Analysis of long-period fibre grating filters
Student thesis: Doctoral Thesis
Related Research Unit(s)
A long-period fibre grating (LPFG) allows light coupling between the guided mode and the cladding modes. The transmission spectrum of a typical LPFG contains a series of attenuation bands centred at discrete wavelengths, leading to extensive studies of its applications as an all-fibre filter. The most distinct feature of LPFGs is the flexibility they offer in achieving the desired transmission characteristics by variation of the grating parameters, for instance, index modulation, grating period, grating length, chirping, phase shifts, etc. In this thesis, LPFG filters in the form of a single LPFG or two parallel LPFGs are analysed in detail. A single LPFG provides a band-rejection output while two parallel LPFGs provide an additional band-pass output. The design of high-contrast filters and the characterization of their transmission spectra constitute the major part of the thesis. A uniform LPFG is the most basic structure in all LPFG-based devices. Useful formulas are derived to provide insights into the characteristics of a uniform LPFG, where the relationship between the coupling coefficient and the side lobes is highlighted. To relax the constraints of a uniform LPFG, a detailed theoretical analysis of apodized phase-shifted LPFGs is performed. Simple analytical formulas are derived to facilitate designs for specific applications. In particular, the conditions for achieving zero or complete transmission at the resonance wavelength with zeroor p-phase shifted gratings are derived. It is shown that index apodization and length apodization can be employed effectively to suppress side lobes, or, in the other extreme, generate large, useful side lobes, as in the case of realizing a comb spectrum by using a binary index apodization profile. While a single LPFG is a natural band-rejection filter, two parallel LPFGs, namely, an LPFG coupler can provide both band-rejection and band-pass outputs, and thus offer additional flexibility in producing new functions. When the two LPFGs are identical and uniform, simple analytical solutions are derived and the conditions for achieving the highest coupling efficiency are highlighted. The theoretical results compare well with experimental data. The study is further extended to the case where the two parallel LPFGs are dissimilar and non-uniform, for which a transfer-matrix method based on the coupled-mode theory is developed. The non-uniformities considered include pitch detuning, chirping, phase shifts, and index apodization. In addition, it is shown that the introduction of an offset distance between the two gratings provides an effective means to increase the coupling efficiency of the coupler, as well as an additional degree of freedom in controlling the transmission spectra of the coupler. Finally, a wavelength-tuneable filter based on bending an LPFG is studied. The bend sensitivity of an LPFG manifests itself as a shift in the centre wavelength of the rejection band with a reduction in the contrast, and the generation of a new rejection band with an increase in the contrast. The original rejection band can be shifted to a longer wavelength or a shorter wavelength, depending on the fibre parameters. A theoretical analysis to explain the bend sensitivity of the resonance wavelength is performed. Taking into account the modal dispersion factor, the pitch modification, and the change in the effective index of the cladding mode, the analysis provides a reasonable explanation of the wavelength shift.
- Electric filters, Wave-guide, Optical fibers, Microwave filters, Diffraction gratings