of the surface plasmon waves and that of the introduced EM field coincide, thereby enabling resonance to take place such that there is maximum modal power delivery from the core mode to the surface plasmon polariton (SPP) mode. A leaky Gaussian core mode energy loss summoned from the incoming light is the primary observation at that match. As the propagation constants are matched, the crossing of the real part of the core and the SPP mode ensures the resonance condition. The relation of the effective refractive index and the propagation constant is stated as [23]:

(2)$${{\boldsymbol n}_{\; {\boldsymbol{eff}}}} = \frac{{{\boldsymbol \beta }({{\boldsymbol \lambda },{\boldsymbol n}({\boldsymbol \lambda } )} )}}{{{{\boldsymbol k}_0}}}$$

Here, ${k_0} = \frac{{2\pi }}{\lambda }$ which is the vacuum wave number. $\beta $ is the propagation constant whereas ${\eta _{eff}}$ stands for the effective mode index.

3. Modelling and numerical analysis

The designed model has a dual slotted D-shape microchannel, introduced on the two sides, portrayed in Fig. 1(a). Air holes with three different diameters da₁, da₂, and da₃ with square lattice have been arranged, with a decrement in the diameters, going outwards to inwards. The two open channels have a radius (r_c) of 2.4µm. The analyte has to be placed outside the fiber. Gold is the plasmonic metal. As gold does not show strong attachment with silica, TiO₂ effectively attaches gold with silica and improves the coupling between the modes. The ideal parameters found from the investigation of the design are da₁= 1.45µm, da₂= 1.65µm and da₃= 2.2µm, the thickness of gold layer t_gold= 80nm and that of TiO₂ is 9nm. The fiber diameter is 19.2µm. The span between successive airholes is termed as the pitch, Λ. The pitch size, Λ is kept at 3µm. Comsol Multiphysics has been utilized as the numerical simulation tool. A non-physical PML kept close to 10% of the fiber diameter with the analyte, ideally works well as the radiation absorber [24]. The PML radius is kept at 12.2µm with a thickness of 1.2µm. The PML absorbs reflected light at the boundary and acts as the boundary condition. Stack and draw technique can be used for building square lattice airholes and the side polishing scheme to polish the fiber for the D-shape and focused ion beaming to implement the microchannel [25]. Chemical vapor deposition (CVD) is widely applied for gold and TiO₂ layer depositions. Atomic layer deposition is the other option [26] (details in Supplement 1). Refractive index for the background material silica ${\eta}_{{si}}$ can be obtained via the Sellmeier equation [23].

(3)$${\boldsymbol \eta }_{{\boldsymbol{si}}}^2({\boldsymbol \lambda } )= 1 + \frac{{{{\boldsymbol B}_1}{{\boldsymbol \lambda }^2}}}{{{{\boldsymbol \lambda }^2} - {{\boldsymbol C}_1}}} + \frac{{{{\boldsymbol B}_2}{{\boldsymbol \lambda }^2}}}{{{{\boldsymbol \lambda }^2} - {{\boldsymbol C}_2}}} + \frac{{{{\boldsymbol B}_3}{{\boldsymbol \lambda }^2}}}{{{{\boldsymbol \lambda }^2} - {{\boldsymbol C}_3}}}$$

Fig. 1. (a) Geometry and (b) Experimental setup for the proposed design

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Here, B_i and C_i are the Sellmeier coefficients for silica, where i =1,2,3

The dielectric function of the gold as the plasmonic material was derived from the Drude Lorentz model [26]

(4)$${\epsilon _d} = {\epsilon _\infty } - \frac{{\omega _D^2}}{{\omega ({\omega + j\gamma D} )\; }} - \frac{{\Delta \epsilon \mathrm{\Omega }_L^2}}{{({\omega ^2} - \mathrm{\Omega }_L^2) + j{\mathrm{\Gamma }_L}\mathrm{\omega \;\ }}}$$

where ɛ_∞ is the permittivity at a very high frequency and its value is 5.9673 [26]. Plasma and damping frequencies are denoted by ω_D and γ_D respectively and the rest of the parameters have been taken from [26].

TiO₂ has a refractive index expressed as [26]

(5)$$n_{Ti{O_2}}^2 = 5.913 + \frac{{2.441 \times {{10}^7}}}{{({{\lambda^2} - 0.803 \times {{10}^7}} )}}$$

in which λ is the wavelength measured in angstrom.

Geometry along with the design for the sensor has been portrayed in Fig. 1(a). The experimental setup for its practical sensing applications comes in Fig. 1(b). An optical source launches light which can be linearly polarized if a polarizer controller is used. After coupling the sensor to an optical fiber to guide light via splicing, an analyte flow channel is introduced on the periphery of the SPR sensor. A pump can control the inlet and outlet of the analyte. The interaction of the analyte with the sensor leads to resonant wavelength shifts with analyte index alterations. Output intensity is measured via photodetector and the wavelength shifts are sensed by passing the light through an optical spectrum analyzer (OSA).

4. Results and discussions

The simulation operation has been carried out utilizing the FEM as a numerical apparatus in COMSOL Multiphysics. Reflected light at the boundary is absorbed by the circular PML. For evaluating the performance analysis, the entire geometry has been meshed with triangular elements. The maximum element size is 0.903µm, which is fractions of the wavelength such that the propagation of the wave is fully resolved. The minimum element size is 3.05 nm, with a maximum growth rate of 1.25 with which the element size can grow from regions of small element size to regions with larger elements. Keeping it around 1 is highly wanted. The curvature factor, which can be defined as the ratio of the boundary element size with respect to the curvature radius, is kept at a very low value of 0.25 so that good accuracies can be gained to provide with a robust simulation environment. The total number of mesh elements are 47,174, with a mesh area of 467.2µm².

When light passes through the fiber sensor, it escapes from the core mode so that the evanescent field interacts with the metal surface electrons, where SPWs are generated. This confinement loss (CL) of light from the core region is stated [24]

(6)$$CL = 8.686 \times {k_0} \times Im({{n_{eff}}} )\times {10^4}\; \; \; ({dB/cm} )$$

where ${k_0} = \frac{{2\pi }}{\lambda }$ which is the free space wave number with λ being the effective wavelength. Im(n_eff) is the imaginary portion of effective index.

4.1 Sensor performance

In Fig. 2(a), b, c light guidance via, the core and SPP mode has been depicted along with their resonance coupling. The field profile enunciates that the incident wave is escorted by the core. Figure 2(a) confirms the same. The surface plasmon polariton mode in Fig. 2(b) portrays the field formation in the metal-dielectric interface where the electronic oscillations take place.

Fig. 2. Field profile for (a) core mode (b) SPP mode and (c) resonance coupling.

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The field profile in Fig. 2(c) is obtained at the resonant conditions. Figure 2(c) shows the electric field that is generated for both the surface plasmon waves and the guided incident light at the resonance wavelength. Figure 3 portrays the crossing of the real parts of the modes, when the analyte index is residing with na = 1.34RI, where the Gaussian shape of the loss curve is ensued because of the incomplete coupling of the modes. The crossing ensures the occurrence of resonance such that maximum modal power transfer takes place. The resonant wavelength, λ corresponds to the zero derivative for the Gaussian propagation loss curve. The lattice design has the potential to sense a wide range of analyte RI from 1.16–1.37. It is always a challenge to sense lower analyte indices and there are very few works on detecting low indices of analytes. However, the proposed dual D-slotted sensor shows fine performance within the wide range, as illustrated in Fig. 4(a), b, c. A birefringent PCF sensor has been able to gain an extra broad span of analyte RI sensing, 1–1.43. But the sensing potential is low for the analyte changes [27]. However, for our proposed senor, the incorporation of the dual slotted open channels, causes the greater interaction of the core with analytes. Hence, analyte changes are more easily detected with a robust sensing performance. The analyte index for pharmaceutical inspections and bio-sensing purposes are mostly located within the range lower than 1.30 [28], which is covered by our proposed sensor.

Fig. 3. Crossing of the real parts of the core and the SPP mode with Gaussian peak at na = 1.34.

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Fig. 4. Gaussian curve shifts for analyte RI changes (a) 1.16–1.23 (b) 1.24–1.30 and (c) 1.31–1.37

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From the observations of Fig. 4, it is noteworthy that, within the broad sensing range, the loss curves show red shifting with the increase of the analyte indices. This also causes successive increments in confinement losses as well. Hence, the Gaussian peak shifting is caused by the corresponding red shifting of the resonance λ. The slight increments of the analyte RI have a pronounced effect on the overall effective indices of the escorted modes. Increasing analyte indices cause better coupling of the modes, which result in more energy transfer between them via evanescent waves. Hence, the CL conducts better for the analyte RI increments. In addition to this, increasing analyte index reduces the RI contrast between the two modes [26]. This causes the crossing of the RI of the two modes to shift to greater λ, leading to the occurrence of the resonance at those higher wavelengths. The highest confinement loss with the highest sensitive nature is observed for na = 1.37. Another noteworthy feature of the analyte alteration response is that the overall peak loss values for each of the analyte indices are quite low.

The highest loss peak is observed for na = 1.37, where the maximum confinement loss is 100.4 dB/cm. High CL impedes the practical realization of the sensor. With the increase of loss, the sensor length has to be minimized thus causing more trouble in getting a viable output [24]. The sensor performance can be evaluated by using the wavelength sensitivity [24].

(7)$${S_\lambda }[{nm/RIU} ]= \frac{{\mathrm{\Delta }\lambda }}{{\mathrm{\Delta }{n_a}}}$$

where, $\mathrm{\Delta }\lambda $ stands for the peak wavelength shifts with respect to the analyte change, $\mathrm{\Delta }{n_a}$. Table 1 summarizes the findings of how well the sensor can perform within the sensing range in accordance with Fig. 4. The sensor shows increasing resonant λ shifts with analyte index increment, resulting in the nonlinear increase of S_λ.

With respect to the amplitude interrogation method, the analyte index changes are picked up by the amplitude sensitivity, depicted in Fig. 5, governed by [24]

(8)$${S_A}(\lambda )[{RI{U^{ - 1}}} ]={-} \frac{1}{{\alpha ({\lambda ,{n_a}} )\; }}\frac{{\delta \alpha ({\lambda ,{n_a}} )}}{{\delta {n_a}}}$$

in which, $\alpha ({\lambda ,{n_a}} )$ is the overall loss. $\delta \alpha ({\lambda ,{n_a}} )$ is the contrast between two successive loss spectra having corresponding analyte index difference $\delta {n_a}$. With analyte RI increment, the S_A increases successively, followed by red shifting of the curves.

Fig. 5. Amplitude sensitivities for analyte RI changes (a) 1.20–1.24 (b) 1.24–1.30 and (c) 1.31–1.36

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Table 1. Sensor Performance Within Analyte RI Range

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The proposed sensor exhibits a maximum S_A= 331 RIU⁻¹ for the ideal structural parameters. S_A starting from na = 1.20 to 1.36 has been shown, as S_A below 1.20 is quite low.

4.2 Study on metal layer thickness variations

The thickness variations of gold and TiO₂ are studied on the sensor performance. Figure 6(a), b elucidates the changes on the confinement loss curves with analyte index alterations. Figure 6(c), d shows the same analysis on S_A. With the gold layer increment from 70nm to 90nm, blue shifting of both the loss curve and S_A is observed. However, due to the greater damping of SPWs because of the thicker gold layer, the evanescent field penetration decreases as confirmed by the slight decrease in loss. TiO₂ thickness increment interlinks the coupling a bit more. So, the propagation loss shows a slight increase. TiO₂ variation effects on S_A is negligible (further analysis provided in Supplement 1).

Fig. 6. Loss curve shifts with respect to variations for analyte RI = 1.34 in (a) gold thickness (b) TiO₂ thickness and amplitude sensitivity shifts for (c) gold and (d) TiO₂ variations.

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4.3 Study on pitch variations

The pitch in between the airholes is varied. The behavior of the loss curves and the amplitude sensitivities is studied and shown in Fig. 7(a), b. Increasing the hole-to-hole distance from 2.9–3.1µm, the structure exhibits blue shifting of both the loss curve and S_A curve. However, the coupling of the modes increases when the air holes are brought closer to each other. The S_A remains almost the same for Λ equal to 3µm and 3.1µm. On the contrary, the S_A is significantly improved for Λ=2.9µm, to more than 950 RIU⁻¹. But the response of the sensor is better for lower analyte RI when the pitch is kept at 3µm. So, 3µm is maintained as the ideal structural parameter for the sensor (further analysis provided in Supplement 1).

Fig. 7. (a) Pitch variations for analyte RI = 1.34 on loss curves and (b) amplitude sensitivity

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4.4 Study on airhole diameter variations and channel radius

There are three types of airholes with different diameters da₁, da₂ and da₃ in the sensor design. The 2 airholes present in between the fiber center and the metal layers have a diameter, da₁. The air hole diameter at the outermost square lattice is da₃. The air holes in between them are da₂. The variation of da₁ from 1.40–1.50µm reveals that, with the increment of the two air holes area, the coupling and the energy transfer between the modes decrease as these air holes directly obstruct the evanescent field to reach out to the SPWs. Increasing da₂ causes a slight red shifting of the loss curve. da₃ variations have a negligible effect on the loss curves. The reason is that, as these annular rings are present in the most outward arena in the sensor design, these have a lesser effect on the coupling. Almost close to 10% variation of the diameter has little or no effect on the sensor response. But the presence of these air holes is of great importance for confining light in the core. Figure 8(a), b, c portrays the diameter da₁, da₂ and da₃ variations on the sensor performance. Fabrication tolerance has been studied on the two open channel radii and portrayed in Fig. 8(d). The channel area increment causes the CL to rise, followed by subsequent slight right shifts. The increase of the channel radius causes more volume of the analyte to interact with the evanescent field. This causes more energy flow from the core arena to the SPWs, which in turn interlinks the coupling a bit more. This results in the increment of the confinement loss.

Fig. 8. Diameter variations on loss curves (a) da₁, (b) da₂ (c) da₃ and (d) Channel radius variations on loss curves.

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4.5 Sensor evaluation and comparative analysis

The sensor resolution is used to evaluate the sensing potential of the design with respect to the wavelength interrogations [24].

(9)$$R = \frac{{\mathrm{\Delta }{n_a}\mathrm{\Delta }{\lambda _{min}}}}{{\mathrm{\Delta }{\lambda _{peak}}}}RIU$$

where, $\mathrm{\Delta }{\lambda _{peak}}$ is the peak shifting with respect to analyte index alteration $\mathrm{\Delta }{n_a}$, considering $\mathrm{\Delta }{\lambda _{min}}$=0.1nm [29], which is the minimum spectral resolution. The R is found to be as low as 2. 94×10⁻⁶ RIU for an analyte RI alteration at na = 1.36. Another significant parameter to judge how well the Gaussian response will be for the the analyte changes is the figure of merit (FOM) [30]

(10)$$FOM = \frac{{{S_\lambda }}}{{FWHM}}$$

in which, FWHM is the fullwidth of the half maximum of the Gaussian response. The highest FOM for the sensor is found to be 153 RIU⁻¹ corresponding to the S_λ at na = 1.36.

Table 2 sheds light on the relative idea of the sensor performance with the most recently developed sensors, where the maximum S_λ and S_A are compared within their respective sensing range. It has been found that, our proposed sensor has the highest wavelength sensitivity within the wide analyte RI, 1.16–1.37. Recently, a D-shape sensor has been proposed, with a wide sensing range, but the wavelength sensitivity is not as high as ours [24]. Though their range of detection of the analyte is satisfactory, the sensing range for our design is wider, with capabilities of detecting low analyte RI.

Table 2. Comparative Study with Recent Publications

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The resonant λ shifts with respect to the analyte index changes are illustrated in Fig. 9(a), which shows a non-linear rise in λ with analyte RI increment. A polynomial fit is applied to the observed changes to find out the characteristic equation of the sensor, which is mentioned in the figure. Our proposed dual D-slotted open channel sensor exhibits a polynomial fitting of the 5^th order.

Fig. 9. (a) Resonant λ shifts for analyte RI alterations and (b) relation between peak confinement loss at resonant wavelengths and analyte index changes.

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Furthermore, the alteration occurring on the confinement loss at the resonant λ is shown in Fig. 9(b). This gives an idea of the intensity changes that will occur at the output of the sensor which can be detected by using a photodetector. The output intensity of light will be less than that of the incident light, because of the occurrence of the energy flow. Any viable output coherent to the relation between the confinement loss and the analyte index proves the occurrence of resonance. The resonant λ shifting is usually detected by a spectrometer.

The input incident light gets transmitted through the fiber sensor. The energy transfer from the core guided light to the surface plasmon waves is the confinement loss or the absorbance of the fiber. The reflectance is negligible compared to the transmittance and the absorbance in the fiber sensor. As the reflectance is comparatively negligible, the dip or fall in the transmittance of the output light from the SPR waveguide is identical to the rise of absorbance in the fiber sensor. The SNR of an SPR sensor depends on how accurately the sensor can detect the resonance λ and the accuracy of detection of the resonance wavelength depends on the width of the transmittance curve [38]. The SNR is inversely proportional to the full width of the half maximum (FWHM) of the transmittance curve [38]

(11)$$SNR = \frac{1}{{FWHM}}$$

As the dip in the transmittance curve is identical to the rise in the absorbance or the confinement loss curve, according to the optical conservation of energy, the SNR of the sensor will depend on the FWHM of the confinement loss curve, which is shown in Fig. 10(a). The SNR is improved for analyte detection at lower analyte RI. The broadening of the loss curve with the increase of the analyte RI causes the SNR to degrade.

A very high value of confinement loss is an impediment to the practical realization of the sensor, as high losses can limit the sensor fabrication length. The sensing length is inversely proportional to the confinement loss [30]

(12)$$L = \frac{1}{{\alpha ({\lambda ,{n_a}} )}}$$

Fig. 10. (a) Signal to noise ratio (SNR) changes for analyte RI alterations (b) sensing length variation with respect to the analyte index changes.

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Here, L is the sensing length and $\alpha ({\lambda ,{n_a}} )$ is the confinement loss, which is a function of the analyte RI. Figure 10(b) indicates that the sensing length starts to decrease from approximately 0.1cm to a few millimeters

4.6 Comparative discussion on design analysis

D-shaped open channel designs are more effective than circular analyte channels. Previously, our recent analysis with circular channels with hexagonal lattice design with reduced airhole diameter in the core could only reach a maximum WS = 1,000 nm/RIU [39]. However, later on, we could improve the maximum WS to 9,000 nm/RIU for benzene detection keeping all airholes equal in size [40]. For acetic acid pH level detection, we have used a modified hexagonal airhole arrangement [41]. Our analysis on adhesive layer comparison using TiO₂ and Si₃N₄ with gold improves the highest WS to 21,000 nm/RIU with a boost in the maximum amplitude sensitivity, AS = 914 RIU⁻¹ [42]. However, the design structure complexity is more due to the presence of 4 open channels. Similar type of works has also been found in [43]-[44] where four D shaped channels are introduced. Our further investigation reveals that a microchannel assisted D-open channel design can improve the maximum WS to 54,000 nm/RIU with a wide sensing range [45]. However, the fabrication impediments are high due to the incorporation of the microchannel. Also, as the microchannel enters deep inside the fiber, this makes the fiber a subject to increased fragility. This may cause the breaking of the sensor. Our analysis with large asymmetrical D-channel ameliorates the highest WS to 80,000 nm/RIU, but that is for a short range of high sensing range 1.42–1.47 RI [46]. Another large D shaped microfluidic channel PCF-SPR sensor has been found but it has an internal sensing approach with comparatively lower WS than our double D shaped PCF sensor [47]. Our analysis with an external sensing approach can detect the same sensing range. But the WS drastically deteriorates [48]. It is quite obvious from the analysis that the presence of D-open channel assists the analyte in interacting more with the core to have an increased range of analyte RI detection with high wavelength sensitivity. Our findings are also supported by another recent work which introduces an open D-channel in the lattice design [24]. Though the FOM deteriorates for higher analyte RI, the design introduced in this work is one of the very first designs which utilizes an open D-channel to accomplish optical sensing for such a broad sensing range and has been the inspiration to future open D-channel assisted lattice designs. The analysis in our work reveals that it is quite possible to have very satisfactory wavelength sensitivity with a broad range of analyte detection with only 2 open D-channels arranged along the same line with airholes arranged in a square lattice. This eases the fabrication complexities and makes the sensor more efficacious in practicality.

5. Conclusions

The proposed sensor design functions on an external sensing mechanism with two D-slotted open channels. As this causes the analyte to interact with the core mode to a greater degree, the sensor is highly sensitive to a broad span of analyte RI changes from 1.16–1.37. Gold and TiO₂ are the metal layers used for enhanced SPR to take place within the sensor. The wavelength interrogations reveal the highest sensitivity of 34,000nm/RIU. The highest amplitude sensitivity is 331 RIU⁻¹ for the ideal structural degrees of freedom. The sensor resolution is found to be as low as 2.94×10⁻⁶ RIU, considering the wavelength interrogations. This sensor bears the attractive feature of low RI detections with low confinement loss, which makes the sensor highly suitable for its practical realization.

Funding

Shahjalal University of Science & Technology (SUST); Independent University, Bangladesh (IUB).

Acknowledgments

This work was supported by Shahjalal University of Science & Technology (SUST) and Independent University, Bangladesh (IUB).

Disclosures

The authors declare no conflict of interest.

Data availability

The data that underpins the results of this research is not currently accessible to the general public, although it may be acquired from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Analyte Index	Loss peak α_peak (dB/cm)	λ_peak (µm)	Resonant peak shift (nm)	S_λ (nm/RIU)
1.16	9.23	1.583	4	400
1.17	9.38	1.587	5	500
1.18	9.54	1.592	6	600
1.19	9.72	1.598	6	600
1.20	9.91	1.604	7	700
1.21	10.12	1.611	7	700
1.22	10.36	1.618	8	800
1.23	10.62	1.626	11	1100
1.24	10.92	1.637	11	1100
1.25	11.27	1.648	14	1400
1.26	11.67	1.662	15	1500
1.27	12.14	1.677	19	1900
1.28	12.7	1.696	22	2200
1.29	13.4	1.718	26	2600
1.30	14.29	1.744	33	3300
1.31	15.47	1.777	43	4300
1.32	17.1	1.820	53	5300
1.33	19.47	1.873	72	7200
1.34	23.25	1.945	100	10000
1.35	30.1	2.045	155	15,500
1.36	45.73	2.2	340	34,000
1.37	100.4	2.54	N/A	N/A

Ref.	Structure	WS (nm/RIU)	AS (RIU⁻¹)	RI Index
[19]	D shaped	46,000	1086	1.33–1.43
[31]	Circular lattice	9000	318	1.34–1.37
[32]	Hollow-core D shaped	2900	120	1.33–1.34
[33]	Circular lattice	1000	118	1.33–1.36
[34]	Two open rings channel	13,000	333.8	1.23–1.29
[35]	Circular lattice	2200	266	1.33–1.36
[24]	D shaped	20,000	1054	1.18–1.36
[30]	Au-TiO₂ based	25,000	1411	1.33–1.38
[36]	Two-sided open channels	5000	396	1.33–1.39
[16]	H shaped	25,900	N/A	1.33–1.49
[37]	Circular slotted lattice	16,000	780	1.4–1.46
Proposed design	Dual D-slotted	34,000	331	1.16–1.37

Analyte Index	Loss peak α_peak (dB/cm)	λ_peak (µm)	Resonant peak shift (nm)	S_λ (nm/RIU)
1.16	9.23	1.583	4	400
1.17	9.38	1.587	5	500
1.18	9.54	1.592	6	600
1.19	9.72	1.598	6	600
1.20	9.91	1.604	7	700
1.21	10.12	1.611	7	700
1.22	10.36	1.618	8	800
1.23	10.62	1.626	11	1100
1.24	10.92	1.637	11	1100
1.25	11.27	1.648	14	1400
1.26	11.67	1.662	15	1500
1.27	12.14	1.677	19	1900
1.28	12.7	1.696	22	2200
1.29	13.4	1.718	26	2600
1.30	14.29	1.744	33	3300
1.31	15.47	1.777	43	4300
1.32	17.1	1.820	53	5300
1.33	19.47	1.873	72	7200
1.34	23.25	1.945	100	10000
1.35	30.1	2.045	155	15,500
1.36	45.73	2.2	340	34,000
1.37	100.4	2.54	N/A	N/A

Ref.	Structure	WS (nm/RIU)	AS (RIU⁻¹)	RI Index
[19]	D shaped	46,000	1086	1.33–1.43
[31]	Circular lattice	9000	318	1.34–1.37
[32]	Hollow-core D shaped	2900	120	1.33–1.34
[33]	Circular lattice	1000	118	1.33–1.36
[34]	Two open rings channel	13,000	333.8	1.23–1.29
[35]	Circular lattice	2200	266	1.33–1.36
[24]	D shaped	20,000	1054	1.18–1.36
[30]	Au-TiO₂ based	25,000	1411	1.33–1.38
[36]	Two-sided open channels	5000	396	1.33–1.39
[16]	H shaped	25,900	N/A	1.33–1.49
[37]	Circular slotted lattice	16,000	780	1.4–1.46
Proposed design	Dual D-slotted	34,000	331	1.16–1.37

Highly sensitive double D-shaped channel photonic crystal fiber based plasmonic refractive index sensor

Abstract

1. Introduction

2. Theoretical considerations

3. Modelling and numerical analysis

4. Results and discussions

4.1 Sensor performance

4.2 Study on metal layer thickness variations

4.3 Study on pitch variations

4.4 Study on airhole diameter variations and channel radius

4.5 Sensor evaluation and comparative analysis

4.6 Comparative discussion on design analysis

5. Conclusions

Funding

Acknowledgments

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (10)

Tables (2)

Equations (12)

Optics Continuum

M. Hussayeen Khan Anik	https://orcid.org/0000-0001-8470-3296
Rubel Chandra Talukder	https://orcid.org/0000-0002-2138-4723
Hriteshwar Talukder	https://orcid.org/0000-0002-6391-6177