Bart Demeulenaere

Confinement factors and gain in optical amplifiers

A new identity is derived which relates the gain and the field distribution (or confinement factor) in a dielectric waveguide with complex refractive indices. This identity is valid for any guided mode of waveguides with an arbitrary cross section. It provides a new check of the accuracy of mode solvers. Also, it can be used in a variational approach to predict the gain or loss of a guided mode based on knowledge of confinement factors. It is shown that a previous analysis that is often used, is not correct. In addition, approximate expressions for the gain in slab waveguides are presented.

Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized modal performance

We present a numerical optical model for calculating threshold material gain in vertical-cavity surface-emitting lasers. It is based on a vectorial solution of Maxwells equations and therefore gives exact results where other approaches fail, e.g., in the case of oxide-confined devices, which have high lateral index contrasts. Results are given concerning the influence of oxide window thickness and position on threshold gain and modal stability. We also propose an intuitive plane-wave model to enhance the physical understanding of these effects.

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.

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.

Simulation results of transverse-optical confinement in airpost, regrown, and oxidized vertical-cavity surface-emitting laser structures

Based on a numerical optical model for calculating threshold material gain in vertical-cavity surface-emitting laser, we investigate the influence of transverse-optical confinement in airpost, regrown, and oxidized structures. In each of these cases, we demonstrate the trade-off that needs to be made between low threshold for the fundamental laser mode and good modal stability.

Design of AlAs-oxidized VCSELs with stable fundamental mode operation

We show that and explain why thin oxide apertures at a node of the optical standing wave pattern enhance stable fundamental mode operation in VCSELs as large as 12 /spl mu/m in diameter.

Rigorous optical VCSEL modelling based on vectorial eigenmode expansion

To enable the further improvement of VCSEL properties, an accurate optical model is needed to study the effects of transverse optical confinement on threshold gain and modal stability. An important example in this respect is the choice of the thickness and the position of an oxide aperture in the design of high-performance VCSELs. We will present different approaches for the optical modelling of these devices based on vectorial eigenmode expansion techniques. These approaches take the vectorial nature of Maxwells equations into account and are therefore fully rigorous, even in the case of devices that are small compared to the wavelength or devices with high index contrasts, as is the case in oxide-apertured devices.

Design of polarisation selective grating structures for surface emitting lasers

posed structures of Au/GaAs polarizerloaded AlAs/GaAs DBR. We define the electric field E, and E/, which are perpendicular and parallel to the grating, respectively. This polarizer has a birefringence in two orthogonal polarization states. Then we can expect the reflectivity decrease for E,/ to control the phase by changing the thickness of polarizer. We show the reflectivity spectrum of samples measured from substrate side. A reflectivity difference for two polarization states is observed due to birefringence. But both the reflectivities have the dip at the cavity resonance wavelength. We examined another type of polarizer as shown in Fig. 2(a), where a X/2 GaAs layer in the DBR of this structure is introduced to make the phase of lasing polarization match to the DBR center. Figure 2(b) shows measured reflectivity spectra for two polarizations. Compared to Fig. l(b), differential reflectivities are obtained for two polarizations. The result shows that the fabricated polarizer is transparent for E,, which is in good agreement with our expectations based on LAMIPOL concept? Further optimization of the polarizer and application to 0.98 km VCSELs are now under study. In conclusion, we present its design and have fabricated a novel Au/GaAs polarizer for polarization control. Bragg wavelength discrimination in reflectivity