Investigation Of The Light Propagation In One-dimensional Photonic Crystal Waveguides Based On The Hermite-Gauss Function Method

Photonic crystals (PCs) are a new kind of optical materials with periodic variation of the optical refractive index. If some defects are introduced in a PC, the light energy will be confined in the defect area and thus a control of light propagation can be realized. This property can be applied to design many kinds of optical devices. Due to the layered structure, the one-dimensional (1D) PCs with defects can be regarded as a special kind of planar waveguide and may have many applications in modern optoelectronic integration technology.In this thesis, we first have a brief review of the concepts, the theoretical methods and the preparation technologies of PCs. Then, based on the Hermite-Gauss function expansion method, we calculate the eigenmodes of1D refractive-index-typed PC defect waveguides. At the same time, a finite-layer approximation based analytical model of this kind of waveguide structures is established and is used to verify the correctness of the calculation. At last, based on the Hermite-Gauss function expansion method, we study the light propagation properties of this kind of waveguide structures.With the Hermite-Gauss function expansion method, the dispersion relations, the mode field patterns, energy control factors and effective refractive indices of the1D PC waveguides with different polarizations and structural parameters are calculated. Based on the numerical results, the following conclusions can be obtained:(1) there are significant differences between the high-ordered modes in1D PC defect waveguides and those in step planar waveguides, and thus an effective control of the transmission of the high-ordered modes can be realized by adjusting the structural parameters of1D PCs.(2) The cut-off frequency of the1D PC defect waveguide is lower than that of a step planar waveguide, so the transmission capacity of the low frequency wave is stronger in1D PC defect waveguides than that in step planar waveguides, and at the same time, however, this property is not beneficial for the realization of a single-mode transmission in the waveguide.(3) In the regions far from the cut-off frequency, the properties of the eigenmodes in the ID PC defect waveguide are significant different from those in the step planar waveguides, if the order of the eigenmode is not smaller than2.(4) The electric field component can be significantly enhanced in the medium/ metal boundary of a1D PC defect waveguide containing metal layers, and the field distribution of the eigenmodes is influenced significantly by the ratio of the thickness of the two component layers.