Open Access
Add to BibSonomyAbstract
The light radiated from the guided mode of a hollow core photonic crystal fiber into free space is measured as a function of angle and wavelength. This enables the direct experimental visualization of the photonic band gap and the identification of localized modes of the core region.
©2005 Optical Society of America
1. Introduction
In a hollow-core photonic crystal fiber (HC-PCF), a large central air hole is surrounded by a number of periods of silica/air photonic crystal cladding, formed by a regular array of air holes in a glass matrix [1] (see Fig. 1). Light coupled into this hollow core is confined by the photonic band gap of the photonic crystal cladding and propagates with low attenuation [2]. Because the fiber is (to a good approximation) invariant along its length, the modes of the hollow core and the “holey” cladding are defined by their propagation constants β along the fiber axis. The frequency (ω) range covered by the band gap evolves in a complicated manner with β. No photonic band gap exists for in-plane propagation (β=0) but gaps can open up for ranges of non-zero values of β, mapping out “finger” shaped regions in the ω-β plane. Alternatively, the same information can be represented as a plot of effective index n eff=β/k against free-space wavenumber k=2π/λ where λ is the vacuum wavelength. In a band gap region satisfying β < k (i.e., n eff < 1), light can propagate in an air core but not in the photonic crystal cladding, so that an air-guided mode can be formed [3].
Fig. 1. Scanning Electron Micrograph (SEM) of the HC-PCF. The size of the hollow core is equal to 7 unit cells of the photonic crystal cladding. The pitch between adjacent holes is 3.7 µm and the air-filling fraction of the holey cladding is ~90%. The holey cladding is surrounded by a solid silica jacket to strengthen the fiber and to bring the outer diameter to 125 µm. The fiber guides light between 1400 nm and 1600 nm wavelength, with a minimum attenuation of around 20 dB/km.
As for conventional fibres, the modal properties of HC-PCFs are most commonly determined by imaging the near field profile of the guided mode at the end of the fiber. A limitation of this technique is the lack of discrimination between different modes that may be excited simultaneously, making it difficult, for example, to compare experimental results to computer simulations. This problem arises because information about the effective indices of the individual modes is lost when the light leaves the fiber.
In contrast, the angular distribution of light escaping through the side of the fiber into a high-index medium preserves this information because the angle of propagation outside of the fiber is directly related to the effective index of the mode by
where n MF is the index of the external medium, here an index-matching fluid with n MF close to that of silica and θ is the angle between the direction of propagation and the fiber’s forward axis. Angularly-resolved observations of escaping light have been used for decades to characterize planar waveguides [4], and have been applied to solid core, index-guiding fiber [5] and to uniform 3D photonic crystals without waveguides [6] as well. A related experiment in photonic crystal fibre involved the angularly-resolved observation of fluorescence emitted by excited Er3+ dopant ions located at the centre of the core of a solid-core PCF [7], but the fiber studied in that case possessed no band gap. In this paper we report, to our knowledge for the first time, the direct experimental visualization of the photonic band gap and guided modes in a hollow-core PCF, based on such angularly-resolved scattering measurements.
2. Optical properties of a HC-PCF photonic band gap cladding
To interpret the experimental results presented in the following it is useful to first consider the optical properties of the fibre cladding. Figure 2 shows the calculated density of states (DOS) (as defined in [8]) of a typical HC-PCF cladding. The photonic band gap is defined by a dark “finger” below n eff=1 within which the DOS falls to zero and light does not propagate. The band gap is surrounded by two “pass-bands” (banded bright regions) where propagation of light in cladding modes is possible.
The properties of the band gap depend on the air-filling fraction and the shape of the air holes, as well as on the regularity of the cladding. For this example, we have assumed a perfectly periodic cladding with struts with a width of 0.041 Λ, separating hexagonal holes whose rounded corners have a radius of curvature of 0.23 Λ. This corresponds to an air-filling fraction of 90% [9]. The pitch Λ=3.7 µm. These parameters closely match those of the fabricated fiber for which experimental results are presented in Section 4.
Fig. 2. Computed Density of States (DOS) for a perfect infinite cladding with an air-filling fraction of 90%. DOS values are shown relative to the vacuum level. The finger of zero DOS around n eff=1 is the fundamental photonic band gap, with regions where propagation is allowed bordering above and below. The zero-DOS region at the top defines the cladding cutoff, the lower edge of which is the effective index of the cladding.
There are two routes for light propagating in a core-guided mode to escape through such a cladding. The most direct path is for light to “tunnel” through the finite-thickness cladding and continues to propagate at a specific angle. In Fig. 2 this would show up as a line at n eff~1. Practical HC-PCFs are usually designed with enough periods of holes in the cladding, however, so that tunneling from the core-guided mode is not the dominant loss mechanism for wavelengths inside the photonic band gap. Therefore we expect that such direct leakage will be observable only close to the edges of the band gap, where the light becomes less well confined. Alternatively light can be scattered into and between other core-guided or cladding modes by small-scale imperfections such as surface roughness at the silica/air interfaces [10], and leak out into free space. Since the propagation constants of these modes form a quasi-continuum and light diffused between them, this indirect loss-path would manifest itself in bright continuous bands, broadly outlining those regions, where propagation in the cladding is possible.
3. Experimental setup
The experimental setup is shown schematically in Fig. 3. A similar setup has been used for measuring the loss properties of solid-core step-index fibers [5] but has, to our knowledge, never been applied to a photonic band gap fiber.
A 5.5 mm section of a 50 m long HC-PCF is placed across the centre of a rotatable 32 mm diameter cylindrical immersion cell. The cell is filled with index matching fluid (Cargille 50350) with a refractive index n MF of 1.449. The rest of the fiber in the cell is surrounded by black tubing, so that it does not contribute to the measured signal. Light escaping from the exposed region of fiber propagates through the cell and is detected by a cooled linear 512-element InGaAs photo-detector array (Hamamatsu C8061). The array is placed approximately one focal length from the lens formed by the curved surface of the cell, so that light propagating at a given angle arrives at the same point along the array, irrespective of its point of origin along the exposed fiber. To increase the signal, an additional cylindrical lens focuses light from a range of azimuthal angles around the fiber. For the given dimensions, the setup achieves an angular discrimination of 40 pixels/degree. An angular range of ~12° around the centre of the photonic band gap can thus be imaged directly onto the array, covering roughly 4 times the width of the band gap of the fiber.
Light from a 7 mW tunable external cavity semiconductor laser is coupled into one end of the fiber. The laser covers the wavelength range from 1510 nm to 1630 nm spanning only one part of the band gap. When used with an integration time on the order of a second, sufficient light is collected to analyze fibers with a loss around 1 dB/km at good signal to noise ratio.
Fig. 3. Experimental setup. The detector is separated from the surface of the immersion cell by roughly one focal length of the cylindrical Fourier lens formed by the cell surface. An additional, orthogonally oriented cylindrical lens serves to increase the signal by covering a larger range of azimuthal angles.
4. Results
4.1 Experimental results
Figure 4(a) shows the measured power of scattered light as a function of wavenumber k and effective index n eff. Corresponding wavelength and angle axes are also provided in the plot. The band gap appears as a distinct dark wedge in the experimental data and corresponds very closely to the location of the calculated band gap shown in Fig. 2. The bright horizontal stripes of high intensity above and below the band gap in Fig. 4(a) correspond to scattering into cladding modes matching similar features, representing a high DOS, in Fig. 2. Sharp lines are also visible close to the band gap edge, especially for smaller wavenumbers, corresponding to direct leakage out of core-guided modes as confinement becomes weaker at the band gap edges.
To aid in identifying the origin of the bright vertical lines, Fig. 4(b) is the measured transmission spectrum recorded when white light is transmitted through a short length (10 m) of fiber. The vertical lines appear at the same wavenumber k as local minima in the transmitted spectrum, which have been previously identified as being due to anti-crossings of the core-guided mode with surface-guided modes [9,11].
Fig. 4. (a) Scattered light signal as a function of n eff and k, normalized to the output power of the fibre and plotted in dB. The band gap manifests itself as a dark wedge in the image, corresponding to combinations of k and n eff for which no scattering is observed. The fine lines within the band gap are due to light tunneling directly out of confined modes. (b) The transmitted spectrum of the fiber, showing that the vertical white bands in (a) correspond to loss peaks (previously identified with surface-mode crossings) at specific wavelengths.
4.2 Comparison to simulation
We have calculated the effective indices of the guided modes of our fiber by performing computations based directly on the SEM shown in Fig. 1 [12]. The results are presented in Fig. 5(a). Figure 5(b) is the corresponding part of the side-scattering measurement from Fig.4(a). The yellow line in Fig. 5(a) is the fundamental HE11-like mode in which the majority of the incident power resides. This appears at the same effective index of 0.993 towards the left of Fig. 5(b), close to the band gap edge where the confinement of the mode is weaker. The line is almost parallel to the k axis, as expected for a low-order core-guided mode predominantly guided in air. Other visible bright lines in the experimental band gap can be identified in Fig. 5(a) as higher-order core-guided modes: TE01, TM01 and HE21-like modes as a single line at n eff=0.986, and the HE12-like mode as a line along the bottom of the band gap around n eff=0.975. The sharp lines towards the top of the experimental band gap towards the left correspond to surface-guided modes, shown as broken lines in Fig. 5(a). These surface modes are more dispersive than the core modes, and their trajectories are not parallel to the k axis.
Fig. 5. (a) Computed modal trajectories, with core modes marked as solid lines and surface modes with broken lines. Not all surface modes are shown. The HE11-like core mode is the top solid line. (b) Zoom of the experimental data to enable identification of the observed modes. Core modes and surface modes appear clearly at smaller wavenumbers.
The bright vertical band for k around 3.99 µm-1 in Fig. 5(b) is caused by the anti-crossing of a surface-guided mode and the HE11-like core mode. The anti-crossing event occurs too deeply within the band gap for it to be directly observed experimentally by tracking mode trajectories, but it is apparent in the numerical results shown in Fig. 5(a). Close to the anti-crossing event, the total scattered power greatly increases because the HE11-like mode hybridizes with the surface mode that has far higher field strength at the air/silica boundaries, leading to enhanced surface roughness scattering. A similar anti-crossing causes the weaker vertical line around k=3.925 µm-1. In this case, the anti-crossing of the lines is clearly evident in the experimental data.
5. Conclusion
Varying the wavelength of light coupled into a hollow-core PCF while observing the angular dependence of the light lost through the fiber walls enables the band gap region to be quickly mapped out in wavenumber and effective index. It also allows the trajectories of core and surface modes to be followed, to the extent that light in these modes can tunnel through the finite-thickness cladding. The results presented here are a direct and sensitive experimental verification of the general optical properties of hollow-core photonic band gap fibers, which could previously only be inferred from measurements of transmitted light, adding a potentially valuable tool for the further development of these fibres.
Measurements on fibers with fewer periods of photonic crystal cladding (or with the outer layers of holes filled in with index matching liquid), and thus deliberately weaker confinement, could make it possible to observe the trajectories of guided mode deep inside the band gap, and would allow mode anti-crossing events between core-guided and surface-guided modes to be tracked experimentally: such events are known to increase loss and to substantially alter dispersion properties [9–11]. Furthermore, observation of the scattering pattern at different positions along the length of a fiber would provide a sensitive test of the homogeneity of the fiber.
References and links
1. J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003). [CrossRef] [PubMed]
2. B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic band gap fiber,” postdeadline paper PDP24 in Optical Fiber Communication Conference 2004 (Los Angeles, 2004).
3. T. A. Birks, P. J. Roberts, P. St.J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic band gaps in silica/air structures,” Electron. Lett. 31, 1941 (1995). [CrossRef]
4. H.-G. Unger, “Planar Optical Waveguides and Fibers” (Clarendon Press, Oxford, England1977).
5. M. E Lines, W. A. Reed, D. J. Di Giovanni, and J. R. Hamblin, “Explanation of anomalous loss in high delta singlemode fibers,” Electron. Lett. , 35, 1009–1010 (1999) [CrossRef]
6. A. F. Koenderink and W. L. Vos, “Light exiting from real photonic band gap crystals is diffuse and strongly directional,” Phys. Rev. Lett. 91, 213902 (2003). [CrossRef] [PubMed]
7. R. F. Cregan, J. C. Knight, P. St. J. Russell, and P. J. Roberts, “Distribution of spontaneous emission from an Er3+-doped photonic crystal fiber,” J. Lightwave Technol. 17, 2138–2141 (1999). [CrossRef]
8. J. M. Pottage, D. M. Bird, T. D. Hedley, J. C. Knight, T. A. Birks, P. St. J. Russell, and P. J. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11, 2854–2861 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2854. [CrossRef] [PubMed]
9. G. Humbert, J. C. Knight, G. Bouwmans, P. St. J. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan, “Hollow core photonic crystal fibers for beam delivery,” Opt. Express 12, 1477–1484 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477. [CrossRef] [PubMed]
10. P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibers,” submitted to Opt. Express. [PubMed]
11. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic band gap fiber,” Nature 424, 657–659 (2003). [CrossRef] [PubMed]
12. S. G. Johnson and J. D Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173 [CrossRef] [PubMed]
