1762 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 9, SEPTEMBER 2002 Air Trenches for Sharp Silica Waveguide Bends Miloˇ s Popovic ´ , Student Member, IEEE, Kazumi Wada, Shoji Akiyama, Hermann A. Haus, Life Fellow, IEEE, Fellow, OSA, and Jürgen Michel Abstract—Air trench structures for reduced-size bends in low- index contrast waveguides are proposed. To minimize junction loss, the structures are designed to provide adiabatic mode shaping be- tween low- and high-index contrast regions, which is achieved by the introduction of “cladding tapers.” Drastic reduction in effec- tive bend radius is predicted. We present two-dimensional (2-D) finite-difference time-domain/effective index method simulations of bends in representative silica index contrasts. We also argue that substrate loss, while present, can be controlled with such air trenches and reduced to arbitrarily low levels limited only by fabri- cation capabilities. The required trench depth, given an acceptable substrate loss, is calculated in three dimensions using an approx- imate equivalent current sheet method and also by a numerical solver for full-vector leaky modes. A simple, compact waveguide T-splitter using air trench bends is presented. Index Terms—Air trench bend (ATB), cladding taper, enhanced lateral mode confinement, low-index contrast, sharp bend loss, silica waveguide. I. INTRODUCTION L OW-INDEX contrast silica bench technology—referred to as planar lightwave circuit (PLC) or silicon optical bench (SiOB)—has gained widespread use in practice in the fabrica- tion of passive integrated optical components by virtue of its use of well-tested integrated-circuit industry manufacturing pro- cesses and technology [1]. Large silica waveguide cross sections offer low fiber-to-chip coupling and propagation losses. A major drawback of SiOB technology is the relatively large component size, where a critical factor is the minimum waveguide bend ra- dius. This radius is large—normally in the millimeters—in the low-index contrasts 0.25%-1.5% found in silica [1]. The low density of integration keeps production cost high and invites yield problems. On the other hand, high-index contrast, such as silicon-on-insulator (SOI)—while offering dense inte- gration, poses challenges of fiber-to-chip insertion loss due to mode shape mismatch and misalignment, scattering loss, and sensitivity to other fabrication defects and tolerances, as well as fabrication processing challenges. Manuscript received November 5, 2001; revised June 12, 2002. This work was supported in part by the Materials Research Science & Engineering Cen- ters (MRSEC) Program of the National Science Foundation under Award DMR 98-08941, by a Natural Sciences and Engineering Research Council (NSERC) of Canada PGS-A scholarship, and by a National Partnership for Advanced Computing Infrastructure (NPACI) supercomputer allocation. M. Popovic ´ and H. A. Haus are with the Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: milos@mit.edu). K. Wada, S. Akiyama, and J. Michel are with the Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA. Digital Object Identifier 10.1109/JLT.2002.802230 A technology that allows a drastic reduction in the bending ra- dius would overcome one of silica’s major obstacles to attaining truly large-scale optical integration. We propose a scheme using air trenches to provide locally enhanced lateral mode confine- ment. We use adiabatic tapering to avoid abrupt junction-in- duced mode mismatch and Fresnel reflection in order to minia- turize optical waveguide bends while preserving low-loss per- formance [13]. In the last 30 years, much attention has been devoted to the de- sign of waveguide bends and the proper analysis of their losses [2]–[5], [11], including the use of air trenches. More recent con- tributions include “deep etching” in InP-ridge waveguide bends [6], and a proposal of more unconventional, low- cavity bends in high-index contrast, such as SOI [7]. Air trenches have been proposed for suppressing bend radia- tion in several ways [6], [10]. When they are used to enhance lat- eral mode confinement, mode mismatch-induced junction loss is incurred at points of abrupt change in refractive index and/or cross-sectional waveguide geometry, limiting the success of the approach [6], particularly in low-index contrast. To our knowl- edge, no attempt has been made to use air trenches to improve bending loss in low-index contrast by properly addressing the mode-mismatch issue introduced by the present air trench, to produce small, low-loss bends. We use judiciously placed air trenches for sharp bending with adiabatic transition to mitigate junction loss. It is generally recognized that adiabatic mode shaping results in low-loss tapers and directional couplers (e.g., see [8]). In this paper, we introduce a pair of “cladding tapers” as an integral part of the etched air trench at the bend (Fig. 1) in order to provide fast mode transition to and from the high-index con- trast trench region with low radiation loss and low reflection. The main high-index contrast region in this case contains the waveguide bend. The result is a reduction in bending radius by a factor of 10–1000 and in total bend structure edge length by a factor of 4–60. The theoretical justification for the proposed idea is presented primarily in terms of two-dimensional (2-D) finite-difference time-domain (FDTD) simulations of air trench bends (ATBs) with index contrast between 0.25% and 7%. In Section II, we describe the ways in which air trenches have been used in prior work and justify our approach to the problem in low-index contrast. In Section III, we first show the perfor- mance and physical size of a regular waveguide bend, without air trenches, for a set of chosen index contrasts. We then de- scribe the method used to produce the ATB structure designs, and, in Section IV, we show 2-D simulation results, including dimensions and performance. In Section V, we discuss mode confinement issues that are important in properly accounting for 0733-8724/02$17.00 © 2002 IEEE