| In integrated and fiber-optic photonics, as in many other areas, computer modeling is very important, sometimes necessary, for design and analysis. The task is basically to numerically solve Maxwell's equations in an efficient and accurate fashion. This thesis is based on the two most popular numerical simulation approaches, the beam propagation method (BPM) and the finite-difference time-domain (FDTD) method, and improves them in their capability and efficiency, with an emphasis on reflective photonic devices.; An bidirectional BPM is proposed, extending BPM's capability to deal with reflective structures while maintaining the computational efficiency of BPM. Components such as AR/HR coatings, gratings and add-drop multiplexers have been simulated to demonstrate the efficiency and accuracy of the algorithm. Furthermore, the proposed bidirectional BPM is improved to cure the inability of the previous algorithm in handling the evanescent field, by using a complex representation for the field propagator. In addition, the bidirectional BPM is extended to model nonlinear reflective devices. The reflection response of nonlinear gratings is calculated and their application for switching and amplification is also simulated. Besides propagation analysis, bidirectional BPM can also be applied to solving for the cavity modes in some cases. It is employed to find the modes of a vertical-cavity surface-emitting laser (VCSEL), predicting the mode profile, lasing wavelength, and threshold gain of the modes. Using this algorithm, several design problems for oxide-confined VCSEL devices are examined.; Time-domain approaches, such as FDTD, are more versatile and powerful because they do not impose assumptions on the geometry of the structures and the propagation direction as in frequency-domain approaches, such as BPM. However, they are generally very time and memory consuming. In this thesis, the efficiency of FDTD method is significantly improved while maintaining the same accuracy by employing an envelope approach. Time-domain methods are also useful for modeling pulse dynamics. A model is established based on FDTD to simulate the passive modelocking dynamics of VCSEL's. Lorentzian model is employed to describe the resonance of the macroscopic polarization and rate equation is used for the carrier dynamics. Stable modelocking pulse train is obtained on a 1D VCSEL example. |
