Refractive index and strain sensitivities of a long period fiber grating

A long period fiber grating (LPFG) fabricated upon the all-solid photonic bandgap fiber by CO2 laser irradiation was investigated, and its resonance wavelength was at 1335.76 nm with a modulation depth of 15 dB and a 3-dB bandwidth of 2.6 nm. We studied its strain, temperature, and index sensor characteristics, the strain sensitivity of 0.992 pm/μɛ was obtained by using linear fit, and the relationship between the refractive index and wavelength obeyed the distribution of quadratic function. Also, we demonstrated its temperature response was relatively insensitive (21.51 pm/°).


Introduction
The optical fiber grating, such as fiber Bragg grating (FBG) [1,2] and long period fiber grating (LPFG) [3], has been in great use in the field of optical communication and sensors. And the LPFG, consisting of a periodic change in the refractive index or the fiber geometry along the fiber length, possesses so many advantages, which has been widely used in sensing applications. Light is coupled from the core mode to the resonant co-propagation cladding modes that are absorbed by the coating causing the characteristic attenuation bands in the transmission spectrum [8]. Lots of methods have been used for fabricating the LPFG such as ultraviolet (UV) laser exposure [3], CO 2 laser irradiation [4], and femtosecond laser exposure [5].
In this paper, we describe an LPFG all-solid photonic bandgap fiber (AS-PBF) fabricated by high-frequency CO 2 laser pulse irradiation. The LPFG with a resonance wavelength of 1335.76 nm with a modulation depth of 15 dB and a 3-dB bandwidth of 2.6 nm was obtained in experiments. Its stain, temperature, and refractive index sensitivities were studied.

Experimental setup
The cross section captured by the optical microscope (Olympus BX51) of the AS-PBF is shown in Fig. 1. The AS-PBF with the cladding diameter of about 123 μm and pitch (Λ) between adjacent air holes of 9.3 μm was used for fabricating the LPFG. Within the fiber, the diameters of the Ge-doped high-index rods surrounded by the F-doped low-index cladding were d 1 =4.06 μm and d 2 =6.9 μm, respectively. characteristic of about 330 μm, and its total length was 9.9 mm. We added a polarization controller (PC) to adjust the depth of the transmission dip, and the transmission spectrum was also recorded by an optical spectrum analyzer (OSA, Yokogawa AQ6370B) with a super luminescent light-emitting diode (SLED) light source, which is shown in Fig.  2(b). The LPFG with a resonance wavelength of 1335.76 nm, a modulation depth of 15 dB, and a 3-dB bandwidth of 2.6 nm was obtained in our experiments.

Strain measurement
The strain sensitivity of the LPFG was studied. The experimental setup for strain investigating is shown in Fig. 3. Two stages were used to hold and keep the LPFG straight: one stage was fixed, and the other was movable to provide the strain. The distance L between two stages was set to 4 cm.  The resonant matching condition of an LPFG can be described in (1), here λ represents the resonant wavelength, Λ represents the period of an LPFG, and core eff n cladding eff n are the effective mode indices of the core and cladding, respectively.
The relationship between the wavelength shift and stain [10] was demonstrated in (2) by a derivative with respect to axial strain (ε): In Fig. 4, the sensitivity of strain was achieved to be 0.992 pm/με, which was about 1.223 times larger than that of the hollow-core photonic crystal fiber [11] and about 1.03 times larger than that of the modal interferometer [12], but about 0.354 times less sensitive than that in [10], negative correlation shows the interference dip moves toward the shorter wavelength (blue shift).

Temperature measurement
The response of the LPFG to temperature was also studied by monitoring the shifts of the dip wavelength in a V-groove of a cylindrical temperature heater with a temperature range from 30 to 100 ℃ , at 10 ℃ intervals. The previous ℃ research results in [13] demonstrated that the temperature response of the LPFG was weakly dependent on the polarization states of input light. Hence in our experiments, we adjusted the polarization controller in front of the LPFG to get the maximum modulation depth of 15 dB, as shown in Fig. 2(a). Figure 5 shows the linear fit of the relationship between the dip wavelength and temperature (Δλ/ΔT), we got the relatively insensitive result of -21.51 pm/℃, but it is about 1.434 times larger than that in [11] and about 1.625 times larger than that of the photonic crystal fiber in the line Mach-Zehnder interferometer [12], because hollow-core photonic crystal fibers (HC-PCFs) used for the temperature sensor have a lower temperature sensitivity [16][17][18].

Refractive index measurement
We know from (3) that the refractive index difference between the core and cladding can be changed gradually when different surrounding refractive indices are added to the cladding of the LPFG, and L in (3) represents the length of the LPFG. The effects of its sensitive characteristic can be investigated for sensing the surrounding medium's refractive index using the equation The experimental setup for the surrounding refractive index investigation is shown in Fig. 6. At last, we used the polynomial fit to the experimental data by just three orders, as shown in Fig. 8, and   In one of these regions, the surrounding refractive index (SRI) lies between 1.33 and 1.36, and the corresponding dip wavelength change is plotted in Fig. 9

Conclusions
In conclusion, we fabricated an LPFG upon the all-solid photonic bandgap fiber by CO 2 laser irradiation and obtained the strain sensitivity of 0.992 pm/με. The relationship between the refractive index and wavelength obeyed the distribution of the quadratic function. Also, we demonstrated its temperature response was relatively insensitive (21.51 pm/℃). Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.