In a nuclear photonic rocket, a nuclear reactor would generate such high temperatures that the light from the reactor would provide thrust. Think of a nuclear light-bulb, with a reflector. The big advantage is that no material leaves the spacecraft, so only nuclear fuel is depleted. The disadvantage is that it takes a lot of power to generate a small amount of thrust this way, so acceleration is very low. The reactor would be constructed of graphite and tungsten.
A variation is the photon rocket proposed by the German rocket scientist Eugen Sänger, using antimatter annihilation as a light source and an electron-mirror as a reflecting medium. None of his mirror designs seem to work in reality, however.
The specific impulse would be 300,000,000 m/s or, expressed as a time, one year. P = mca, i.e. the net power needed to accelerate 1 kg 1 m / s2 would be 300 MW.
See also: spacecraft propulsion