光子晶体自从被提出后，在光学物理、凝聚态物理、电磁波、信息技术等领域引起了人们广泛的关注。在这短短的二十年里，光子晶体在理论研究和实验研究方面均取得了显著的成果，并且在某些领域也有了一定的应用。但这毕竟是一种全新的概念，对它的研究还不够深入和广泛，其很多特性还没有得到很好的应用，有必要开展进一步的研究，尤其是在可见光波段全向禁带的实现与展宽方面。本文分析了一维和二维光子晶体周期不均匀性对光子晶体禁带的影响，指出了一定的周期性破缺对光子晶体禁带具有很好的展宽效果。发现在一定的不均匀条件下，二维正方格子型光子晶体也能实现全向禁带，并在不均匀性达到一定程度时，得到的全向禁带宽度最大。重铬酸盐明胶因具有厚度大、信噪比高等优点可被用来制作光子晶体。在制作的过程中，我们尽可能严格控制实验条件，并通过改变重铬酸盐明胶的后处理工艺来增加膨胀的不均匀性，以此来实现宽的禁带结构。在实验制作的过程中，通过改变后处理工艺得到了具有宽带隙特性的一维全息光子晶体，同时得到了一些有奇特“谱分叉”现象的实验结果。本文分析了重铬酸盐明胶的物理特性和膨胀机理，首次在重铬酸盐明胶的膨胀系数中引入服从高斯分布的随机数来描述实验中的不确定因素，提出了随机调制的线性膨胀模型，解释了奇特的“谱分叉”现象，并对实验结果的不确定性和不可预测性给出了合理的解释。该模型对全息光子晶体禁带的展宽有一定的指导作用。考虑到全息方法在制作复杂结构方面的优势，本文设计了一种用全息方法实现的二维八重准晶结构，并结合全息记录材料的感光阈值特性，提出了线性曝光模型和非线性曝光模型。用平面波展开方法分析了准晶结构在不同的模型参数下的禁带特性，发现全息记录材料的感光阈值对禁带有很大的影响，当全息记录材料感光特性不太灵敏、容易达到饱和阈值的情况下最容易实现对TEM波的全向禁带，且在一定条件下能实现全向禁带。为了充分了解什么样的结构有利于全向禁带的形成，本文以完全渐变的二维方格子模型（即线性曝光模型）、完全突变的方格子模型以及渐变和突变相结合的方格子模型（即非线性曝光模型）为例，用平面波展开方法来研究它们的禁带结构。发现渐变和突变相结合的模型更有利于TEM波全向禁带的实现。考虑材料的磁性，从广义布儒斯特角出发，理论上分析了一维二元光子晶体实现全向禁带的必要条件，并把一维二元光子晶体分为四类，发现一类特殊的光子晶体总是具有全向禁带特性，构成这类光子晶体的两种材料的折射率相同或相反，并给出了全向禁带展宽的两种方法：其一是降低环境介质的折射率，其二是提高构成光子晶体两种材料的阻抗对比度。针对光子晶体在抑制自发辐射和带边激光器制作方面的应用，本文以一维阶跃型光子晶体为例，研究了光子晶体内部的光子态密度受光子晶体结构及其环境等因素的影响，给出了用于自发辐射抑制和带边激光器方面的优化结构参数。

Since proposing the concept of photonic crystal in 1987, photonic crystal has attracted great attention in the fields of optical physics, condensed matter physics, electromagnetic waves and information technology. Lots of achievements related to theoretical and experimental studies have been reported. However, it is still a novel study topic, the research works on it is still not profound and wide enough, and further studies are necessary to understand it more thoroughly and apply it better, especially at the achievement of the large omnidirectional band gaps in the visible range.In this dissertation, we discussed the influence of non-uniform property of the period of photonic crystals on the width of band gaps. It is found that the broken of the periodicity will broaden the band gaps. Also, this method was applied to two-dimensional photonic crystal with square lattice. It is found that the omnidirectional band gaps can be obtained under some certain conditions.The dichromated gelatin has several advantages and can be used to fabricate holographic photonic crystals. During fabrication, some techniques were developed to enlarge the non-uniform property in hologram so that band gaps can be broadened. One-dimensional holographic photonic crystals with wide band gaps were obtained in our experiment. Also, a peculiar phenomenon in diffraction spectra in our experiments was found. In order to explain theoretically this phenomenon, we analyzed the physical properties and expansion mechanism of the material dichromated gelating (DCG), and a random number was firstly introduced in the expansion coefficient to describe the effect of uncertain factors in experiments. At last, a new linear expansion model modulated by the random numbers was proposed. This model can be used to explain the peculiar “bifurcation” phenomena in the diffraction spectra and the general properties of volume hologram. This model also gives a reasonable explanation for uncontrollable and unpredictable properties of the experimental results. Generally, the modulation of the refraction index of the holographic recording materials is not high enough. To achieve omnidirectional band gaps, a quasi-crystal structure with eight-fold symmetry was designed. Considering the exsistence of the exposure threshold value of the holographic recording materials, linear and nonlinear exposure models were discussed. And the properties of the band gaps based on different models were investigated. It shows that omnidirectional band gaps could be achieved under certain conditions.In order to learn what structure is advantaged to form the omnidirectional ban gaps, we also studied the effect of three models of the variation of the refractive index on the band gap structures, the three models are the gradual change model, the abrupt change model and the model combining gradual and abrupt changes respectively. It is found that the model combining gradual and abrupt changes is benefitial to obtain omnidirectional band gaps for TEM wave. Considering the effect of the magnetic properties of materials, the necessary condition to achieve omnidirectional band gaps was deduced theoretically. It is found that a special kind of 1-D photonic crystal always possesses omnidirectionan band gaps. And two methods for broadening band gaps are suggested. Finally, the effects of the refractive index of the enviroment materials and the surface truncation of the photonic crystals on the electromagnetic mode density in photonic crystals were investigated. And further, the optimization of the structure of photonic crystals was proposed for some applications (band-edge laser).