I. Introduction
Vertical-cavity surface-emitting lasers (VCSELs) possess characteristics such as low power consumption, circular beam output for efficient laser-fiber coupling, single longitudinal mode lasing, and scalability in two-dimensional arrays. Therefore they are suitable to be used in combination with multimode fibers as the low-cost solutions for short-haul optical data communication [1]. To satisfy the need for rack-to-rack communications in large data centers which require error-free transmission over long-distance fiber links at high data rate, it is crucial to employ VCSELs with single transverse mode or narrow spectral width for reduced modal and chromatic dispersion so that signal integrity can be maintained [2]. For conventional oxide-confined VCSELs [3], the common practice is to reduce the oxide aperture diameter so that the higher order modes are cut off. Such approach has enabled error-free transmission at 17 Gb/s over 1-km OM3 MMF [4] and 25 Gb/s over 600-m [5]. For the conventional oxide-confined VCSEL, the oxide aperture in the mirror is also used for current confinement, so reduced current aperture size implies increased operating current density, which is detrimental to device lifetime [6]. Moreover, small aperture VCSELs exhibit series resistances in excess of the maximum values allowed by standard drivers, and at very small aperture sizes, a small composition nonuniformity of the oxide layer across the wafer will reduce the yield of the VCSELs with uniform parameters. Transverse mode control such as a shallow surface relief can also reduce the number of transverse modes and such VCSELs have demonstrated 25 Gb/s error-free transmission over 500-km [7], though the current density exceeds the 10- industrial benchmark for high-reliability operation [6].