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We propose a novel photonic crystal fiber refractive index sensor which is based on the selectively resonant coupling between a conventional solid core and a microstructured core. The introduced microstructured core is realized by filling the air-holes in the core with low index analyte. We show that a detection limit (DL) of 2.02 × 10−6 refractive index unit (RIU) and a sensitivity of 8500 nm/RIU can be achieved for analyte with refractive index of 1.33.
©2011 Optical Society of America
1. Introduction
In recent years, optical fiber refractive index sensors have achieved considerable attention especially in the context of label-free fiber-optic biosensor, in which biomolecules are unlabeled or unmodified [1–4]. For example, Rindorf et al. demonstrated a sensitivity of 1.4 nm shift of a long-period grating resonance per nm biolayer (1.4 nm/nm) [1], and Ott et al. [4] reported a biosensor using the inherent nonlinearity of the photonic crystal fiber (PCF) for FWM-based label-free biosensing, which predicted a sensitivity of 10.4 nm/nm.
PCFs can provide a flexible platform for optical sensing of a wide range of analyte refractive index in a variety of configurations. PCF index sensors can be based on a Bragg or long period grating (LPG) [1,3,5], surface plasmon resonances [6,7], photonic bandgap properties of the PCF [8,9], or resonant coupling [10–15], nonlinear process of modulational instability [4]. Recently, Hassani and Skorobogatiy [6] have investigated a microstructure optical fiber sensor based on surface plasmon resonance, the detection limit of the sensor for measuring changes in the aqueous analyte was found to be 5 × 10−5 RIU, assuming a 1% amplitude change detection limit in the shift of a plasmonic peak. Huy et al. have shown that a fiber sensing system based on photowriting fiber Bragg gratings in a six-hole microstructured optical fiber can achieve a detection limit of 4 × 10−3 RIU for analyte refractive index close to 1.33 [16]. In addition, by using a three-hole fiber a resolution of 3 × 10−5 RIU for analyte refractive index as low as 1.33 can be achieved [17]. Photonic crystal fiber grating sensors with a high sensitivity of 1500 nm/RIU and low detectable index change (2 × 10−5) have been demonstrated by Rindorf and Bang [5].
Sensors based on dual-core PCFs configuration have been shown to be capable of achieving enhanced sensitivity for refractive index sensing [13–15]. In particular, a dual-core microstructured optical fiber realized by using the exponential dependence of intercore coupling on analyte refractive index, has the potential for use over a wide range of analyte refractive index with high sensitivity [13]. For example, for analyte with refractive index around 1.44, the sensitivity of the device is 167,911%/RIU. Very recently, a refractive index sensor based on a twin-core coupler in an all-solid photonic bandgap guiding optical fiber shows a highly sensitivity of 70,000 nm/RIU [14]. By operating in the bandgap guiding regime the proposed sensor is capable of measuring refractive indices around that of water. A microfluidic refractive index sensor based on a directional coupler architecture using solid core photonic crystal fibers, has been demonstrated experimentally by Wu et al. [15]. The sensor can achieve very high sensitivity by coupling the core mode to a mode in the adjacent fluid-filled waveguide. A detection limit of 4.6 × 10−7 refractive index units with a sensitivity of 30,100 nm/RIU can be achieved. However, the device is restricted to measuring analyte index higher than the silica host. It has now been shown that coating the holes and using flourinated polymer microstructured optical fibers can extend the regime of operation to low indices, such as water [18].
In this article, we present a novel PCF-based low-index sensor, the wavelength-selective resonant coupling in a dual-core directional geometry with an analyte-filled microstructured core can detect analyte with refractive index as low as 1.33. Numerical simulation demonstrates that a detection limit of 2.02 × 10−6 refractive index unit (RIU) and a sensitivity of 8500 nm/RIU can be achieved.
2. Numerical simulation
High sensitive detection for high-index fluid can be realized by exploiting selectively resonant coupling in dual-core PCFs. The inclusion of analyte in the center of core can effectively increase the overlap between the evanescent field and the analyte, which increases the detection sensitivity of the device [15]. In this section, we will focus on the detection of analyte with refractive index na = 1.33. However, for a dual-core PCF composed of a conventional solid core and an analyte-filled channel as shown in Fig. 1 , the inclusion of low-index material in the core reduces effective fundamental index of the core, which makes the index-matched coupling between the fundamental modes in the two cores impossible. The remedy is to increase the effective fundamental index of the analyte-filled core by increasing its core area. This can be realized by eliminating several air-holes to form a large core and then introducing a large analyte-filled channel in the center. There are some disadvantages in this method which we will discuss further in Sec. 3.3. Another method is the introduction of analyte-filled microstructured core. Microstructured core optical fibers have been investigated by several groups [19–22]. The microstructured core, which is composed of air-holes or all-solid configuration, forms an effectively step-index core. Recently, a directional coupler fiber has been reported in the THz regime and demonstrated a 3 dB coupler with a broad bandwidth of 0.6 THz centered at 1.4 THz [22]. The broadband coupling is achieved by microstructuring the cores of a dual-core PCF.
The cross-section of an analyte-filled microstructure configuration, which is composed of seven analyte channels embedded in a silica background, is shown in Fig. 2(a) . The refractive index of the analyte is set as na. The centers of all air holes and channels are arrayed in a regular triangular lattice and the center-to-center distance of the two nearest air-holes is set as Λ. We set the diameter of the cladding holes as d and the diameter of the channels as da in this article. Figure 2(b) shows the z-component of the Poynting vector with the configuration parameters chosen as d/Λ = da/Λ = 0.4, Λ/λ = 1.661 and na = 1.33. We can see that the fundamental mode field is similar to that of a conventional PCF except that the field distribution is more complex.
Fig. 2 (a) Cross-section of an analyte-filled microstructured core optical fiber. The dark area denotes pure silica, the black areas denote analyte-filled channels and the white areas represent air holes. (b) Mode field profile of the microstructured core optical fiber.
We solve the modes of the individual cores in the proposed fiber by semi-vectorial beam propagation method [23]. Figure 3 plots the effective indices of the fundamental modes in the two cores of the dual-core PCF with d/Λ = da/Λ = 0.4. The inset shows the proposed structure with a conventional solid core (core A) and a microstructured core (core B). Owing to the fact that index-matching is reached at the frequency where Λ/λ = 1.661, we expect the effective coupling can appear at this point. Therefore, if the index-matched coupling happens at the wavelength of 1.55 μm, the pitch Λ should be 2.575 μm.
Fig. 3 Effective indexes curves of core A and core B for the vertical polarization with d/Λ = da/Λ = 0.4, and na = 1.33. The inset shows the cross-section of the proposed fiber.
It’s found the coupling characteristics of the dual-core fiber are slightly dependent on polarization state of the input signal. In this case, the resonant wavelength difference between the horizontally polarized (x-polarized) and the vertically polarized (y-polarized) modes is 1.5 nm. The coupling length difference for the two different polarizations is less than 0.2 mm. We will only consider the coupling characteristics of vertically polarized state. The horizontally polarized mode can be eliminated by inserting a polarizer before the OSA [15]. The coupling length of the structure at the wavelength of 1550 nm is Lc = 2.25 mm. We plot in Fig. 4 the evolution of the field distribution at different propagating distance, where the y-polarized mode at the resonant wavelength is injected into core A. We can clearly observe that at the distance of z = Lc, all the power injected from core A is transferred to core B and the transition is a smooth one. Obviously, the deviation of the wavelength from the resonant wavelength will lead to the rapid reduction of the power transferring between the two cores.
Fig. 4 The field distributions of the y-polarized mode in the proposed dual-core sensor at propagation distance (a) z = 0 mm, (b) z = 0.75 mm, (c) z = 1.50 mm, and (d) z = 2.25 mm.
Typically, a refractive index sensor has a resonant feature whose resonant wavelength λr depends on the refractive index of the analyte na. The sensitivity of the sensor is defined as and the detection limit is formulated as, where λFWHM is the full width at half maximum of the resonance, and SNR is in linear units (e.g., 50 dB gives 10(50/10)) [24]. The evolution of the normalized power transmission at the output port of core B as a function of the operating wavelength after a propagation length of Lc, is plotted in Fig. 5 . The blueshift of the resonant wavelength between na = 1.33 and na = 1.3304 is 3.4 nm, which corresponds to a sensitivity of S = 8.5 × 103 nm/RIU. The spectral width λFWHM of the resonance at na = 1.33 is only 0.46 nm. Assuming a signal-to-noise ratio of 50 dB, we can get a detection limit of 2.02 × 10−6 RIU.
The detection limit and sensitivity as a function of analyte index for the fiber with L = 2.25 mm has been investigated. The results are shown in Fig. 6 . It should be noted that the sensitivity is only slightly changed with the analyte index, whereas the detection limit gets worse when the analyte index is deviated from the optimum value. By requiring the detection limit should be lower than 5 × 10−5 RIU, then we can get the dynamic range is Δn = 0.012 ranging from 1.324 to 1.336.
Fig. 6 Variation of detection limit and sensitivity as a function of analyte index for the fiber with L = 2.25 mm.
The fiber sensor proposed here can be fabricated by two steps. Firstly, a PCF with the core of which realized by the omission of one air-hole is fabricated by the stacking-and-draw procedure. Secondly, the seven air-holes are selectively filled with the anaylte by the similar technique proposed previously [15].
3. Discussion
3.1 Tolerance and temperature stability analysis
One important issue about PCF coupler is the tolerance of the structure parameters. As shown in Fig. 7 , the deviation of the fiber length from the optimum value will lead to a linear increase of the detection limit while the sensitivity is only slightly changed. As shown in Sec. 2, the detection limit for the fiber with fiber length L = 2.25 mm for the detection of analyte with dynamic range Δn = 0.012 is 5 × 10−5 RIU. We can see that the fiber with ± 7% variation in fiber length with respect to the optimum value can still have detection limit lower than 5 × 10−5 RIU. Therefore, the fiber can allow relatively large tolerance of the fiber length deviation.
Fig. 7 Variation of sensitivity and detect limit as a function of deviation of fiber length from the optimum length.
It’s also possible the sensitivity and the detection limit will be influenced by the environmental temperature. For the fiber with L = 2.25 mm, the sensitivity of which is around 8500 nm/RIU for analyte with refractive index around 1.33, that is, the shift of 1 nm in resonant wavelength corresponding to 1/8500 RIU variation. The detection limit of this sensor is 5 × 10−5 RIU for the dynamic range Δn = 0.012. Therefore, if the resonant wavelength shift induced by temperature variation is within ± 0.2 nm, then the shift implies refractive index change is less than ± 2.5 × 10−5, which is well below the detection limit and will not be detected. We have calculated the shift of resonant wavelength as a function of temperature variation. The thermo-optic coefficient of fused silica is set to be 1 × 10−5/°C [25]. Figure 8 shows the shift value of the resonant wavelength as a function of temperature variation. Based on the figure, we can get the temperature variation should be in the range of ± 2 °C, such that the resonant wavelength shift induced by the temperature variation will be within ± 0.2 nm.
3.2 sensitivities and detect limits for different analytes
In this section, we will discuss how the sensitivity and detect limit change as different analytes are selected. Figure 9 shows the calculated effective fundamental indices of the two cores as functions of normalized frequency. It is evident that the index curves of the two cores will meet at different wavelengths for different analyte refractive indices. Figure 10 shows resonant wavelengths and coupling lengths as a function of analyte refractive index. As seen from Fig. 10, the change in coupling length can be approximated simulated by an exponential function. Although the high sensitivity and low detect limit detection of analyte is limited to a dynamic range of refractive index, the fiber with the same configuration can be used for the detection of analyte with a wide refractive index range by the appropriate selection of fiber length.
Fig. 9 Effective indexes of the fundamental modes of the two cores, as a function of the operating wavelength λr, at different analyte indices.
Fig. 10 Variation of resonant wavelength and coupling length in the proposed fiber as a function of analyte refractive index.
Table 1 depicts the corresponding resonant wavelength λr, sensitivity S, spectral width λFWHM, and detect limit DL of the proposed sensor for the detection of analyte with refractive index around 1.33, 1.35 and 1.42, respectively. As shown in Table 1, the sensors designed for analyte with high refractive index show better performance. This can be attributed to the fact that a high analyte refractive index (or low index difference between the analyte and the background material) leads to strong overlapping between the optical field of the fundamental mode of core B and the analyte channels. Furthermore, a narrower spectral feature width λFWHM leads to lower detection limit. It’s also expected that if the background material of the PCF has lower refractive index, better detection limit can be achieved.
Table 1. Numerical Results of the Proposed Fiber for the Detection of Different Analyte Refractive Indexes
3.3 Analysis of single channel fiber sensor
As we have stated in Sec. 2, it’s also possible to realize wavelength dependent coupling by introducing a large analyte-filled hole in a core. In this section, we will discuss and compare the transmission properties of these two types of fiber sensors. We define the microstructured core dual-core fiber as Fiber І. And the dual-core fiber composed of a small core and a large analyte-filled hole core is named as Fiber ІІ, the configuration of which is shown in Fig. 11 . Firstly, we will compare the sensitivity of the two fibers. The analyte index is assumed to be 1.40, using the same configuration as shown in Fig. 3, we can get the resonant wavelength λr to be 902.9 nm for Fiber I. By using the same configuration except that the microstructured core is replaced by a single large anaylte-hole, Fiber ІІ can be constructed. By requiring that index-matched coupling will also be meet at the wavelength of 902.9 nm for Fiber ІІ, we get the diameter of the large hole to be w = 3.622 μm. The numerical results are shown in Table 2 . We can see that although they have the same sensitivity, the spectral width of Fiber І is much narrower than that of Fiber ІІ. As a result, Fiber І has considerably better detect limit than Fiber ІІ. This can be explained based on the effective index difference between the fundamental modes of the two cores. As shown in Fig. 12 , both of the fibers have the same index curve for core A, whereas the different core B leads to different index curves. The index curves of the core B for the two fibers meet only at the resonant wavelength. There is always a small index difference between the effective fundamental index of core A and core B for Fiber ІІ. In contrast, as the wavelength is away from the resonant wavelength, the effective fundamental index of core B for Fiber I shows quite large index difference with that of core A, which leads to lower coupling efficiency and therefore, shorter spectral width.
Table 2. Comparison of Two Different Couplers
Besides the merits of low detection limit, Fiber І can be used for the detection of a wide rang of analyte refractive indices. Although Fiber ІІ can also detect analyte with refractive index lower than that of the fiber material, it would be difficult to detect analytes with much lower refractive indices. Firstly, the fundamental mode of core B will be extended to the silica background for a low index analyte, which will lead to a decreased overlap between the optical field and the analyte. As a result, the sensor will have low sensitivity. Secondly, the extension of the optical field to the background will lift the effective index of the fundamental mode. As a result, index-matched coupling with the solid core would be difficult. In contrast, the analyte-filled microstructure core in Fiber І leads to an effectively low index core, which ensures the wavelength-dependent coupling between the two cores and a uniform distribution of the modal field. As a result, low detection limit can be achieved.
4. Conclusion
In conclusion, we proposed in this article the design of an ultra-sensitive microstructured optical fiber refractive index sensor, which can be used for the detection of analyte with refractive index lower than that of the background index of the microstructured optical fiber. It’s also found that the detection limit reduces when the refractive index of the analyte is close to that of the background material of the PCF, which means that lower detection limits can be achieved for low analyte refractive index if the PCF is composed of lower index material.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (NNSFC) (Grant No. 10904051), National Basic Research Program of China (Grant No. 2010CB327801), and the China Postdoctoral Science Foundation (Grant No. 20080441070 and 200902505).
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