1. Introduction

Efficient light guidance can be achieved in optical fibers using photonic bandgaps created by a core and its surrounding periodic structure, as an alternative to the total internal reflection (TIR) that has been widely utilized in conventional single-mode fibers (SMFs) and index-guiding holey fibers [1]. Photonic bandgap fibers (PBGFs) have been classified into two types: hollow-core (HC) and solid-core (SC) types. The HC-PBGFs consist of a central hollow core surrounded by a periodic array of air holes in a silica background, which can provide low-scattering propagation along with unique optical properties [2]. Despite very successful experimental demonstrations, the HC-PBGFs still suffer from highly elaborated fabrication processes and a low tolerance against mechanical perturbations. To circumvent these shortcomings, the SC-PBGFs have replaced the air-hole structures in the HC-PBGFs with high-index materials embedded in the silica background. In early attempts, high-index fluids have been infiltrated into the air holes of the index-guiding holey fibers [3], and all-solid (AS) PBGFs have been subsequently developed to achieve long fiber length and high stability against temperature and other environmental effects [4,5].

Guidance in the AS-PBGFs has been described by the anti-resonant reflecting optical waveguide (ARROW) model [6–9], where incident light is reflected to the central core by the periodic high-index rods in the cladding. Thus far, most of the investigations into the AS-PBGFs have been confined to step-index rods [4–9], parabolic-index rods [10,11], and those surrounded by depressed-index trenches (DITs) [12,13]. Recently, a new type of an AS-PBGF with high-index rods surrounded by graded-index pedestals (GIPs) has been reported [14], which showed very contrasting transmission spectra depending on the fiber length: flat transmission without bandgaps for a long fiber and typical anti-resonant bandgap transmission for a short fiber. Despite these unusual transmission properties, detailed investigations of transmission changes under mechanical perturbations have not been further pursued, nor has the guiding mechanism been explained yet.

In this paper, the origin of the contrasting transmission spectra of the AS-PBGF with the GIPs is qualitatively explained, and we report spectral responses of the new AS-PBGF under both bending and twisting. The bending and twisting over a long fiber segment induced variable optical losses over flat transmission at specific spectral locations which coincided with the bandgap centers predicted by the plane-wave expansion method [15]. We investigated the potential of the unique responses of the proposed AS-PBGF under bending and twisting as a new type of a non-phase-matched band-rejection filter with variable rejection efficiency, for the first time.

2. Light guidance in the proposed AS-PBGF with the GIPs – a qualitative perspective

In recent years, various efforts in the AS-PBGF design have been reported to achieve a low transmission loss over a long distance. One of the successful methods is to introduce the DITs around the high-index rods as in Fig. 1(a) to strengthen the light confining capability in the ARROW structure [12,13]. The DIT structures are known to induce a higher loss at the resonance and a lower loss at the anti-resonance providing prominent photonic bandgaps in the transmission spectrum as schematically shown in the solid line in Fig. 1(b).

 

Fig. 1 (a) Refractive-index profile of the highly confining defects with the DITs and (b) its schematic transmission spectra. (c) Refractive-index profile of the weakly confining defects with the GIPs and (d) its schematic transmission spectra. In (b) and (d), the solid lines are for the straight fibers and the dotted lines are for the deformed fibers.

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The efficiency of the ARROW guidance can be tailored by the detailed refractive-index profiles at individual high-index rods. In this study, we proposed the unique GIPs around the high-index rods for the AS-PBGF [14] as in Fig. 1(c). When the DITs are replaced by the GIPs, the optical guidance is significantly altered to reduce the anti-resonance guidance, which subsequently results in a flat transmission spectrum with suppressed bandgaps as schematically shown in the solid line in Fig. 1(d).

When mechanical perturbations such as bending or twisting are applied to the AS-PBGF with the DITs, it has been reported that transmission decreases near the edges of photonic bandgaps to result in narrow bandwidths along with slightly attenuated peaks [12,13]. These effects are schematically shown in the dotted line of Fig. 1(b). In the case of AS-PBGF with the GIPs, there has been no report on the effects of mechanical deformations on their transmission spectra to the best knowledge of the authors, and we report detailed spectral changes in transmission for the first time. As the guiding mechanism in the AS-PBGF with the GIPs is opposite to that of the AS-PBGF with the DITs, schematically shown in Figs. 1(a) and 1(c), respectively, we found that the transmission changes near the bandgaps show opposite characteristics in the two AS-PBGFs under same mechanical deformations. The changes in transmission by mechanical deformations in the AS-PBGF with the GIPs are schematically shown in the dotted lines in Fig. 1(d), where the peaks in the bandgaps experience the most of the induced loss in contrast to Fig. 1(b) where the bandgap edges suffer the most of the induced loss.

The precise mechanism of the induced loss in the AS-PBGF with the GIPs is still not fully understood and is being investigated by the authors. In the following sections, we will describe the fabrication of the AS-PBGF with the GIPs and detailed experimental results for transmission measurements under bending and twisting.

3. Fiber fabrication and optical characteristics

The AS-PBGF with the GIPs was fabricated by the conventional stack-and-draw technique [1] with the silica background and hexagonal arrangements of the Ge-doped rods in five-ring layers. The high-index rods on the GIPs were fabricated using modified chemical vapor deposition (MCVD), whose preform profile is shown in Fig. 2(a) . Note that the index difference is about an order of higher than that of the conventional SMFs. The graded index was intentionally achieved by controlling the ratio of GeO₂ and SiO₂ in each glass layer during the MCVD process.

 

Fig. 2 (a) Profile of the 1-mm-diameter preform for the weakly confining high-index rods surrounded by the GIPs. (b) Cross-sectional micrograph of the fabricated AS-PBGF.

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The core of the AS-PBGF was formed by placing an undoped silica rod at the center. The final assembly of the stacked rods was enclosed in a silica jacketing tube, which was drawn into a fiber with a desirable outer diameter. The cross section of the fabricated AS-PBGF with the GIPs is shown in Fig. 2(b) with the core diameter of 15.4 μm, the high-index-rod diameter of 7.4 μm arranged in hexagonal symmetry with a pitch of 11.5 μm.

For the given geometrical parameters, the corresponding bandgap map of the fabricated fiber was obtained by using the plane-wave expansion method [15] and the results are summarized in Fig. 3(a) . The shaded regions represent the non-zero photonic density of states (DOS) in the high-index rods and high-loss guiding into the central core by the resonance. The white regions indicate the zero photonic DOS (i.e. bandgaps) in the high-index rods and low-loss guiding into the core by the anti-resonance. The horizontal solid blue line is the refractive index of SiO₂. Here the material dispersion of SiO₂ has no significant impact in the qualitative analysis as in [10] and is neglected. The bandgaps are denoted as integers and three bandgaps near 1700, 1200, and 900 nm are expected within the measurable wavelength range of a conventional optical spectrum analyzer (OSA), which are denoted as #3, #5, and #6, respectively.

 

Fig. 3 (a) Bandgap map calculated by the plane-wave expansion method. (b) Normalized transmission spectra of the AS-PBGF for 10 cm (solid black) and 120 cm (dotted red) in length.

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Transmission of the fabricated fiber was measured using a white light source (WLS, Yokogawa AQ4305) and an OSA (Agilent 86142A). An SMF with the core diameter of 4.5 μm was precisely aligned to the center of the AS-PBGF to avoid direct coupling of light into the high-index rods in the cladding. The AS-PBGF was kept straight with a very small tension to remove any kind of mechanical deformation such as bending and twisting. Transmission spectra of the AS-PBGF with the GIPs were normalized in reference to the output of the SMF and the results are shown in the solid and dotted lines in Fig. 3(b) for two different lengths of 10 and 120 cm, respectively. For the 10-cm fiber segment, the transmission spectrum (solid black) shows a typical photonic bandgap spectrum whose band center locations were in a good agreement with the predicted bandgaps of #3, #5, and #6 in Fig. 3(a).

The transmission spectrum of the 120-cm fiber segment is shown in the dotted red line of Fig. 3(b). It is noted that the bandgap structure is no longer prominent to result in almost flat transmission. This result is consistent with the qualitative explanation shown in Figs. 1(c) and 1(d): degradation of ARROW guidance due to the GIPs along the long propagation distance. Therefore, we experimentally confirmed that the proposed AS-PBGF with the GIPs could provide highly fiber-length dependent transmission characteristics in contrast to the prior AS-PBGFs.

4. Spectral responses to bending and twisting

To further investigate the guiding properties of the AS-PBGF with the GIPs, we measured the transmission spectra of the 120-cm-long fiber by applying bends and twists over the fiber in a systematic manner. For the bending experiments, we made one loop at the middle of the AS-PBGF with the GIPs around cylindrical mandrels with various radii R suppressing any torsional stress as shown in Fig. 4(a) . For the twisting experiments, both ends of the straight AS-PBGF were mounted on rotational stages, which is about 45 cm from the center as shown in Fig. 4(b). Transmission spectra for bending and twisting experiments are shown in Figs. 4(c) and 4(d), respectively, which were normalized in reference to the output of the straight AS-PBGF.

 

Fig. 4 Measurement setup for spectral responses by (a) bending and (b) twisting. Normalized transmission spectra of the 120-cm-long AS-PBGF with the GIPs under (c) bending and (d) twisting. The insets in (c) and (d) show spectral variations in the bandgap #3 along the bend radius and the number of turns, respectively.

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In contrast to bandwidth narrowing in the conventional AS-PBGFs with the DITs [12,13] as schematically shown in Fig. 1(b), the proposed AS-PBGF with the GIPs showed distinctive loss peaks at the center of each bandgap region whose spectral locations were predicted in Fig. 3. The assigned numbers on the absorption bands in Figs. 4(c) and 4(d) correspond to those of bandgaps in Fig. 3. It is noticed that the transmission changes under mechanical deformations are most prominent at the bandgap #3 near the wavelength of 1.55 μm (the C-band in optical communications), whose spectral variations of the peak value and the full width at half maximum (FWHM) are shown in the insets in Figs. 4(c) and 4(d) under bending and twisting, respectively. It is observed that the smaller bend radius resulted in the larger amount of loss at the peak and the wider FWHM as in Fig. 4(c). In the case of twisting, the larger rotation angle resulted in linear increases in the loss at the peak yet the FWHM did not change much in comparison to the case of bending. The range of tunable band rejection at the bandgap #3 was over 2.5 and 1.5 dB for bending and twisting, respectively. The FWHM tuning ranges at the bandgap #3 were 90~200 nm and 45~75 nm for bending and twisting, respectively. The band rejection peaks showed a blue shift of ~50 nm under the bending, but only a negligible shift in the case of twisting.

These distinctive responses in the bandgap #3 can be attributed to the smaller index mismatch between the guided core mode and the photonic band than others [11]. The slope of the blue edge of the bandgap #3 is shallower than other cutoff lines as shown in Fig. 3(a), which makes the guided mode more sensitive to external perturbations. Ripples near the band gaps in Fig. 4(c) are due to the partial resonance among high-index rods by bending [11].

The spectra in Fig. 4 are very similar to those of long-period fiber gratings (LPFGs) [16–18], yet the physical origins are entirely different. In the conventional LPFGs, rejection bands occur at spectral locations to satisfy the phase-matching conditions; λ_m = (n_core–n_clad^m)Λ, where λ_m is the resonant wavelength, Λ is the grating pitch, and n_core and n_clad^m are the effective indices of the fundamental core mode and the mth-order cladding mode, respectively. However, band rejection peaks in Fig. 4 are evidently caused by a non-phase-matched condition. Note that the bent AS-PBGF does not have any periodic index change. Twisting LPFGs usually shifts the peaks, but the twisted AS-PBGF did not show a significant shift as in Fig. 4(d). Furthermore, in comparison to the conventional LPFGs’ pitch of ~500 μm, the helical pitch by twisting is ~3 cm, an order of magnitude larger.

It is speculated that the band rejection might be attributed to the light coupling from the core to the high-index rods by the GIPs and further theoretical investigations are being pursued by the authors.

5. Conclusion

We successfully fabricated the AS-PBGF with the high-index rods surrounded by the GIPs to intentionally provide a weakly confining ARROW structure. The straight fiber showed two contrasting transmission spectra; typical bandgaps for 10-cm length and flat transmission for 120-cm length, which is attributed to the unique GIPs to reduce ARROW effects along the core. Non-phase-matched tunable band rejections were observed by applying bends and twists over the fiber. The spectral locations of the band rejection coincided with the bandgap centers. Tunable rejection efficiency over 2.5 and 1.5 dB were achieved for the bend radius of 0.6 cm and 15 turns of twists, respectively. The FWHM could be also controlled by bending in the range of 90~200 nm centered within the C-band near the wavelength of 1.55 μm.