1. Introduction

All-solid photonic bandgap fibers (ASPBGFs) have attracted great attention in the past ten years due to their special bandgap-guiding mechanism, modal property and compatibility with conventional fibers. Typically, ASPBGF consists of some triangular-lattice high-index glass rods embedded in a low-index background glass [1–3]. Thanks to this all-solid structure, ASPBGFs are usually easier to be fabricated and spliced with no regard for air-hole collapse, compared with holey microstructured optical fibers (MOFs) [4]. By optimizing the refractive index difference between the background glass and the high-index rods, ASPBGFs can be designed to support single-mode guidance with very large mode areas and have been applied in high-power fiber lasers [5–7].

Another active research area based on ASPBGFs is related to sensing application. By splicing a section of ASPBGF to standard single-mode fibers (SMFs) with a certain amount of core offset, a Mach-Zehnder interference (MZI) between two core modes or core-cladding modes has been demonstrated for high-temperature measurement [8, 9]. An ASPBGF-based Michel-son interferometer for distributed pressure sensing was reported as well [10]. Grating inscription is another post-processing technique to fabricate ASPBGF-based device. In 2007, L. Jin et al. inscribed a fiber Bragg grating (FBG) in an ASPBGF consisting of a pure silica core and germanium-doped high-index rods. This grating peak appeared a directional response to curvature [11]. Long-period gratings (LPGs) written by CO₂ laser or femtosecond laser in ASPBGFs were reported as well for temperature [12] and refractive index sensing [13].

Moreover, ASPBGF also can be employed for dual-parameter sensing application. In 2012, Z. Wu et al. reported on an MZI composed of a microtaper and an LPG in a same section of ASPBGF for the simultaneous measurement of curvature and temperature [14]. MOF-based dual-parameter sensors recently received increasing interest for achieving higher accuracy and eliminating the cross impact between different parameters. These MOF-based dual-parameter sensors can be composed with various schemes, for example, a holey MOF based MZI cascaded with an FBG [15] or LPG [16] in SMFs; fabricating LPGs in both an MOF and an SMF [17]; combining a Fabry-Pérot interference with photonic bandgap effect [18], and so on. They have been demonstrated for simultaneous measurements of curvature and temperature [15], Strain and temperature [19], refractive index and temperature [16], or humidity and temperature [20].

In this paper, we demonstrate a compact ASPBGF-based sensor by combining a cladding Bragg grating resonance with an MZI. Theoretical investigation verifies that the Bragg grating dip stems from a cladding LP₀₁-like supermode (LP: linear-polarized) and the MZI occurs between LP₀₁ core mode and a cladding LP₀₁-like supermode. The axial-strain sensitivities of the supermode grating dip and one MZI dip are measured to be 9.023 × 10⁻⁴ nm/με and −2.968 × 10−4 nm/με, respectively. While they response to temperature with the sensitivities of 12.56 pm/°C and 50.94 pm/°C, respectively. Thanks to these different responses, this sensor finds a useful application in the simultaneous measurement of temperature and axial strain.

2. Configuration & fabrication

The ASPBGF used in this work is fabricated by Yangtze Optical Fiber and Cable Co., Ltd., and its cross section is shown as the scanning electron microscopy (SEM) image in Fig. 1(a). It consists of a pure silica background embedded with 5-layer triangular-lattice high-index rods. The core is formed by replacing the central high-index rod with a pure silica rod. These high-index rods are prepared from a same preform which is composed of a germanium-doped silica cylinder surrounded with an index-depressed layer (fluoride-doped silica), as illustrated as the inset in Fig. 1(b). The corresponding refractive index profile of this preform is shown in Fig. 1(b). The additional index-depressed layer has been proved to decrease effectively the transmission loss and bending loss of the ASPBGF by weakening the coupling between adjacent high-index rods [3]. The outer diameter is about 125 μm. The pitch Λ_r, the distance between the centers of adjacent rods, is about 9.26 μm. The normalized radii of the germanium-doped silica cylinder and index-depressed layer are 0.181 Λ_r and 0.3786 Λ_r, respectively.

 

Fig. 1 (a) SEM image of the ASPBGF cross section; (b) refractive index profile and structural diagram (inset) of the high-index-rod preform; (c) the proposed sensor configuration.

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The configuration of the proposed sensor is shown in Fig. 1(c). It was fabricated by two steps: grating inscription and then core-offset splicing. The grating in this ASPBGF was inscribed by using scanned phase-mask method [21]. Before the grating inscription, the ASPBGF was photosensitized via hydrogen loading at 12 Mpa for one week. The ultraviolet (UV) light was generated from a continuous wave 244 nm frequency-doubled Argon laser and its power was about 70 mW. The period of phase mask was 1070.2 nm, corresponding to the grating with a pitch of 535.1 nm. The inscription length of was 10 mm. In order to monitor the evolution of grating generation and compare the grating effects of the core mode and cladding mode, one end of the ASPBGF was spliced to a SMF without core offset while the other end was spliced to another SMF with a certain amount of core offset. Then, it was connected to a broadband light source and an optical spectrum analyzer through a circulator. The red curve in Fig. 2(a) was measured when the ASPBGF was spliced with SMF without core offset. It is corresponding to the reflection spectrum collected from the core region of the ASPBGF. An obvious peak located at 1543.95 nm was obtained. It should come from a Bragg reflection of the fundamental core mode. Two very weak resonant bands around 1550.0 and 1555.8 nm, respectively, were found as well. When we switched to the other end with the core-offset splicing, however, the peak located at 1543.95 nm disappeared and a much stronger reflection peak at 1555.81 nm was measured, shown as the black curve in Fig. 2(a). Due to the core offset, this strong reflection peak should come from a Bragg resonance of a cladding mode.

 

Fig. 2 (a) Reflective spectra of the ASPBGF with grating under different splicing conditions; (b) transmission spectrum of the proposed sensor.

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After the grating fabrication, the next step is the improvement of the Mach-Zehnder interference. The ASPBGF was cleaved from the connections to SMFs and then re-spliced to SMFs by optimizing the core offset [22]. Since the ASPBGF was relatively short, such cleaving and re-splicing processes of two ends were conducted one after the other. The improved transmission spectrum is shown in Fig. 2(b). The extinction ratio of the interference is lager than 3 dB and the average span of adjacent interference dips is about 5.29 nm. After re-splicing, the length of the ASPBGF was measured to be ∼15.3 mm under a microscopy.

3. Mechanism discussion

In order to further figure out the generation mechanism of the interference and the Bragg resonances, a simulation on the guided modes in the ASPBGF was conducted by using the full-vector finite-element method. The material refractive index of pure silica was set as 1.444. The indices of those high-index rods were described with the rods’ coordinates and a distribution function, which was fitted from the refractive index profile of the preform and then scaled down from the preform diameter to the ASPBGF pitch Λ_r. Figure 3 shows some representative guided modes around 1550 nm in this ASPBGF. These guided modes can be sorted into two categories: core modes and cladding supermodes. There are two core modes – LP₀₁ and LP₁₁ modes, shown as Figs. 3(a) and 3(b), respectively. Whereas, the photonic-crystal cladding supports many guided supermodes distinguished by their electric field distributions. Referring to the designation of LP modes in step-index fibers [23], some low-order guided supermodes can be denoted with LP_mn-like supermodes. For example, Figs. 3(c)–3(i) are corresponding to LP₀₁-, LP₁₁-, LP₂₁-, LP₀₂-, LP₃₁-, LP₁₂-, and LP₀₃-like supermodes, respectively. Besides, there are several tens of higher-order supermodes with more complicate electric field patterns. It is noteworthy that the effective refractive indices (n_eff) of these guided supermodes are very close. Even the n_eff difference between the first order (LP₀₁-like) and the highest order supermodes is less than 2×10⁻⁴. It indicates that the maximum difference on resonant wavelength is only around 0.2 nm if the grating pitch is 535.1 nm. Moreover, LP₀₁-like supermode is more easily excited under common launching condition, compared with higher-order supermodes. Therefore, only LP₀₁-like supermode will be considered in the following discussion.

 

Fig. 3 Electric field distributions of typical guided modes in the ASPBGF: (a)–(b) LP₀₁ and LP₁₁ core modes; (c)–(i) LP₀₁-, LP₁₁-, LP₂₁-, LP₀₂-, LP₃₁-, LP₁₂-, and LP₀₃-like cladding supermodes. (j) Grating pitches against wavelength for different mode couplings. (k) Group refractive index difference between LP₀₁ core mode and cladding LP₀₁-like supermode and the corresponding theoretical MZI fringe spacing against wavelength.

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Based on the calculated effective refractive indices and the phase-matching condition of fiber Bragg grating, ${\mathrm{\Lambda }}_{\text{FBG}}={\lambda }_{\text{res}}/(n_{\text{eff},1}^{+}+n_{\text{eff},2}^{-})$, the grating pitches of different mode couplings can be derived [21]. Here, Λ_FBG is the grating pitch, and λ_res is the Bragg resonance wavelength. n_eff,1 and n_eff,2 are the effective refractive indices of two modes involved in the resonance coupling. They can be two identical or non-identical modes. Superscripts “+”and “−” represent the forward-propagating and backward-propagating modes, respectively. Figure 3(j) illustrates the calculated grating pitches against wavelength in the range of 1530–1570 nm. For a given grating pitch of 535.1 nm, the resonant wavelengths of different modes were theoretically predicted and listed in the second column of Table 1. Compared with the experimental result shown in Fig. 2(a), they match well to each other.

Table 1. Resonant wavelengths of different mode couplings.

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Considering the impact of dispersion, the fringe spacing Δλ_c of MZI is related to the physical length L and the group refractive index difference Δn_g between two interfering modes, Δλ_c = λ²/(Δn_g · L). Δn_g depends on the dispersion of effective refractive index difference Δn_eff with the form Δn_g = Δn_eff −λ·(dΔn_eff/dλ). Assuming that the physical length L equals to 15.3 mm and the interference occurs between LP₀₁ core mode and LP₀₁-like supermode, Δn_g and Δλ_c can be derived on the basis of the calculated n_eff of these two modes and then plotted in Fig. 3(k). As shown, the calculated fringe spacing Δλ_c is around 5.5 nm for the wavelength range of 1530–1570 nm. It is very close to the experimental result measured from Fig. 2(b).

4. Application

After fabrication, the proposed sensor was clamped on two translation stages to characterize the response to axial strain. One stage was fixed, while the other one was moved to the opposite direction to stretch fiber. Since the ASPBGF’s cross-sectional area and Young’s modulus are almost same as those of the lead-in SMFs, the axial strain ε can be calculated by the equation ε = Δl/l. Here, Δl is the change in fiber length and l is the original length of the fiber between two stages. When the axial strain was increased from 0 to 1164.17 με, the supermode grating dip shifted to the longer wavelength. Whereas the MZI fringe moved wholly to shorter wavelengths as shown in Fig. 4(a). We denoted the strain response of the MZI by following the movement of Dip A, which was located around 1552 nm in Fig. 2(b). The corresponding sensitivities of Dip A and supermode FBG dip, as shown in Fig. 4(b), are measured to be about −2.968×10⁻⁴ nm/με and 9.023×10⁻⁴ nm/με, respectively.

 

Fig. 4 Spectral shifts of Dip A and supermode grating dip with varying axial strain (a) and temperature (c); responses of Dip A and supermode grating dip to axial strain (b) and temperature (d).

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Then, the thermal response of this sensor was calibrated by using a high-accuracy column oven. The fiber with the sensor head was put into the oven and stretched with a tiny tension to keep the fiber straight. As shown in Fig. 4(c), both Dip A and supermode grating dip shifted to longer wavelengths as the sensor was heated from room temperature to 90 °C step by step. Their sensitivities to temperature are about 50.94 pm/°C and 12.56 pm/°C, respectively, as shown in Fig. 4(d). Compared with the grating resonant dip, the MZI dip shows a much higher temperature sensitivity. It is caused by the difference on thermo-optical coefficient between the doped-silica cladding and pure silica core.

Since the MZI dip and the cladding supermode FBG dip response differently and linearly to axial strain and temperature, this sensor can be applied to measure strain and temperature simultaneously by using the following matrix [21,24]:

5. Conclusion

We have demonstrated the generation of a strong cladding Bragg resonance in an all-solid photonic bandgap fiber (ASPBGF) by inscribing a Bragg grating in the ASPBGF and then splicing it to SMFs with a certain amount of misalignment. Meanwhile, a Mach-Zehnder interference was formed as well due to the core-offset splicing. Theoretical and experimental results verified that the Bragg resonance originated from the coupling of counter-propagating cladding LP₀₁₋like supermodes and the interference worked between the LP₀₁-like supermode and LP₀₁ core mode. This supermode grating resonant dip showed quite different sensitivities to temperature and axial strain from the interference fringe. Thus, this device can be applied to discriminate temperature and axial strain.