1. Introduction

In the large family of Photonic Crystal Fibers (PCFs) [1-4], Photonic BandGap Fibers (PBGFs) are probably the most original ones as the light in these structures is confined in a low index core conversely to all the other fibers. Such confinement leads to very unusual and interesting dispersive and spectral properties [5-8]. Among these PBGFs, the totally solid ones [1,8,9], made of pure and doped silica, are particularly interesting as they present the great benefit to associate the original properties of PBGFs (in terms of chromatic dispersion and spectral filtering) with the advantages of all-solid fibers (relatively easy to fabricate, to splice, to actively dope and to insolate for Bragg gratings realization). Since the first realization of 2D all-solid PBGFs in 2004 [9], significant progress have been made, both in terms of attenuation [1] and comprehension of these fibers properties [10-12].

In this paper, we propose to further investigate experimentally the quantitative importance of bend loss in these fibers. We also propose and realize a new fiber design that allows a decrease of the bend sensitivity for these low index contrast PBGFs.

The outline of this paper is the following: after demonstrating that our previous loss record [1] was in fact limited by bend loss, we propose and realize a new design, based on the addition of a holey ring, to reduce both the confinement and bend losses of all-solid PBGFs. The benefit of this new design will be experimentally verified and discussed in the fifth section of this paper and some conclusions will be drawn in its last section.

2. Bend loss: a limiting factor?

In Ref. [1] we reported the lowest loss obtained in 2D all-solid PBGFs. However the measured total loss (around 18 dB/km) was about 20 times higher than the one predicted by numerical simulation using a commercial vectorial Finite Element Method (FEM) with Perfectly Matched Layers (PML) (COMSOL 3.2b software) [13]. The effect responsible for this discrepancy could be the appearance of important bend losses. In order to investigate the relative importance of such losses, we performed series of cut-back measurements for the fiber described in Ref. [1] wrapped on spools of different radii. The results are summarized on Fig. 1(a) (limited to the 3^rd PBG window of our fiber) and Fig. 1(b) (overview from the 3^rd to 6^th PBG). On both graphs, the green, red and blue curves were obtained for respectively 7.9, 10.5 and 15.8 cm spools radii.

 

Fig. 1. Loss spectra obtained by cut-back measurements of the all-solid PBGF [1] wrapped on spools of different radius R: R=7.9 cm (green), R=10.5 cm (red) and R=15.8 cm (blue). a) zoom on the 3^rd bandgap; b) overview from the 6^th to the 3^rd bandgap.

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Firstly, note that the fiber minimum loss of ∼ 18 dB/km obtained previously for R = 7.9 cm is reduced to only ∼ 6 dB/km for R = 15.8 cm (Fig. 1(a)). More importantly, this reduction by about a factor three of the minimum loss demonstrates that our previous record was indeed strongly limited by bend loss. Secondly, the transmission window associated to the 3^rd PBG increases significantly with R, reaching a bandwidth of 140 nm (1480-1620 nm) of less than 20 dB/km attenuation for R=15.8 cm, showing that bend loss is also a limiting factor for our fiber in term of bandwidth.

Finally, let’s mention that we also observed, as T.A. Birks et al. [12] did recently albeit on a different fiber with significantly larger bend loss, i) that bending our all-solid PBGF reduces more the transmission window on the shorter wavelength side of the PBG than on the longer wavelength side ii) that even PBGs are more sensitive to bend loss than odd ones. For example, the estimated extra losses due to a decrease of R from 15.8 to 7.9 cm are of 740 dB/km for the 4^th PBG whereas they are “only” of 12 dB/km and 170 dB/km for the 3^rd and 5^th PBGs (cf. Fig. 1(b)). An interpretation of these surprising results can be found in Ref. [12].

3. New design

As bend loss appears to have a major impact on the transmission properties of low index contrast PBGFs, we investigated a new design to reduce the fiber bend sensitivity.

3.1 Principle

A well-known solution to reduce bend loss for conventional fiber is to add a low index region in the fiber cladding [14]. This low index region acts as a barrier to avoid coupling of the light between the core region and the effective higher index cladding (due to the bend [14]) on the outside of the bend. We thus propose the new design shown in Fig. 2. It is based on both the reduction of the number of doped rings and the addition of an extra holey ring to help the confinement of the core mode both for the straight and bent fiber. The number of doped rings will come from a compromise between a large number that will reduce the confinement losses of the straight fiber but lead to a thicker fiber and a small number that is likely to present the disadvantage of diminishing the PBG effect in favor of the more conventional Total Internal Reflection (TIR) due to the proximity of the core and the holey region. In the case of a large number of doped rings, the bend sensitivity reduction is also anticipated to be less efficient as the low index region is further away from the core. More precisely, it is expected that a larger inner cladding will support cladding modes with effective indices more “affected” by the bend (for a fixed R) as the perturbation increases away from the core. This will lead to an increase of the coupling between the core mode and inner cladding modes and thus produces bend loss either on the outside or inside of the bend as explained in Ref. [12].

 

Fig. 2. Schematic representation of the proposed double-clad PBGF. (a) transversal cut (b) index profile along axis x with the definition of the pitch Λ, the doped region diameter d and the hole diameter d_H.

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Note that, for simplicity of fabrication, we kept the same pitch, Λ, for the doped and air hole rings but allowed the doped region diameter, d, and the holes diameter, dH, to be different.

This new design, called hereafter Double-Clad (DC) PBGF, appears as an alternative to the one proposed recently by J.M. Stone et al. consisting in using annular doped rods [15], but the two solutions are not incompatible and can indeed be implemented together.

3.2 Modeling

In order to facilitate the comparison between the two designs (with and without the air holes), we used the same parameters than in Ref. [1] for the doped regions i.e., a parabolic profile with a maximum refractive index difference, Δn, of 3.10^-2 and a ratio, d/Λ, of 0.683. According to the above discussion, the numbers of rings have been fixed to 3 and 1 for respectively the doped region and the holey ring. The last parameter d_H/Λ has been fixed to 0.63 since such a value is expected to lead to similar minimum confinement loss (∼ 1 dB/km around 1550 nm) than for our previous design (this theoretical value has been deduced from the FEM used to perform the simulations).

Our new design has the obvious advantage to reduce the number of doped rods from 168 (7 rings) to 36 (3 rings) whereas keeping the confinement loss to a low level. As a direct consequence, the fiber diameter (generally rather large to insure low loss transmission in these class of low index contrast PBGFs) is then also significantly reduced. The advantage of this new design against bend loss will be demonstrated experimentally in section 5.

 

Fig. 3. Theoretical plot of the bandgaps (white). For simplicity, the silica refractive index is kept constant and equal to 1.45 (upper blue curve). Also shown the fundamental space filling mode of the air clad (n_FSM, lower blue curve) and the effective index of the fundamental core mode in the 3^rd and 4^th bandgap (dark lines).

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To predict the optical properties of such fibers, the PBGs for a triangular lattice of parabolic high index rods embedded in a silica background have been calculated using a Plane Wave Expansion method developed at the MIT (MPB) [16] with the above opto-geometrical parameters (but without the holey ring). The PBGs are displayed in Fig. 3 assuming a constant refractive index for the background.

The second clad (i.e. the holey ring) will act as a lower index region compare to the inner cladding. The effective index of this region will be, for simplicity, approximated in the following by the effective index of the fundamental space filling mode (n_FSM) calculated using the analytical relationships given in Ref. [17]. Its evolution against wavelength has been plotted in blue on Fig. 3 (lower blue curve). Also shown are the fundamental modes for the band gaps # 3 and # 4 (dark curves). In the high effective index region (above n_silica), the mode of the whole ensemble of rods gather into a discrete ensemble of single rod modes. A label placed above Fig. 3, gives the nature of these LP_lm modes.

As can be seen, nFSM is smaller than the effective index of the core modes (modes of the PBG fiber), leading to a conventional TIR confinement of these modes by the holey ring (note however that these modes are still leaky as the light can escape from the inner cladding to the outside silica jacket through this holey region made of only one ring with rather large silica bridge compare to the wavelength). This explains that similar confinement losses can be obtained for these modes with fewer high index doped rings that for our previous all-solid PBGF embedded in silica outside jacket.

A possible drawback of this new fiber is that higher order core modes will also be better confined in the ‘defect’ core by the depressed cladding, as long as their effective indices are higher than n_FSM. However, we verified numerically that, for the design described above, the differential loss between the first higher order mode and the fundamental mode is still significantly large (> 2 orders of magnitude between 1400-1600 nm) to practically ensure singlemode operation. Note also that it is possible theoretically to modify n_FSM (by simply changing d_H) in order to adjust it between the fundamental and the first higher order core mode effective indices. Doing this, one can expect to increase the differential loss between these two modes as the depressed cladding will act as a conventional confinement layer only for the fundamental core mode. However this may work efficiently only for some specific wavelengths and will add strict requirements on the holes diameters. As we want to keep the fabrication as simple as possible we have discarded such possibility.

One should also note, that the holey ring will act as a low index layer compared to the high index doped microstructured region. Thus, any cladding modes with effective index higher than n_FSM will also benefit from the confinement offered by the depressed clad region. In particular, all the cladding modes with effective index lower than n_silica were leaky in our previous design, whereas some of these modes will be allowed to propagate along the fiber with relatively low losses. Because of the loss reduction of these unwanted modes, one has to avoid realizing a depressed clad with a too low refractive index and with a too large section. This is also why we limit ourselves to only one ring of hole with relatively low d_H/Λ (compared to conventional air-clad structure for which d_H/Λ is generally larger than 0.8-0.9).

4. Fabrication

DC PBGFs have been realized in a way similar to the one used for our previous all-solid PBGFs [1]. A graded-index doped preform provided by Draka-Comteq has been drawn into canes which have been used to realize a hexagonal stack with a pure silica rod in its center. We added an extra ring of capillaries of pure silica with an original d_H/Λ of 0.63. The stack was then inserted in a jacket tube and drawn directly into fiber.

 

Fig. 4. Scanning Electron Micrograph (SEM) of the DC PBGF. The fiber diameter is 187 μm for a core diameter of 20 μm, a pitch, Λ, of 15 μm and an average hole diameter d_H of 10.6 μm.

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Figure 4 shows a SEM picture of our DC PBGF. The outside fiber diameter is 187 μm i.e., 38 % less than our previous realization, whereas the doped microstructured region has very similar parameter Λ ≈ 15 μm, d/Λ ≈ 0.67. The final d_H/Λ ≈ 0.71 is slightly larger than the initial capillaries due to an overpressure in the holes during the fiber drawing.

Because the exact size of the holes is not as critical as for other PCFs the fabrication difficulty is not significantly increased compared to our previous all-solid PBGF. Similarly, the eventual air holes collapse during splicing is not as crucial as for others air-silica PCFs. In our case these holes are indeed not essential for the light confinement on such short propagation length. Thus the fabrication and use of this DC PBGF are indeed very similar to previous all-solid PBGFs.

5. Experimental characterization of DC PBGF.

In order to facilitate the study of the air-clad addition impact, we used the same set-up as in [1] to characterize our new fiber. In particular, all the spectra described below were obtained by butt-coupling a super continuum source to the input of the fiber under test whereas the fiber output was butt-coupled to a standard telecom single mode fiber (∼ 10 m of SMF28) connected to an Optical Spectrum Analyser (OSA) with a 1 nm resolution.

5.1 Preliminary results

Figure 5(a) shows the transmission spectra of 460 m (blue curve) and 10 m (red curve) of the DC PBGF wrapped on a 7.9 cm spool radius. Let’s first focus on the spectrum of the short fiber piece. We clearly observe the “conventional” bandgap structure [1]: roughly the 3^rd bandgap from 1400 to 1645 nm, the 4^th bandgap from 1108 to 1172 nm and the 5^th bandgap from 897 to 930 nm. In these wavelength ranges, we verified that the output mode profile (cf. for example Fig. 5(c)) was indeed very similar to the one observed in our previous all-solid PBGF. This confirms that, in these conditions, the PBG is still the dominating guiding mechanism.

 

Fig. 5. (a) Transmission spectrum of the DC PBGF through 460 m (blue) and 10 m (red) with the bandgap number. (c) and (d) are the mode profiles observed at 1150 nm for respectively L = 10 m and L = 460 m. e) and g) are the mode profiles observed for L = 460 m at respectively 1190 et 1500 nm. Note that if (d) and (e) show all the solid microstructured cladding, (c) and (g) are zoomed on the core mode, whereas (b) and (f) are zooms on few doped rods respectively at 950 and 1190 nm.

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The transmission spectrum obtained for the long fibre piece (blue curve) looks first also very similar to conventional bandgaps spectra, but a more careful study reveals quickly that it is in fact rather different. In order to develop this point let’s first discuss the case of the transmission band around the 4^th bandgap. This transmision band presents a clear dip at 1161 nm and has a surprisingly higher longer wavelength limit than the one for the shorter piece : ∼ 1220 nm against ∼ 1175 nm. Actually only the shorter side of this band (< 1161 nm) is related to the conventionnal core mode guided by PBG as shown in Fig. 5(d) whereas the longer wavelength band is due to cladding modes with most of the light guided in doped rods (cf. Fig. 5(e) and 5(f)). The observation of LP₁₂ modes like in that case is in agreement with the ARROW model predicting that the 4^th bandgap is limited in the upper wavelength regime by the coupling of the core mode to the LP₁₂ modes of the high index rods. Conversely to previous all-solid PBGFs, such modes can be guided in our structure with relatively low loss for wavelengths above the isolated rods cut-off thanks to the presence of the air-clad structure (as long as their effective index is higher than the depressed clad one). These modes, only poorly excited at the PBGF input, have for some wavelengths lower losses than the fundamental core mode and thus can be clearly isolated for fiber length long enough. However, as the light is not core-guided, these modes are a priori of poor interest for applications.

This phenomenom is even more dramatic in the vicinity of the 5^th bandgap where only the cladding modes can be observed through the 460 m piece with LP₀₃-like modes in the high index region (cf. Fig. 5(b)). In opposite, the fundamental core mode of the 3^rd bandgap is clearly observed (Fig. 5(g)) for L = 460 m and the cladding modes contribute significanlty to this transmission spectrum only for wavelength higher than 1615 nm (Fig. 5(a)).

Note that the bandgap-like transmission of these cladding modes (for example the transmission window from 922 to 952 nm for L= 460 m), poorly excited at the fiber input, can be understood as a consequence of i) an efficient power coupling from the core mode to these modes only for wavelengths around the cut-off of the isolated rods and ii) an increase of their losses with the wavelength as their effective index become closer to n_FSM (cf. Fig. 3).

5.2 Validation of bend losses reduction

We now focus on the 3^rd bandgap centered around 1550 nm. Figure 6 shows the total loss spectra obtained by cutting back the DC PBGF from around 500 m to 10 m for two bend radius, R = 7.9 cm (dark green curve) and R= 15.8 cm (dark blue curve). In order to facilitate the comparison between the two designs we also add to this graph, in bright colors, the corresponding loss spectra for the all-solid PBGF described in section 2.

 

Fig. 6. Loss spectra of the DC PBGF obtained by the cut back technique for bend radius of 15.8 cm (dark blue curve) and 7.9 cm (dark green curve). The red circle points out an artifact due to the existence of extra confined modes. The corresponding spectra for the all-solid PBGF are represented in bright colors.

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First of all, note that the original behavior on the long wavelength side (> 1615 nm) of the bandgap (marked by the red circle on Fig. 6) is not related to the loss of the fundamental mode of the fiber but is an artifact due to the existence of low loss cladding modes described in the previous section.

Except for this particularity, the loss spectra for the largest bend radius (R= 15.8 cm, blue curves) are very similar for both fibers, demonstrating experimentally the confinement properties of the extra air holes ring. Note that the experimental minimum losses of our new design are about 10 times higher than the one expected from confinement loss calculations done for the ideal structure described in section 3. The exact origin (OH contaminations, transverse and longitudinal defect of the structure…) of this discrepancy is under current investigations.

However, the advantage of the new design clearly appears for R = 7.5 cm. Thus, while the impact of bend loss is obvious for the all-solid PBGF (increase by a factor of 3 of the minimum loss, narrowing by roughly 50% of bandgap width), the transmission of the DC PBGF is not significantly affected by this reduction of R: no visible effect on the minimum loss and only a slight narrowing (< 10%) on the red side of the bandgap.

To demonstrate further the advantage of the new fiber design, we studied the sensitivity of the transmission spectra to sharper bends for shorter fiber length. The results are summarized on Fig. 7-a (all-solid PBGF) and 7-b (DC PBGF), both fibers lengths being around 4.5 m. The blue curves were obtained for the fibers bent on 3 loops of diameter larger than 35 cm and by taking care that the rest of the fiber was as straight as possible. These spectra will be referred in the following as the ‘straight’ fiber transmission spectra as this experimental condition should not lead to any significant bend loss, at least in the wavelength range of interest here. All the other transmission spectra were obtained for 10 loops of fiber wrapped on a mandrel of diameter R (6, 4.5, 3.75, 3 cm) whereas the rest of the fiber was maintained as straight as possible.

 

Fig. 7. Transmission spectra of the all-solid PBGF (a) and of the DC PBGF (b) for different bend radii: 6 cm (pink), 4.5 cm (yellow), 3.75 cm (cyan) and 3 cm (purple). For each of these spectra 10 turns of the fiber were wrapped on a mandrel of the corresponding radius. The dark blue curves, referred as ‘straight fiber’, were obtained for 3 very large loops of diameter higher than 35 cm.

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The decrease of sensitivity to bend loss of our new design is obvious when comparing Fig. 7(a) and 7(b). For the larger bend radius (R= 6 cm, pink curve), 10 loops are enough to significantly reduce the transmission of the all-solid PBGF (compared to the ‘straight’ case) whereas the output power of the DC PBGF is not modified on most (1450 to 1600 nm) of the bandgap transmission range. This improvement is even more visible in the case of 10 loops of 4.5 cm bend radius (yellow curve): the output transmission of the all-solid PBGF decreases by 12 dB for the less affected wavelength (∼ 1572 nm) while the DC PBGF transmission decreases at most of 1.5 dB on a large wavelength range (∼1460 to 1600 nm). For the smaller studied bend radii, R= 3.75 and 3 cm, only the DC PBGF has a significant transmission, represented on Fig. 7(b) respectively in cyan and purple.

Comparisons with the results obtained by other authors [15,18] with low index contrast PBGFs are not straight forward either because their designs do not lead to a bandgap at 1550 nm or by lack of information. However, we believe that our new design significantly improves the fiber properties against bend loss especially for relatively long wavelength (1.5μm) and for reasonable value of pitch and Λn.

6. Conclusion

We demonstrated that our previous loss record was in fact limited by bend loss. We then proposed and realized a new fiber design consisting in the addition of a ring of air holes around the all-solid photonic bandgap microstructure. We proved that this new fiber, called DC PBGF, has the important benefit to reduce significantly both the fiber diameter and its sensitivity to bend loss. We believe that this fiber improvement could lead to the use of low index contrast PBGF as large mode area fiber with relatively low bend loss.