We develop a complete two-dimension transmission line laser model (TLLM) to analyze the proposed twodimension vertical cavity surface emission laser (VCSEL) based wavelength converter. Modified connecting matrices are used to model the Bragg reflectors. The longitudinal variations of carrier density, photon density and the amplified spontaneous emission noise are taken into account. Therefore, extinction ratio, frequency chirping, optical pulse patterns and dynamic characteristics can be accurately estimated. In this paper, extinction ratio and frequency chirp of the output signal have been calculated for various parameters such as wavelength, input signal power, cavity diameter and facet reflectivity.