Analysis of leaky modes in deep-ridge waveguides using the compact 2D FDTD method

Abstract

The compact 2D finite difference time domain method combined with the uniaxial anisotropic perfectly-matched-layer (UPML) absorption boundary condition and the Padé approximation transform has been employed in a novel method to analyse leaky modes in deep-ridge semiconductor waveguides. Compared with frequency-domain mode solvers based on complex root searching, this method is easy to implement and can calculate the mode loss and the propagation constant separately and reliably.Introduction: Deep-ridge waveguides have been widely employed to fabricate semiconductor devices such as arrayed waveguide gratings (AWGs) and Mach-Zehnder (MZ) modulators. A general concern with deep-ridge waveguides is that owing to their strong lateral optical confinement it is easy to induce higher-order lateral modes, which could degrade the device performance. To control these leaky modes the leaking loss must be well determined. The mode leaking loss can be calculated from the imaginary part of the mode effective index, which is generally several orders of magnitude smaller than the real part. It is rather challenging to accurately calculate such complex effective mode indices with such small imaginary parts through numerical simulations. Several methods have been used to solve this problem, such as the finitedifference method [1], the imaginary beam propagation method based on the finite-element scheme [2, 3], the eigen-equation solving method based on the finite-element scheme [4,5], and the spectral index scheme [6]. These methods search the complex effective indices in the complex plane through iteration processes and are generally initial-guess sensitive. A method based on real propagation has also been used to estimate the leaking loss [7]. In this Letter, the compact 2D finite difference time domain (FDTD) method [8] is employed to analyse the higher-order leaky modes in deep-ridge semiconductor waveguides. The compact 2D FDTD method is a full vectorial method based on the finite-difference scheme which treats the 3D waveguide as a 2D cavity. The 2D cavity resonance modes represent the 3D propagation modes of the waveguide. To employ the FDTD method to solve for the leaky modes, two points are very important: one is the absorption boundary condition (ABC); the other is the transforming tool which changes the FDTD data from the time domain to the frequency domain. For the first point, the so-called uniaxial anisotropic perfectly-matched-layer (UPML) [9] boundary conditions were adopted in the simulation to efficiently truncate the FDTD lattices. For the second point the Padé approximation transform (PAT) [10] was used which can obtain high spectral resolution through short FDTD data sequences. Through the compact 2D FDTD method, combined with the PAT technique, the mode loss can be calculated separately from the mode propagation constant, which we think is a significant advantage when compared with the frequency-domain complex-root searching methods.

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