Direct Measurement of VCSEL Transverse Mode Correlation and <inline-formula> <tex-math notation="LaTeX">$k_{\mathrm {mpn}}$ </tex-math></inline-formula>

Abstract

The correlation properties of vertical-cavity surface-emitting laser (VCSEL) transverse modes determine the noise impairments of VCSEL-based high-speed links. The cross-correlation statistics between VCSEL mode pairs and the autocorrelation statistics for each VCSEL mode are directly measured using real-time 40GSs synchronous observations of spatially separated modes. Anticorrelation was found to be different for different mode pairs along with some positive correlations between modes, contradicting the assumptions of the IEEE model for mode partition noise in VCSEL multimode fiber links. These correlation results are used to estimate the mode partition parameter $k_{\mathrm { {mpn}}}$ yielding different values of $k_{\mathrm { {mpn}}}$ for the same VCSEL at the same bias, again in contrast with the IEEE model assumption.