Abstract

We report the fabrication, characterization and modeling of an all-solid photonic bandgap fiber (PBGF) based on an array of oriented rectangular rods. Observed near-field patterns of cladding modes clearly identify the cut-off rod modes at the bandgap edges. The bend losses in this fiber depend on the bend direction, and can be understood by the directional coupling properties of the different rod modes and the modeled density of cladding states.

©2006 Optical Society of America

1. Introduction

All-solid photonic bandgap fibers (PBGF) are a relatively new [1, 2, 3, 4] member of the family of microstructured optical fibers. They are interesting both for their contribution to our understanding of the nature of photonic bandgaps in optical fibers [5] and for certain technological applications [6]. The cladding of a solid PBGF is formed by a regular arrangement of unconnected high-index rods embedded in a lower-index matrix, which can confine guided modes to a core formed from the lower-index material through the appearance of cladding band gaps. Spectrally, the locations of these bandgaps are determined by the resonance properties of the high index inclusions, and are readily calculated. Corresponding simple analysis is not possible for hollow-core PBGFs, in which the lower-index material – air or vacuum – would not support the structure if the high-index regions were not connected. Consequently, our understanding of hollow-core PBGFs is conceptually more complicated and we can gain new insights through studies of the simpler all-solid structures.

Previous research has concentrated on fibers in which the raised-index cladding elements are circular, either rods [1, 2, 3] or rings [4]. In this paper, we report the fabrication of an all-solid PBGF based on an array of oriented rectangular (line-like) rods. Near-field patterns of cladding modes at the band edge clearly identify the cut-off rod modes at their corresponding bandgaps, demonstrating the generality of ARROW (anti-resonant reflecting optical waveguide [7]) guidance in solid PBGF. We have studied the directional dependence of bend losses in this fiber, relative to the orientation of rectangular rods, and show that it can be explained by coupling to different rod modes when bent in different directions. Our modeling of the density of states in the cladding explains the experimental spectral properties of the bandgaps, and can be used to explain the direction-dependent bend losses in the fiber.

 figure: Fig. 1.

Fig. 1. (a) Optical micrograph of a cane with a rectangular inclusion made from an array of raised-index rods; b) scanning electron micrograph of the final fiber; c) close-up of the core region in b), rod pitch: 13.8μm, length (D)/width (W): 7/1, D/Λ=0.67.

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2. Fabrication

The cladding of our all-silica fiber comprises an arrangement of isolated high index rectangular rods in a lower-index background. The rectangular rods in the cladding are all aligned. Canes of 0.98mm outer diameter and containing one rectangular inclusion [illustrated in Fig. 1(a)] were obtained by drawing down a hexagonal stack composed of three layers of Ge-doped step-index silica rods (comprising a central doped region surrounded by an undoped cladding) located in the middle of a stack of undoped silica rods. The index step in the original step-index preform was 2.03% and the core-to-cladding diameter ratio was 0.88. The aspect ratio for the raised-index rectangle was designed to be 7:1.

In forming the stack for the final fiber from the canes we paid special attention to the orientation of each cladding rod, to ensure that they were all approximately parallel in the final fiber. We first stacked thin wall capillaries (inner-to-outer diameter ratio=0.85) with 1.02mm inner diameter (just slightly larger than the canes) in the desired array. We then inserted a cane into each capillary, rotating the cane to obtain the correct orientation. By drawing the stack down with an additional jacketing tube we obtained final fibers with several different diameters. The final ratio of the length of each rectangle to the pitch, D/Λ, was measured to be 0.67. Using the electron microscope image shown in Figs. 1(b) and 1(c), we measured the pitch of the fiber with 245μm outer diameter fiber to be 13.8 μm.

3. Numerical modeling of band structure

 figure: Fig. 2.

Fig. 2. Calculated DOS for a triangular lattice of step-index rectangular rods in a low-index background as described in Section 2. The geometry of the rectangular rods and lattices were chosen to be the same as the fiber displayed in Fig. 1.

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We used a fully-vectorial fixed-frequency plane-wave method [8] to calculate the photonic density of states (DOS) of a perfectly periodic triangular lattice of isolated parallel high-index rectangular inclusions (nH=1.47288) in a low-index pure silica background (nL=1.457). We have chosen the refractive index and dimensions of the structure to match the experimental fiber in Fig. 1 as closely as possible. The resulting photonic band structure was mapped as a function of frequency ω and propagation constant β, represented in Fig. 2 by normalized frequency kΛ = ωΛ/c and (β-nk)Λ. The bands with non-zero DOS are shown as a gray scale. In between are the photonic bandgaps with zero DOS, which are highlighted in red to contrast with regions of small but non-zero DOS. The first 6 bandgaps are displayed in Fig. 2. The bands arise from the waveguide modes of the high-index rods [7]. These are designated Emn, where m and n are the numbers of intensity peaks along and across the rods respectively [9, 10]. The rod modes E11,E21…E71 and E12 are labeled in Fig. 2. They define the edges of the first 6 bandgaps. We see that the E12 mode is shifted towards higher frequencies to be close to the E71 mode, due to the high ratio of the rod’s length to its width. Compared with the other rod modes, E12 has a flattened dispersion curve, and indeed passes through almost all the bandgaps defined by the modes from E11 to E71, affecting the vertical depth of each bandgap. Overall, the higher order bandgaps are affected more profoundly by the E12 mode and are shallower: the unconfined E12 mode has no overlap with E11 mode, while the depth of the 6th bandgap is completely determined by the E12 mode.

4. Transmission windows & near field patterns

We measured the spectral transmission of about 25cm of the fiber shown in Fig. 1 using a fiber-based supercontinuum source. The bandgap fiber was butted up against an endlessly single-mode photonic crystal fiber (PCF) at each end. We coupled the supercontinuum light into one of the PCFs, and measured the spectrum transmitted from the other using an optical spectrum analyzer (OSA). The alignment of these three fibers was adjusted to maximize the power in the core, as monitored by the OSA. The fiber was kept straight during the measurement. As shown in Fig. 3, we see that there are a series of low-loss transmission windows corresponding to light being guided in the core, which was confirmed by imaging the near field pattern at the bandgap fiber’s output end and using bandpass filters. By measuring otherwise-identical fibers with different pitches (from 5.6μm to 14μm), we were able to observe 6 low-loss transmission bands in visible and near infrared regions (350nm to 1750nm), which is in good agreement with the modeling results for cladding bandgaps shown in Fig. 2. The long wavelength bandgap centered at 1220nm is the second, followed by 3 to 6 at shorter wavelengths as marked in Fig. 3. The intrinsic transmission loss of this fibre was measured to be 0.2 dB/m at the wavelength of 1220nm by the cut-back method. The first bandgap (which is comparatively narrow) and sixth bandgap (which is shallow) are more lossy than the middle four. The first band could only be observed in the near-infrared region using a fiber with a smaller pitch, such as 7μm. This fiber is not expected to have large birefringence, because of its large core size and very small refractive index contrast.

 figure: Fig. 3.

Fig. 3. Transmission spectrum of the fiber shown in Fig.1 as a function of normalized frequency (kΛ) and wavelength in central diagram. The top 4 pictures A, B, C and D show the near field patterns in the middle of bandgaps 3 to 6, respectively. The bottom four A’, B’, C, and D’ present the near field patterns at the corresponding bandgap edges. Images E and F are enlarged images of the cladding region in images B’ and D’ respectively.

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The near-field patterns at the fiber’s output face were measured by imaging onto a CCD camera with appropriate magnification. A scanning monochromator with a 3 nm passband was added between the supercontinuum source and the input PCF. After optimizing the alignment to couple the spectrally filtered light into the bandgap fiber core, a series of near-field images were recorded, as displayed in Fig. 3. As the dotted arrows show, the top four near-field images from A to D correspond to the middle position of four low-loss transmission ranges (i.e, bandgaps) from 3 to 6, while the bottom four correspond to the high-loss band edges. In the band edge images from A′ to D′, the light patterns in the cladding rods clearly present the rod modes E41, E51, E61 and E12 respectively at their cut-off wavelengths. By similarly observing the near-field patterns in the lower bands (from 1 to 3) through a 125μm outer diameter fiber (7μm pitch), E11, E21 and E31 mode patterns were also identified clearly at the corresponding band edges.

Due to the large 7:1 aspect ratio of the rectangular rod, the E12 mode is strongly shifted in frequency, having a higher cut-off frequency than the E61 mode, which means the wavelengths of the first 5 bandgaps at the low-index line are completely determined by the modes of E11 to E61 in order. From near field image E (the close-up of image B′), we find that the coupling of the neighboring cladding rods (E51 mode in image E and B′) is stronger between rods in the same layer, and weaker between the adjacent layers. The rod layer is defined according to the “horizontal” direction in Figs. 1 and 3. This coupling property is also found for modes E21, E31, E41 and E61, by checking their corresponding near field images. In fact, by scanning the wavelength from the centre of each of the bandgaps 2-5 to the edge, we observe that the light in the core tends to leak in the “horizontal” direction much more quickly than in the “vertical” direction. Note that near field image D′ is obviously different from the other three band edge images: coupling of the adjacent rod modes doesn’t occur in the same layer but between the neighboring layers; the regions located between the neighboring rods in the same layer become dark, instead of being bright in images A′, B′ and C′. This is particularly clear in image F, the close-up of image D′.

5. Directional bend losses

We measured the directional dependence of bend loss in this fiber by bending the fiber in two directions, one in the plane of the rectangular rods in the cladding and the other perpendicular to this plane. The bend diameter used was 16cm and the bent length was 8cm, the remainder of the fiber being held straight. One end of the fiber was butted against an endlessly single mode PCF coupled to the supercontinuum source. By checking the near field image at the output end, we rotated the fiber to an angle at which the cladding rods were horizontal. Another piece of endlessly single mode fiber was then butted up against the output end with the alignment adjusted to maximize the power in the core, and an OSA was used to record the spectrum when the fiber is straight and bent. The bend loss measurement for the other direction was carried out in a similar way. The bent length and bend radius were kept identical for the two measurements.

Figure 4 shows that the susceptibility of the fiber to bend loss varies across bandgaps 2-5, and is also dependent on the direction of bending. The difference in bend loss in the two bending directions is especially great for bandgaps 2 and 4, with in-plane bending giving the greatest loss. Conversely, in bandgaps 3 and 5 there is a smaller difference between the two bending directions, and out-of-plane bending gives the greater loss. These differences are most obvious for bandgaps 2 and 3, when we bend the fiber with smaller diameter than that shown in Fig. 4.

In Ref [5] it was shown that the bend loss of a bandgap-guiding PCF structure can be understood in terms of the cladding bandstructure by considering the ‘depth’ of bandgaps, i.e. the offset between the fundamental guided mode and the nearest band edge. If the offset is small, the fiber is more susceptible to bend loss than when it is large. The different behavior of the bandgaps in the fiber described in this paper can also be understood by reference to the DOS plot in Fig. 2.

Figure 4 shows that bandgap 2 is the most resilient to bend loss, and bend loss susceptibility increases with frequency (and hence bandgap number). This can be explained by the shape of the DOS plot in Fig. 2: the depth of each bandgap decreases as frequency increases, largely as a result of the dispersion of the E12 mode, and it is therefore expected that the susceptibility to bend loss also increases with frequency. In order to understand the directional dependence of bend loss, it is necessary to consider the different bandgaps in detail. Consider first bandgaps 3 and 5. The E41 and E61 modes define the high-frequency edges of these bandgaps, but these modes broaden relatively slowly below cutoff. As a result, the floors of the bandgaps are defined over much of their width by the E12 mode. As shown in Sec. 4, the E12 mode is most strongly coupled between adjacent rods in the out-of-plane direction, and therefore we can expect these bandgaps to be more sensitive to out-of-plane bending than to in-plane bending.

 figure: Fig. 4.

Fig. 4. Directional bend losses. a) the orientation of the cladding rods; b) the fiber bent in-plane and out-of-plane; c) transmission spectra of 30cm of fiber for different bend directions. The length of bent region in this fiber was about 8cm with the bend diameter of 16cm. The fiber was straight (black solid line), bent out-of-plane (red solid line) and bent in-plane (blue dashed line).

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Bandgaps 2 and 4 are defined at their high-frequency edges by the E31 and E51 modes. These modes broaden more quickly below cutoff than the E41 and E61 modes. The floor of bandgap 2 is consequently defined by the E31 mode over much of the bandgap width at the cutoff line; the E12 and E51 modes are both found to appear close to the floor of bandgap 4 at the low-frequency part, while the high-frequency part of the bandgap 4 is completely determined by E51 mode. Because E31 and E51 are both strongly coupled between adjacent rods in the in-plane direction, we expect bandgaps 2 and 4 to be particularly susceptible to in-plane bending, and especially so at their high-frequency edges. The increased susceptibility of the high-frequency edges of bandgaps 2 and 4 to in-plane bending is particularly evident in Fig. 4.

6. Conclusion

A new kind of all-solid photonic bandgap fiber based on an array of oriented rectangular rods was fabricated and a series of low-loss transmission bands was measured. From the near-field patterns of modes at the band edges, the rod modes defining their corresponding bandgaps were easily identified, coinciding with the numerical modeling of cladding band structures. Directional dependence of bend losses in this fiber, relative to the orientation of the rectangular rods, was measured. The detailed directional bend loss properties for each bandgap were explained according to the density of states of the cladding and the directional coupling properties of different cladding rod modes.

Acknowledgments

We would like to acknowledge assistance in fabricating this fibre from Mr Alan George. This work was funded by the U.K. E.P.S.R.C.

References and links

1. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic band gap fiber,” Opt. Lett. 29, 2369–2371 (2004). [CrossRef]   [PubMed]  

2. A. Argyros, T. Birks, S. Leon-Saval, C. M. Cordeiro, F. Luan, and P. S. J. Russell, “Photonic bandgap with an index step of one percent,” Opt. Express 13, 309–314 (2005). [CrossRef]   [PubMed]  

3. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, “Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm,” Opt. Express 13, 8452–8459 (2005). [CrossRef]   [PubMed]  

4. J. M. Stone, G. J. Pearce, F. Luan, T. A. Birks, J. C. Knight, A. K. George, and D. M. Bird, “An improved photonic bandgap fiber based on an array of rings,” Opt. Express 14, 6291–6296 (2006). [CrossRef]   [PubMed]  

5. T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, “Bend loss in all-solid bandgap fibers,” Opt. Express 14, 5688 (2006). [CrossRef]   [PubMed]  

6. A. Wang, A. K. George, and J. C. Knight, “Three-level neodymium laser incorporating photonic bandgap fiber,” Opt. Lett. 31, 1388–1390 (2006). [CrossRef]   [PubMed]  

7. N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. White, R. C. McPhedran, and C. M. de Sterke, “Resonances in microstructured optical waveguides,” Opt. Express 11, 1243–1251 (2003). [CrossRef]   [PubMed]  

8. section I and II of G. J. Pearce, T. D. Hedley, and D. M. Bird, “Adaptive curvilinear coordinates in a plane-wave solution of Maxwell’s equations in photonic crystals,” Phys. Rev. B 71, 195108 (2005). [CrossRef]  

9. J. E. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J. 48, 2133–2160 (1969).

10. E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell. Syst. Tech. J. 48, 2071–2102 (1969).

References

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  1. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic band gap fiber,” Opt. Lett. 29, 2369–2371 (2004).
    [Crossref] [PubMed]
  2. A. Argyros, T. Birks, S. Leon-Saval, C. M. Cordeiro, F. Luan, and P. S. J. Russell, “Photonic bandgap with an index step of one percent,” Opt. Express 13, 309–314 (2005).
    [Crossref] [PubMed]
  3. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, “Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm,” Opt. Express 13, 8452–8459 (2005).
    [Crossref] [PubMed]
  4. J. M. Stone, G. J. Pearce, F. Luan, T. A. Birks, J. C. Knight, A. K. George, and D. M. Bird, “An improved photonic bandgap fiber based on an array of rings,” Opt. Express 14, 6291–6296 (2006).
    [Crossref] [PubMed]
  5. T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, “Bend loss in all-solid bandgap fibers,” Opt. Express 14, 5688 (2006).
    [Crossref] [PubMed]
  6. A. Wang, A. K. George, and J. C. Knight, “Three-level neodymium laser incorporating photonic bandgap fiber,” Opt. Lett. 31, 1388–1390 (2006).
    [Crossref] [PubMed]
  7. N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. White, R. C. McPhedran, and C. M. de Sterke, “Resonances in microstructured optical waveguides,” Opt. Express 11, 1243–1251 (2003).
    [Crossref] [PubMed]
  8. section I and II of G. J. Pearce, T. D. Hedley, and D. M. Bird, “Adaptive curvilinear coordinates in a plane-wave solution of Maxwell’s equations in photonic crystals,” Phys. Rev. B 71, 195108 (2005).
    [Crossref]
  9. J. E. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J. 48, 2133–2160 (1969).
  10. E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell. Syst. Tech. J. 48, 2071–2102 (1969).

2006 (3)

2005 (3)

2004 (1)

2003 (1)

1969 (2)

J. E. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J. 48, 2133–2160 (1969).

E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell. Syst. Tech. J. 48, 2071–2102 (1969).

Argyros, A.

Bigot, L.

Bird, D. M.

Birks, T.

Birks, T. A.

Bouwmans, G.

Cordeiro, C. M.

de Sterke, C. M.

Douay, M.

Dunn, S. C.

Eggleton, B. J.

George, A. K.

Goell, J. E.

J. E. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J. 48, 2133–2160 (1969).

Hedley, T. D.

section I and II of G. J. Pearce, T. D. Hedley, and D. M. Bird, “Adaptive curvilinear coordinates in a plane-wave solution of Maxwell’s equations in photonic crystals,” Phys. Rev. B 71, 195108 (2005).
[Crossref]

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic band gap fiber,” Opt. Lett. 29, 2369–2371 (2004).
[Crossref] [PubMed]

Knight, J. C.

Leon-Saval, S.

Litchinitser, N. M.

Lopez, F.

Luan, F.

Marcatili, E. A. J.

E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell. Syst. Tech. J. 48, 2071–2102 (1969).

McPhedran, R. C.

Pearce, G. J.

Provino, L.

Quiquempois, Y.

Russell, P. S. J.

Russell, P. St. J.

Stone, J. M.

Usner, B.

Wang, A.

White, T.

Bell Syst. Tech. J. (1)

J. E. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J. 48, 2133–2160 (1969).

Bell. Syst. Tech. J. (1)

E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell. Syst. Tech. J. 48, 2071–2102 (1969).

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. B (1)

section I and II of G. J. Pearce, T. D. Hedley, and D. M. Bird, “Adaptive curvilinear coordinates in a plane-wave solution of Maxwell’s equations in photonic crystals,” Phys. Rev. B 71, 195108 (2005).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. (a) Optical micrograph of a cane with a rectangular inclusion made from an array of raised-index rods; b) scanning electron micrograph of the final fiber; c) close-up of the core region in b), rod pitch: 13.8μm, length (D)/width (W): 7/1, D/Λ=0.67.
Fig. 2.
Fig. 2. Calculated DOS for a triangular lattice of step-index rectangular rods in a low-index background as described in Section 2. The geometry of the rectangular rods and lattices were chosen to be the same as the fiber displayed in Fig. 1.
Fig. 3.
Fig. 3. Transmission spectrum of the fiber shown in Fig.1 as a function of normalized frequency (kΛ) and wavelength in central diagram. The top 4 pictures A, B, C and D show the near field patterns in the middle of bandgaps 3 to 6, respectively. The bottom four A’, B’, C, and D’ present the near field patterns at the corresponding bandgap edges. Images E and F are enlarged images of the cladding region in images B’ and D’ respectively.
Fig. 4.
Fig. 4. Directional bend losses. a) the orientation of the cladding rods; b) the fiber bent in-plane and out-of-plane; c) transmission spectra of 30cm of fiber for different bend directions. The length of bent region in this fiber was about 8cm with the bend diameter of 16cm. The fiber was straight (black solid line), bent out-of-plane (red solid line) and bent in-plane (blue dashed line).

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