TABLE OF CONTENTS For axially varying waveguides, the beam propagation method described in the preceding chapter is the most powerful technique for investigating linear and nonlinear lightwave propagation phenomena. In comparison with BPM, the staircase concatenation method is a classical technique that has been utilized for the analysis of axially varying waveguides. As explained in Chapter 7, the step size of numerical analysis in BPM is something between a fraction of the wavelength and several times the wavelength. Therefore calculation time and rounding errors will increase in the analysis of optical devices of several centimeters length. The staircase concatenation method is suitable for the analysis of such long devices. In this chapter, the basic concepts and procedures of the staircase concatenation method are explained via the example of fused-taper fiber couplers.
We will investigate here the transmission characteristics of the fused-taper (fused and elongated) coupler [1, 2] shown in Fig. 8.1. The fused-taper coupler is fabricated by first fusing the two parallel fibers with a burner or heater and then elongating it. The total diameter of the minimum waist region reaches about 20 30 m from the original diameter of the two fibers. In this case, the core diameter of each fiber becomes about 1 m (one-tenth of the original core diameter). Therefore, most of the light is not confined in the core region, and it spreads to the entire cladding. Light confinement is then provided by the air cladding. Since the refractive-index difference between...
