Recently, photonic integration technology has made great progress, where the silicon-based photonic integrated circuits (PICs) are the most significant candiates. The rapid development of silicon-based PIC is not only dependent on the matured CMOS processing, but also on the efficient computer aided design softwares for optical waveguides and photonic devices (O-CAD). With the increasing of the integrated density in PICs and the applications of new materials or structures, O-CAD softwares are greatly required. Numerical methods for optical waveguides and photonic devices are the cores of O-CAD softwares. In this thesis, several efficient numerical techniques for optical waveguides and their devices are proposed, aiming at solving some problems from the classical reported methods or providing new solutions to the special design requirements.
Firstly, the basic electromagnetic equations for optical waveguides are derived from the Maxwell’s equations. Then an improved full-vectorial finite difference mode solver is proposed. By optimizing the accuracy order of differential discretization scheme, the computational efficiency is improved.
To slove the widely existed discontinuity problem in optical waveguides, an efficient numerical method based on Denman-Beavers iterative algorithm is proposed. The present method has advantages of faster convergence rate and better stability than traditional method. Moreover, more complex three-dimensional (3D) semi-vectorial and full-vectorial analysis models are proposed; especially, in the full-vectorial analysis model, the longitudinal field component is strickly included.
Next, the wide beam propagation method (WA-BPM) and bidirectional beam propagation method (WA-BPM) are studied. A WA-BPM based on Denman-Beavers iteration is proposed. Typical numerical tests show that the present method has the advantages of fast convergence and the ability of properly dealing with evanescent waves. A WA-BPM based on shifting-beam scheme is proposed for waveguides whose structure slowly varies in the propagation direction. By using a simulation window of proper size, this method can effectively improve the computational efficiency and have little effect on the accuracy. For effiecient analysis of the planar lightwave circuits, an ef?cient 3D semivectorial horizontally WA-BPM based on the alternating direction implicit scheme is proposed. This method transforms the 3D problem into two-dimensional calculation, which greatly improves the computational efficiency. Moreover, a stable and accurate preconditioner for the Bi-BPM is proposed, which improves the convergence speed of the Bi-BPM. In addition, an improved bidirectional propagational operator is proposed, which allows a larger propagation step to ensure accuracy, and can correctly simulate the true physical characteristics of the evanescent waves.
Moreover, the highly accurate multi-domain pseudospectral method (MD-PSM), which has attracted attention in the analysis of photonic devices in recent years, has been studied. A full-vectorial mode solver based on MD-PSM for electric fields is proposed. The model can obtain accurate results with only a few collocation points and its computational load is much smaller than the classic finite difference method. Moreover, an ef?cient re?ective BPM based on the MD-PSM is developed. By imposing the lateral boundary conditions through a weighting technique, a transverse characteristic operator like that in the ?nite-difference method (FDM) is constructed so that the BPM techniques for FDM are available.
In addition, a finite difference frequency domain method (FDFD) is developed for the design of silicon based photonic devices. A novel polarization rotator (PR) for silicon-based cross-slot waveguides using subwavelength gratings is proposed and analyzed by the FDFD. Numerical results show that a PR of 12.6 μm in length at a wavelength of 1.55 μm is achieved, where the polarization conversion efficiency (PCE) and insertion loss (IL) are, respectively, 97.2% and 0.71 dB, and the reflection loss is below ?20.5 dB for both cases. Moreover, a wide bandwidth of ～260 nm for both polarizations is obtained for keeping the PCE over 90% and IL below 1 dB.
Finally, the conclusion of our work is drawn and the outlook for future work is presented.