FOURIER-ANALYSIS AND SYNTHESIS OF ADIABATIC TAPERS IN INTEGRATED-OPTICS

Tapered optical waveguides are of increasing importance for use as mode-size transformers in integrated optics. We present a new Fourier integral interpretation of the first-order coupled-local-mode theory of the mode-conversion loss in adiabatically tapered waveguides that provides a new degree of perspective on taper behavior. On the basis of this interpretation, we introduce a technique for synthesizing tapers with desired length-versus-loss characteristics. Since this technique involves a Fourier integral, we are able to take advantage of the existing substantial body of literature on filter design. We demonstrate this new technique by analyzing and synthesizing two examples of taper structures, a tapered directional coupler and a mode-size controller, and introduce a class of (near-) optimal tapers from this synthetic approach. We also prove the adiabaticity theorem in tapered waveguides, starting from Maxwell's equations, on which our first-order perturbation approach is premised.