Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system

Abstract

By analyzing the propagating behavior of the supermodes in a coupled-waveguide system, we have derived a universal criterion for designing adiabatic mode transformers. The criterion relates , the fraction of power scattered into the unwanted mode, to waveguide design parameters and gives the shortest possible length of an adiabatic mode transformer, which is approximately 2/ 1/2 times the distance of maximal power transfer between the waveguides. The results from numerical calculations based on a transfer-matrix formalism support this theory very well. [7,8]. Two schemes have been implemented to realize the mode transformationresonant coupling and adiabatic coupling. In a resonant coupler, by designing the coupling region to be of a half beat length, the light transfers from one waveguide to the other [8]. The coupler length can be made very short in this manner; however, it is practically difficult to determine the exact beat length, rendering the efficiency of power transfer uncertain and the resulting devices of dubious value. An adiabatic coupler, on the other hand, does not require a precise definition of power-transfer length [1,9,10], but it has to be sufficiently long to satisfy the adiabatic condition to reduce the coupling of power into other unwanted modes. Clearly a longer coupler not only reduces the component density but also suffers from higher transmission losses and higher probability of material defects and fabrication imperfections. The optimal design procedure of adiabatic mode transformers has been proposed in different ways. Love et al. first studied the fiber tapers, suggesting that for a given taper length the optimal delineating curve should have the local taper angle inversely proportional to the local beat length [1,11]. This design principle was also employed in experiments [10,12]. Another design concept is based on equalization of the "single-step loss" (defined as the overlap integral of the modes in two adjacent segments) along the taper [13,14]. Based on the stationary field distributions rather than the wave propagation behavior, those analyses did not point out the shortest taper length with which a certain coupling efficiency could be achieved. In this Letter we derive a universal criterion for the adiabatic mode transition in a coupledwaveguide system and suggest the shortest length of an adiabatic mode transformer for a given maximal tolerated scattering from the wanted mode into other modes during power transfer.The mode transformer to be analyzed here is based on a coupled-waveguide system shown in Fig. 1. It consists of two waveguides, waveguide 1 and waveguide 2, placed in close proximity to each other. The refractive index or geometry of at least one waveguide is gradually varied along the propagation direction z. Light is coupled into this transformer at input plane z = z i ͑=0͒ and out at output plane z = z f . The normalized local modes (or "supermodes"), denoted as e e for the even mode and e o for the odd mode, of this coupled-waveguide system are expressed as col...

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