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Abstract
We propose and demonstrate a novel type of sampled Bragg gratings by combining a helically twisted fiber and a Bragg grating. A comb-like spectrum with a series of harmonic narrow resonances is observed, and the influence of geometrical parameters on the resonances is studied. As a special application, the intrinsic nature of the device that contains the Bragg grating and helical fiber spectral responses permits the temperature to be detected from the former, whereas the mechanical torsion is extracted from the latter, suggesting a potential for the simultaneous measurement of these two parameters. The proposed configuration features simplification, easy fabrication, high flexibility, stability, and low cost, and therefore has good prospects for sensor applications, as well as other applications, such as multi-channel filters, distributed Bragg reflectors, etc.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber Bragg gratings (FBGs) are important components for both the optical telecommunication and sensing systems, acting as wavelength selective filters with controllable wavelength operation, reflectivity, bandwidth, and low insertion loss [1]. A sampled fiber Bragg grating (SFBG) is a complex grating which is normally realized by superimposing a periodic amplitude or phase modulation to a Bragg grating structure [2–23], and the resultant spectrum exhibits a sampling function of the modulation. SFBGs have shown numerous potential applications, such as distributed Bragg reflectors [5], multi-wavelength fiber filters/lasers [6–9], dispersion compensators [10], and multiply sensors [11–17]. In the past many efforts have been made to develop various kinds of SFBGs. For example, they can be realized by shuttering an ultraviolet beam over a phase mask upon a fiber [2,3,9–13] or by introducing a specially designed amplitude mask in the inscription process [5,15–17]. However, these methods may be affected by the apodization arising from multiple laser exposures [3] or restricted by the fixed envelope of the amplitude mask. Fang et al. have obtained an SFBG by periodically heating a fiber Bragg grating through CO2 lasers [18]. This method has an optional modulation profile, but the thermal stability is constrained by the heating process. Recently, the point-by-point technique of a femtosecond laser has offered a flexible tool for implementing an SFBG or other types of gratings with customized periods, amplitudes, and phases. But the difficulty is the complicated and expensive fabrication system with an accurate control of the laser power, irradiation times, and positions of exposures [19,20]. In addition, phase-only SFBGs [21–23] have shown the advantage of a decreased index modulation compared to the amplitude ones and moreover, the phase sampling has no change in the amplitude so that the apodization profile for the multi-channel is the same as that for the seed grating, which could reduce the realization difficulty. Nowadays, however, almost all these previous studies are limited to purely changing the material refractive index along the fiber length [1–23], to the best of our knowledge.
On the other hand, one of the most advantageous applications of the SFBGs is sensing of a variety of parameters, such as axial strain, refractive index, curvature, temperature, or a combination of them [11–17], due to their compactness, high sensitivity, and high integration with a fiber system. However, the reported SFBG structures typically cannot be used for detection of mechanical torsion because of low sensitivity originated from the cylindrically symmetric fiber form. Recently, helically twisted optical fibers have been intensively studied in both conventional step-index fibers [24–34] and microstructure fibers [35–37], which show potential applications in polarization control, elimination of higher-order modes from fiber lasers, spectral filters, orbital angular momentum generation, and etc. The twisted fibers can in general show high sensitivity to the mechanical torsion different from conventional fiber gratings [31–33]. But the measurement could be influenced by the temperature variation with a cross effect [31–33]. Thereby it is essential to detect the temperature and the mechanical torsion simultaneously in a practical application.
In this paper, we report a new type of SFBGs by combining a helically twisted fiber and a Bragg grating. It shows a comb-like spectrum with a series of regularly spaced harmonic resonances, and the influence of structural parameters on the resonances is investigated. Moreover, the intrinsic characteristics of the hybrid structure can allow the temperature to be measured from the FBG response, whereas the mechanical torsion to be derived from the helical fiber response with the temperature having been compensated for, suggesting a potential of simultaneous sensing of these two parameters. Our structure is featured with compactness, simple configuration, easy fabrication, high flexibility, stability, and low cost, and thus has good prospects for practical applications.
2. Configuration and spectral characteristics
Figure 1 shows the schematic of the proposed SFBG, which contains a Bragg grating inscribed in a helically twisted fiber. The helical pitch is Λhelical (yielding a twist rate of α = 2π/Λhelical), the pitch of the FBG is ΛFBG, and the total length of the SFBG is L. A standard single-mode fiber (Corning SMF-28) is used for fabrication of the SFBG. First, the SMF-28 fiber is mounted onto two fiber holders of a secondarily developed splicer machine (Fujikura FSM-100P + ). One fiber holder is unrotated whereas the other one is rotatable driven by a built-in rotation motor. A slight tension is applied along the fiber length to keep the structure strictly straight. Both the fiber and the holders as a whole can move along the axis with a constant speed driven by a translation stage. A pair of electrodes is to produce arc discharge to heat the fiber material to the glass-softening temperature (~1700 °C), with the arc intensity modified by an electric current. When the arc is down, the fiber structure begins to soften and is slowly deformed under a twisting stress applied. Because of some core-cladding eccentricity of the fiber and the faultiness of its drawing process in a realistic condition, the fiber core follows a helicoidal path inside a cylinder cladding as the fiber is axially twisted [25, 30–34]. The fiber geometry is optimized by modifying the rotating speed of the fiber holder and the moving speed of the translation stage in combination of the arc intensity. Subsequently, a uniform FBG is inscribed into the helical-core fiber by use of a 193nm ArF excimer laser exposure and phase mask technique. The fiber is placed parallel to a phase mask with a distance of ~100μm and a cylindrical lens is used to focus the laser beam onto the fiber. The single-pulse energy of the laser pulses is ~2.5 mJ, which produces an energy density of ~100 mJ/cm2 on the surface of the fiber. The repetition rate, scanning speed, and scanning times of laser pulses are 200 Hz, 0.1mm/s, and ~3, respectively. By control of the inscription location of the grating with a translation stage, the proposed SFBG is finally formed, as shown in Fig. 1.
Fig. 1 Schematic of the proposed SFBG, combined by a helically twisted fiber and a Bragg grating. The helical pitch is Λhelical (yielding a twist rate of α = 2π/Λhelical), the pitch of the FBG is ΛFBG, and the total length of the SFBG is L.
Figure 2 records typical spectral characteristics of an SFBG with Λhelical = 504.0 μm (yielding α = 12.47 rad⋅mm−1), ΛFBG = 544.6 nm, and L = 5.0 mm, monitored by an unpolarized broadband light source (1250 ~1650 nm) and an optical spectrum analyzer with a resolution of 0.1 nm. There are a distinct broad dip observed around 1507.63nm and a comb-like spectrum corresponding to a series of harmonic reflection peaks around 1576.67nm, respectively. The former is induced by the twist of the fiber while the latter is by the FBG inscription. It has been observed that the inscription of the FBG has induced a redshift of the former dip with ~94.15 nm and an increment of the dip depth with ~3.53 dB, which can be attributed to the increasing of the average refractive index of the fiber core. It has been demonstrated that the Ge-doped core in the utilized fiber exhibits relatively higher photosensitivity compared to the silica fiber cladding [38]. The inset of Fig. 2 shows an enlarged view of the harmonic FBG resonances in the spectra. There are seven resonant channels observed at 1570.06nm, 1572.27nm, 1574.47nm, 1576.67nm, 1578.88nm, 1581.09nm, and 1583.30nm, respectively. The inter-channel wavelength spacing is almost uniform at ~2.21nm but the channel intensities are highly nonuniform. As shown in the inset of Fig. 2, the maximum dip depth of channels in the transmission spectrum is ~5.01dB @ 1578.88nm, corresponding to a reflectivity of not more than ~68.5%. The reflection of the SFBG is relatively low and can be enhanced by improving the refractive index modulation depth of the seed FBG (e.g., through decreasing the scanning speed or increasing the scanning times in the FBG writing process) or elongating the length of the SFBG. As shown in Fig. 2, the finalized device shows an off-resonance transmission loss of ~1.56 dB.
Fig. 2 Typical spectral characteristics of an SFBG, with Λhelical = 504.0μm (yielding α = 12.47 rad⋅mm−1), ΛFBG = 544.6 nm, and L = 5.0 mm. The inset shows an enlarged view of the harmonic FBG resonances in the spectra.
To understand the mode coupling effects, the twisted core in a step-index fiber can be regarded as a perturbation to the field distributions of guided modes. Such a phenomenon has recently been studied using various perturbative approaches [26–29] and the general selection rules for resonant coupling between the core and cladding modes have been established, with βco−βcl−lmα = 0 (phase-matching condition) and Mco− Mcl ± lm = 0 (angular momentum-matching condition), where βco,cl (here we assume βco > βcl especially for the step-index fiber) and Mco,cl are propagation constants and angular momenta for the core mode and the cladding mode, respectively, l is the rotational symmetry number of the structure of the utilized fiber, and m is a positive integer. In cases of strong perturbation, the higher-order couplings (m>1) and the couplings to the modes of opposite handedness can be achieved [26,27]. Presently, however, the core offset is extremely smaller compared to the core size in our utilized fiber with l = 1. For this case the lower-order coupling (m = 1) is dominant, as predicted in [28,29] and experimentally observed in [30,31]. Polarization insensitivity is obtained as a result of couplings to HE2,N+ (with a spin direction opposite to the helical core of the fiber) and TE0,N/TM0,N (N = 1,2,3…) cladding modes, which are degenerated in the weak guidance approximation [27,28]. This effect can demonstrate the presence of the resonant dip related to the helical-core fiber as described in Fig. 2. On the other hand, according to the theoretical model of a general SFBG, the effective index modulation profile of the seed FBG is modulated by a periodic sampling function s(x), with δn(x) = Δn(x) cos(2πx/Λ + ϕ(x)) s(x) [21,22], where δn(x) is the resultant index variation of the SFBG, x is the coordinate along the fiber length, and Δn(x) and ϕ(x) are the maximum index modulation and local phase of the seed FBG, respectively. Assuming that the seed FBG is uniform and there is no chirp, we can have Δn(x), ϕ(x) ≈constant. The sampling function s(x) can be further expanded by the Fourier series, with s(x) = , where Sk is the Fourier coefficient and P is the period of the sampling function. Then, based on the coupled-mode equations [21,22], the harmonic resonant wavelength for the SFBG can be obtained with
where Δβ = π(2nco/λ−1/Λ) is the detuning of the seed FBG. The central Bragg wavelength corresponding to k = 0 is expressed as λFBG = 2ncoΛ, and the wavelength separation between the resonances is Δλ≈λΛ /P. The number of the channels in the SFBG is determined by the number of the coefficient Sk as shown in Eq. (1). Currently, a clear formula about the sampling function for our SFBG is still unavailable, but it can be related to the presence of the helical core of the fiber with P = Λhelical. Since the core offset of the utilized fiber is very small, we approximately have Λ = ΛFBG. By substituting the parameters λ = 1576.67nm, ΛFBG = 544.6nm, and Λhelical = 504.0 μm in Fig. 2 to Eq. (1), we obtain Δλ≈1.70nm. The calculation can agree with the experiment result. The small discrepancy may be attributed to the fabrication error in pitches of the structures.To investigate the influence of structural parameters on the harmonic resonances, Fig. 3 gives reflection spectra for a number of SFBGs with (a) different helical pitches but the same FBG pitch and (b) different FBG pitches but the same helical pitch, respectively. As shown in Fig. 3(a), the wavelength separation between the resonances are measured to be Δλ = ~2.41 nm, ~2.13 nm, and ~1.94 nm, for Λhelical = 453.6 μm, 504.0 μm, and 554.4 μm, respectively, with ΛFBG = 535.2 nm. The value of Δλ is inversely proportional to Λhelical; but the central Bragg wavelength stays almost unchanged at ~1550.26 nm due to the fixed ΛFBG, consistent to the analysis of Eq. (1). As shown in Fig. 3(b), the measured central Bragg wavelengths are 1550.26 nm, 1566.11 nm, and 1576.67 nm, and the wavelength spacings between the resonances are Δλ = ~2.13 nm, ~2.17 nm, and ~2.21 nm, for ΛFBG = 535.2 nm, 540.8 nm, and 544.6 nm, respectively, with Λhelical = 504.0 μm. Both the central Bragg wavelength and the wavelength separation Δλ increases with an increase of ΛFBG, consistent to the analysis in Eq. (1). Figures 3(a) and (b) demonstrate a high flexibility for achieving the SFBGs with simplicity, easy fabrication, robustness, and low cost, showing great promises for applications of multi-channel fiber filtering, distributed Bragg reflecting, and etc.
Fig. 3 Reflection spectra for a number of SFBGs with (a) different helical pitches but the same FBG pitch and (b) different FBG pitches but the same helical pitch, respectively.
3. Potential for the simultaneous measurement of mechanical torsion and temperature
The hybrid structure that contains both the helical fiber and FBG resonances demonstrates different mode coupling effects as previously stipulated, which may exhibit different responsivities to the mechanical torsion and temperature variations. We characterize the thermal response of the SFBG by placing the device into a resistance furnace in air. The furnace temperature is modified by an electric circuit and recorded by a thermometer. Figure 4(a) gives the transmission spectra at 26 °C and 95 °C, respectively, and Fig. 4(b) details the wavelength shifts as a function of temperature, with Λhelical = 504.0 μm, ΛFBG = 544.6 nm, and L = 5.0 mm. Both the helical fiber and FBG resonant dips are found to redshift with an increase in the temperature, but show different sensitivities. Within the temperature range of 26 – 95 °C, the wavelength shifts are Δλhelical = ~4.37 nm and ΔλFBG = ~0.71 nm for the helical fiber and FBG resonances, respectively. By linearly fitting the experimental data, we obtain the temperature coefficients of SThelical = 60.51 pm/°C and STFBG = 10.12 pm/°C. It is clear that the temperature sensitivity of the helical fiber is much higher than that of the FBG. As shown in Fig. 4(b), the good linear characteristics can allow us to calibrate the correlation between the temperature and the wavelength shifts for the respective structures in applications.
Fig. 4 (a) Transmission spectra at 26 °C and 95 °C, respectively, for the SFBG with Λhelical = 504.0 μm, ΛFBG = 544.6 nm, and L = 5.0 mm. (b) Measured wavelength shifts as a function of temperature for the helical fiber and FBG responses, respectively, of the SFBG.
The spectral response of the SFBG to the mechanical torsion is characterized by fixing one end of the structure with a fiber holder while rotating the other end using a rotation stage. A slight tension is applied along the fiber axis to keep the structure strictly straight. The mechanical torsion rate αM can be worked out from the angle of rotation and the distance between two fixed fiber ends. Figure 5(a) shows the transmission spectra at different mechanical torsion rates of αM = −0.075 rad·mm −1, 0, and 0.075 rad·mm −1, respectively, and Fig. 5(b) details the resonant wavelength shifts as a function of αM for both the helical fiber and FBG resonances, respectively, for the SFBG with Λhelical = 504.0 μm, ΛFBG = 544.6 nm, and L = 5.0 mm. This experiment is performed at a constant room temperature (~26 °C). It is found that the helical fiber resonant dip blueshifts as αM is co-directional to the geometric twist α, i.e. αM > 0, while it redshifts as αM is contra-directional to α, i.e. αM < 0. Within a range of αM from + 0.075 to −0.075 rad·mm −1, the total wavelength shift is Δλhelical = 9.36 nm. A linear fit to the measurements produces mechanical torsion sensitivity of SMhelical = 64.64 nm·mm·rad−1. From Fig. 5(b), the helical fiber can have a good linear response and high sensitivity, as well as the ability to distinguish negative from positive mechanical torsion without the need for pre-twisting of the structure, which is important for the sensor to be used in the real-world applications [31–33]. In contrast, however, the FBG resonances are almost unvaried with the change of the mechanical torsion, demonstrating that the fundamental core mode of the fiber is almost unaffected by the twist of the structure. By combining Figs. 4 and 5, it is possible for us to derive the temperature information solely from the FBG spectral response and then use it to compensate the thermal contribution from the helical fiber response, leaving a net effect of the mechanical torsion, with
From Eq. (2), both the temperature variation ΔT and the mechanical torsion rate αM can be obtained given that the helical fiber and FBG resonant wavelength shifts, Δλhelical and ΔλFBG, are known, which suggests a potential for simultaneous measurement of the two parameters. Note that a vibration to the sensor device may introduce additional disturbance to the output spectrum. The structure should be kept stable to improve the measurement accuracy in the real situation.Fig. 5 (a) Transmission spectra at different mechanical torsion rates of αM = − 0.075 rad·mm −1, 0 rad·mm −1, and 0.075 rad·mm −1, respectively, for the device with Λhelical = 504.0 μm, ΛFBG = 544.6 nm, and L = 5.0 mm. (b) Measured wavelength shifts as a function of the mechanical torsion rate αM for the helical fiber and FBG responses, respectively, of the SFBG.
4. Conclusion
In conclusion, we have proposed and demonstrated a new type of SFBGs formed in helically twisted fibers. It exhibits a comb-like spectrum with a series of regularly spaced harmonic resonances. The influence of structural parameters on the resonances is investigated. Particularly, the hybrid structure that contains both the helical fiber and FBG spectral responses can show different sensitivities to the mechanical torsion and temperature, which suggests a possibility for us to realize simultaneous measurement of the parameters. The proposed device has advantages of simplicity, flexibility, stability, and low cost, and thereby has prospects in in-fiber sensors as well as other applications such as multi-wavelength filters, distributed Bragg reflectors, and etc.
Funding
National Science Fund for Distinguished Young Scholars of China (61225023); National Natural Science Foundation of China (NSFC) (61575083); Guangdong Natural Science Funds for Distinguished Young Scholars (2014A030306040); Guangdong Natural Science Foundation (2014A030313364).
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