在本論文，我們著重於拉伸式以及無拉伸式長週期光纖光柵之頻譜響應以及模態色散特性之探討研究。我們使用Mathematica 7.0來解三層結構下(纖核、纖殼以及周圍介質)長週期光纖光柵之不同模態等效折射率，並且使用LabVIEW 2010來計算色散值。我們假設對稱性的耦合模態下，不同的拉伸比例、不同折射率的周圍介質，模擬各個不同模態的等效折射率。模擬結果顯示，具有些微拉伸結構的長週期光纖光柵，由於模場較集中在纖核，和沒有拉伸結構的相比，具有以下特性：1.在空氣中，些微拉伸的長週期光纖光柵，在同樣的光柵週期以及纖殼模下，具有較長的共振波長。2.當周遭介質折射率改變時，具些微拉伸結構的長週期光纖光柵共振波長飄移比未拉伸的小；這顯示具些微拉伸結構的長週期光纖光柵在環境擾動下較穩定。3.在空氣中，具些微拉伸結構的長週期光纖光柵，其纖核模與纖殼模之色散值差異較大。 因此，對於非用為感測應用的長週期光纖光柵而言，具些微拉伸結構之長週期光纖光柵相較於未拉伸之長週期光纖光柵在環境擾動影響下具有較穩定特性，且具些微拉伸結構之長週期光纖光柵的色散特性使其可用為穩定的色散調製元件。In this thesis, we focus on the study of resonance spectral response and dispersion characteristics of tapered and non-tapered long-period fiber gratings (LPFG). We use Mathematica 7.0 to simulate the effective indices of different modes of LPFGs with three layer structure: core, cladding and surrounding media; and use LabVIEW 2010 to calculate the dispersion values. We assume symmetric mode coupling to simulate the effective indices and dispersion of LPFGs with different taper ratio and surrounding media. The simulated results show that slightly tapered LPFGs have the following characteristics compared to non-tapered LPFGs: 1. In the air, slightly tapered LPFG will have longer coupling wavelength compared to non-tapered LPFG with the same grating period and cladding mode. 2. When the refractive index of surrounding medium is changed, the coupling wavelength shift of slightly tapered LPFG is smaller than that of non-tapered LPFG; it means that the slightly tapered LPFG is more stable to environmental fluctuations compared to non-tapered LPFG. 3. In the air, the dispersion difference for core and cladding modes of slightly tapered LPFG is larger than that of non-tapered LPFG. As a result, for non-sensing related LPFGs, slightly tapered LPFGs are more stable to environmental fluctuations than non-tapered LPFGs, and the dispersion characteristics of slightly tapered LPFGs make them suitable for dispersion compensation devices.
