1. Introduction

Long-period fiber gratings (LPFGs) have been significantly advanced in recent years because of their various advantages of wavelength-selective operation, small size, low backreflection, and low insertion loss, which are attributed to their versatile applications to dense wavelength division multiplexed systems and optical fiber sensors [1–4]. Y. J. Rao et al. discussed fiber optic sensors based on LPFGs with the asymmetrical index variation by exposing a conventional single mode fiber to high frequency CO₂ laser pulses [4]. Recently holey-fiber (HF)-based LPFGs have been intensively investigated for optical fiber sensors [5–10]. Since the HF has periodic structure of air holes in the cladding, they can offer distinct modal and dispersive properties. Furthermore, optical sensors based on HF-based LPFGs can provide the unique characteristic of temperature insensitivity because of a single material composition like silica [6]. The asymmetrically-induced refractive index change can provide high sensitivity of the LPFG to the external bending change [9].

In this paper, we propose and experimentally demonstrate transmission characteristics of a LPFG inscribed into a HF with the bending curvature change depending on an axial rotation angle. In previous reports, a CO₂ laser or an electric arc was exploited to fabricate LPFGs with HFs because of no photosensitivity within silica of HFs and the undesirable asymmetric resonant peaks are created, which result to the complicated transmission spectrum and the weak transmission peak depth of LPFGs [6–9]. Y. Zhu et al. proposed a strongly resonant LPFG with symmetrically deformed gratings by using the specially established setup with a CO₂ laser, which can induce mechanical strength degradation of the HF-based LPFG. In this work, however, we can fabricate the HF-LPFG with a UV laser and obtain the strong and fine resonant peak (~20dB) since the proposed HF has a germanium-doped core with photosensitivity. We investigate bending sensitivity of the HF-based LPFG depending on an axial rotation angle. Since the proposed HF has a low bending loss of less than ~0.04 dB [11], the HF-based LPFG has bending insensitivity under a certain range of the bending curvature (< 3.9 m^-1). When the bending curvature is higher than 4 m^-1, the center wavelength of the grating is shifted into the shorter wavelength. The peak depth of the grating is reduced by the applied bending because of the reduction of the coupling strength between the core and the cladding mode. The bending sensitivity of the HF-based LPFG strongly depends on rotational orientation, which can be changed as the axial rotation angle increases. We measure transmission characteristics of the HF-based LPFG with the ambient index change. The resonant wavelength shift and the peak dept variation are measured to be less ~0.1 nm than ~0.02 dB, respectively, as the external refractive index is changed from 1 to 1.64.

2. Transmission characteristics of the HF-based LPFG with the fiber bending curvature change depending on rotational orientation and with the ambient index change

The HF is composed of a germanium (Ge)-doped core, one-layered air holes, and silica cladding. The Ge-doped core and silica-cladding diameters of the HF were 8.7 μm and 125 μm, respectively. The relative index difference (Δ) was 0.3 %. The scanning electron microscopy (SEM) images of the cross-section of the HF for the fabrication of LPFGs are shown in the inset of Fig. 1. The air hole size and the pitch between the air holes were measured to be 24.4 μm and 27.5 μm, respectively. The splicing loss was 0.23 dB. The proposed HF has the low bending loss because the core mode can be effectively confined by the large air hole, which was measured to be less than ~ 0.04 dB under the bending radius of 2.5 mm [11]. The HF was exposed to a 244-nm Ar⁺ laser with the power of ~70 mW through an amplitude metal mask by using a beam scanning technique. The travel speed of the translation stage for the beam scanning of the Ar⁺ laser was 100 μm/sec. The length and the period of the LPFG were 4 cm and 350 μm, respectively. The hydrogen-loading process for 7 days at 100 bars should be run to further enhance photosensitivity of the Ge-doped core region. After fabricating several LPFGs, we annealed all LPFGs during 24 hours to remove unreacted hydrogen and to stabilize quality of the HF-based LPFGs.

 

Fig. 1. Experimental scheme for measurement of bending sensitivity of the HF-based LPFG.

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Figure 1 show the experimental setup for measurement of the bending characteristics of the HF-based LPFG. Both ends of the grating were fixed at the two rotational fiber holders. The HF-based LPFG was positioned at the middle of two rotational fiber holders as seen in Fig. 1. As the one of translation stages moves inward, the bending along the grating can be induced. The induced curvature (C) along the grating can be written as

where d is the bending displacement at the center of the grating and L (=12 cm) is the half of the distance between two rotational fiber holders. As the bending is applied to the grating, the cladding modes coupled from the core mode have the modified profile and their effective index can be changed [9]. Consequently the center wavelength and the peak depth of the LPFG can be changed by the fiber bending. The dependence of the center wavelength in the HF-based LPFG on the bending curvature can be written as [8]

where λp is the center wavelength of the grating, m is the cladding mode order, and Λ is the grating period. n_core and n_clad are the effective index of the core and cladding modes, respectively. In order to measure the rotational angle dependence of the transmission characteristics of the HF-based LPFG, we changed the axial rotation angle of the grating by using two rotational holders. The scotch tape flags attached to both ends of the fiber indicate the axial rotation of the grating.

Figure 2 shows the transmission characteristics of the HF-based LPFG as the bending curvature increases. When the bending curvature was changed in a range from 0 to 3.9 m^-1, the center wavelength shift of the grating was measured to be as small as -0.1 nm. Its peak depth could be increased to be -24.5 dB at C = 3.9 m^-1 because the coupling coefficient between the core and cladding mode could be maximized. We believe that the bending effect on the effective index change of both the core and the cladding mode is small because of bending insensitivity of the proposed HF with the strong field confinement. When the bending curvature was increased up to 4 m^-1, however, the center wavelength of the grating was shifted into the shorter wavelength and the peak depth was reduced. Since the variation of the cladding mode effective index is higher than that of the core mode effective index when the large bending curvature is applied to the grating, the center wavelength shifts into the shorter wavelength [9]. The transmission peak depth was reduced by the high bending curvature because the modification of the field confinement by the bending could reduce the coupling coefficient. Figure 3 shows the variation of the transmission and the center wavelength of the HF-based LPFG as a function of the bending curvature change at the axial rotation angle (θ= 0°). For the conventional LPFG fabricated with a single mode fiber, the center wavelength shifts into the longer wavelength or the peak splitting occurs as the bending curvature increases because the bending modifies the cladding mode effective index or the symmetric property of the cladding modes to be asymmetric [2]. For the asymmetric LPFG fabricated with a CO₂ laser, the mode splitting occurs as the bending is applied to the LPFG [9]. Since the asymmetric LPFG is sensitive to rotational orientation, the center wavelength of the grating is shifted into the longer or the shorter wavelength depending on their pristine axial orientation. In the proposed HF-based LPFG, no peak splitting induced by the fiber bending was created because the symmetric cladding mode was coupled by the UV-induced symmetric index modulation. However, the bending sensitivity of the center wavelength strongly depends on rotational orientation.

 

Fig. 2. Transmission spectra of the HF-based LPFG with the bending curvature change.

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Fig. 3. Variation of the transmission and the center wavelength of the HF-based LPFG as a function of the bending curvature (θ= 0°).

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Figure 4 shows the dependence of the center wavelength on the axial rotational angle (θ). The amount of the center wavelength shift was changed as the axial rotational angle increased. When the bending curvature was 6.3 m^-1, the center wavelength shifts for θ= 0° and 180° were measured to be -0.42 and -10.8 nm, respectively. The center wavelength and the peak depth of the HF-based LPFG were not changed when the HF-based LPFG was twisted in the twist ratio of 25 rad/m without fiber bending as seen in the inset of Fig. 4. We believe that those differences are attributed to the dependence of the cladding mode profile and its effective index on the slight deformation of the air holes as the large bending curvature is applied. In addition, since the fiber bending induces the asymmetric cladding mode coupling from the symmetric core mode, the bending sensitivity of the center wavelength in the HF-based LPFG can be changed by rotational orientation [5]. It means that the bending sensitivity of the HF-based LPFG can be controlled by the axial rotation angle. It can provide the great potential for the rotation or twist sensing application using the HF-based LPFG.

 

Fig. 4. Center wavelength shift as a function of the applied bending curvature depending on the axial rotational angle (θ). The variation of the center wavelength of the grating with the twist rate without fiber bending was shown in the inset.

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Fig. 5. Transmission spectra of the HF-based LPFG with the ambient index change.

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Figure 5 shows the transmission characteristics of the HF-based LPFG with the ambient index change. Since all cladding modes in the silica inner cladding are well confined by air holes, the HF-based LPFG has ambient index insensitivity as seen in Fig. 5. Figure 6 shows the variation of the transmission and the center wavelength of the HF-based LPFG as a function of the ambient index change. The resonant wavelength shift and the peak dept variation were measured to be less ~0.1 nm than ~0.02 dB, respectively. The experimental results can provide high quality of the LPFG after recoating of the LPFG.

 

Fig. 6. Variation of the transmission (a) and the center wavelength (b) of the HF-based LPFG as a function of the ambient index change (θ= 0°).

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3. Discussion and conclusion

In summary, we investigated bending characteristics of a LPFG inscribed into a HF depending on an axial rotation angle. Since the proposed HF has a low bending loss, the HF-based LPFG has bending insensitivity under a certain range of a bending curvature (< 3.9 m^-1) and the wavelength shift was as small as -0.1 nm. When the bending curvature was higher than 4 m^-1, the center wavelength of the HF-based LPFG was shifted into the shorter wavelength because of the modification of the effective cladding mode index. The peak depth was reduced by the applied bending because of the reduction of the coupling strength between the core and cladding mode. We also investigated the dependence of the bending sensitivity of the HF-based LPFG on an axial rotational angle. The bending sensitivity of the HF-based LPFG was changed by rotational orientation. The center wavelength shifts for θ= 0° and 180° were measured to be -0.42 and -10.8 nm, respectively, at the bending curvature of 6.3 m^-1. By adjusting rotation orientation, we could control bending sensitivity of the HF-based LPFG. The dependence of the HF-based LPFG on the ambient index change was measured. The air holes in the inner cladding of the HF could provide ambient index insensitivity to the HF-based LPFG. The resonant wavelength shift and the peak dept variation were measured to be less ~0.1 nm than ~0.02 dB, respectively. The experimental results are very useful for applications to structural bending sensors and rotation/twist sensors with ambient index intensively.