This is a good one to show off my sci-fi, geek knowledge. We do actually have a pretty good idea of how lightsabers are supposed to work, thanks to the extensive technical manuals written by the Lucas team.
The first thing you need to know is the beam is not actually made out of light. The name is a misnomer, like how tin foil is made of aluminum, not tin, shooting stars are not stars, pencil lead does not contain lead. The most common and consistent description is that the lightsaber creates a powerful arc of plasma and then via magnetic fields and the focusing , that arc is pushed out into a very long thin arc.
We actually already have something very similar, as far as the essential technology and function of a lightsaber goes. Every day we use 'beams' of superheated plasma, some in excess of 40,000 degrees, to easily slice through several inches of metal in factories all over the world.
The device is a plasma arc cutter/torch/welder/sprayer. Unfortunately, this is where the similarities end. Firstly, the actual arc is very small. This tiny yet very hot arc ignites a gas that is continually pumped through the nozzle and the gas carries away the heat produced in a 'beam' that acts as the working medium of this tool.
So we want a handheld weapon that can cut through various materials, has an extendable blade and glows? The closest thing to that we might be able to make would be with a few strands of carbon nanotube wire. These are then pulsed with electromagnetic field vibrations and/or plasma to give them some extra cutting power. This would effectively create a type of 'energy vibro-sword' – but without a solid backing behind the length of it you would get a whip and not a blade.
Perhaps some kind of telescoping portion behind the cutting edge could contain a bundle of carbon-nano tube threads that are held in place and energised with plasma, creating a burning edge. The rigid edge would be thin enough on one edge to follow through the hot cutting edge and thick enough at the other side to make a rigid parrying weapon.
To preserve the threads as long as possible, and reduce energy and waste heat, they would not be energised until just before they hit.
You would still need a very large power pack (maybe a backpack) possibly with some exotic energy storage medium, and you would need heat protection for your hands and arms, as well as special flare-compensating glasses for your eyes.
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