1. Introduction

Thanks to the unique characteristic of helicity, the helical-type long-period fiber gratings (HLPG) have recently attracted a great research interest and have been found a lot of applications in the fields of optical communication and optical sensor [1–8]. On the other hand, recently the phase-shifted long-period fiber gratings (LPG) have attracted a lot of research interests [9–17], attributed to the their superior properties, such as the narrow bandwidth for the resulted loss peak, high sensitivity to the environmental parameters which makes them the ideal roles for being utilized as the all-fiber-type biochemical sensor, optical switching, and all-optical processing elements (such as the optical differentiator and sub-picosecond pulse shaper) etc. To date, various methods have been developed to fabricate the phase-shift LPGs. In general the phase shift can be permanently inserted into a fiber grating by using either the UV post-processing, or the post-etching technique, or by directly inserting a certain space at middle of the grating during its fabrication [9–17]. Most recently, we have developed an approach to fabricate HLPG by using CO₂ laser [18,19], where unlike most of the previous writing approaches, a sapphire tube is particularly designed and utilized instead of the conventionally-used focal lens, which allows us to repeatedly fabricate the HLPGs with both the high quality and high yielding-rate. Furthermore, a phase-shift produced in a LPG by using the CO₂ laser technique has been reported recently [20]. However, among all the above methods, the real magnitude of the phase-shift formed in a HLPG has rarely been measured in practice. Moreover, the in situ measurements for the resulted phase-shift in HLPG have never been accomplished to date, which is, however, very important and strongly desirable while the phase-shifted HLPG is fabricated and practically utilized as either the all-optical signal processing component or as the high-sensitive fiber devices.

In this study, based on the sapphire-tube writing technique (previously proposed by us in [18]), firstly, we demonstrate a simple and robust method to write a phase-shifted HLPG. Secondly, we propose and demonstrate a new method enabling to quantitatively characterize the phase-shift formed in HLPG, which is realized by directly observing and analyzing the imaging pattern of the fabricated grating with a stereo microscope but under a white light illumination. Unlike most of the previous methods [21–23], which are indirectly realized either by measuring the transmission spectrum of the fabricated HLPG or by analyzing the differential interference contrast (DIC) microscopy of the fabricated HLPG, the proposed method can be utilized to well estimate the local grating-period as well as the magnitude of the phase-shift inserted at any position of the HLPG in situ, which would considerably facilitate the fabrication of the HLPG by using CO₂ laser technique [24].

2. Fabrication and experimental results for the phase-shifted HLPGs

The setup for fabrication of the phase-shifted HLPGs is shown in Fig. 1, where there consists of a CO₂ laser, three translation stages, a fiber rotation motor, and a testing system for measuring the transmission spectrum of the fabricated HLPG. In our experiment, the sapphire tube is fixed at a spatial position while the fiber can continuously move through the tube by driving the motorized stage 3. Since the sapphire tube rather than the fiber is directly heated by the CO₂ laser, the passed fiber within the tube region can be homogeneously heated and twisted, and thus period of the HLPG can be precisely controlled just by changing the speeds of both the moving stage 3 and the rotator [18,19]. As matter of fact, the setup shown in Fig. 1 is the same as the one what we had utilized for fabrication of a HLPG in [18]. However, in order to simultaneously insert a phase-shift in a HLPG during its fabrication, we made some changes to the original principle scheme as shown in Fig. 2(a). For comparison, the principle scheme for a conventional HLPG is also given as shown in Fig. 2(b), where the HLPG has a constant period of Λ and no phase-shifts are inserted. To compare the one shown in Fig. 2(a) with that of Fig. 2(b) carefully, one can see that except for the parts of L₂ and L₁, the two schemes are totally identical. Without losing the generalities, here the grating period in part of L₂ is assumed to be Λ_1, which may be a little different from the period Λ in the part of L₁. If the condition that both the regions of L₁ and L₂ (as shown in Fig. 2) are much less than the total length of the grating L is satisfied, an equivalent phase-shift formed in HLPG can be expected to obtain, which is expressed by

 

Fig. 1 Experimental setup for fabrication of the phase-shifted HLPG based on CO₂ laser.

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Fig. 2 Principle scheme for the formation of a phase-shifted HLPG, where (a) an accumulated phase-shift is inserted at end of the local part L₂. (b) Index-change profile without a phase-shift inserted.

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Here it must be noted that the phase-shift $\theta$ obtained is an accumulated one and can be regarded as the one inserted right at end of the part L₂. Therefore, an arbitrary phase-shift inserted can be obtained just by changing the length of (L₂-L₁) accordingly. Moreover, unlike those post-processing methods in which the phase shift is formed after the fabrication of LPFG is completed, here both the grating and the inserted phase-shift are fabricated simultaneously.

To confirm the principle scheme (shown in Fig. 2(a)), three kinds of phase-shifted HLPGs with a phase shift of 0, π, and 1.5π, respectively were fabricated. Figure 3 shows the transmission spectra of three typical gratings, where the grating length and grating period were adopted as 2.6 cm and 648 μm, respectively. Two different phase-shifts were arranged to insert into the grating just by adjusting the length of L₂ and L₁, respectively, where the length of L₂ adopted was about 3 mm. Figures 3(a) and 3(b) show the results corresponding to the gratings with a phase-shift of π, and 1.5π, respectively. For comparison purpose, the transmission spectrum for the grating with 0 phase-shift is also shown in these two figures. From these two figures, one can easily find that attributed to the inserted phase-shift, the original loss band is split into two attenuation bands. When the phase shift inserted is equal to π as shown in Fig. 3(a), it can be seen that within the wavelength range of 1520-1620 nm, there exists two nearly identical attenuation-bands. While for the case of 1.5π as shown in Fig. 3(b), since the inserted phase-shift is larger than π, the new resulted band with a larger loss-dip appears on the left side (short-wavelength side). All the above results agree well with the previous ones shown in [17] and [20], respectively, which in return means that the proposed scheme shown in Fig. 2(a) works well and the phase-shift formed here is equivalent to a traditional one which is introduced within one period the grating.

 

Fig. 3 Transmission spectra of three phase-shifted HLPGs, where the phase shifts inserted at middle part of the HLPG are (a) 0 and π, and (b) 0 and 1.5π, respectively.

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3. Characterization of the phase-shift formed in a HLPG by using the microscopic imaging method

To verify the above results and make sure that the resulted phase-shifts in the gratings corresponding to the results of Figs. 3(a) and 3(b), are exactly the π and 1.5π, respectively, we further developed a simple imaging method which enables to well estimate the local period and the resulted phase-shift while the HLPG is fabricated. The measuring setup is shown in Fig. 4, where a stereo microscopy system (E-Zoom 6V, Edmund Optics), a white light sources (Olympus Epi-illuminator), and the tested HLPG are included. The first two devices can be arranged as auxiliary ones which are added to the fabrication setup of Fig. 1 for on-site measurement. By fine adjusting the working distance and zoom objective magnification of the stereo microscope, a clear top-view of the fabricated HLPG can be obtained like the one shown in Fig. 5(a). To exam this figure, it is very interesting to find that, besides the main body of the fiber (i.e., the central white-line part as shown in Fig. 5(a)), there exist two periodical structures (fringes) on the upper and lower edge of the HLPG, respectively, which have the same period but the one appeared on the upper edge has a π phase delay (advance) to the lower edge one. To exam and verify the periodical features of these two fringes, we also investigated the line scanning intensity distribution of the Fig. 5(a) at line XX’, which are shown in Fig. 5(b). Since periods of these fringes obtained in Fig. 5(b) have a fix ratio to the real magnitude of the HLPG, we make sure that this kind of fringes result from to the reflection light of the HLPG through the white-light illumination and are attributed to the periodically helical structures existed on the fiber surface.

 

Fig. 4 Experimental setup for microscopic image of the fabricated phase-shifted HLPG.

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Fig. 5 Imaging pattern of one typical HLPG obtained by using the setup shown in Fig. 4, where (a) Imaging pattern, (b) XX’ line scanning intensity distribution of the Fig. 5(a).

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Based on the above results, one certainly thinks that not only the local period of HLPG but also the phase-shift inserted can be visualized by checking the periodical features of the reflection fringes which are obtained with the setup as shown in Fig. 4. Noted that for fringe measurement, the phase accuracy is mainly depended on the spatial resolution of the stereo microscopy system utilized. In our case, the spatial resolution is about 2.2 μm. Three kinds of the HLPG with the inserted phase-shift of 0, π, and 1.5π, respectively have been considered, and here the last two gratings considered are the same as the ones whose spectra have already been shown in Fig. 2, respectively. Figure 6 shows the imaging patterns of these HLPGs but only within the central region of several millimeters, where Figs. 6(a), 6(b), and 6(c) represent the ones in which the phase-shift of 0, π, and 1.5π, are inserted, respectively. For further visualized, the line scanning intensity distributions for the upper fringes are also shown in Fig. 7. By counting the same numbers of the fringes and comparing them each other in Figs. 7(a) and 7(b), Figs. 7(a) and 7(c), respectively, it is easily to find that at end of the central part, the accumulated phase difference are exactly the π and 1.5π, respectively, which once again means that the proposed scheme shown in Fig. 2(a) really works and the proposed calibration approach shown in Fig. 4 is also available to the phase-shifted HLPG.

 

Fig. 6 Imaging patterns of the three kinds of HLPGs with (a) zero phase-shift, (b) π phase-shift, and (c) 1.5π phase-shift inserted at central part of the grating.

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Fig. 7 Line scanning intensity distributions of the three imaging patterns as shown in Fig. 6, where (a) 0 phase-shift, (b) π phase-shift, and (c) 1.5π phase-shift is inserted at central part of the grating.

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4. Conclusions

We have proposed and developed a stereo microscopy method to characterize a helical long-period fiber grating (HLPG), which is realized by directly measuring and analyzing near-field diffraction pattern of the fabricated HLPG under a white light illumination. Unlike most of the previous methods which are indirectly realized, the proposed method can be utilized to directly measure the local-period of the grating as well as the magnitude of the phase-shift while the HLPG is fabricated, which would considerably facilitate the fabrication technique of the HLPG by using CO₂ laser.