Transistor laser can drive recent innovative technologies like optical antennas and rectennas. To this end, this semiconductor device requires an accurate electromagnetic model capable of determining the antenna characteristics like radiation pattern, directivity, gain, bandwidth, and polarization. Nonetheless, the current semiconductor models of transistor laser describe the absorption and emission of light mainly by simplified expressions and circuit models. These models usually overlook the actual physical geometry and full-wave light-emitting analysis of the device. In this article, a comprehensive computational electromagnetic modeling and characterization is presented for transistor laser. The existing semiconductor and electromagnetic equations are reorganized in a systematic fashion, coupled, and solved numerically to get the electromagnetic field components emitted or absorbed by the device. These fields determine the radiation pattern, directivity, gain, bandwidth, and polarization of transistor laser in transmit and receive modes. The equations involved in the above electromagnetic model are the Poisson and continuity equations incorporating radiative and non-radiative recombination rates, the vector magnetic potential equation interacting with the Hamiltonian operator of electrons in valance and conduction bands, the equation of the dielectric properties fluctuations of semiconductor layers, and the Poynting vector determining the power flow. The constructed model demonstrates agreement with the general performance of the device in experimental reports.