The Particle-Wave duality of light is very well known and documented. Yes, the Michelson-Morley experiment using an interferometer confirms, without a doubt, that the speed of light is constant despite whatever material, or lack thereof, exists along a path. That's because light travels the absolute smallest possible distance at the absolute smallest possible unit of time. It's hard to explain if you don't have a solid knowledge of calculus, and even then it's no easy task, but think about it this way. If you slice a unit of time to an infinitesimally, but real, small unit of time (continually slice time in half an infinite amount of times), then you come to a "quantized" amount of time. That's the amount of time it takes light to travel from a quantized amount of distance. Nothing can exceed this speed because time can't get smaller than infinitely small (approximately 0). This is essentially part of the explanation as to why nothing can travel faster than light (relativity is another issue... as you go faster you actually get heavier and so it becomes infinitely difficult to apply an acceleration force-- it basically begins to require infinite force due to an approaching infinite mass to move matter at light speed... but I digress).

That's speed and why it requires no medium (btw, all mediums respond essentially the same to light-- it's hit by a photon which causes the admitting of another photon-- if something else gained momentum from the photon, like an electron excitation, then the photon that's emitted is of a different wavelength, etc etc). The only thing is that if a photon travels without hitting anything it never stops. There is a momentum associated with photons and the effects of friction, etc., are negligible due to the incredible speed associated with photons. They don't need a medium through which they propagate because photons are, in many ways, particles with an associated momentum (though no associated mass). This, in fact, is part of the evidence for photons being particles, as well as our ability to detect single photons since they always are detected in definite packets of energy. These quanta (quantitative packets of energy) are defined as the amount of energy from E/M radiation divided by some integer which always ends up being the same number. This is how much energy a single photon carries.

Evidence of the wave like nature comes from interference patterns detected through "split" experiments, as well as explaining the ability of certain wavelengths to be seen/absorbed/pass through, etc, and also can very accurately determine the energy of such waves. It also explains the radial spread of E/M energy.

E/M radiation is actually made up of an electrical energy wave and an orthogonal magnetic energy wave traveling in phase with each other...