Application of modified finite-difference formulas to the analysis of z-variant rib waveguides

Abstract

Abstract-Modified finite-difference formulas for a general position of an interface are applied to the propagating beam analysis of -variant rib waveguides. The modified formula based on the semivectorial H-field is found to be more insensitive to variation in an interface position than that on the E-field. A discretization error is satisfactorily reduced in tilted and tapered rib waveguides.

Analysis of rib waveguides by a fourth‐order accurate finite‐difference beam‐propagation method

“…(17) is approximated in Eqs. (14) and (15) If the refractive index profile is uniform, the improved finite-difference formula coincides with the finitedifference formula derived from the conventional Taylor series expansion. Therefore, the algorithm of the improved finite-difference formula can be used regardless of existence of the refractive index discontinuity.…”

“…In the formulation, the alternate direction implicit method (ADIM) is used, resulting in an accurate and fast three-dimensional BPM, while the advantage that the discontinuity position of the refractive index can be chosen arbitrarily is utilized [13,14].…”

“…In the present paper, a three-dimensional analysis [12] using the fourth-order improved accuracy finite-difference formulation (IFD4) for the electric or magnetic field component is discussed in detail. In the formulation, the alternate direction implicit method (ADIM) is used, resulting in an accurate and fast three-dimensional BPM, while the advantage that the discontinuity position of the refractive index can be chosen arbitrarily is utilized [13,14].…”

Finite difference split step method for non-paraxial semivectorial beam propagation in 3D

“…A full vectorial analysis would require a large computational effort; however, in most devices, the index contrast is only moderately high and a semivectorial approach can be used. As such several semivectorial methods have been developed which are mainly used for modal analysis of devices or for low angle propagation (Stern 1988a,b;Vassallo 1992Vassallo , 1997Kim and Ramaswamy 1989; D. Bhattacharya · A. Sharma (B) Physics Department, Indian Institution of Technology Delhi, New Delhi 110016, India e-mail: asharma@physics.iitd.ac.in Hoekstra et al 1992;Wijnands et al 1995;Yamauchi et al 1997Yamauchi et al , 2000Liu et al 1993;Mitomi and Kasaya 1998). Few semivectorial methods have been used for wide-angle beam propagation but only in devices with low index contrast (Shibayama et al 2006a,b).…”

A Computational Solution of Natural Convection Flow in a Rotating Fluid with Radiative Heat Transfer

“…The temperatures involved are assumed to be very high so that the radiative heat transfer is significant, which renders the problem highly non-linear even with the assumption of a differential approximation for the radiative heat flux. Yamauchi et al [8] presented modified finite-difference formulas for a general proposition of an interface that they applied to the propagating beam analysis of z-variant rib waveguides. They observed that a discretization error is satisfactorily reduced in tilted and tapered rib waveguides.…”