Calculation Of The Transverse Modes Of Waveguide By Using The Beam Propagation Method

With the development of integrated optics, many kinds of optical waveguide devices which have different functions and structures appeared. Designing waveguide by experimental method is very time consuming, but using Computer Aided Design (CAD) method to design waveguide can overcome such difficulty. This method can also be used to analyze the characters of optical waveguide and leading to the designation of optical waveguide quickly. So, many algorithms are used to analyze integrated optical waveguide, among these algorithms, the beam propagation method is the most effective method which is used widely.In this paper, the current situation and developing direction of integrated optics are introduced, and we also introduce the optical waveguide mode theory: the mode theory of three layers planar waveguide and deformed fiber. Then on the basis of Maxwell equations and the paraxial limit, the formula that is needed in calculating finite difference beam propagation method (FD-BPM) is deduced. The transverse mode for ridge waveguide and fiber using the FD-BPM are also calculated here. When m=0, 1, 2, 3 and 4, we found that it is the ideal mode while working at the fundamental mode (m=0). Only strong peak value appears in the beam center and present "single one" at this moment. This kind of beam has the minimal angle of divergence with the highest luminance, and can be coupled effectively with fiber. It can also focus on the minimum spot through the simple optical system; this is very favorable to application of the laser instrument. When working at the m >1 axially symmetric same spot appeared with lower intensity of light. Then it has a bigger angle of divergence, and can not be coupled effectively with the fiber. The result indicated that it is very favorable for the computing on the deformed fiber.