Strong optical coupling is a carrier extraction method for hot-carrier solar cells, where carriers are extracted as photons from an absorber material and then reabsorbed by a conventional photovoltaic (PV) cell. The design and working principle of this kind of optically coupled device is investigated using a relaxation-time model with practical operating conditions. This investigation is performed in the so-called "down-conversion" configuration, where the band gap of the absorber material is the same as that in the final photovoltaic cell. In this configuration, carrier impact ionization rates that are faster than thermalization rates by at least 50 times are needed to effectively down-convert the hot carriers' energy to the electronic band edge. Photon emission through radiative recombination must be enhanced by more than 500 times through photonic engineering in order to reduce Auger loss during carrier extraction. The strong luminescence from the PV cell feeding back to the absorber material will further limit the optical extraction in the near-field coupled structure, reducing the overall conversion efficiency to be lower than the ideal expectation reported previously. The strong similarity between the hot-carrier down-conversion and carrier multiplication also suggests the possible application of such optical extraction for multiple-exciton-generation solar cells, making it potentially a general carrier extraction approach for third-generation solar cells.