1. Introduction

Hollow Core Photonic BandGap fibers (HC-PBG fibers) present numerous advantages as the possibility to combine a photonic bandgap effect with a high non linearity and damage threshold [1–3], low bending loss [3], and high birefringence [4]. These fibers have also a huge potential for all applications requiring a high overlap between light and gas as for example in sensors and lasers [5,6]. However, HC-PBG fibers suffer from some important drawbacks among which a tricky fabrication and splicing to other fibers. Furthermore, surface modes appear in these structures, limiting significantly the fiber properties [7,8]. Moreover, it would be very challenging to realize rare-earth doped amplifier or laser based on these fibers or to write Bragg gratings which are widely used in photonics.

Consequently, Solid-Core Photonic BandGap fibers (SC-PBG fibers) [9–14] appear to be very attractive because they associate the specific bandgaps properties (unique spectral and dispersion characteristics) with the possibility to dope the fiber core either for Bragg grating inscription or for lasing/amplifying system. Furthermore all-solid versions of PBG fibers should be easier to fabricate and splice as no collapse can occur in these hole-free structures.

So far, several techniques have been used to produce SC-PBG fibers but they all led to short fiber lengths or and to relatively high losses (~dB/m). For example, J. Jasapara et al. [11] made a SC-PBG fiber from a conventional Photonic Crystal Fiber (PCF) by filling the air holes with a high-index liquid. Such approach has been used to make tunable PBG fibers [12]. A. Argyros et al [13] also used a conventional PCF approach but with filling the air hole of a small PCF preform with conventional multimode fibers. A modified stack and draw techniques, starting from homogenous rods of two different glasses, have also been reported [14]. Finally, Bragg fibers [15], which are 1D structure, are also a kind of SC-PBG fiber. They can be made by MCVD techniques [16] but the fiber lengths used are short and losses still high whereas the fabrication technique is not as versatile as the stack and draw techniques [17] used to build a 2D structure.

In this paper, we report on the fabrication and characterization of a 2D SC-PBG fiber with a low-loss region around 1550 nm and we discuss on potential new designs and applications of such fibers.

2. Fabrication

Our fibers (Fig. 1) have been made by the conventional stack and draw technique [17] but we used a graded-index doped preform provided by Draka-Comteq to build the periodic structure of the cladding.

 

Fig. 1. Scanning electron micrograph of the SC-PBG fiber. The bright cylinders correspond to germanium-doped regions. The fiber diameter is 300 μm for a core diameter of 20 μm and a pitch, ʌ, of 15.2 μm.

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This preform has a central doped part with a quasi parabolic index profile embedded into a region of constant refractive index (equal to the pure silica one). The maximum refractive index difference, compared to pure silica, is close to 3.10^-2. The ratio between the doped region diameter and the entire perform diameter (similar to the d/ʌ of conventional PCF) is 0.683. We drew this perform into hundreds of rods in order to stack them in the desired hexagonal structure. A pure silica rod has been placed in the structure’s centre to form the core of the final fiber. We finally drew directly this stack into fiber, allowing the production of long fiber length with minimum deformation (as the stacking was tightly packed).

The fiber diameter (d) and pitch (ʌ) are respectively 300 μm and 15.2 μm. The periodic structure contains 7 periods around the central core. If we can see clearly the existence of the doped regions on the fiber SEM picture (the bright cylinders on Fig. 1), the size of these regions can not be determined accurately from this picture. We assumed that the refractive index profile has not been significantly modified during the drawing process and then that the doped region diameter (similar to the so-called d parameter in conventional PCF) is 10.4±0.2 μm leading to a core diameter of 20 μm.

3. Losses and mode profile

3.1 Bandgap orders and losses

Figure 2(a) represents the transmission spectrum for a fiber length of 4 m. This spectrum has been obtained (Fig. 2(b)) by butt-coupling the light of a supercontiuum source [18] into the PBG fiber core and by collecting the output signal with a fiber (multimode or singlemode) connected to a conventional Optical Spectrum Analyzer (OSA - ANDO AQ 6135A). A camera allowed us to control that only the light coming from the PBG fiber core was coupled into the collecting fiber (a diaphragm aperture was used to block any light coming from the cladding).

The experimental transmission curve (Fig. 2(a)) shows the existence of 5 well defined bandgaps in the range 630 to 1715 nm. In particular, we can see the bandgap of interest here, spreading from about 1410 nm to 1650 nm.

First of all, unlike A. Fuerbach et al. [19] a high resolution transmission spectrum (0.05 nm) did not show any fine structures that could limit the bandgap properties (the very fine structures on the bandgap left is coming from our source and not from the fiber under test).

 

Fig. 2. (a) Transmission spectrum of the PBG fiber shown on Fig. 1 (L= 4 m). Full curves: experimental data with 2 nm (black) and 0.05 nm (dark blue) resolution. The hatched regions represent the range of wavelength for which new modes appear in the high index inclusions (cf. Table 1). (b) Schematic representation of the set-up used for transmission measurements

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Secondly, we want to point out that this bandgap is not the fundamental one but the third one. This can be demonstrated using the ARROW model [20]. This model predicts that bandgaps lie between high loss transmission regions which appear each time the high-index inclusions of the cladding support new modes. The mode cut-offs of these high-index regions are determined using the results given by T.L. Lukowski et al. [21] assuming a perfect parabolic profile, a doped diameter of 10.6 μm and a maximum refractive index difference of 3.10^-2. The results are summarized in table 1 where only the extreme values of cut-off for each modes family are shown. The ranges of wavelength corresponding to the appearance of these groups of modes correspond to the hatched areas on Fig. 2(a). As one can see, there is a good agreement between these domains and the high loss regions showing once again that the simple ARROW method can predict correctly bandgap positions. It is clear from the table 1 that the bandgap of interest (centered on 1530 nm) is the 3^rd one (the 2^nd and 1^st bandgaps are respectively between λ= [1.95 μm; 2.81 μm] and λ = [2.8 μm; ∞]).

Table 1. Mode cutoffs of the high-index inclusions of our 300 μm fiber according to the results published in [21]. Each range of wavelength for which a group of modes appears in high index inclusions has been represented by hatched areas on Fig. 2.

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We also confirmed experimentally this result by drawing the preform to a smaller diameter in order to shift the two first bandgaps in our detection range. For example, with a fiber diameter of 110 μm, we observed the third bandgap around 570 nm (in agreement with the fiber scale reduction) as well as the second bandgap centered on 880 nm and the beginning of the first one above 1200 nm.

The reasons we chose to work in the third bandgap are due to the following compromise: working in higher bandgap should reduce confinement loss but the widths of higher bandgap are more sensitive to variations of size, shape and refractive index of the high index regions (these variations would lead to a spread out of the many cutoffs that limit the high loss regions and then shrink the associated bandgap width) [22]. Furthermore, if we keep the numbers of periods constant (same preform), working in higher bandgaps at a fixed wavelength (for example 1550 nm), would require larger ʌ and so thicker fibers. Alternatively, for a fixed wavelength (1550 nm) and confinement loss level (~1 dB/km), there is no advantage to work in a higher bandgap to reduce the fibre size as, for example, working in the 5^th bandgap will lead to an increase of the pitch of a factor ~1.7 whereas the number of rings decrease only from 7 to 5 (a factor ~1.4).

 

Fig. 3. Loss transmission spectrum of the 300 μm diameter fiber. The spectrum was obtained by cutting the fiber from 387 m to 10 m.

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The attenuation spectrum of the 300 μm fiber (Fig. 3) has been obtained by the standard cut-back technique (the fiber length was cut from 387 m to 10 m). Care has been taken that only the light coming from the fibre core is collected. The fiber presents a low-loss transmission window ranging from 1520 nm to 1600 nm with a minimum loss of 18.7 dB/km at 1576 nm. To the best of our knowledge, this is two orders of magnitude better than previously reported results in similar structures [11,13,14,22].

Confinement losses have been calculated numerically in the case of a perfect periodic structure and are on the order of 1 dB/km. We believe that our experimental level of loss is limited by contaminations during drawing and stacking process. This level can probably be reduced further by using adequate cleaning process as it has been done for conventional PCF. Better fiber design (optimizing the refractive index profile, the relative core size …) could also contribute to reduce the fiber losses. The impact of other loss mechanisms (diffusion, transversal and longitudinal structure variation…) in these fibers is under current investigations. Anyway, this level of loss is already low enough to realize a lot of practical experiments such as Bragg gratings inscription, active doped photonic bandgap fibers, and high threshold stimulated Raman propagation fibers…

Finally, we want to point out that even with a core diameter of 20 μm, the fiber does not suffer from significant bending losses as long as the bend radius is higher than 4.5 cm (corresponding to a loss of 1 dB/turn at 1550 nm), making this fiber very attractive to transport high power beam with a good spatial quality beam as presented below.

3.2Mode profiles

The modal properties of the fiber have been studied by injecting the light from a tunable laser into different fiber lengths and by imaging the fiber output end on an infrared camera. The Fig. 4(a) shows an example of the intensity profiles observed for a fiber length of 59.5 cm. The mode is mainly confined in the core region but with some intensity extended into the 6 high-index inclusions closer to the core. This “star” shape is similar to the one predicted by N.M. Litchinitser et al. [20]. Figure 4(b) represents the light intensity along the two red lines of Fig. 4(a). The experimental data (black curves) can be very well fitted by a Gaussian profile (red curve) in the X direction with a waist diameter (at exp(-2)) of 21.2±0.8 μm and relatively well in the Y direction (waist diameter of 25.3±1 μm).

 

Fig. 4. (a) Near field image of the guided mode observed at 1470 nm for a fiber length of 59.5 cm. (b) Experimental intensity profiles (black curves) along the two axes X and Y shown on Fig. 4 (a). The red curves represent a Gaussian fit of the experimental data.

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In order to determine if the fiber can support other modes, we tried different injection conditions (off-axis, small spot….) and mode coupling (by bending, twisting the fiber) for different fiber lengths and different wavelengths. We never observed any other mode than the one described before as long as the fiber length was higher than 60 cm. However, for very short fiber lengths (typically smaller than 30 cm), higher order modes can be observed but only if the fiber is kept straight between the fiber holders. As for many other fibers [3,23], this fiber is then not intrinsically single mode but the differential of loss between the fundamental mode and higher order modes is so important that the fiber can be considered in practice as single mode.

These results suggest that this all-solid PBG fibers can be used with confidence as a single-mode fiber with a large mode area and relatively low bending losses.

4. Guiding properties

4.1 Chromatic group velocity dispersion

The fiber chromatic Group Velocity Dispersion (GVD) plays an important role for short pulse propagation and/or non linear effect. We used two techniques to measure this dispersion: a phase shift method and a low coherence interference method.

For the phase shift technique, the signal of a tunable laser diode is modulated at a frequency F=2 GHz and amplified by an Erbium-Doped Fiber Amplifier (EDFA) before being injected into the SC-PBG fiber. The signal transmitted through 377 m of fiber is then converted electronically and analyzed using a phasemeter that deduces the phase delay between this signal and the reference. This phase delay is related to the group delay and then to the GVD. The results are plotted on Fig. 5 (red curve). Because of the limited bandwidth of the amplifier, the measurement could be done only on a short wavelength range, from 1525 nm to 1570 nm. In this domain, the dispersion increases almost linearly from 52 ps/(nm.km) to 83 ps/(nm.km).

In order to increase the accessible range of wavelength, we used a low coherence interference method [11]. A 65 cm-long fiber was inserted in the fixed arm of a Mach-Zehnder interferometer. A supercontinuum generated in a PCF fiber is used as broadband source. The frequency at which the dispersion is measured is selected thanks to a 7 nm bandwidth monochromator placed at the output of the interferometer. A lock-in amplifier associated to a computer allows us to record the interference pattern as a function of the position of the mobile mirror of the Mach-Zehnder. The inset of Fig. 5 shows an example of the interference pattern observed. The chromatic dispersion, D, was deduced from the mirror position corresponding to the maximum visibility of the fringes.

The results are plotted on the Fig. 5 (blue curve). First of all, there is a very good agreement between the values obtained by both methods even if the fiber lengths used are very different (from 65 cm to 377 m) showing that the GVD can be considered as constant along the entire fiber length. Secondly, we can see that the zero dispersion wavelength, λ₀, is on the short wavelength side of the bandgap, around 1450 nm. For shorter wavelength, the dispersion is normal (<0) whereas for longer wavelength the dispersion is anomalous (>0) and increases as we approaches the edge of the bandgap (around 200 ps/(nm.km) at 1650 nm). This result is typical of all PBG fibers as the GVD of such fibers is mainly governed by the bandgap effect. However, in contrary to HC-PBG fibers, the dispersion of our silica core is not completely negligible and is indeed positive at these wavelengths. This material dispersion is at the origin of the shift to shorter wavelength (compared to HC-PBG fiber) of λ₀. We verified this assumption by measuring the dispersion in the 5^th bandgap (ranging from 895 to 955 nm) where the material dispersion is normal. We did observe that the λ₀ appears near the long wavelength edge of this bandgap, confirming that the material dispersion plays a role on the relative position of λ₀ in the bandgap.

 

Fig. 5. GVD measured with the phase modulation method (red curve) and the low coherence interference method (blue curve) inside the fiber’s 3rd bandgap. Inset shows an example of an interference pattern observed in the case of the interference method.

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4.2 Polarisation mode dispersion

The ideal fiber has no birefringence because of its sixfold symmetry. However, defects appearing during the fabrication break this symmetry, leading to some level of birefringence in the real fiber. When these unintentional defects are constant on fiber length, it is possible to associate a well-defined value and axes to the birefringence [3]. However, in our case we didn’t observed such fixed birefringence axes: it was still possible to extinguish the light coming out of the fiber by the wavelength scanning method [4] but the polarizer’s orientations were wavelength-dependent even for fiber length as short as few meters. These phenomena are well known in low birefringence fibers and can be explained by a spatial distribution of the birefringence. In this case, the most relevant parameter is then the Polarization Mode Dispersion (PMD).

The PMD of our fiber has been determined by using the fixed analyzer method [4]. The light from a broadband source (1450–1650 nm) is injected into the fiber core after passing through a polarizer. The output light is then analyzed by another polarizer and an optical spectrum analyzer. The PMD is then determining by subtracting the transmission spectra (in dB) obtained for two orthogonal directions of the input polarizer and by counting the number of extrema, N_e, or zero crossing points, N_m, per unit of wavelength [24]. The Fig. 6(a) shows an example of such subtracting transmission spectra for a fiber length of 347 m. It is clear from this figure that the extrema (or zero crossing points) density increases with the wavelength showing an increase of the PMD inside the bandgap as has already been observed in HC-PBG [3]. The calculated group delay τ and its associated error (variance’s square root [24]) are plotted versus wavelength on Fig. 6(b). Note that we used the formula for the long length regime as our ratios N_e/N_m is closer to 1.54 than 1 [24]. The group delay increases from 1.6 ps at 1530 nm to 5.4 ps at 1600 nm leading to relatively low PMD coefficients, respectively 2.7 ps/km^1/2 and 9.2 ps/km^1/2.

 

Fig. 6. (a) Result of the substraction of two transmission spectra obtained for orthogonal directions of the input polarizer (L_fiber = 347 m) and (b) the corresponding calculated group delay τ.

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5. Conclusion

An all-solid PBG fiber has been made and characterized. This fiber presents a low-loss transmission region around 1550 nm corresponding to the 3^rd bandgap of the periodic structure. A minimum loss of 18.7 dB/km has been obtained, corresponding to an improvement of about two orders of magnitude compared to the previously published results. This level of loss is already acceptable for many applications and could be reduced further by fabrication process improvements. The measured fiber dispersion is typical of bandgap fibers but with a zero dispersion close to the shorter wavelength edge of the bandgap because of the positive dispersion of the core material at this wavelength. The fiber’s PMD, due to fabrication defects, remains at a satisfactory level (few ps/km^1/2) for most applications.

This fiber has a large core diameter of about 20 μm but remains single-mode with a mode profile close to a Gaussian profile. As the fiber bending losses are also relatively low, this fiber is a good candidate to transport high power beam. Furthermore it is possible to dope the core and write Bragg grating in this kind of SC-PBG fibers making these fibers very attractive for all-fiber high-power-amplifier/laser systems delivering a high quality beam.