A photon rocket is a propulsion technology which produces thrust via the emission of intense light.
While photons do not have mass, they do still carry linear momentum and so create a small reaction force when emitted or absorbed. This is the basis of laser cooling. As photon rockets provide the maximum exhaust velocity (c) and the minimum exhaust mass (zero), they represent the theoretical maximum in specific impulse, but provide very low thrust, given by 2PR/c, where P is the emission power in watts and R is the efficiency of the reflection/collimation apparatus.
Currently proposed photon rocket designs include the Nuclear Photonic Rocket and the Antimatter Photonic Rocket (first proposed by Eugen Sanger in the 1950s). In a Nuclear Photonic Rocket, a nuclear fission reactor is used to directly heat tungsten coils or graphite blocks to white-heat at the focus of a parabolic reflector. While using a laser to produce the light beam would provide much better collimation, this is offset by the reduction in efficiency incurred by powering a laser rather than using black-body radiation directly (a nuclear fission reactor will generally output at least 5 to 10 times more energy as heat than it can the electricity it could generate).
The Antimatter Photonic Rocket first proposed by Eugen Sanger used electron/positron annihilation to generate gamma rays, but he was unable to solve the problems of how to reflect and collimate the beam as all atomic matter is opaque and non-reflective to gamma rays except at grazing incidences. Thus, feasible APRs are similar to NPRs, involving annihilation of protons and anti-protons inside a block of tungsten or graphite in order to heat it until it glows white. An APR would have 1000 times more energy available per kilogram of fuel than an NPR.
Photon rockets could be thought of as a type of space drive, in that they do not require the expulsion of reaction mass and do not push on anything external to themselves. Note, however, that they are pushing on something- the photons that are their propellant.
Solar sails operate on the same principle as photon rockets, deriving thrust from the tiny transfer of momentum that occurs when photons are emitted from a surface or bounce off of a reflector. They key difference is that a solar sail depends on an external light source, and its manueverability is limited by the direction of that light source, while a photon rocket carries its own light source along with it.
The broomsticks from Donald Moffet's science fiction novel The Jupiter Theft were photon rockets powered by mass-energy conversion with a high enough power output to produce a full g of acceleration. At that intensity, the energy density in the exhaust beam led to particle-antiparticle pair production, making the beam visible from the side.