3392 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 12, DECEMBER 2003 Rigorous Beam Propagation Analysis of Tapered Spot-Size Converters in Deep-Etched Semiconductor Waveguides B. M. A. Rahman, Senior Member, IEEE, W. Boonthittanont, S. S. A. Obayya, T. Wongcharoen, E.O. Ladele, and K. T. V. Grattan Abstract—A rigorous study of a tapered spot-size converter in a deep-etched GaAs/AlGaAs optical modulator is reported through the use of full vectorial approaches. Mode beating in the tapered section, the expansion of the spot-size, and the consequent enhance- ment of the coupling to an optical fiber are also reported. Index Terms—Beam propagation method, finite-element method, optical coupling, spot-size converters. I. INTRODUCTION I N the design of semiconductor optical waveguides, power splitters, bends, lasers, modulators, and amplifiers, two dif- ferent manufacturing technologies creating different design ap- proaches are often used. The first type, the shallow rib type de- signs [1], [2], are more widely used; however, the performance of the devices often critically depends on the etch depth, and in this approach, the resulting optical mode shape is also diffi- cult to control. On the other hand, by deep-etching through and beyond the core to part of the lower cladding [3], the modal be- havior of the structure would be less sensitive to the etch depth. Besides, due to the strong horizontal confinement, the bending losses would be greatly reduced [4], [5] and consequently a more compact optoelectronic system design would be possible, which will lead to an increased functionality of the subsystems than would be allowed by using the shallow-etching approach. This type of deep-etched waveguide structure has been used for the design of multimode interference (MMI)-based power split- ters [6], [7], delay lines, and high-speed modulators [8]. For many semiconductor devices, such as lasers, modulators, and amplifiers, their optical spot-sizes are small in size and often highly nonsymmetrical. If such a device is directly butt-coupled to a single-mode fiber (SMF), which has a much larger and cir- cular field profile, often 90% or more of the optical power would be lost due to the mismatch between their field profiles. In the design of a deep-etched semiconductor waveguide, effectively single-mode operation is possible [3] for a much wider wave- guide by controlling the lower cladding index to radiate out all the higher order modes. In this case, the resulting spot-size is Manuscript received May 29, 2003; revised September 3, 2003. This work was supported by EPSRC. B. M. A. Rahman, W. Boonthittanont, S. S. A. Obayya, E. O. Ladele, and K. T. V. Grattan are with the School of Engineering and Mathematical Sciences, City University London, EC1V 0HB London, U.K. (e-mail: B.M.A.Rahman@ city.ac.uk). T. Wongcharoen is with Bangkok University, Bangkok, Thailand. Digital Object Identifier 10.1109/JLT.2003.821753 slightly bigger and more symmetrical, but not yet comparable with that of a SMF. As an example, in the design optimization of high-speed GaAs modulators [8], often values of the wave- guide core width of between 3.0 to 5.0 m with heights between 1.5 to 3.0 m are used, which may yield 30-40% coupling ef- ficiency. However, these spot-sizes need to be improved further to reduce significantly the coupling loss with the SMFs and to minimize the packaging costs. Recently, in the design of a semiconductor photonic compo- nent or a subsystem, monolithically integrated spot-size con- verters (SSCs) have often been incorporated to improve the cou- pling efficiency along with the much relaxed alignment toler- ances. In the design of such an SSC, often the primary guide is tapered down [9]–[13] to push the mode to the secondary guide, which is designed to have a similar spot-size to that of a SMF. In this work, a SSC converter compatible with deep-etched semi- conductor photonic components is investigated, by using rig- orous vectorial approaches to study the spot-size transformation and the resultant enhancement of the coupling efficiency. II. NUMERICAL METHOD The expansion of the spot-size is often achieved by reducing the core dimension to a sufficiently small value [9]–[13] so that the primary guide cannot support any guided mode and consequently the optical power is pushed out of this core to a secondary core. Often a closely spaced twin-core superstructure may be used, with one core being axially nonuniform and the resultant waveguide cross-section can be quite complex in shape. To study the mode-shape and the evolution of the optical beam, both a modal solution and a beam propagation-type evolutionary approach would be necessary. Over the last two decades, many numerical methods have been reported for the eigenmode solutions of the optical waveguides. However, many of these approaches would not be accurate for optical waveguides operating near their modal cutoff conditions. In this respect, the -field based full-vectorial finite-element method (FEM) [14] has established itself as one of the most rigorous full vectorial approaches for the characterization of a wide range of optical waveguides [14], [15]. In the FEM approach, the waveguide cross section is represented by a large number of triangles, and since these triangles could be of different shapes and sizes, any waveguide cross-section can be accurately represented. The full vectorial -field formulation (VFEM) is used here, which allows each of these elements to have different 0733-8724/03$17.00 © 2003 IEEE