Intermodal interference in photonic crystal fibres, single mode over long lengths, is measured over a short length. Akin to conventional fibres, this poses a potential problem for practical device utilisation of photonic crystal fibres. We note that given the existing widespread fabrication capability of this fibre and indications that some commercial use in devices will come to fruition, the need for standardising measurement techniques, analogous to ITU standards for conventional fibre, specific to photonic crystal fibres will be required.
© 2004 Optical Society of America
Intermodal beating in multi-mode fibres is an inherent problem of all fibre-based technology where over short lengths even traditionally single-mode fibre can sustain sufficient optical intensity in higher order modes [1–5]. For short devices and short lengths of fibre, modal interference leads to decoupling of light into the lossy higher order mode – the loss is further enhanced by non-ideal splicing where matching of the NA and geometries is not perfect. Such is the problem that ITU standards now exist to help alleviate this issue within systems work. On the other hand, intermodal interference has also been practically useful: for example, it forms the basis of a modal Mach Zhender interferometer used to study bulk UV-induced index changes in photosensitive fibres . More significantly, the high sensitivity of the modal interferogram as a function of varying fibre parameters allows optical diagnostics and hence control of fibre parameters for fibre manufacturers . Given the burgeoning interest in photonic crystal fibres and their variants, such as photonic bandgap fibres  and Fresnel fibres [8,9], and the possible role of modal interference, both problematic and useful, we explore in this paper intermodal interference in a index guiding photonic crystal fibre in the near IR. The fibre is single mode over lengths of a couple of hundred meters at 1.5µm, but supports two modes over shorter lengths (10cm).
The photonic crystal fibre was fabricated by the now routine method of bundling capillaries to form a preform that is then drawn into optical fibre. More details of the method we employ are given in . An SEM image of a cleaved cross-section of the triangular lattice is shown in Fig. 1. The core diameter is 13µm, average hole diameter 2.6µm and pitch 7.1µm. Its propagation loss at 1500nm was measured using a commercial loss rig to be <6dB/km over 350meters. To meet international standards most commercial systems require long lengths of fibre when determining single-mode operation . As a result there is a discrepancy between single-mode behaviour of long lengths over short lengths, giving rise to the issue of modal interference over short lengths when splicing is not perfect. The large loss difference between fundamental and higher order modes in photonic crystal fibres is determined in part by leakage between the holes of the transverse component of the propagation vector describing the modes (confinement loss), which is much larger for the higher order modes. For the fibre described in these experiments the fundamental mode has a propagation loss <6dB/km. Further, since confinement is determined mostly by leakage between air-holes, deformation of the lattice by bending can significantly affect the presence and position of shorter wavelength loss as well as the loss differential between the modes . This factor is important because standard telecommunication fibre loss measurements involve set bend radii that can affect single-mode measurements of photonic fibres markedly. Thus there are grounds for reevaluating fibre loss measured to an international standard analogous to the ITU standard for conventional fibre. Certainly, for the purposes of this paper, over straight short lengths of ~10cm, the higher order mode is confined sufficiently for clear observation of modal interference.
Modal interference between the lowest order modes traditionally occurs between the LP01 and LP11 modes. Whilst a reasonable representation is an analogous LP01 and LP11 set of modes in the photonic crystal fibre, it should be recognised that the high index contrast found in photonic crystal fibres leads to a fine splitting of the four vectorial modes that make up the LP11 mode in low-index conventional fibres. Therefore, in our description of these fibres, and since the modes of a photonic crystal fibre are leaky modes, the lowest order mode is HE11-like, which is doubly degenerate. The next analogous LP11 modes are the TE01-like (single degenerate), HE21-like (double degenerate) and TM01-like (single degenerate) modes [13, 14]. The higher order mode classes are almost degenerate and when linear superpositions are taken give rise to an LP11-like profile. It should be noted that the splitting of the higher order modes can also result from the symmetry of the structure - in this paper we assume no asymmetry in the numerical analysis.
For the experimental measurement of the modal interference, we used a setup consisting of a broadband halogen lamp, monochromator, 3D micro stage and photodetector. The front face of the fibre was located at the slit of the monochromator and the end face on the 3D micro stage. A standard fibre served as the aperture detection piece. The photonic crystal fibre was adjusted accordingly, using the translation stage, to maximise the observed interference fringe and fringe contrast, as summarised in Fig. 2. The measurement was performed with unpolarised light.
3. Results and discussion
The spectral dependence of the signal recorded over the wavelength region 700nm to 1050nm, where the fibre is two-moded is shown in Fig.3. Curve A in this figure is the measured signal (its spectral variation) when the photonic crystal fibre and detection fibre are aligned as shown in Fig. 2 A. Curve B similarly corresponds to the photonic crystal fibre and detection fibre aligned as shown in Fig. 2 B (symmetrically opposite to A). The fact that phases of the signals measured with those positions are opposite indicates that interference is occurring between a symmetric and an antisymmetric mode – beating between the analogous LP01 and LP11-like modes. This is consistent with the measurement being carried out in a spectral range where two modes are present. Note that the propagation constants of the TE01, HE21, and TM01 modes are so closely matched that we are unable to resolve the interference between them.
A common sign of modal interference within telecommunication fibres is the existence of an interference centre (equalisation wavelength), which is a consequence of an extreme of difference between phase constants of interfering modes (see Fig. 4 or Ref. ). However, no indication of such an extreme is observed in Fig. 3; at least not in the wavelength area where interference was observed. Another significant difference between modal interference in the photonic crystal fibre and standard telecommunication fibres is that the variation in wavelength period measured across the spectrum is much smaller in this photonic crystal fibre. The wavelength period is so small (~11.2nm) that it is convenient for modal interference studies to use short samples of the fibre (we use 7.3cm). It is also practically convenient to measure the modal interference in short samples of PCF since the interference at longer wavelengths can also be readily observed – over longer lengths the higher order mode will not be observed. Spectra for the longer wavelength regions are shown in Fig. 5.
Intermodal interference occurs in single-mode fibres because higher order modes exist for wavelengths above the cut-off wavelength although only the fundamental mode is strongly guided. In conventional fibres the ITU recommended method for determining single mode guidance  are made over a relatively long length of fibre over which the higher order modes are considered lost. These higher order modes are lost through radiation leakage over relatively short lengths (typically a few millimetres when the wavelength is far from cut-off wavelength and few tens of cm for a wavelength near cut-off wavelength). From a practical point of view, the length of the fibre convenient for intermodal interference observation depends also on the spectral width of the monochromator (or the resolution of the spectral analyser), because the period of variation is proportional to reciprocal fibre length.
Also shown are fitted harmonics to estimate the average period across these regions. The spectral period is a little longer than those observed at shorter wavelengths in Fig. 3. It is 12.1nm and 12.7 nm in vicinity 1100nm and 1500nm, respectively. Increasing the wavelength period with increasing wavelength indicates that an extreme difference in phase constants might be at much longer wavelength (if it exists). Generally, the period variation over the total wavelength span measured is small (~11–13nm) for PCF which is considerably less than that observed for standard telecommunications fibres - according Fig. 4 from 7 to 20nm (depending on distance from interference centre) in ten times longer fibre. The fact that the period in the PCF is much smaller than in the standard telecommunication fibre confirms the idea that extreme difference of phase constants is very far from the wavelength region where the intermodal interference measurement has been performed.
There is good accordance between experimentally determined wavelength periods with those periods theoretically calculated for the PCF. Small discrepancies are most likely attributed to the measurement of hole positions and dimensions from the SEM images (±5% error). Calculations were done by numerical simulation of the fibre structures using the recently developed algorithms of Issa and Poladian .
Figure 6 shows the periodicity of the interference signal as calculated for the photonic crystal fibre (shown in Fig. 1), where good agreement is obtained between theory and experiment. It should be noted that the numerical method is exact and hence it was possible to estimate the interactions of the lowest order modes with all quasi-degenerate modes of the higher order modes that are not orthogonal to each other. A consequence of the high index contrast, the breaking of the degeneracy of the higher order mode results in further interference between the TE01-like mode and the HE21-like mode. The spectral period for this is calculated to be ~700nm at ~1.3µm and increases substantially at shorter wavelengths (~850nm at 1µm). The simulated intensity profiles of the fundamental mode and example intensity profiles resembling those observed in the experiment for light guided in higher order modes are shown in Fig. 7. The calculated losses for higher order modes (TE01, HE21 and TM01) are ~40dB/m at 1.5µm.
In conclusion, we have measured for the first time equivalent modal interference in a photonic crystal fibre, an issue that will be critical to future systems work involving these fibres. We have found that as a result of a much greater index contrast and the strong wavelength dependency of the effective indices of the core and the cladding, the dispersion, or wavelength dependence, of the interference is significantly less than conventional fibres. Analogous to conventional fibre, modal interference may prove problematic in applications where short lengths of fibre are spliced into components or systems. Whilst splicing of these fibres with themselves is straightforward, significant improvements in splicing with other non-matched conventional fibres are required. Alternatively, practical use of intermodal interference such as that mentioned in the introduction can also be envisaged. Finally, we have also noted that some review of existing standards for fibre measurements such as loss and eventually those defining modal interference, will be required to ensure that a similar standardisation of methodology employed for conventional fibres is applied to photonic crystal fibres prior to future systems deployment.
This work was funded largely by an Australian Research Council Discovery Project grant. J. Zagari and J. Digweed at the Optical Fibre Technology Centre are thanked for their assistance in fabricating the fibre. The authors also thank to Faculty of Electrical Engineering of the University of Žilina for supporting this work.
References and links
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