Silica Optical Fiber Technology for Devices and Components: Design, Fabrication, and International Standards

CHAPTER NINE

Fiber Mode Analysis Using OFACAD

9.1   THEORETICAL REVIEW ON CASCADED BOUNDARY MATRIX METHOD

In Chapter 2, we have reviewed the basis of the waveguide properties in a step-index cylindrical fiber with a single core–cladding boundary. As explained in Chapter 4, we need more than simple step refractive index profile to cope with various optical specifications for current optical communication networks. There have been extensive researches on numerical modeling of an optical fiber with an arbitrary structure to predict and analyze the guiding properties [1–4]. Recently fiber design tools [5,6] are also commercially available based on various numerical techniques.

In this book, we will provide a fiber analysis software, optical fiber analysis computer-aided design (OFACAD) [7]. OFCAD is an efficient Maxwell’s equation vector solver including effects of material dispersion. The fundamental approach in OFACAD is to divide a given arbitrary refractive index profile of an optical fiber into meshes within which the index profiles are approximated as a step index. The boundary conditions at the interface between the neighboring meshes will then be the same as in equations 2.59–2.64. The vector components of the electric field and magnetic field are related as in equation 2.73 in terms of Bessel functions. The boundary conditions in each mesh will add up to form a cascaded matrix whose determinant will be used to find the effective index at a given frequency. We named this efficient ...