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To solve the phase matching and analyte filling problems in the microstructured optical fiber (MOF)-based surface plasmon resonance (SPR) sensors, we present the D-shaped hollow core MOF-based SPR sensor. The air hole in the fiber core can lower the refractive index of a Gaussian-like core mode to match with that of a plasmon mode. The analyte is deposited directly onto the D-shaped flat surface instead of filling the fiber holes. We numerically investigate the effect of the air hole in the core on the SPR sensing performance, and identify the sensor sensitivity on wavelength, amplitude and phase. This work allows us to determine the feasibility of using the D-shaped hollow-core MOFs to develop a high-sensitivity, real-time and distributed SPR sensor.
© 2015 Optical Society of America
1. Introduction
Surface plasmon resonance (SPR), characterized by its high sensitivity to refractive index (RI) of the material in contact with the metal, and has been implemented in numerous sensing structures, such as Kretschmann-Raether prism, optical waveguides and fibers [1–10]. Among these SPR configurations, optical fibers-based SPR sensor offers miniaturization, high degree of integration and remote sensing capabilities, shows great potential in chemical and biomedical sensing. In most of fiber-based SPR sensors, cladding is partially or completely stripped from the fiber and the exposed part is coated with a metal layer and then exposed to an analyte. The light launched into the fiber core can couple with a plasmon mode at a certain wavelength, and the RI of the analyte can then be followed by monitoring spectral or power characteristics of the transmitted light. To couple with the plasmon mode, the phase matching condition between the core mode and plasmon mode has to be satisfied, which theoretically amounts to the equality between their mode effective RIs (neff) [11,12]. However, phase matching between the two modes is not easy to achieve. In the case of a single mode fiber, the neff of its core mode is close to that of the core material, which for most practical materials is higher than 1.45 (fused silica). And the neff of the plasmon mode is typically close to that of the bordering analyte, which in the case of water is 1.33. Only at higher frequencies the neff of the plasmon mode becomes high enough to match that of the core mode. High frequency of operation limits plasmon penetration depth into the medium, thus reducing the sensitivity of the sensor. Although the phase matching problem can be alleviated by coupling to a plasmon mode via a certain number of high-order modes of multimode fibres [9,10,12], only a small fraction of the launched power can be coupled to the plasmon mode, which will also reduce the sensitivity.
Recently, SPR sensors based on microstructured optical fibers (MOFs) [11–17] attract the most research interest because of their flexible design of microstructures, which provides a new method to achieve phase matching between the core mode and the plasmon mode. To implement the sensors for liquid analytes, metal films are selectively [11–15,18] or completely [16,17] incorporated into fiber holes. And the analyte can be filled into the metallized holes. However, note that if the analyte changes during the measurement period, emptying and re-filling of the fiber is required. This makes their use impossible for real-time, fast-response or distributed sensing applications. Moreover, either coating the holes of a MOF with metal films or filling them with analyte is difficult and time-consuming work.
To solve above problems, we present a D-shaped fiber SPR sensor based on hollow-core MOF. For sensor operation, the MOF is side-polished to form a flat plane [19,20]. And the plane is coated with a gold film and then contacted directly with the analyte. Compared with the inside coating of the fiber holes [11–18], the outside coating should be much easier to operate and provide more potential for fast-response, real-time and distributed sensing. Making a hole in the core of the MOF can lower the RI of the core mode to match with that of the plasmon mode at lower frequencies, thus increasing the sensor sensitivity. We numerically investigate the effect of the introduced air hole in the core on the SPR sensing performance, and identify the sensor sensitivity on wavelength, amplitude (power) and phase of the transmitted light for the analyte RI at na = 1.33 (aqueous solution).
2. Design and analysis
The schematic of the D-shaped MOF based SPR sensor is shown in Fig. 1. The lattice pitch is Λ = 2 µm, the diameters of the center and cladding holes are dc = 0.2Λ and d = 0.8Λ, respectively. And the polishing depth is h = 0.45Λ. The thickness of the gold film is 40 nm.
The electromagnetic mode of the sensor fiber is solved by finite element method (FEM) [11–17,19,20]. The RI of the MOF material is assumed to be 1.45 (fused silica), the RI of the gold layer is given by the Drude model [21] and the RI of the analyte (na) is altered from 1.33 to 1.34 to assess the sensitivity of the sensor at na = 1.33 [11,16].
Figure 2 shows dispersion relations and electric field distributions of the core mode and the plasmon mode with na = 1.33 and dc = 0.2Λ. Here, we use the Gaussian-like modes as the core modes [11,12,16,17], and it is best suited for the excitation by standard Gaussian laser sources. As shown in Fig. 2, the core modes exhibit strong birefringence, with one mode (x-polarized mode) being polarized essentially parallel to the gold surface and the other (y-polarized mode) orthogonal to this [see Figs. 2(a) and 2(b)]. And only the y-polarized mode could couple to the plasmon mode, gauged from the imaginary part of the neff [Im(neff)] curve of the y-polarized core mode (blue solid curve) which is proportional to the mode loss. The S-shaped kink on the real part of neff [Re(neff)] curve of the y-polarized core mode (black solid curve) expose that the phase of the transmitted light is modified by the SPR [20]. Significant increase in the loss of y-polarized core modes (blue solid curve) is observed at phase matching point, where the Re(neff) of the y-polarized core mode and that of the plasmon mode coincide, indicates the nature of the coupling and the transfer of energy from the y-polarized core mode to the plasmon mode. The electric field distributions in Figs. 2(b) and 2(c) allow clear differentiation of the nature of the two modes. In the phase matching point, the two modes become strongly mixed [Fig. 2(d)], with losses of the y-polarized core mode increasing dramatically due to the energy transfer into the lossy plasmon mode. Thus, an obvious peak in the loss spectrum of a y-polarized core mode is observed at this wavelength range. When na is varied, the plasmon dispersion relation displaces accordingly, thus leading to the shift in the position of the phase matching point with y-polarized core modes. Consequently, the loss spectrum of y-polarized core modes varies strongly with the na variation.
Fig. 2 Left: Dispersion relations of core modes (black and blue curves) and a plasmon mode (red curve) with na = 1.33 and dc = 0.2Λ. Right: Electric field distributions of the (a) x-polarized core mode at λ = 600nm, (b) y-polarized core mode at λ = 560nm, (c) y-polarized plasmon mode at λ = 560nm and (d) y-polarized core mode at λ = 648nm (phase matching point).
3. Results and discussion
The na variation will induce changes of the phase matching point between the y-polarized core mode and the plasmon mode, thus leading to different loss spectra. And the na variation can be identified by measuring the peak wavelength (phase matching point) shift or transmitted power change at the certain wavelength of the y-polarized core mode, and also by measuring the phase shift of the core mode [20,22].
Figure 3(a) shows the different spectra of a y-polarized core mode when the na changes from 1.33 to 1.34. For reference, losses in decibels per meter are defined as [17]:
Here, k0 = 2π/λ is the wavenumber with λ being in meters. In our simulations, the primary variable is the dc. By varying the dc, as in Fig. 3(b), the neff of the core mode can be readily tuned, thus changing the peak wavelength and the sensor sensitivity.Fig. 3 (a) Loss spectra of a y-polarized core mode with analyte na at 1.33 and 1.34 when the dc is 0.2Λ. (b) Re(neff) at the phase matching point and the peak wavelength of a y-polarized core mode for various values of the dc.
3.1 Wavelength sensitivity
In the wavelength interrogation mode, the na variations are detected by measuring the shift of the resonance peak Δλpeak. In this case, the sensitivity in term of refractive index units (RIU) is defined as [12]:
As shown in Fig. 3(a), the Δλpeak is 29nm for the na changing from 1.33 to 1.34 (Δna = 0.01), and the corresponding spectral sensitivity is 2900nm/RIU. As the dc increasing, the Re(neff) of the core mode will decrease, as in Fig. 3(b), and the peak wavelength increases correspondingly. The increasing wavelength will enhance plasmon penetration depth, thus increasing the Δλpeak [see Fig. 3(b)]. Therefore the wavelength sensitivity increases, as in Fig. 4(a), but the peak loss decreases correspondingly. This fact is easy to understand by noting that the larger size of a center hole reduces the mode presence near the gold interface, as the insets in Fig. 4(b), thus reducing the coupling efficiencies between the core mode and the plasmon mode, and leading to a decreasing peak loss.
Fig. 4 (a) Wavelength sensitivity and peak loss of the y-polarized core mode for various values of the dc. (b) Loss spectra of the y-polarized for different values of the dc = 0Λ, 0.2Λ and 0.4Λ when the na is 1.33. And insets show the corresponding electric field distribution of the core mode at wavelength λ = 590 nm.
3.2 Amplitude sensitivity
As mentioned above, in the vicinity of the phase matching wavelength, the loss of the core mode varies strongly with the na variations. Thus in the amplitude interrogation mode, the transmitted light power is monitored at a fixed wavelength [11,12,16]. The advantage of this method is its simplicity and low cost as no spectral manipulation is required. The sensitivity parameter is defined as [16]:
This parameter S is valid for a sensor of length 1/α1.33, with α1.33 denoting the modal loss for the case na = 1.33.Figure 5(a) shows the sensitivity S for various dc = 0Λ, 0.2Λ, 0.4Λ. Take the sensitivity curve with dc = 0.2Λ as obtained from the data of Fig. 3(a), for example, the maximum S of the sensor is 120 RIU−1 at 145 nm for the na range from 1.33 to 1.34. As the dc increasing, as shown in Fig. 5(b), both the maximum S and its wavelength increase. The larger sized hole increases the Δλpeak for the na changing from 1.33 to 1.34 [see Fig. 3(b)], hence increasing loss changes in the different loss spectra (Δαloss), thus resulting in the higher S according to Eq. (3) with the decrease of mode loss α1.33 [see Fig. 4(b)]. The maximum Δαloss always locates in the vicinity of the peak wavelength, thus the operated wavelength of the maximum S will also correspondingly increase with dc.
Fig. 5 (a) Amplitude sensitivity comparison of the y-polarized for different values of the dc = 0Λ, 0.2Λ, 0.4Λ. (b) Maximum amplitude sensitivity and its wavelength of the y-polarized for various values of the dc.
3.3 Phase sensitivity
In phase interrogation, referring to the reports [20,22], the incident coherent light is split into a vertical component and a horizontal component with respect to the D-shaped plane. By injecting a periodic phase, the phase difference between the two electrical field components can be extracted by a lock-in amplifier. The phase difference is defined as [20]:
Where L is the length of sensor region, Re(np) is the real part of the neff for SPR cases (y-polarized modes), and Re(ns) represents that in the non-SPR cases (x-polarized modes).Figure 6(a) shows the phase difference Φd and its shift for na changing from 1.33 to 1.34. Vertical line represents the wavelength of the incident light, and its crossing points with the curves give the phase differences for each na. The maximum phase shift is 503deg/cm at 676 nm, and the corresponding maximum phase sensitivity is 50300 deg/RIU/cm.
Fig. 6 (a) The phase difference of two modes Φd with na at 1.33 and 1.34 when the dc is 0.2Λ. Vertical lines represent the wavelength of the incident light for the maximum phase shift. (b) Maximum phase sensitivity and maximum Φd value of the sensor for various values of the dc with na at 1.33.
The maximum phase sensitivity for different dc is shown in Fig. 6(b). Different from the wavelength and amplitude sensitivity, the phase sensitivity decreases as the dc increasing. This phenomenon is attributed to that the increasing dc reduces the maximum Φd, as shown in Fig. 6(b). The maximum phase shift always occurs near the maximum Φd, therefore the maximum phase sensitivity decreases.
4. Conclusion
We numerically investigate a D-shaped fiber SPR sensor based on hollow-core MOF. The gold film and the analyte are both deposited onto the fiber plane, which are much easier to operate than those into the fiber holes [11–18]. The air hole in the fiber core can reduce the RI of the core mode and promote phase matching between the core mode and the plasmon mode at lower frequencies, thus increasing the wavelength and amplitude sensitivity of the sensor. Unlike the all-solid D-shaped fibers [19,20,22] are limited by the required core-cladding index contrast, the all-air holes D-shaped MOFs can further reduce the RI of a core mode to increase the sensitivity by increasing the size of the centre hole, benefiting from the air holes cladding. Simulation results show that the increasing diameter of the center hole can improve the wavelength and amplitude sensitivity because of the increasing peak wavelength and its shift (Δλpeak) for the same na changing, but reduce phase sensitivity due to the decreasing maximum Φd of the core modes. Considering the potential for fast-response, real-time, distributed sensing of the D-shaped fiber and these demonstrated SPR sensing characteristics, The D-shaped fiber SPR sensor based on hollow core MOF will be more competitive in the chemical, biological and industrial applications.
Acknowledgments
This work is supported by the National Key Basic Research and Development Program of China (Grant No. 2010CB327801).
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