Reinhold Pregla

Numerical techniques for modeling guided-wave photonic devices

Accurate modeling of photonic devices is essential for the development of new, higher performance optical components required by current and future high-bandwidth communications systems. This paper reviews several key techniques for such modeling, many of which are used in commercial design tools. These include several mode-solving techniques, the beam propagation method, the method of lines, and the finite-difference time-domain technique.

Hybrid-Mode Analysis of Arbitrarily Shaped Planar Microwave Structures by the Method of Lines

This paper presents a method for analyzing arbitrarily shaped planar microwave structures, which is based on the method of lines and applies to both resonant and periodic structures in microstrip, slotline, and finline circuits. Numerical results are presented for some selected structures.

Beam-propagation algorithm based on the method of lines

We extend the method of lines [ ItohT., ed., Numerical Techniques for Microwave and Millimeter Wave Passive Structures ( Wiley, New York, 1989), pp. 381– 446] for application as a beam-propagation algorithm with absorbing boundary conditions. We thus avoid reflections from the computational window edges. The new algorithm has in principle none of the restrictions of standard beam-propagation methods (propagation under paraxial conditions in low-contrast media and relatively small propagation steps) and is applied to planar waveguides with high-refractive-index steps (e.g., straight or S-bend slab waveguides) and to rib waveguides.

Method of lines for the analysis of dielectric waveguides

This paper is concerned with the application of the method of lines (MoL) to the analysis of general dielectric waveguides that are uniform along the direction of propagation, lossfree, and passive. Hybrid-mode dispersion curves, field and intensity distributions for integrated optical waveguides are presented. >

Comparison of optical VCSEL models on the simulation of oxide-confined devices

We compare the results of different optical vertical-cavity surface-emitting laser models on the position-dependent effects of thin oxide apertures. Both scalar and vectorial models as well as hybrid models are considered. Physical quantities that are compared are resonance wavelength, threshold material gain, and modal stability. For large device diameters and low-order modes, the agreement between the different models is quite good. Larger differences occur when considering smaller devices and higher order modes. It is also observed that the spread in the resonance wavelengths is smaller than that for the threshold material gain.

Efficient analysis of periodic structures

An algorithm which allows the analysis of optical periodic structures with a very large number of periods with minimum numerical problems is presented, For this purpose the stable impedance transfer is combined with Floquets theorem. Numerical results for a Bragg grating with up to 20000 periods are presented featuring the very moderate numerical effort.

Method of lines for the analysis of strip-loaded optical waveguides

The analysis of planar strip-loaded optical waveguides with the vectorial method of lines is described. The main feature of this method is its semianalytical approach, which yields accurate results with less computational effort than other techniques. Hybrid-mode dispersion curves and field and intensity distributions of a sample waveguide are presented.

Analysis of a deep waveguide Bragg grating

Spectral properties of a very deep Bragg grating operating in a first diffraction order on a single-mode planar waveguide have been studied theoretically. It is shown that the scattering loss can be low (a few percent), the reflectivity very high (over 90%), the reflection band is shifted against the ‘Bragg’ wavelength toward the shorter wavelengths, and its spectral shape is very different from that of a shallow grating. Inside a reflection band, a part of the input optical power penetrates through the grating even if it is infinitely long. These properties are predicted by modelling using two independent computer codes based on different modelling methods, namely the bi-directional mode expansion and propagation method (BEP), and a method of lines (MoL). The first method is discussed in some detail here. The work has been performed within the framework of European Action COST 240.

The method of lines for the analysis of dielectric waveguide bends

The analysis of a wide class of waveguide bends using the method of lines is suggested. The discretization is performed in radial direction. The cross section of the waveguide may consist of many inhomogeneous layers. Loss can be taken into account by using complex permittivities. The radiation loss is calculated by the use of absorbing boundary conditions. The presented algorithm is verified by the analysis of a rib waveguide bend. The results are in good agreement with those published in the literature.

The analysis of general axially symmetric antennas with a coaxial feed line by the method of lines

The use of the method of lines in the analysis of various circular antennas-circular patch antennas and various forms of monopoles is proposed and substantiated. The antennas considered are fed by coaxial lines. Impedance/admittance transfer procedures are developed, which allow to calculate the antenna input impedance by a successive transfer from the aperture through the different sections. The described relations are also useful for other applications.