1. Introduction

Being extremely sensitive, small size, label-free, capable of multi analyte detection and online distributed sensing, the optical fiber surface plasmon resonance (SPR) sensor has gathered continuous research interests in medical diagnostics, food safety control, environmental control, and drug detection [1]. To implement SPR sensing, one prerequisite is to fulfill the phase matching condition which mathematically equates the propagation constants of a plasmonic mode and a core-guided mode at a given wavelength [2]. In the past decades, Photonic Crystal Fibers (PCFs) or Holey Fibers (HFs) with a regular hexagonal array of holes running along the fiber length have promoted the development of fiber optic SPR sensors [3–12]. M. A. Schmidt et al. are the pioneers to introduce plasmonic PCF in the experiment, they have successfully fabricated metallic nanowires with high quality through different methods and observed the SPR phenomenon experimentally [8–10]. The SPR sensors based on HFs are products of the combination of photonic technology, plasmonic science and coating technique, which have provided a perfect solution to the phase matching condition and packing issues [7]. The HF-SPR sensors are paving a way towards closed-form all-in-fiber sensors with excellent performance. However, among these extensively investigated HF-SPR refractive index (RI) sensors, which all share the feature of introducing a small air hole in the core area to lower the effective refractive indices of the core modes. To some extent, the phase matching condition between the core-guided mode and plasmonic mode is restricted [4, 5, 11, 12]. Moreover, the analytes are always infiltrated in several closely arranged cylindrical metalized channels, the interference between neighboring channels cannot be ignored. The resonances between fundamental core mode and higher order plasmonic modes give rise to multiple resonance peaks, which would broaden the resonant spectrum and deteriorate the signal-to-noise ratio (SNR). All in a word, the multiple resonance peaks and relative limited dynamic RI detection range, and the nonlinearity of sensitivity are not always desirable in the practical applications.

Recently, a subseries of PCFs—multi-core fibers, both solid type and holey type, have attracted considerable attention due to their design flexibility and the matured stack-and-draw fabrication technology. They have found ways in the field of optical communications, fiber sensors, fiber lasers and optical imaging, et al. [13–16]. In this work, we report a closed-structure optical SPR sensor design utilizing the index-guiding multi-core holey fibers (MCHFs), and present a comprehensive numerical analysis based on the finite element method (FEM). A single-resonance and highly sensitive character of the fundamental mode is utilized to perform the sensing. We find for this novel sensor design a large dynamic RI detection range, as well as high sensitivity and linearity, which is to our knowledge the largest among the reported HF-SPR sensors. A detailed structure design and theoretical modeling is given in the next section, which will be followed by the simulation results, and the conclusions in the last section.

2. Structure design and theoretical modeling

The schematic of the MCHF-SPR sensor with six identical cores is shown in Fig. 1(a) , which is a single-material optical fiber that can be obtained by the well developed stack-and-draw fabrication process. The index-guiding MCHF consists of three layer of air holes arranged in a hexagonal way, the cores are formed by omitting corresponding air holes in the second layer, which are substituted by six silica rods. These cores are numbered 1-6 clockwisely with the Arabic numbers indicating the corresponding core. The remaining second layer air holes, and those in the first, third layers constitute the lower index cladding. For each individual core, the index-guiding mechanism and total internal reflection condition will be naturally established. It should be addressed that, the introduction of a smaller air hole in the core center is not necessary to perform the phase matching condition, which is widely employed in the previous configurations [4, 5, 11, 12]. Our novel design with six identical solid cores contributes to the increase of dynamic RI detection range. Different from the previous configurations, the only one analyte channel is positioned in the center of the whole MCHF cross section, rather than several closely arranged analyte channels surrounding the central core. The main advantages of our novel sensor design lies in four aspects: (i) The consumption of gold and analyte volume is greatly reduced and it is less time-consuming to coating and infiltrating the analyte channel. (ii) The interference between neighboring analyte channels can be effectively eliminated. (iii) The uniformity of the micro-channel is easier to keep in the real world. (iv) The six identical solid cores feature a C_6v rotational symmetry with respect to the metalized analyte channel, which guarantees a polarization independent propagation characteristic. Both the x-polarized and y-polarized light can excite surface plasmon polaritons (SPPs) equally.

 

Fig. 1 (a) Cross section of the index-guiding MCHF-SPR sensor with six identical cores of homogenuous material index. (b) FEM mesh and boundary conditions for computation.

Download Full Size | PDF

We assume the MCHF is made of silica glass with the RI of 1.45, cladding holes are filled with air n_air = 1.0, while metalized microchannel is infiltrated with aqueous sample with n_a varying from 1.33 to 1.53. The dielectric constant of gold in the visible and near-IR region is defined by the Drude model [5]. The pitch of the underlying hexagonal lattice is Λ = 2μm the diameters of the central analyte channel and cladding air holes are d_c = 0.8Λ and d = 0.5Λ, respectively. The thickness of gold layer is fixed to t = 40nm. Here, we use the commercially available software package Comsol Multiphysics to investigate the mode characters and find the complex propagation constants of the core-guided and plasmonic modes. Benefiting from the geometrical symmetry, only a quarter of the MCHF cross-section is needed to be computed. As the FEM mesh in Fig. 1(b) shows, the vertical and horizontal boundaries of the calculation area are assigned with Perfect Electric Conductor (PEC) and Perfect Magnetic Conductor (PMC) artificial boundary conditions, separately. A perfectly matched layer (PML) is used to matching the outmost layer. We use the triangular sub-domain to discretize the computation area. The computational region is meshed into 14576 elements, and the 40nm thick gold layer contains 252 elements. The number of degrees of freedom equals to 102457.

3. Numerical results

3.1 Mode analysis

We begin with the analysis of various core-guided modes supported by the MCHF to get a comprehensive understanding about the resonance properties. By introducing six identical hexagonal ordered solid cores (See Fig. 1.(a)), the MCHF is treated as a superstructure, and the lights propagate in the MCHF are analyzed by the full-vectorial FEM solver. The structure parameters are d_c = 0.8Λ, d = 0.5Λ, t = 40nm, n_a = 1.43, λ = 500nm. The obtained electric field distributions and effective refractive indices of the relevant electromagnetic modes are illustrated in Fig. 2 . It is readily to recognize that the discrete core-guided modes interact with each other, forming core-guided supermodes [17], and each supermode has different electric field direction at a given wavelength and analyte RI, shown by the arrows (both white and blue) in Fig. 2. It should be noted that the mode field distributions have a Gaussian profile, rather than a splitting nature as a higher order mode features in a standard single mode fiber, so it is not appropriate to name these modes as higher order modes.

 

Fig. 2 Calculated electric field distributions and effective refractive indices of three guided-modes that can excite and resonant with plasmonic modes. The arrows (both white and blue) represent the direction of the electric field. Calculated for d_c = 0.8Λ, d = 0.5Λ, t = 40nm, n_a = 1.43, λ = 500nm.

Download Full Size | PDF

The figures in Fig. 2 are arranged according to the real parts of effective indices, which are (a) 1.4458, (b) 1.445808, (c) 1.445987, the corresponding electromagnetic modes are named supermode 1 (s1 mode for short), supermode 2 (s2 mode), and fundamental mode (fund. mode), respectively. The supermode can be viewed as the electric field superposition of the individual core with different directions. Concerning the propagation loss (Defined in decibels per meter [5], α(dB/m) = 40πIm(n_eff)/(ln(10)λ)), which is in proportional to the imaginary part of the mode effective RI, the s1 mode and s2 mode exhibit a much larger loss property than the fund. mode. The electric field directions in the six cores are co-directional for the fund. mode, while for the s1 mode and s2 mode the electric field distributions in the neighboring cores are in different orientations. For each supermode, there is another degenerate one with the same real part of effective RI but electric filed orientation perpendicular to each other, within our computation accuracy. Though the effective RI difference between the three supermodes is quite small, in the order of 10⁻⁶RIU (Refractive Index Unit), all the three guided-modes are able to excite and resonant with plasmonic modes, with distinguishable coupling properties.

There are three SPP modes that are involved with the coupling between the specific core-guided modes. The electric field distributions and corresponding dispersion relations of the 1^st-order, 3^rd-order and 5^th-order SPP modes are illustrated in Fig. 3 . The origin of these SPP modes can be explained by the ray model proposed in [18]. The discrete SPP modes can be viewed as spiraling plasmons, which means the fields of these SPP modes on opposite sides of the inner surface of the analyte channel do not interact but simply spiral around the inner surface of the microchannel. The integral number of field nodes around the circumference of the metalized channel is the mode order of the corresponding discrete SPP mode.

 

Fig. 3 Wavelength dependence of the real parts of the effective indices and modal loss of s1 mode (Red), s2 mode (Purple), and fund. mode (Blue) of the MCHF-SPR sensor design. The solid green lines represent the dispersion relations of SPP modes with specific mode orders excited on the interface between the metal and analyte. The loss spectra of the s1 mode are magnified by a factor of 10 for clarity. Insets are mode fields of the specific SPP modes (1^st-order, 3^rd-order and 5^th-order) and supermodes at resonance ((a) for s1 mode, (b) for s2 mode and (c) for fund. mode). (I) and (II) for lower RI n_a = 1.43 and 1.44, (III) for higher RI n_a = 1.47. (IV): Illustration of incomplete coupling between fund. mode and 1^st-order SPP mode for n_a = 1.47.

Download Full Size | PDF

3.2 Phase matching and incomplete coupling

Among the HF-SPR sensor designs reported up to now, the resonant spectra of the fundamental core-guided modes feature multiple peaks [4, 5, 11, 12], which are resulted from the coupling of the fundamental mode with higher order SPP modes supported by the cylindrical analyte channels. The several closely ordered aqueous channels would interference with each other, resulting a broadened main resonant peak, which is the most sensitive one to the variation of sample RI. Besides, the reported upper detection limit of analyte RI are relatively low, typically below 1.42 [11, 12]. This is due to the breaking down of the phase matching condition for higher RI analytes, as the small air hole in the central core lowers the effective RI of the fundamental core mode, while that of the SPP mode is still higher than the fundamental mode. To some extent, the upper detection limit and some other physical phenomenon beyond phase matching in HF-SPR sensor designs are not investigated sufficiently enough in the previous literatures. A few configurations have endeavoured to increase the upper detection limit [19], which is necessary for some high RI organic chemical liquid samples, such as benzene, nitrobenzene and phenylamine. The solid core MCHF-SPR sensor proposed in this work with relatively large effective RI of core modes is able to measure a liquid sample with RI as large as 1.53, which can be further increased with an optimized structure.

To investigate the coupling properties of the MCHF-SPR sensor, we exemplarily depict the resonant curves for three analyte RI values n_a = 1.43, 1.44 and 1.47. The simulated results are presented in Fig. 3 with structural parameters d_c = 0.8Λ, d = 0.5Λ, t = 40nm. We desire to demonstrate the single resonance feature of the fundamental mode supported by the MCHF and lay emphasis on the phase matching and loss matching coupling mechanism of the fundamental mode. Generally speaking, the resonant coupling between core-guided mode and plasmonic mode can only occur if their propagation constants are equal, which requires the dispersion relations of the relevant modes should intersect [4, 5]. Resonance is characterized by an obvious peak of the core-guided mode loss spectrum, which indicates the largest energy transfer from the core-guided mode to the plasmonic mode. The fundamental SPP mode have much higher effective RI than the core modes and can never couple with them, whereas the higher order SPP modes, namely 1^st-order, 3^rd-order and 5^th-order SPP modes have much smaller effective refractive indices. The effective refractive indices of the s1, s2 and fund. mode are close to each other, so they can all intersect with the specific SPP modes. The dispersion relations of s1, s2 and fund. mode are partially plotted around the corresponding resonant wavelengths for clarity. By tracking the loss spectra of the fund. mode under three analyte RI values n_a = 1.43, 1.44 and 1.47, we find that each of them features only one resonant peak, resulting from the strongly energy transfer from the fund. mode to the 1^st-order SPP mode. The insets (c) in Fig. 3(I), (II) and (III) show the electric field distributions of the three fund. modes at the resonant wavelengths. We can see an obvious electromagnetic field overlapping between the fund. mode and the 1st-order SPP mode, the phase matching coupling phenomenon can also be confirmed by the coincidence of the loss peak and the intersection between the dispersion relations of the fund. mode and 1^st-order SPP mode, see points (c) in Fig. 3(I), (II) and (III). It is worthy to note that the fund. mode loss spectra do not show any resonance peaks in the short wavelength range. They share a single-resonance feature, which is not influenced by the other higher order plasmonic modes. Being the most sensitive resonance peaks, these single main resonance peaks are highly sensitive to the analyte RI variation and free from the broadening caused by the neighboring higher order resonance peaks [11].

For the s2 mode, the loss spectra in Fig. 3 show three relatively weak resonance peaks in the short wavelength range. Each loss spectrum exhibits a single-resonance character too, which is incurred by the resonance between the s2 mode and the 3^rd-order SPP mode. It can be verified by the electric field distributions of the s2 mode at resonance in Fig. 3, insets (b) and points (b) of (I), (II) and (III). While for the s1 mode, the resonance depths are so weak that they are multiplied by 10 for clarity. These resonances come from the phase matching between the s1 mode and the 5th-order SPP mode, which can be confirmed by the crossing points between the dispersion relations of the s1 modes and 5th-order SPP modes, see insets (a) and points (a) of (I), (II) and (III). Now we can get a general coupling property that the fund. mode only couples with the 1^st-order SPP mode in the whole wavelength range. The single sharp resonant peak of the fund. mode is the strongest and most sensitive one to the variation of analyte RI. While the s2 and s1 mode can only resonant with the 3^rd-order and 5^th-order SPP mode in the shorter wavelength range, respectively. They are weakly coupled and less sensitive to the RI change, thus the following study will concentrate on the coupling and sensing properties analysis of the fund. mode. The resonant characteristics of the three core-guided modes are summarized in Table 1 .

Table 1. Summary of Resonant Characteristics of the s1, s2 and Fund. Mode

View Table | View all tables in this article

Apart from the loss spectrum of the fund. mode, the 1^st-order SPP mode loss curve is also helpful for understanding the coupling properties. In our calculation for analyte with n_a ≤1.47, the imaginary part of 1^st-order SPP mode is in the order of 10⁻³ (RIU), which is much larger than that of the fund. mode at the resonant wavelength. Consequently, the loss curves of the fund. mode and the 1^st-order SPP mode can never intersect, shown in Fig. 3(IV). The figure illustrates a phase matching coupling between the two modes. It is obvious to see the notable difference between the two mode losses, though the phase matching condition is well satisfied. An incomplete coupling indeed happens when the two coupling modes have equal real parts of effective refractive indices but different imaginary parts. This can be confirmed by examining the transformation course of electric field distributions of the fund. mode and 1^st-order SPP mode depicted in insets of Fig. 3(IV). At shorter wavelength away from the phase matching point, the fund. mode and 1^st-order SPP mode are well confined in the core and metal-analyte surface. A little amount of fund. mode energy transfers to the SPP mode with approaching to the phase matching point. The largest energy transfer takes place at the intersection between the two dispersion curves. The transferred energy from the fund. mode to the 1^st-order SPP mode returns to the core region with increasing wavelength. Table 1 indicates that the fund. mode resonant loss grows fast with the increase of n_a, which means the resonant coupling gets stronger and more energy is transferred to the 1^st-order SPP mode. Insets (c) in Fig. 3(I), (II) and (III) also gives a well understanding of the incomplete coupling phenomenon under the phase matching condition.

3.3 Loss matching and complete coupling

Though there is not a complete coupling between the fund. mode and 1^st-order SPP mode in the whole course when n_a ≤1.47, the coupling will be very different when n_a is larger than 1.48. In our simulation, the phase matching condition is maintained until n_a = 1.47, and the resonant coupling for n_a varying from 1.33 to 1.47 is incomplete. This is because the imaginary parts of the fund. mode and 1^st-order SPP mode effective refractive indices cannot match, so the fund. mode energy is only partially transferred to the SPP mode (See Fig. 3(IV)). Although the loss curves of the two coupling modes do not intersect, a dip on the 1^st-order SPP mode curve and a peak on the fund. mode loss curve appear at the phase matching point at the same time. Most importantly, the peak loss of the fund. mode increases dramatically with increasing n_a, while the dip loss of the 1^st-order SPP mode decreases slowly. As a result, the dip-to-peak difference gets smaller with larger n_a, and the coupling becomes stronger and stronger, too. We can predict that with large enough n_a, the dip-to-peak difference will disappear and the loss curves would intersect to form a loss matching condition.

We calculated the dispersion relations and loss curves of the fund. mode and 1^st-order SPP mode with large enough n_a (n_a = 1.50), the results are presented in Fig. 4 . It can be seen from Fig. 4(a) that the originally intersecting dispersion curves for the fund. mode and 1^st-order SPP mode will split into another two new modes due to the avoided crossing effect. The insets in Fig. 4(a) illustrate the avoided crossing transition of the two coupling modes. At the shorter wavelength range away from the anti-crossing point, the fund. mode energy is mainly confined in the core area, more energy is transferred to the 1^st-order SPP mode with increasing wavelength. Near the avoided crossing point, the electric field distribution of the fund. mode and 1^st-order SPP mode are almost the same, thus it is difficult to distinguish between them. Gradually, the energy is thoroughly transferred into the 1^st-order SPP mode at longer wavelengths. For the 1^st-order SPP mode at shorter wavelength, the field transition is just contrary to that for the fund. mode. And finally, the energy is totally diverted into the fund. mode at longer wavelengths. The completely energy transfer can also be understood from the losses of the two coupled modes. From Fig. 4(b), the mode loss exhibited by the green curve follows the fund. mode part at shorter wavelengths, and switches to the 1^st-order SPP mode after passing through the avoided crossing point (1480.3nm). For the red curve, the mode loss undergoes an opposite transition, from 1^st-order SPP mode to fund. mode. Different from the loss curves in Fig. 3(IV), the two loss curves in Fig. 4(b) really intersects, indicating that the coupled modes have the same imaginary parts of effective refractive indices. The intersection is the avoided crossing point, and the complete coupling incurred by anti-crossing effect is under loss matching condition in nature [20].

 

Fig. 4 Wavelength dependence of the real part (a) and modal loss (b) when a complete coupling happens. Dashed curves represent the dispersion relations of fund. mode and 1^st-order SPP mode respectively without coupling at all. The insets are electric field distribution of coupled modes at specific wavelengths. The analyte RI n_a equals to 1.50.

Download Full Size | PDF

Actually, the complete coupling takes place when the analyte RI is larger than 1.48, the results are presented in Fig. 5 . Considering the real part of effective refractive indices, we can get that it experiences a stronger coupling with wider transition wavelength range, with the increase of analyte RI. The avoided crossing point shifts towards longer wavelength with increasing n_a. It is interesting to note that almost all the intersections between the fund. mode and 1^st-order SPP mode loss curves have the same loss value. This is because the losses of the two coupled modes vary contrarily with the increase of n_a in Fig. 5(b), which is in agreement with the phenomenon depicted in [20]. Now, we can draw a conclusion that not only phase matching but also loss matching condition plays an important role in the mode coupling in the HF-SPR sensor. For n_a ≤1.47 the phase matching condition is well satisfied, and the incomplete coupling between the fund. mode and 1^st-order SPP mode happens. While for n_a ≥ 1.48 the loss matching condition is fulfilled, and the complete coupling accompanying with the avoided crossing effect takes place. During the avoided crossing, the electric field of the fund. mode undergoes a spatial transition into the 1^st-order SPP mode in spite of the real parts of their effective refractive indices not being equal. From the whole coupling progress, the two coupling modes exchange their roles and the real parts of their effective refractive indices diverge. The avoided crossing effect and complete coupling we observed are also consistent with the phenomenon reported in [21, 22]. Note that there are kinks in the dispersion relations of the 1^st-order SPP mode of Fig. 5(a) when the analyte RI is large enough, for example, 1761.7nm for n_a = 1.53. It originates from the avoided crossing between the s1 mode and the 1^st-order SPP mode.

 

Fig. 5 Real part (a) and loss (b) as a function of wavelength when loss matching condition is satisfied and complete coupling happens. The analyte RI n_a varies from 1.48 to 1.53.

Download Full Size | PDF

During the whole simulation, we find out that the coupling experiences a transition from incomplete coupling to complete coupling with increasing analyte RI. The theoretical explanation based on the coupled mode theory presented in Ref [20]. is helpful to understand the coupling process. We calculate three sets of resonant spectra for n_a equals to 1.465, 1.475 and 1.485 to make out the transition from incomplete coupling to complete coupling, the results are exhibited in Fig. 6 . For lower n_a (1.465, 1.475), the coupling coefficient κ is relatively small, while δ_i the imaginary parts detuning factor (Defined as δ_i = Im[(β_f -β_p)/2], where β_f and β_p are the propagation constants of the isolated fund. mode and the 1^st-order SPP mode, respectively) is relatively large. When κ is smaller than the absolute value of δ_i, the fund. mode and 1^st-order SPP mode have equal real parts but different imaginary parts. The coupling between them is incomplete coupling. The fund. mode energy is partially transferred to the 1^st-order SPP mode. With increasing n_a, the coupling coefficient κ increases, and δ_i decreases at the same time. Thus, κ becomes larger than the absolute value of δ_i once n_a is large enough (for example, 1.485). The coupling experiences a transition from incomplete coupling to complete coupling, and fund. mode energy is nearly entirely transferred to the 1^st-order SPP mode.

 

Fig. 6 Imaginary parts of effective indices of the fund. mode and 1^st-order SPP mode for three analyte RI, n_a = 1.465, 1.475 and 1.485. Insets are electric field distributions of the fund. mode at the resonant wavelengths.

Download Full Size | PDF

4. Sensing performance

In Section 3.2 and 3.3, we present a comprehensive investigation on the core-guided modes supported by the MCHF which can resonant with the specific SPP modes. The summary of the resonant properties in Table 1 shows that the fund. mode is the most sensitive one to sense the analyte RI, with the highest coupling efficiency. In this section, we focus our attention on the MCHF-SPR sensor performance by calculating the resonant spectra of the fund. mode in a large dynamic RI range to find the corresponding resonant wavelength, without loss of generality. The results are presented in Fig. 7 .

 

Fig. 7 Linear fitting lines of the fund. mode resonant wavelength versus analyte RI, (a) for lower analyte RI of 1.33-1.42 and (b) for higher analyte RI of 1.43-1.53. Simulated parameters: d_c = 0.8Λ, d = 0.5Λ, t = 40nm.

Download Full Size | PDF

Recently, the extensively investigated ultrasensitive HF refractometers are based on a dual-core coupling effect, the air holes in one core are selectively filled with aqueous analyte to tune the coupling properties of the dual-core HF. Typically they are implemented on two schemes: (i) Analyte channel formed waveguide [23–25], the sensing capability was enforced by the phase matching of dissimilar waveguides, the analyte filled one and the solid one. Due to the index-guiding property of the newly formed analyte channel waveguide, it was restricted to detecting analyte indices higher than the silica background. (ii) Analyte replaced air holes in the core area [26, 27], the sensing was performed under the tuning of the core-mode effective indices by the analyte. To preserve the index-guiding character of the original waveguide, the sensor was limited to analyte with RI lower than that of the background material. The MCHF-SPR sensor we proposed here overcomes these limitations, the large dynamic detection range makes it more competitive in the chemical, biological and industrial applications.

The sensitivity of a resonant-based RI sensor is often defined by the resonant wavelength shift caused by unit analyte RI change, which is given in units of nm/RIU. It is preferable to get an average sensitivity within a given analyte RI range, rather than a local sensitivity determined by only two measurands. We find that the resonant wavelength shift with respect to the analyte variation exhibits a nonlinear feature, the scatter points of higher analyte RI owns a larger local slope compared to the lower RI analytes. It is easy to rationalize that the sensitivity of a SPR sensor is intrinsically different for lower and higher RI analytes [28]. What’s more, the average sensitivity and calibration linearity is dependent on the dynamic sensing range. With this consideration in mind, we investigate the MCHF-SPR sensor sensitivity in two parts, the lower RI range of 1.33-1.42 and higher RI range of 1.43-1.53. It is also impartial to compare our sensor performance with others in the same sensing range (1.33-1.42). The corresponding linear fitting lines of peak wavelength with respect to analyte RI are presented in Fig. 7(a) and 7(b). The regression equations are

So far the sensitivity, dynamic operation range and linearity have been considered, the spectral width is another parameter crucial for the sensor operation. The accuracy of the detection of SPR wavelength depends on the width of the response curve, which is characterized by the full-width-at-half-maxima (FWHM). In a practical SPR sensing system a smaller FWHM is favorable, as it would filter the spectral noise more effectively, which results in not only lower spectral deviation from the actual center of the resonant wavelength, but also the suppression of non-resonance confinement loss [29]. The FWHM and resonant mode loss in the sensing range 1.33-1.53 are presented in Fig. 8 . The minimum FWHM is only 17nm for n_a = 1.48, which is the beginning of the complete coupling. The resonant losses of fund. mode and 1^st-order SPP mode vary contrarily with increasing analyte RI, and finally they coincide with each other due to the avoided crossings. Consider a SNR of 60dB, an average FWHM of 30nm, a spectral resolution of 1pm, using a rigorous definition for the detection limit of the SPR sensor proposed in [29] (δn_l = FWHM/(4.5 × S × SNR^0.25), S is the average sensitivity in 1.33-1.53), a high sensor resolution of 3.72 × 10⁻⁴ RIU is achievable. The changes in peak loss for incomplete coupling can be analyzed by an exponential function, which would be used to derive the transmittance characteristic as a function of sample RI in a certain sensing length. This is due to the fact that the mode field overlapping between the evanescent field and the analyte increases exponentially with increasing analyte RI.

 

Fig. 8 Dependence of the fund. mode peak loss (Red, Logarithm coordinates), 1^st-order SPP dip loss (Blue, Logarithm coordinates), and FWHM (Green) on the analyte RI. The operation wavelength is 400-1850nm.

Download Full Size | PDF

Table 2 compares the performance of the MCHF-SPR sensor proposed in this work with the other optical fiber based SPR sensor designs in terms of dynamic detection RI range, operation wavelength, average sensitivity and linearity. For lower RI analytes, the sensitivity of our MCHF-SPR sensor is comparable to the other HF-SPR sensors, but the linearity is much higher than the counterparts. While for higher RI analytes, the novel design shows higher average sensitivity and better linearity. We believe the closed-form all-in-fiber MCHF-SPR sensor proposed in this work is competitive and outstanding among numerous optical fiber based SPR sensors, with really large dynamic detection range and high linearity, of which the others are out of reach. The sensing performance and detection upper limit can be improved with an optimized structure and the further work is ongoing.

Table 2. Comparison of Various Fiber-SPR Sensor Performances

View Table | View all tables in this article

Concerning the experimental feasibility, larger sensor length will facilitate the coating and infiltration process, and ensure sufficient interaction between the core mode and analyte. Though the peak loss is about several dB/mm and the millimeter scale length is challenging in the experiments, a 6mm long PCF selectively filled with gold nanowire has been successfully characterized in the experiment reported in Ref [8]. We believe that using a special designed fiber holder, three dimensional translation stages and precise alignment system, our millimeter scale sensor can be successfully implemented. Furthermore, the propagation loss of the sensor can be reduced by careful tuning of the structure parameters, for example, by increasing the gold layer thickness and cladding air hole diameters [5]. Thus, the sensor length can be extended to a centimeter scale. Selective excitation of the core guided supermodes is of great importance in the real world, which can be realized by a coaxial or off axial input beam with a Gaussian profile [32, 33]. The fundamental mode guided by the MCHF can be selectively excited by coaxial injection and controlling the input Gaussian beam mode field radius [32].

5. Conclusions

We have proposed a closed-form all-in-fiber MCHF-SPR sensor design with six identical solid cores surrounding one metalized analyte channel, which not only reduces the consumption of gold and sample volumes, but also is free from the interference between neighboring analyte channels. We have also revealed that both the phase matching and loss matching coupling mechanisms are significant for the MCHF-SPR sensor. Simulation results confirmed that the MCHF-SPR sensor is able to work in a large dynamic RI range from 1.33 to 1.53 with high sensitivity and linearity.