A new variational method of incorporating loss in the analysis of coupled multiple-quantum well three-dimensional waveguides

We have developed a simple method of calculating the imaginary part of the propagation constant in a lossy waveguide that closely follows the effective-index method of finding the real propagation constant of a rectangular dielectric guide. The method gives values much in agreement with the exact values obtained by the circular-harmonics method. The method has been used in the improved coupled-mode analysis of coupled-multiple-quantum-well waveguides developed by Tsang and Chuang. Three different configurations of coupled waveguides have been considered: slab, buried-channel, and strip-loaded waveguide directional couplers, where excitonic electrorefraction in multiquantum wells has been utilized to accomplish the switching. The output power-electric field curves calculated by using the above method agree closely in all three cases with similar curves obtained by using a complex propagation constant calculated by a numerical two-dimensional root-searching technique. The present method simplifies the design and optimization of coupled-waveguide devices and its application is illustrated in the case of multiple-quantum-well directional couplers