1. Introduction

Attributed to its helicity characteristics which are especially suitable for controlling the polarization and orbit-angular-momentum state of the light in optical fiber, helical long-period fiber grating (HLPG) has attracted a great research interest and has found versatile applications, such as the temperature and torque sensors, all-fiber band-rejection filter, mode-converter for micromanipulation, and conversion of orbital angular momentum beams, etc [1–10]. To date, various methods to fabricate the HLPG have been proposed and demonstrated, which includes the ones by homogeneously twisting a fiber with a noncircular core cross-section [1, 2] where the special fibers with a high birefringence in the core are generally demanded, and the others by creating a helical surface deformation along the fiber [3, 4] where the conventional single-mode fiber (SMF) and the point-to-point direct writing technique using on a focused CO₂ laser [11, 12] are generally used, however the fabricated HLPGs inevitably undergo the drawbacks of low yielding-rate and the weak resistance to stretching and bending, and therefore are not available to some practical applications especially for bending and strain sensors. Most recently, based on the utilization of CO₂ laser, we have proposed and developed another approach to fabricate HLPG [7, 8], where a sapphire tube is particularly utilized in place of the focal lens [13], which thus enables to robustly and repeatedly fabricate HLPGs with a high quality and moreover, even the conventional SMF fiber is available.

On the other hand, as is well known that long-period fiber grating (LPG) is one kind of fiber grating in which the strong couplings occurs only between the forward fundamental core-mode and the matched discrete cladding-modes. As a result, LPG can generally be used as an optical band-rejection filter with a bandwidth of several tens of nanometers, which is almost one to two order broader than that of fiber Bragg gratings [14, 15]. However, it is extremely difficult to precisely control the profile of the resulted notch during the LPG’s fabrication. Especially for a LPG with a broad flat-top rejection-band, although it is one of the key components and strongly desirable in fiber communication system as well as fiber sensing system, there has rarely been practically realized due to some unrealistic demands in the grating’s fabrication. To date, mainly three methods have been proposed and demonstrated to realize the LPG-based flat-top filter [4, 16–22]. The first is the one based on UV exposure technique [16] where the LPG is designed by using the inverse scattering method [17], as a result, the required grating’ length is generally longer than 0.5 meter, which is too long to be realized due to the packaging and fabrication limitations. Furthermore, in order to obtain a flat-top type filter, sinc-like apodization is generally demanded, which is extremely difficult or even impossible to be realized by using the CO₂ laser writing technique [16, 17]. The second method is the one based on the phase-shifted LPG, where several discrete phases are assumed to insert into the LPG, as results of the simulations, flat-top rejection-band can be obtained [18–22], however how to precisely control the phase magnitude at particularly position of LPG become a critical challenge, which make this kind of LPGs not be obtained in practice until now. The third is the one based on utilization of two cascaded HLPG proposed by Shin et al. [4], where a tunable band-rejection filter with bandwidth of several tens nanometer has been successfully obtained, however, a large separation (>10cm) between the two LPGs are adopted. As a result, the spectral interference are inevitable due to the polarization scrambling effect and fluctuation of the loss-depth is so large (>10 dB) that a flat-top band-rejection filter cannot be realized.

In this study, we propose and demonstrate a novel method for the fabrication of flat-top band-rejection, which is realized by fabricating two HLPGs but with opposite helicities with using CO₂ laser and the sapphire tube technique [7, 8] and successively cascading these two LPGs. The proposed HLPGs have a relative short length (less than 4.6 cm) and do not require a complex apodization in grating’s amplitude, which makes this kind of HLPGs particularly suitable to be fabricated by using the robust CO₂ laser writing technique.

2. Experimental results and principle analysis for the spectrum of the successively cascaded HLPGs

2.1 Experimental setup and measuring results for the spectrum of the cascaded HLPGs

The setup for fabrication of the HLPGs is shown in Fig. 1, in which there consists of a CO₂ laser, translation stages, a fiber rotation motor, and a testing system for measuring the transmission spectrum the fabricated HLPG. To fabricate HLPG, firstly the selected fiber (fixed at the clamp and the center of rotator) is homogenously heated to softly fused status through a sapphire tube, meanwhile the heated fiber is homogenously twisted through the rotation motor. In addition, a small weight (8g) is added on the left side of the fiber as shown in Fig. 1, which can provide a little longitudinal stress to the fiber and thus makes the fiber straight all the time during the fabrication process. Period of the HLPG is precisely controlled by the speeds of the fiber-moving stage and the rotator. Noted that in our experiment, the sapphire tube is fixed at a spatial site but the fiber is moveable, which can continuously move through the tube by driving the motored 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, which facilitates the fabrication of HLPG with almost 100% yielding-rate [8].

 

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

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In order to realize a flat-top band-rejection filter, two HLPGs which are successively cascaded but with opposite helicities were utilized here as shown in the inset of Fig. 1. The detailed procedures are described below. At beginning, the first section of the SMF was heated and continuously twisted to the clockwise direction (observe in the direction from right to the left side) until the cHLPG was completely fabricated, which has a grating period of 648 μm and a length of 22.68 mm (35 periods). Transmission spectrum of this grating is shown in Fig. 2(a) as labeled by black solid line. It is seen that like the general LPGs, there exists a deep notch (loss band) in the transmission spectrum, and the loss depth and its peak-wavelength are ~26 dB and 1574.50 nm, respectively, which may be attributed to the coupling between the core mode and the LP₁₂ cladding mode in our case [8]. Sooner after the cHLPG was produced, the neighboring part of the utilized SMF was then successively twisted to the counterclockwise direction until the fabrication of ccHLPG was completed, which has the same period and grating length as those of the first grating (i.e., cHLPG).

 

Fig. 2 (a) Transmission spectrum of the cascaded HLPGs, where the solid black line shows the spectrum of the first grating cHLPG, and (b) magnification part of the Fig. 2(a) near the center wavelength region.

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Then we measured the transmission spectrum of these two cascaded HLPGs, which was shown in Fig. 2(a) labeled by the red solid line. Frank speaking, the result obtained here is totally beyond our expectations: a fine flat-top filter with a rejection-band of ~15 nm@0.5dB and ~20 nm@1dB has been successfully obtained. The increase of the bandwidth is achieved by sacrificing the rejection ratio of the notch filter. If a larger rejection rate is furtherly demanded for the rejection band, each of the two HLPGs should be more strongly written, i.e., larger refractive index-change in the core is demanded, which would be a challenge for us while keeping such a short length of HLPGs. Fig. 2(b) shows a magnification part of the Fig. 2(a) at the central wavelength of 1574.50 nm region. It is obviously seen that there exists two small peaks (labeled with an arrow of LCP and RCP) in the flat-top band and central wavelength of the band almost lies in the same position as that of the cHLP (i. e, black line shown in Fig. 2(a)). To make further clear the mechanism of the resulted band-rejection filter, we also investigated the polarization dependence of the transmission spectrum by adding a fiber polarizer (Thorlabs: IPP1550SM-FC) and a fiber polarization controller (PC) right after the ASE source, the measuring results are shown in Fig. 3, where two particularly polarization status for the input light: a left circular polarization (LCP) and a right circular polarization (RCP) are particularly selected. However, due to the polarization scrambling effect most probably existed in the connecting fiber (SMF) between the PC and the two HLPGs, 100% of LCP and RCP light cannot be obtained in our case, where a small portions of the light with a random-polarization (RP) status are inevitable. To compare Fig. 2(b) with the Fig. 3, it can be seen that the two peaks existed in the flat-top band are strongly dependence on the polarization status of the incident light, which may be attributed to the two kinds of circular polarization light, respectively. Recently, it has been reported by Wong et al. that there exists newly-created circular-birefringence in a twisted photonic crystal fiber [23, 24]. In our case, due to the core-cladding eccentricity in the pristine fiber [5–8], it is believed that the newly circular birefringence may also be generated, which would split the degenerated HE₁₁ mode (with effective index of n_eff) into two de-degenerate modes: one is the right circular polarization (RCP) mode with effective index $n_{eff}^{RCP}$ and the other is the left circular polarization (LCP) mode with effective index$n_{eff}^{LCP}$. Although the cladding mode LP₁₂ may undoes the same de-degeneration procedure, the two cascaded HLPG will become the one with a phase-shift at middle of the grating, i.e., there will inevitably result in a phase shift of$\Phi$ between ccHLPG and cHLPG for LCP light; a phase shift of -$\Phi$ for RCP light; and a phase shift of zero for the random polarization light. Therefore it is believed that the transmission spectrum shown in Fig. 2(b) can be regarded as the superposition one resulted from three individual gratings but without any interference.

 

Fig. 3 Polarization properties for the transmission spectrum of the cascaded HLPGs.

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2.2 Numerical analysis for the flat-top band-rejection filter based on the successively cascaded HLPGs

To verify the above proposal for principle of the resulted band-rejection filter, we had done some numerical simulations for the phase-shift LPGs using the transfer matrix method [25–27] under the conditions of different polarizations of the incident light. For convenience, we limit our calculations to a HLPG where there only exists a coupling between the core mode (LP₀₁) and the hybrid cladding mode LP₁₂ within the wavelength region of 1500-1610 nm [7, 8]. More specifically, the parameters such as the radii of the core a₁ and cladding a₂, the refractive indexes of the core n₁ and cladding n₂, and the surrounding material n₃, are particularly chosen as: a₁ = 8.2, a₂ = 125 μm, n₁ = 1.4580, n₂ = 1.4536, and n₃ = 1.0. All the other parameters related to the HLPGs such as the grating period and grating length are the same as the ones used in our experiments. Following the assumptions proposed in above section, the successively-cascaded HLPG may be regarded as the superposition of the three kind of LPGs which are depicted as shown in Fig. 4, where the Fig. 4(a) represents a phase-shift HLPG with a phase shift ${\Phi }_1$expressed as

 

Fig. 4 Schematic diagram for the principle of the band-rejection filter based on two cascaded HLPGs.

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Fig. 5 Theoretical simulation for the transmission spectrum of the cascaded HLPGS, where the red line in Fig. 5(a) shows the superposition spectrum of the other three individual gratings, and Fig. 5(b) shows superposition spectra of the LCP and NP, RCP and NP, respectively.

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3. Conclusions

A simple and robust method enabling to fabricate Helical LPG with a flat-top rejection-band has been proposed and demonstrated. Unlike most of the previous approaches, the proposed LPGs have a relative short length (less than 4.6 cm) and do not require a complex apodization in grating’s amplitude, which makes this kind of HLPGs particularly suitable to be fabricated by using the robust CO₂ laser writing technique. As an example, a flat-top band-rejection filter with a bandwidth of ~13 nm@0.5dB and ~15 nm@1dB has been obtained, which is the broadest one reported to date, based on our knowledge, and may find further applications to the fields of fiber communication, fiber sensing, and all-optical information processing.