Jan Haes

The bidirectional mode expansion method for two-dimensional waveguides : the TM case

The mode expansion propagation method is a modelling technique for a large variety of waveguide components. Until now only the case with TE modes has been reported; we give details on the mode expansion propagation method for TM modes. Instead of one type of overlap integral in the TE case, a TM analysis requires two kinds of overlap integrals. The inclusion of radiation modes in this method is discussed. The modifications in the algorithm to include waveguides with gain or loss structures are also considered.As an example, the method was used for analysing a grating-assisted codirectional coupler. In particular, the radiation loss is calculated and compared with calculations when TE modes, instead of TM modes, propagate through the codirectional coupler. The radiation losses are found to be much higher for TM modes.

Monolithic integration of a spot size transformer with a planar buried heterostructure InGaAsP/InP-laser using the shadow masked growth technique

We present a vertically tapered InGaAsP/InP planar buried heterostructure (PBB) laser for low loss coupling to single-mode fibers. To achieve the vertical tapering we make use of the shadow masked growth technique. Tapered lasers with beam divergences of 15/spl deg/ in both lateral and transverse directions were realized. In comparison with untapered lasers, the coupling losses to cleaved single-mode fibers could be reduced by 4.8 dB down to 5.8 dB.<<ETX>>

Confinement and modal gain in dielectric waveguides

Two exact expressions are derived for the effective mode indices of dielectric slab waveguides with complex refractive indices. One is for TE modes, the other for TM modes. The identities are valid for any guided mode of any dielectric slab waveguide and can be successfully employed to check the accuracy of mode solvers. They explain why TE gain can be much greater than TM gain even when the confinement factors are comparable. Also, it is shown that an often used approximation for the TM gain is unreliable under practical conditions. A correct approximation is given.

A comparison between different propagative schemes for the simulation of tapered step index slab waveguides

The performance and accuracy of a number of propagative algorithms are compared for the simulation of tapered high contrast step index slab waveguides. The considered methods include paraxial as well as nonparaxial formulations of optical field propagation. In particular attention is paid to the validity of the paraxial approximation. To test the internal consistency of the various methods the property of reciprocity is verified and it is shown that for the paraxial algorithms the reciprocity can only be fulfilled if the paraxial approximation of the power flux expression using the Poynting vector is considered. Finally, modeling results are compared with measured fiber coupling losses for an experimentally realized taper structure.

Spot size expansion for laser-to-fiber coupling using an integrated multimode coupler

Efficient coupling of light from a semiconductor waveguide to an optical fiber is difficult to achieve due to the inherent differences in the spot sizes. The problem is particularly severe in the vertical dimension. The use of a uniform, untapered, intermediate coupler structure which consists of a multimode waveguide is proposed. This structure has potential for integrating with the semiconductor waveguide. The basic design rules for this coupler are worked out using coupled-mode theory, and the detailed designs are based on direct calculation of the mode profiles in the coupler. A range of realistic examples is examined, and it is shown that the butt coupling efficiency from a typical semiconductor laser to an optical fiber can be improved by up to 5 dB. The dependence of performance on fabrication tolerances is also studied. >

Difference between TE and TM modal gain in amplifying waveguides: analysis and assessment of two perturbation approaches

The commonly used confinement factor-based formula for modal gain in amplifying waveguides – gmod=Γgmat, with Γ a confinement factor – is well established and accurate for TE modes. The TM case is rarely, and sometimes erroneously, described in the literature. Using a variational formulation the fundamental difference between TE and TM modal gain is illustrated. An accurate expression, correct up to first order, for the TM modal gain is then derived from a known general perturbation formula. However, as this does not lead to a true confinement factor formulation, some approximations are introduced, leading to a unified formulation of both TE and TM modal gain. A second method to calculate the modal gain, based on the analyticity of the dispersion equation, is also discussed. Simulation and comparison with modal gain values from a complex mode solver will finally illustrate the validity of the different approaches.

Design of adiabatic tapers for high contrast step index waveguides

Tapered waveguides are frequently used to obtain a good matching between the modes of two butt coupled waveguides having different guiding properties. The design of these tapered waveguides is in most cases conservative because of the lack of precise modelling guidelines and accurate modelling tools. This paper discusses in the first place a quantitative approach for taper design by considering the whole taper with arbitrary shape as a succession of short linear taper fragments. As a result that radiation loss per relative thickness reduction as a function of index contrast, taper angle and thickness is obtained. These simulations require a highly accurate beam propagation method (BPM) able of handling large index contrasts and thereby principally exceeding the applicability range of paraxial algorithms. Therefore a novel BPM which solved directly the non-paraxial 2D Helmholtz equation by decomposing an arbitrary input field in local eigenmodes of the waveguide is used.

Monolithic integration of a single quantum well laser diode and a mode-size convertor using shadow-masked metalorganic vapour phase epitaxial growth

Abstract In this paper we propose the monolithic integration of quantum well InGaAs/GaAs 0.98 μm lasers with passive mode-size convertors using the shadow-masked growth technique. The full width at half maximum (FWHM) of the far-field in the transverse direction could be reduced from 47° to 30° without a significant increase of Ith and even a slight increase of νd. Values down to 21° could be reached although a small penalty in threshold current had to be paid. Along the tapered sections, a bandgap increase up to 130 meV has been measured providing transparent windows near the laser facets. Adjusting the nominal layer structure of the laser should allow the realization of reliable 0.98 μm pump lasers for erbium-doped fibre amplifiers showing an improved coupling efficiency in single mode fibres and an enhanced reliability.

Benchmark tests and modelling tasks

In this chapter we describe benchmark tests and modelling tasks to mutually compare the performance of various beam propagation methods and other software developed and/or currently in use in various laboratories. Two sets of tasks for testing the behaviour of beam propagation methods applied to both lossless and lossy (absorbing) waveguide structures are described in the next section. Theoretical background required to understand the latter task is presented in Section 3.2. Then, an important problem of modelling light propagation in waveguide tapers, both symmetric and asymmetric, is discussed in Section 3.3. Comparative modelling of an example of optical waveguide devices containing thin metal films that can support propagation of surface plasmon waves is described in Section 3.4. In the last section, results of truly bi-directional modelling of light propagation in a very deeply etched Bragg waveguide grating filter are presented. The work described in this chapter was organised within the framework of the Action COST 240.

Analytical study of birefringence in slab waveguides

For a number of optoelectronic components it is important to estimate the amount of waveguide birefringence in order to reduce or eliminate a possible polarization dependence. Several important structures (e.g. buried or ridge) can be analysed with sufficient accuracy by the effective index method which reduces the original 2-D problem to two 1-D problems. We therefore look at waveguide birefringence for the 1-D case.