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Abstract
Symmetrical dual D-shape photonic crystal fibers (PCFs) for surface plasmon resonance (SPR) sensing are designed and analyzed by the finite element method (FEM). The performance of the sensor is remarkably enhanced by the directional power coupling between the two fibers. We study the influence of the structural parameters on the performance of the sensor as well as the relationship between the resonance wavelengths and analyze refractive indexes between 1.36 and 1.41. An average spectral sensitivity of 14660 nm/RIU can be achieved in this sensing range and the corresponding refractive index resolution is 6.82 × 10−6 RIU. The characteristics of a single D-shape PCF-SPR sensor with the same structural parameters are compared with those of the dual PCFs sensor and the latter has distinct advantages concerning the spectral sensitivity, resolution, amplitude sensitivity, and figure of merits (FOM).
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface plasmon resonance (SPR) is an optical phenomenon referring to excitation of electron density oscillations (known as surface plasmon wave, SPW) at the metal-dielectric interface caused by p-polarized light or TM (transverse magnetic) wave [1–5]. SPR arises from coupling of the surface plasmon wave on a metal surface when irradiated with total internal reflection (TIR) evanescent waves under certain conditions [2, 6]. SPR has emerged to be a promising sensing technique in the fields of chemistry, biomedicine, and environmental monitoring because surface plasmons are extremely sensitive to variations in the refractive index of the surrounding medium [6–10]. There are many operating platforms to excite SPR on the basis of the TIR mechanism using prisms, optical fibers, and photonic crystal fibers (PCF). Among them, the Kretschmann-Raether prism configuration suffers from the bulky sensor [1, 11, 12]. Although optical fibers instead of a prism offer miniaturization and remote sensing capabilities, conventional fiber-based SPR sensors have low sensitivity as a result of the single structure [13, 14].
PCFs with a regular array of air holes along the propagation direction are attractive for SPR sensing due to the flexibility in structural design [15–17]. The fundamental principle of PCF-based SPR (PCF-SPR) sensors is phase matching between the core-guided mode and surface plasmon polaritons (SPPs) mode [18]. In particular, the D-shape PCF-SPR (the side-polished PCF) sensors have drawn much attention because the incident light can be coupled out of the polished D-shaped PCF into a metallic film coated onto the polished surface [19, 20]. From the perspective of device fabrication, it is also a good alternative to deposit metal thin films on the polished surface of the D-shaped fibers. J.N. Dash and R. Jha [21] designed a sensitive D-shape PCF sensor based on SPR for near infrared region showing a spectral sensitivity of up to 5200 nm/RIU. Ming Tian et al. [22] studied an all-solid D-shaped PCF-SPR sensor which showed a refractive index sensitivity of at least 7300 nm/RIU and An et al. [23] described a high-sensitivity refractive index sensor based on the D-shaped PCF with a rectangular lattice exhibiting a spectral sensitivity of 8129 nm/RIU. It is obvious that the sensing performance of these sensors depends on the structures and in spite of recent advances, the average spectral sensitivity of D-shape sensors is still less than 10000 nm/RIU. To improve the sensing sensitivity, a strategy is to increase the coupling efficiency between the core-guided mode and plasmonic mode by optimizing the structures. The coupling effect includes the interaction at adjacent multi-plasmonic sensors, which has been applied to dual parallel fibers. However, there have been little efforts to develop dual parallel D-shape PCF-SPR sensors.
Here, we describe a symmetrical dual parallel D-shape PCF-SPR sensor and systemically investigate the sensing performance by the finite element method (FEM). Our results reveal an average spectral sensitivity of 14660 nm/RIU and the performance of the dual D-shape PCFs-SPR sensor is better than that of the single fiber structure, exhibiting great potential in the fields of chemistry, biomedicine, and integrated optics.
2. Numerical modeling
This study focuses on 2D simulation of the dual D-shape PCFs-SPR sensor and the mode characteristics are investigated by the FEM with the COMSOL Multiphysics software. The SPR sensor for the analyte refractive index (nana) is composed of two symmetrical dual D-shape photonic crystal fibers as shown in Fig. 1(a). The blue background material is pure silica glass and an array of regular air holes (the air refractive index nair = 1) is introduced to the edge of silica glass to lower the average refractive index of the edge. As shown in Fig. 1(b), the air holes confine light in region A and regions A and B represent the fiber core and cladding, respectively. Silver layers are put on the vertical planes as the plasmonic materials and the relative permittivity of silver (εAg) is obtained by the L4 model (which may be reduced to the extended Drude model) for wavelengths between 180 nm and 2000 nm [24,25]:
Fig. 1 (a) Cross-section of the symmetrical dual D-shape PCFs-SPR sensor; (b) Electric field intensity distribution of the fundamental mode.
The parameters of the L4 model are obtained from Ref [24]. The silver layers can be deposited by wet chemical deposition or physical vapor deposition, which is convenient for the internal surface of the fiber holes [26]. An artificial boundary condition of the perfectly matched layer (PML) is added to the outer computational region to absorb radiation energy [27]. The perfect magnetic conductor (PMC) and perfect electric conductor (PEC) are used as the boundary conditions in the theoretical model at the outer boundaries, respectively.
As shown in Fig. 1(a), ra = 100 nm, tAg = 50 nm, d = 900 nm, and r = 12 um represent the radius of the air holes, thickness of the silver layer, distance between two fibers, and distance between the air hole array in an arc-shape and center of a single fiber, respectively. is the distance between adjacent air holes in an arc shape and is the distance between vertically arranged adjacent air holes. The space outside the fibers is filled with the analyte (aqueous solution) with refractive indexes (nana) between 1.36 and 1.41. In this model, the confinement loss αloss is used to evaluate the properties of the sensor and it is defined as [28, 29]:
where λ stands for the wavelength of the incident light in vacuum with a unit of nanometer (nm) and Im(neff) is the imaginary part of the effective refractive index of the guide mode.3. Results and discussion
Figure 2 presents the electric and magnetic field distributions of the core-guided modes for the even mode and odd mode in the x and y directions. The black arrows and blue arrows represent the direction of the electric and magnetic fields, respectively. Figures 2(a), 2(b), 2(c) and 2(d) show the even mode distribution in the x-polarized direction (x-even mode), odd mode distribution in the x-polarized direction (x-odd mode), even mode distribution in the y-polarized direction (y-even mode), and odd mode distribution in the y-polarized direction (y-odd mode), respectively. It can be observed that coupling of the core guided mode to the SPPs mode is stronger in the x-even mode.
Fig. 2 Electric and magnetic field distributions of the core-guided modes: (a) x-even mode; (b) x-odd mode; (c) y-even mode; (d) y-odd mode.
To determine the appropriate mode, the loss spectra of the four core-guided modes are plotted in Fig. 3 for analyte refractive indexes from 1.39 to 1.40. The resonance wavelength is defined as the wavelength corresponding to the maximum spectrum loss in order to describe changes in the loss spectra. Figure 3 shows that when the analyte refractive index increases from 1.39 to 1.40, the intensity of the resonance peak increases for the even mode and odd modes for both x-polarization and y-polarization. The confinement loss in the x-polarized direction is two orders of magnitude bigger than that in the y-polarized direction. The even modes for x-polarization and y-polarization show more confinement loss than the odd modes. In addition, the resonance wavelengths for the even mode and odd mode in the x and y directions red-shift as the refractive index of the analyte increases from 1.39 to 1.40. The changes in the resonance wavelengths are 141 nm, 30 nm, 3 nm, and 12 nm for the x-even mode, x-odd mode, y-even mode, and y-odd mode, respectively, indicating that the x-even mode is more sensitive to the analyte refractive index than the other modes. Therefore, we focus on the x-even mode in the subsequent investigation.
Fig. 3 Loss spectra of the even and odd modes for analyte refractive indexes of 1.39 and 1.40 for (a) x-polarization direction and (b) y-polarization direction (nair = 1, ra = 100 nm, tAg = 50 nm, r = 12 μm, and d = 900 nm)
Figure 4 shows the dispersion relationship between the SPPs mode and x-even mode. The black curve represents the confinement loss of the x-even mode and the blue and red lines stand for the real parts of the effective refractive indexes of the SPPs mode and x-even mode, respectively. The results reveal a strong dependence on the wavelength. The real parts of the effective refractive indexes for the x-even mode decrease gradually with increasing wavelength and there is an intersection (point Q) between the two lines of the real parts of the effective refractive indexes at 984 nm. The curve of the confinement loss exhibits an obvious absorption peak at the same wavelength and coincidence of the absorption peak and intersection (point Q) confirms the phase matching coupling phenomenon. Moreover, as shown in insets (a) and (c), the coupling efficiency at the resonance wavelength of 984 nm is higher than that at 870 nm. In addition, it is noted that the confinement loss of the proposed sensor in this work is lower than those results in Ref [16, 18]. This is attributed to that the introduction of air holes in the first layer leads to the lower refractive index of the microstructured cladding. This, in turn, increases the core-cladding refractive index contrast, hence increasing modal confinement in the core region, and resulting in lower modal loss due to coupling to a metal surface [28]. Similar results were also reported in Ref [21, 26].
Fig. 4 Dispersion relationship of the x-even mode (red), SPPs mode (blue), and loss spectrum (black). Inset (a) shows the x-even mode at 984 nm, inset (c) shows the x-even mode at 870 nm, and inset (b) shows the SPPs mode at 984 nm (nair = 1, nana = 1.40, ra = 100 nm, tAg = 50 nm, r = 12 μm, and d = 900 nm)
The performance of the SPR sensor depends on the plasmonic materials and in most cases, silver or gold is used. Figure 5 shows the loss spectra of the x-even mode for gold and silver as plasmonic materials when the analyte refractive indexes increase from 1.36 to 1.38. The resonance wavelengths of silver and gold are nearly equal for the same analyte refractive index. However, silver shows a sharper resonance peak than gold resulting in enhanced sensing accuracy. Therefore, silver is selected as the plasmonic material in our sensor.
Fig. 5 Loss spectra of the x-even mode for gold and silver with the analyte refractive indexes increasing from 1.36 to 1.38 (nair = 1, ra = 100 nm, tAg = 50 nm, tAu = 50 nm, r = 12 μm, and d = 900 nm).
In general, the intensity of the resonance peak and the resonance wavelength are affected by the geometric parameters of the sensor. Figure 6 shows the influence of the radius of the air holes on the loss spectra for the x-even mode. When the radius decreases from 600 nm to 100 nm, the resonance wavelength exhibits a slight red-shift and the intensity of the peak increases gradually. It can be explained by that smaller holes at the edge promote leakage of the modal field from the fiber cores and so more light is coupled to the metallic surface and less light is confined to the cores.
Fig. 6 Loss spectra of the x-even mode for different air hole radii (nair = 1, nana = 1.40, tAg = 50 nm, r = 12 μm, and d = 900 nm)
Figure 7 displays the dependence of loss spectra of the x-even mode on the distance (r) between the air holes in the arc shape and fiber center. The resonance wavelength remains approximately constant and the intensity of the resonance peaks increases gradually as the distance goes up from 9 μm to 12 μm. This phenomenon is attributed to that the core-guided mode field is closer to the silver layer and the contact area between the silver layer and the mode field broadens when the distance increases leading to coupling of more light to the metallic surface and consequently higher confinement loss.
Fig. 7 Dependence of loss spectra of the x-even mode on the distance between the air holes in the arc shape and fiber center (nair = 1, nana = 1.38, ra = 100 nm, tAg = 50 nm, and d = 900 nm)
For the dual PCF-SPR sensor, it is obvious that the distance (d) between two fibers is one of important parameters to determine the position and intensity of the resonance peak. Figure 8 exhibits the influence of the distance (d) on the loss spectra of the x-even mode for analyte refractive indexes between 1.40 and 1.41. When the analyte refractive index is 1.41, there is a secondary peak in the loss spectra and the resonance peaks move to shorter wavelength. The resonance intensity decreases gradually when the distance increases from 860 nm to 900 nm. The results imply that light confinement in the core is enhanced and there is less light penetration through the cladding. Although the resonance is strongest at d = 860 nm, the main peaks of d = 900 nm are more distinctive than those of other distances, thereby improving the sensing accuracy. Therefore, d = 900 nm is adopted for the sensor.
Fig. 8 Dependence of loss spectra of the x-even mode on the distance between two fibers for different analyte refractive indexes: (a) nana = 1.40 and (b) nana = 1.41 (nair = 1, ra = 100 nm, tAg = 50 nm, and r = 12 μm)
Figure 9 displays the dependence of loss spectra of the x-even mode on the analyte refractive indexes between 1.36 and 1.41. The resonance peaks move to longer wavelength and the intensity of the resonance peaks increases gradually with increasing analyte refractive indexes. The corresponding resonance wavelengths change from 683 nm to 1416 nm. For the PCF-SPR sensors, the spectral sensitivity (S(λ)) is one of the most important parameters and is defined as [30]:
where Δλ and Δnana denote the shift of the resonance wavelength and analyte refractive index variation, respectively. When the analyte refractive indexes are 1.36-1.41, each variation of 0.01 in the refractive index causes a shift of 146.6 nm in the resonance wavelength on the average, indicating that an average spectral sensitivity of 14660 nm/RIU can be attained. This value is much higher than 3700 nm/RIU and 5700 nm/RIU described in Ref [31, 32], respectively. A maximum spectral sensitivity is up to 43200 nm/RIU higher than the maximum spectral sensitivity of 17000 nm/RIU reported in Ref [33]. The higher sensitivity may be attributed to the enhanced strong-interaction coupling of the dual D-shaped fibers. Supposing that the wavelength resolution is Δλmin = 0.1 nm, the refractive index resolution (R) of the sensor can be expressed as [34]:Fig. 9 Dependence of the loss spectra of the x-even mode on the analyte refractive indexes for the dual D-shape sensor (nair = 1, ra = 100 nm, tAg = 50 nm, r = 12 μm, and d = 900 nm)
Here, Δλmin = 0.1 nm and S(λ) = 14660 nm/RIU leading to an average sensing resolution of 6.82 × 10−6 RIU between refractive indexes of 1.36 and 1.41.
For comparison, the performance of a single D-shape PCF-SPR sensor with the same structural parameters is investigated. Figure 10 shows the influence of the analyte refractive indexes on the loss spectra, and inset (a) exhibits the modal field distribution of the single fiber structure. According to Figs. 9 and 10, the two sensors have the same refractive index range between 1.36 and 1.41, whereas the resonance wavelength shift of the dual fiber structure is more obvious. By analyzing the single D-shape sensor, an average spectral sensitivity of 4740 nm/RIU is obtained corresponding to an average resolution of 2.11 × 10−5 RIU for refractive indexes between 1.36 and 1.41. From the viewpoint of sensing sensitivity and resolution, it can be concluded that the dual D-shape PCFs-SPR sensor is more suitable for refractive index detection.
Fig. 10 Dependence of loss spectra of the x-even mode on the analyte refractive indexes for the single D-shape sensor (nair = 1, ra = 100 nm, tAg = 50 nm, r = 12 μm, and d = 900 nm)
Besides, the amplitude sensitivity is considered and can be expressed as [33]:
where α(λ, nana) is the overall loss where analyte refractive index is equal to nana and ∂α(λ, nana) is the difference between two adjacent loss spectra due to a small change in refractive index of the analyte, ∂nana is the change of refractive index of the anlayte. Figure 11 displays variation of amplitude sensitivity with wavelength for the dual and single D-shape sensor. The dual D-shape sensor shows the amplitude sensitivities of 636, 801, 1010, 1222, and 1003 RIU−1 at wavelengths of 722, 771, 846, 987, and 1420 nm for the analyte refractive index regions of 1.36 to 1.37, 1.37 to 1.38, 1.38 to 1.39, 1.39 to 1.40, and 1.40 to 1.41, respectively. Similarly, the amplitude sensitivities of the single D-shape sensor are 520, 616, 738, 889, and 1076 RIU−1 at wavelengths of 702, 735, 778, 833, and 910 nm, respectively. For most refractive index regions, the amplitude sensitivity of the dual D-shape sensor is much higher than that of the single D-shape sensor except for 1.40 to 1.41. Additionally, the maximum amplitude sensitivity of 1222 RIU−1 can be achieved at 987 nm when the analyte refractive indexes are varied from 1.39 to 1.40 for the dual D-shape sensor. This value is much higher than 418 RIU−1 and 148 RIU−1 described in Ref [18, 19], respectively.Fig. 11 Variation of amplitude sensitivity with wavelength for analyte refractive indexes change of 0.01. (a) the dual D-shape sensor; (b) the single D-shape sensor (nair = 1, ra = 100 nm, tAg = 50 nm, r = 12 μm, and d = 900 nm)
The spectral width and signal-to-noise ratio are two other performance parameters that affect the detection limit. They can be described using the widely accepted figure of merits (FOM) [35, 36]:
where m is the slope of resonance peak position per refractive index unit and FWHM is the full-width at half-maximum of the resonance peak. A larger FOM means a better detection limit [35]. Figure 12 shows the dependence of FOM for the two sensors on the analyte refractive indexes. It is obvious that the FOM of the dual D-shape sensor is higher than that of the single D-shaped sensor. The decrease in the FOM for the dual fiber structure at nana = 1.41 arises from the secondary peak in the loss spectra in Fig. 9. By conducting comparative analyses, it can be concluded that the performance of the dual fiber structure is better than that of the single fiber structure.Fig. 12 Dependence of FOM of the two sensors on the analyte refractive indexes (nair = 1, ra = 100 nm, tAg = 50 nm, r = 12 μm, and d = 900 nm)
4. Conclusions
A symmetrical dual D-shape PCF-SPR sensor with a silver sensing layer is described and analyzed. The x-even mode is determined to analyze the intensity of the resonance peak and shift of the resonance wavelength. The average spectral sensitivity of the dual D-shape sensor reaches 14660 nm/RIU and the corresponding sensing resolution is 6.82 × 10−6 RIU in the refractive index range between 1.36 and 1.41. The maximum amplitude sensitivity of 1222 RIU−1 can be achieved when the analyte refractive indexes are varied from 1.39 to 1.40 for the dual D-shape sensor. Besides, the dual D-shape sensor has a higher FOM implying a better detection limit in refractive index sensing. Compared with the single D-shape sensor with the same structural parameters, the performance of the dual D-shape sensor is better and exhibits great potential in the fields of chemistry, biomedicine, and integrated optics.
Funding
National Natural Science Foundation of China (NSFC) (51474069); China Postdoctoral Science Foundation funded project (2016M591510); Natural Science Foundation of Heilongjiang Province (E2016007); City University of Hong Kong Applied Research (9667122); City University of Hong Kong Strategic Research (7004644).
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