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Optica Publishing Group
  • Conference on Lasers and Electro-Optics
  • OSA Technical Digest (Optica Publishing Group, 1993),
  • paper CTuM7

Modal reflectivity of quarterwave mirrors in vertical-cavity lasers

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Abstract

The cavities of vertical semiconductor lasers are as long as a few wavelengths and typically involve quarterwave mirror (QWM) or bulk sections with no lateral waveguiding. Very high plane-wave reflection coefficients can be oh tamed with practical semiconductor QWMs, but for beams of finite width, the reflectivity of a mirror with no lateral guiding will be limited by diffraction. This is particularly pronounced in long wavelength vertical cavity lasers (VCL) with epitaxial mirrors fabricated using InGaAsP/InP, where due to the larger mirror penetration depth and the longer wavelength, the modal reflection is much smaller than in AlAs/GaAs mirrors. We have quantitatively verified this by calculating the modal reflectivity of both of the mentioned QWMs. A simplified vertical cavity laser structure used in this analysis is shown in Figure 1; it consists of a waveguide and a laterally-unguided QWM. The incident field pattern is defined by the top waveguide, while the reflected field is calculated by a linear superposition of the plane waves reflected from the QWM at various angles and. polarizations. We consider the fundamental and first higher mode of a cylindrical dielectric waveguide (core index = 3.17, air cladding), and the three lowest order modes of a cylindrical metal waveguide. The calculations have been performed for tire mirrors listed in Fig. 1, and the results for the dielectric waveguide case are shown in Figures 2 and 3. It is evident that, for AlAs/GaAs mirrors at 980 nm, the modal reflection is very high even for diameters as small as 5 μm. The calculated influence of diffraction in the modal reflection agrees well with the experiments performed by Lee et al.1 The coupling loss of long wavelength InGaAsP/InP mirrors is an order of magnitude larger for all diameters. It is clear that for small mode diameters (<15 μm), these mirrors must be guided to provide the reflectivities necessary in practical VCLs.

© 1993 Optical Society of America

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