Global Optimization of Silicon Nanowires for Efficient Parametric Processes Dragana Vukovic, Jing Xu, Jesper Mørk, Leif Katsuo Oxenløwe, and Christophe Peucheret Department of Photonics Engineering Technical University of Denmark DK-2800 Kgs. Lyngby, Denmark e-mail: drvu@fotonik.dtu.dk Abstract—We present a global optimization of silicon nanowires for parametric single-pump mixing. For the first time, the effect of surface roughness-induced loss is included in the analysis, significantly influencing the optimum waveguide dimensions. Keywords— Silicon nanowires; four-wave mixing. I. INTRODUCTION Silicon-on-insulator (SOI) technology is an attractive platform for nonlinear photonic devices since it enables the design of waveguides with enhanced nonlinearity due to strong confinement, which have been exploited for the demonstration of all-optical signal processing functionalities [1-3]. In particular, the efficiency of parametric processes based on four- wave mixing (FWM) strongly depends on the waveguide nonlinearity and the fulfillment of the phase matching condition, which itself is conditioned to dispersion engineering. Numerous studies have therefore naturally been concerned with the optimization of the dispersion and nonlinear coefficient of various silicon nanowire structures by tailoring the waveguide dimensions [4-7]. However, since the principal loss mechanism in silicon waveguides is scattering loss induced by surface roughness [8], changing the dimensions of the waveguide will affect the field distribution, hence its overlap with irregularities at the core- cladding interface, which in turn will determine the loss. Consequently, the dispersion and nonlinear coefficient optimization cannot be considered independently from the loss. To the best of our knowledge, this effect has not been taken into account in the optimization of silicon nanowires so far. In this paper, we incorporate this new dimension and highlight the impact of scattering loss on the design of silicon nanowire structures optimized for efficient parametric wavelength conversion. We show how taking scattering loss into account in the design affects the optimum waveguide dimensions (both cross-section and length) maximizing the conversion efficiency and, consequently, impacts the achievable conversion bandwidth. II. CONVERSION EFFICIENCY OPTIMIZATION The structure considered in this study consists of a strip waveguide made from a silicon rectangular core on top of a buried silicon oxide layer. The structure is covered with an SU8 polymer upper cladding. The material dispersion of Width [nm ] Height [nm] 200 400 600 800 1000 100 200 300 400 500 50 100 150 200 Width [nm ] 200 400 600 800 1000 2 4 6 a) b) Fig. 1. (a) Nonlinear coefficient (in W -1 ⋅m -1 ) and (b) scattering loss (in dB⋅cm -1 ) for the fundamental quasi-TE mode of the SOI waveguide at 1550 nm. silicon and silicon oxide are accounted for by standard Sellmeier equations while the refractive index of the SU8 upper cladding is taken equal to 1.57. The fundamental quasi- TE 0 mode is considered throughout the study. A vectorial finite-difference mode solver [9] is used to calculate the mode field distribution, from which the effective mode area A eff can be derived by taking into account the non-transverse nature of the mode in the high confinement regime [10]. The nonlinear coefficient γ is then calculated according to γ =2πn 2 /λA eff , where n 2 is the nonlinear refractive index of silicon, taken equal to 6×10 -18 m 2 /W. The calculated nonlinear coefficient is represented as a function of the waveguide core dimensions in Fig. 1(a). As the core size decreases, the evanescent field increases and the fractional power in the cladding can exceed that in the core, resulting in the observed reduction of the nonlinear coefficient for thin and narrow waveguides. The best nonlinear coefficients are achieved for core widths around 400 nm and heights between 200 and 300 nm and reach 235 W -1 ⋅m -1 . Loss in optical waveguides originates from three sources: absorption, radiation and scattering. Scattering loss due to fabrication imperfections, in particular the roughness of the etched surfaces, are dominant in silicon waveguides at 1550 nm. Assuming that only the sidewall roughness contributes to the scattering loss, the model of [8] can be used to calculate the attenuation as a function of the dimensions of the waveguide core. The values of the roughness standard deviation and correlation length used in the calculations are 2 nm and 50 nm, respectively. It is clear from Fig. 1(b) that the loss strongly depends on the waveguide cross section and that the waveguide dimensions minimizing the loss do not coincide with those maximizing the nonlinear coefficient. The loss is The authors acknowledge financial support from Villum Fonden via the NATEC center. 115 ThP6 (Contributed) 17:30 – 17:30 978-1-4673-5804-0/13/$31.00 ©2013 IEEE