We present and numerically characterize a liquid-core photonic crystal fiber based plasmonic sensor. The coupling properties and sensing performance are investigated by the finite element method. It is found that not only the plasmonic mode dispersion relation but also the fundamental mode dispersion relation is rather sensitive to the analyte refractive index (RI). The positive and negative RI sensitivity coexist in the proposed design. It features a positive RI sensitivity when the increment of the SPP mode effective index is larger than that of the fundamental mode, but the sensor shows a negative RI sensitivity once the increment of the fundamental mode gets larger. A maximum negative RI sensitivity of −5500nm/RIU (Refractive Index Unit) is achieved in the sensing range of 1.50-1.53. The effects of the structural parameters on the plasmonic excitations are also studied, with a view of tuning and optimizing the resonant spectrum.
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Being extremely sensitive to the properties of the dielectric surrounding the metal layer, optical fiber surface plasmon resonance (SPR) sensors are the most promising biosensing platforms due to their unique feature of label-free sensing [1–3]. In the past decades, Photonic Crystal Fibers (PCFs) with a regular hexagonal array of holes running along the fiber length have opened a new way towards the closed-form optical fiber plasmonic sensing [4–6]. The SPR sensors based on PCFs are products of the combination of photonic technology, plasmonic science and coating technique, which have solved the phase matching and packing issues perfectly [7–10]. Among them the selectively coating of the air holes in the PCF using the neck-down region and a syringe to fabricate the nanometric scale silver films has been demonstrated by X. Zhang et al. . The PCFs with embedded gold and silver nanowires have also been fabricated successfully by M. A. Schmidt et al., and the SPR phenomenon in PCFs was experimentally observed and characterized for the first time [8,9]. However, among these extensively studied PCF-SPR refractive index (RI) sensors, only the plasmonic mode effective indices are influenced by the varied analyte, the effective indices of the core-guided mode are almost independent of the analyte [3–6,11]. An interesting feature of the PCFs is that their properties can be modified by filling the air holes partially or wholly with liquids. A hollow core microstructured polymer optical fiber with all the air holes filled with liquid to perform a RI sensor was reported , by measuring the bandgap edge shift. The optical properties of a series of water core PCFs were numerically studied. The numerical results showed dramatically improved loss and overlap of light with the sample, indicating a direct improvement of sensor performance . Therefore, it is of great importance to tune the core mode effective index dynamically to enhance the interaction between light and sample, which can be realized by introducing a liquid-filled core to replace the solid glass core, benefitting from the convenience of making holes in the PCFs. The newly developed liquid-filled core PCF refractive index sensors are based on a dual-core directional coupler model [14,15], the sensing capability is enforced by the phase matching of two dissimilar waveguides, i.e., the liquid-core mode and the solid glass-core mode. However, the PCFs with liquid core have not been investigated in the plasmonic sensing platform, which is free from the precise control of the coupling length like that of the directional coupler architecture. Moreover, the plasmonic sensor with high RI analyte formed liquid cores are able to detect some high RI samples, while most of the previously reported PCF-SPR sensors have an upper detection limit lower than that of the silica glass.
In this work, we report a closed-form optical SPR sensor design utilizing the liquid-core photonic crystal fiber (LCPCF), and present a comprehensive numerical analysis based on the finite element method (FEM). The negative RI sensitivity is found for the first time in the plasmonic sensing scheme, to the best of our knowledge. The novel sensor design also opens a new way to detect the analyte with RI higher than that of glass. The paper is organized as follows: A detailed LCPCF-SPR sensor design and theoretical modeling are presented in Sec. 2. The sensing performance is analysed in Sec. 3, which is followed by the tuning of plasmonic excitations in Sec. 4, and finally is concluded in Sec. 5.
2. Structure design and theoretical modeling
Figure 1(a) depicts the cross section of the proposed LCPCF-SPR sensor. The index-guiding LCPCF consists of three layers of air holes arranged in a hexagonal way, and the six liquid cores are formed by infiltrating the corresponding air holes in the second layer with an analyte of RI greater than the silica substrate. These cores are numbered 1-6 clockwise with the Arabic numbers indicating the corresponding core. For each individual core, the index-guiding mechanism and total internal reflection condition will be guaranteed by the higher RI analyte. The new design is quite different from the previously PCF-SPR sensor configurations, which incorporate several closely arranged metallic analyte channels [4,6]. The single metallic channel in Fig. 1(a) eliminates the interference between neighboring channels effectively. Thus, the signal-to-noise ratio (SNR) of the sensor can be improved and the uniformity of the metallic channel can be easily guaranteed.
The pitch of the underlying hexagonal lattice is Λ = 2μm, the outer diameter of the central metallic analyte channel, diameters of cladding air holes and liquid-cores are dc = 0.8Λ, d1 = 0.5Λ and d2 = 0.8Λ, respectively. The thickness of gold layer is fixed to t = 40nm. We assume the LCPCF is made of silica glass with the RI of 1.45, and cladding holes are filled with air nair = 1.0. The analyte with na varies from 1.45 to 1.53. The dielectric constant of gold is defined by the Drude model . We employ the full-vectorial FEM solver with perfectly matched layer condition to find the complex propagation constants of the fundamental mode and the surface plasmon polaritons (SPP) mode. Only a quarter of the LCPCF cross section is needed to be computed due to the geometrical symmetry shown in Fig. 1(b). We use the triangular sub-domain to discretize the computation area. The computational region is meshed into 15,272 elements, and the number of degrees of freedom equals 10,7337. The vertical and horizontal boundaries of the calculation area are assigned with perfect electric conductor (PEC) and perfect magnetic conductor (PMC) artificial boundary conditions, respectively. A perfectly matched layer (PML) is used to matching the outmost layer.
3. Numerical results
The six identical liquid cores feature a C6v rotational symmetry with respect to the metalized analyte channel, which guarantees a polarization independent propagation characteristic. The proposed design is actually a multi-core fiber which can be treated as a superstructure, and the LCPCF can support a set of supermodes except for the fundamental mode. A detailed mode analysis can be referred to Ref . In this work, only the y-polarized fundamental mode of the degenerate pair is analyzed, and the resonant spectra for na = 1.46 is presented in Fig. 2 .
The propagation loss (Defined in decibels per meter , α(dB/m) = 40πIm(neff)/(ln(10)λ)) of the fundamental mode exhibits a distinct peak at the wavelength of 1036nm, which is the corresponding resonant wavelength and indicates the largest energy transfer from the fundamental mode to the SPP mode. The coincidence of the loss peak and the intersection (point (c) in Fig. 2) confirms the phase matching coupling phenomenon . From the insets in Fig. 2, we can see an obvious electric field overlapping between the fundamental mode and the SPP mode at the resonant wavelength (inset (c)), while the fields are well confined in the liquid-core and metal-analyte interface at a wavelength away from the resonant wavelength (insets (a), (b), (d) and (e)). Our previous work has analyzed that the fundamental mode loss spectrum does not show any resonance peaks in the short wavelength range , i.e., the fundamental mode loss spectrum exhibits a single-resonance feature, which is not influenced by the other higher order plasmonic modes. Being extremely sensitive to the analyte RI variation and free from the broadening caused by the neighboring higher order resonance peaks, the LCPCF-SPR sensor shows unique performance. The calculated results for na varying from 1.45 to 1.49 are shown in Fig. 3 .
We can see that the peak wavelength shifts towards longer wavelength with the increase of analyte RI, but simultaneously the peak loss value decreases gradually. It is attributed to the fact that the dispersion relation of SPP mode moves upward, resulting in a red-shift of the phase matching point. Meanwhile, the fundamental mode field confinement increases due to the enhanced core-cladding index contrast, with the increasing na. A maximum positive RI sensitivity of 3700nm/RIU is achieved when the RI varies from 1.45 to 1.46, while the corresponding resonant wavelength shifts from 999nm to 1036nm. Assuming a spectral resolution of 10pm, the detection limit of the LCPCF-SPR sensor is 2.7 × 10−6 RIU (Refractive Index Unit), which is comparable to the results reported in Ref , in terms of detecting high RI analytes.
It should also be noted that the red-shift experiences a decrease with increasing na, thus, the sensitivity for higher RI analyte decreases slightly. It is quite different from the previous designs that the sensitivity is larger for higher RI samples . This phenomenon comes true as both the fundamental mode and SPP mode effective indices are sensitive to the varying analyte in the proposed LCPCF plasmonic sensor design, while only the plasmonic mode dispersion relation is dependent on the sample RI in the previous configurations. We calculate the dispersion relations and resonant spectra for different analyte RI to understand the decreased sensitivity, and the results are presented in Fig. 4 .
Figure 4 shows that not only the SPP mode dispersion relation, but also that of the fundamental mode moves upwards when the analyte RI increases from 1.45 to 1.47. The increment of the fundamental mode effective index makes the originally phase matching point (c) experiences a blue-shift and moves to point (b). The originally phase matching point is the intersection between the fundamental mode and SPP mode dispersion relations, when the fundamental mode effective index is independent on the varied analyte. In the calculated wavelength range 900-1200nm, the effective index increment of the SPP mode Δneff,spp is larger than that of the fundamental mode Δneff,core. For example, at the phase matching point (b) λ = 1063.4nm, Δneff,spp equals 1.7158 × 10−2 and Δneff,core is 1.1048 × 10−2. Δneff,spp is so larger than Δneff,core that the resonant wavelength moves towards a longer wavelength finally (From point (a) to (b)). The wavelength separation between the phase matching points (a) and (b) is smaller than that between the points (a) and (c). It is a common phenomenon among the plasmonic sensors that the resonant wavelength experiences a red-shift with increasing analyte RI. But once the core mode is greatly tuned by the varied analyte, i.e., the Δneff,spp is no longer larger than Δneff,core, the LCPCF-SPR sensor features some different characters. We calculate the resonant spectra for higher RI analytes from 1.50 to 1.53 and the results are presented in Fig. 5 .
It is quite different from Fig. 3 that the negative RI sensitivity phenomenon is found, i.e., the resonant wavelength moves towards shorter wavelength with the increase of na. The peak wavelength is 1098nm, 1080nm, 1044nm and 989nm, with the corresponding analyte RI of 1.50, 1.51, 1.52 and 1.53. The loss value at the resonant wavelength decreases simultaneously, due to the enhanced core-cladding index contrast. Lower resonant loss indicates weaker energy transfer from the fundamental mode to the SPP mode, as a result the resonant spectrum broadens. The FWHM (full-width-at-half-maxima) is 30nm, 41nm, 56nm, and 84nm, when the analyte RI equals 1.50, 1.51, 1.52 and 1.53, respectively. On the other hand, one can increase the interaction length to the centimeter scale to compensate the weakened coupling. A maximum negative RI sensitivity of −5500nm/RIU can be obtained when the RI increases from 1.52 to 1.53. Consider a SNR of 60dB, an average FWHM of 40nm, using a rigorous definition for the detection limit of the SPR sensor proposed in Ref  (δnl = FWHM/(4.5 × S × SNR0.25), S is the sensitivity), a high sensor resolution of −5.8 × 10−4 RIU is achievable.
To understand the origin of the negative sensitivity for analyte RI larger than 1.50, we investigate the resonant features of the fundamental mode and SPP mode for na = 1.50 and na = 1.52. The calculated results are shown in Fig. 6 . Similarly, both the fundamental mode dispersion relation and that of the SPP mode are affected by the varied analyte RI. The effective indices of the fundamental mode and SPP mode increase when the analyte RI varies from 1.50 to 1.52. In the simulated wavelength range 900-1300nm, the effective index increment of the SPP mode Δneff,spp becomes smaller than that of the fundamental mode Δneff,core. For instance, at the phase matching point (b) λ = 1038nm, Δneff,spp equals 1.2306 × 10−2 and Δneff,core is 1.5803 × 10−2. Δneff,core is much larger than Δneff,spp and the increase of fundamental mode effective index plays a dominant role in the sensing. Finally, the phase matching point moves towards a shorter wavelength (From point (a) to (b)), while the originally phase matching point (c) lies in the longer wavelength range. With the analyte RI larger than 1.50, the fundamental mode effective index is greatly tuned and plays a dominant role. The negative RI sensitivity phenomenon, i.e., the blue-shift of the phase matching point with increasing analyte RI is helpful to take full advantage of the limited optical source bandwidth. As the operation wavelength range for 1.45-1.53 is between 900nm and 1200nm, there is no need to employ the expensive supercontinuum light source.
With the increasing of sample RI, the resonant wavelength experiences a red-shift for relative lower RI, and then goes through the blue-shift. Therefore, there is an overlap of the resonant wavelength, i.e., two samples with different RI feature the very same resonant wavelength. It is of great importance to distinguish the tested analyte RI. We plot the resonant wavelength and peak loss of the proposed design in the working range of 1.45-1.53 in Fig. 7 . It is clearly that the dependence of the resonant wavelength on the analyte RI is parabolic, and the largest resonant wavelength is 1100nm when the testing analyte RI equals 1.495. But the peak loss decreases monotonically with increasing na, which means for a constant sensor length, the transmitted light intensity gets stronger for higher analyte RI. Taking full advantage of the monotonous decrease feature of the resonant loss, we are able to distinguish the tested sample RI. For example, at the resonant wavelength of 1051nm, the corresponding analyte RI can be 1.466 (Point A) and 1.517 (Point B). Obviously, the resonant loss is quite different for the two possible analyte RI. The peak loss indicated by point a which corresponds to the lower analyte RI (1.466) is 65.45dB/cm, while point b which refers to the higher analyte RI resonant loss is 10.84dB/cm. The peak loss for the lower RI analyte is five times larger than that of the higher one, though the resonant wavelengths of the two samples locate at the same position. In the real applications, we can record the resonant wavelength and transmission intensity simultaneously to make sure weather the testing sample RI locates in the range of 1.45-1.495 or in 1.495-1.53.
4. Tuning of the plasmonic excitations
A PCF based plasmonic sensor is structure-sensitive, the resonant spectrum can be readily tuned by varying the PCF structural parameters. The following will discuss the effect of three main device parameters, namely, the central metallic analyte diameter dc, cladding air hole diameter d1 and liquid-core diameter d2.
The resonant spectrum is highly sensitive to the metallic analyte channel diameter, Fig. 8 depicts the influence of dc on the resonant spectrum for na = 1.46. The peak wavelength experiences a red-shift with increasing dc, which is 944nm, 1036nm and 1132nm for dc = 0.7Λ, 0.8Λ and 0.9Λ, correspondingly. There is also an obvious augment in the peak loss with the increase of dc, which indicates the coupling between the fundamental mode and SPP mode is strengthened. These effects are resulted from the upwards moving of the plasmonic mode dispersion relation, while that of the liquid-core guided mode are not affected. Thus, the phase matching point shifts towards longer wavelength. We can effectively tune the peak wavelength to a desired value by adjusting the size of the central metallic micro-channel.
The influences of cladding air hole diameter d1 and liquid-core diameter d2 are illustrated in Fig. 9(a) and Fig. 9(b). For a constant dc and d2, the resonant wavelength moves towards longer wavelength with increased d1, while the peak loss decreases, and the FWHM increases simultaneously. The resonant wavelength is 1021nm, 1036nm and 1053nm, for d1 = 0.4Λ, 0.5Λ and 0.6Λ, respectively. The corresponding FWHM is 30nm, 35nm and 40nm. The tuning effect is owed to the fact that the liquid-core mode effective index decreases when the cladding air holes get larger, while that of the plasmonic mode is independent of the variation of d1. For practical applications, a smaller cladding air hole diameter d1 is preferred to achieve better SNR.
The responses of the LCPCF-SPR sensor to liquid-core diameter d2 are also considered, the calculated results are presented in Fig. 9(b). It is clearly to see that the resonant wavelength undergoes a blue-shift with the increasing liquid-core diameter d2, and the peak loss decreases slightly. The resonant wavelength is 1059nm, 1036nm and 1016nm, for d2 = 0.6Λ, 0.8Λ and 1.0Λ, respectively. This phenomenon can be attributed to the tuning effect on the liquid-core guided mode dispersion relations, which means the effective index of the fundamental mode increases when the liquid-core diameter d2 gets larger, while that of plasmonic mode is free of influence of d2. As a result, the intersection between the fundamental mode and the plasmonic mode moves towards shorter wavelength range.
By tuning the structural parameters, the resonant wavelength can be designed to a desirable value, as well as the resonant loss. More importantly, some unique features the proposed LCPCF-SPR sensor design possesses are the negative RI sensitivity and the decreased resonant loss, with the increasing of analyte RI. Last but not least, the proposed design is quite suitable for high RI samples, the sensor length can be the centimeter scale and longer, due to the relative low resonant loss. Thus, it is easier to implement in a real world and the interaction between light and testing sample can also be greatly enhanced. To reserve the index-guiding character of the liquid-cores, the proposed LCPCF-SPR sensor only works for analytes with refractive indices no less than that of the silica glass background. However, the detection lower limit can still be lowered to refractive index ranges of water based solutions. On one hand, we can tune the structural parameters to make smaller liquid-core diameters, thus the surrounding silica area guarantees the index-guiding mechanism. On the other hand, the fluorinated polymer PCFs can be utilized to replace the silica substrate PCFs. The fluorinated polymer PCFs have refractive indices comparable to that of water , so the LCPCF-SPR sensor could be carried over to RI ranges close to water.
In conclusion, we have proposed a closed-form all-in-fiber LCPCF-SPR sensor design with six identical liquid cores surrounding one metalized analyte channel. The novel design not only guarantees the uniformity of the metallic micro-channel, but also is free from the interference between neighboring analyte channels. The sensing performance is investigated through the FEM method, and the negative RI sensitivity phenomenon is found for the first time among the PCF based plasmonic sensors. Simulation results show that both the fundamental mode effective index and that of the SPP mode are sensitive to the varied analyte RI. The LCPCF-SPR sensor features a positive RI sensitivity when the increment of the SPP mode effective index is larger than that of the fundamental mode, but the sensor shows a negative RI sensitivity once the increment of the fundamental mode gets larger. The effects of the geometrical parameters on the resonant spectrum are also investigated, and the resonant wavelength can be readily tuned to a desired value by adjusting the structural parameters.
This work was supported by the International Cooperation Projects between China and Singapore (No. 2009DFA12640) and the Fundamental Research Funds for the Central Universities, HUST: 0124182015 & 0109230960.
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