摘要
光子晶体光纤是近年来出现的一种新型光纤,其特点是包层排列有规则或随机分布的波长量级的空气孔。包层中的微结构使得光子晶体光纤能够呈现出许多传统光纤不具备的特性,其中之一就是在可见光和近红外波段能够呈现反常色散。具有这种色散特性的光子晶体光纤在飞秒激光领域具有极大的应用前景。本论文从理论上对光子晶体光纤的色散特性进行了研究。论文的主要内容包括:
1、采用全矢量有效折射率模型研究了光子晶体光纤的色散特性。首次提出了研究光子晶体光纤色散特性的全矢量有效折射率模型,并研究了光子晶体光纤包层基模的分类。研究发现,类比于传统光纤的模式分类方法,光子晶体光纤包层基模也可以归于HE1 1模。通过优化相关参数,全矢量有效折射率模型的计算结果与测量结果以及其他数值方法的计算结果吻合得很好,而标量有效折射率模型则带来较大的误差。
2、采用半矢量有限差分法研究了光子晶体光纤的色散特性。数值计算表明,半矢量有限差分法与测量结果以及其他方法的计算结果吻合得很好。采用半矢量有限差分法研究了光子晶体光纤色散受某一层空气孔尺寸单独变化的影响,结果表明第一、二层空气孔因为靠近纤芯,因而对色散的影响最大。研究了空气孔在角向和径向偏离理想位置对色散的影响,发现空气孔在径向偏离理想位置比在角向偏离理想位置对色散的影响更显著。最后,研究了一类光子晶体光纤-孔助光纤(hole-assisted lightguide fiber)的色散受空气孔参数的影响,结果表明增加包层空气孔的数目、大小以及使空气孔靠近纤芯都有助于零色散波长向短波长移动。
3、设计了在800 nm附近具有零色散和平坦色散的光子晶体光纤。首次考查了在不同比例系数下采用色散无量纲化方法计算光子晶体光纤色散时的准确性,并结合全矢量有效折射率模型进行了在800 nm附近具有零色散和平坦色散的光子晶体光纤的设计。
A new type of fiber, known as photonic crystal fiber, has emerged in the past several years. These fibers are characterized by wavelength-scale air holes running along the entire fiber length in the cladding region, which have resulted in some unusual properties unattainable with conventional optical fibers. In particular, photonic crystal fibers can display anomalous dispersion in the visible and near-infrared wavelength range, and, therefore, have great potential in the field of femtosecond laser technology. The dispersion properties of photonic crystal fibers are investigated theoretically in the present dissertation. The main results are summarized as follows.
1 The dispersion properties of photonic crystal fibers are investigated using a fully vectorial effective index method (FVEIM) that we proposed. In analogy to conventional mode classification, the fundamental space filling mode of photonic crystal fibers is classified as HE1 1mode. With optimized fiber parameters, FVEIM yields results in agreement with experimental data and other numerical values, while the scalar effective index method causes considerable discrepancies.
2 A semi-vectorial finite difference method (SFDM) is used to characterize the dispersion of photonic crystal fibers. Numerical results by SFDM agree well with those measured and by other methods. The influence on photonic crystal fiber dispersion of the size of air holes in different rings within the cladding is studied. It is demonstrated that photonic crystal fiber dispersion is most sensitive to the air hole size variation in the first two rings. In addition, the angular and radial deviations of the air holes from their ideal positions are investigated separately, revealing that the former has less influence on fiber dispersion than the latter. Finally, the dispersion characteristics of hole-assisted lightguide fibers are analyzed. It is found that more air holes, larger air holes, and air holes closer to the fiber core all help to reduce the zero dispersion wavelength.
3 Photonic crystal fibers with zero dispersion and flattened dispersion around 800 nmare designed. The normalized dispersion technique is shown for the first time to our knowledge to be applicable under different scaling parameters, and then used in combination with FVEIM to design photonic crystal fibers with zero dispersion and flattened dispersion around 800 nm.
引文
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