A variational mode expansion mode solver

Abstract

A variational approach for the semivectorial modal analysis of dielectric waveguides with arbitrary piecewise constant rectangular 2D cross-sections is developed. It is based on a representation of a mode profile as a superposition of modes of constituting slab waveguides times some unknown continuous coefficient functions, defined on the entire coordinate axis. The propagation constant and the lateral functions are found from a variational principle. It appears that this method with one or two modes in the expansion preserves the computational efficiency of the "standard" effective index method while providing more accurate estimates for propagation constants, and well-defined continuous approximations for mode profiles. By including a larger number of suitable trial fields, the present approach can also serve as a technique for rigorous semivectorial mode analysis.

Multi-domain spectral method for modal analysis of optical waveguide

“…The used parameters are w = 4 µm, h = 3 µm, n s = 1.506, and n c = 1.512 at 1.32 µm wavelength. Table 9 shows the QTE effective indexes for the studied 3D coupler waveguide as obtained by the presented method (MDSM) and by various previously published methods Ivanova et al (2007). As can be observed, the results of the different methods highly agree with each other.…”

“…The parameters of this rib waveguide are shown in Table 5 and the used wavelength is 1.15 µm. This structure has been studied heavily for numerical methods comparisons (Ivanova et al 2007;Vassallo 1997Vassallo , 1995Hadley and Smith 1995;Koshiba et al 1994;Huang and Xu 1993;Vassallo and Wang 1990;Stern et al 1990;Rahman and Davies 1985). In this paper, the results presented by Vassallo (1997) as normalized propagation constant β and obatained using Modal transverse resonance method (MTRM) are used for comparison, where …”

“…7. It was studied recently by Ivanova et al (2007) using various methods. The used parameters are w = 4 µm, h = 3 µm, n s = 1.506, and n c = 1.512 at 1.32 µm wavelength.…”

“…It can be represented as eigenmode expansion or matrixes exponential. Variational Mode Expansion (VME) (Ivanova et al 2007) is another mode expansion method. As can be noticed from the name, the modes are approximated using functional variational procedure.…”

Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment

“…Assuming a separable form of the respective principal field component, one arrives at an EIM-like procedure through a second restriction step. The formalism is similar to what has been applied in the context of scalar and vectorial mode solvers in Ivanova et al (2007Ivanova et al ( , 2008Ivanova et al ( , 2009). …”