Based On The Study Of [(p-1) / P] Pad¨¦ Approximation Of The Beam Propagation Method

In this thesis, Beam Propagation Method (BPM) is studied and analyzed thoroughly, and the reasoning and developing procedure of the new Pade approximant employed in the BPM is presented, in order to damp the evanescent modes in the numerical simulation of the waveguide.After the introduction of calculating the mode properties of optical fibers by Feit and Fleck 1977, the beam propagation method at present is the most widely used tool employed in the study of guided wave optics, largely owing to its numerical speed and simplicity. These attractive properties result chiefly from the use of the paraxial approximation which in turn severely limits the formalism, especially for the wide-angle propagation. To overcome those limitations, some methods have been reported. Wide-angle beam propagation method is one of those methods. It is the most widely used tool employed in the design and simulation of waveguide devices as simplicity and high efficiency.At present, the most common method is the [p/p] Pade approximant formalism. This approach offers substantial improvements in both wide-angle propagation and index variation tolerance while incurring only a modest numerical penalty. But the wide-angle BPM based on the traditional [p/p] Pade approximant can't damp the evanescent modes for the algorithm itself. Now a new BPM base on a direct approximation to the propagator using [(p-1)/p] Pade approximant is presented. It is simple to construct and has the desired damping effect for the evanescent modes. In this paper, the method is applied to tapered waveguide for TE polarized waves .based on the energy conserving improvement of the one-way Helmholtz equation, and Numerical results are compared with other variants of the BPM.Based on the results of the new method, we found that although it is not as accurate as the [p/p] Pade as far a the propagating modes are concerned, the new method of [(p-1)/p] Pade approximant can obviously suppress the evanescent modes,and can be more accurate to the propagating modes with the increase of p.