Your shield is moving at nearly the speed of light. The peanut-sized chunk of space debris you're approaching isn't. Best case, the peanut rips through the shield at nearly the speed of light and hits your ship anyway. Worst case, when the peanut hits the shield, the shield burns up in a glorious glow of fusion, which you appreciate just before being consumed by the firestorm. (That XKCD is probably the most commonly linked XKCD on this site.)
The basic problems of shields have been known or guessed-at by SciFi writers for decades. It's why they stick with the ubiquitous "deflectors," which are never actually explained and magically move all potential debris out of the way, much like cows vs. the cow sweeps on old steam trains.
The problems with your proposed shield are (at least) ...
- It's not impenetrable (a massive + dense enough object will always go through it).
- It's consumable (it's not self-repairing or self-replacing).
- It will react to impacts (deliver enough energy over a large enough amount of area and it'll burn up like any other solid material).
- The energy needed to keep it in front of you must be at least equal to the impact energy of anything that hits it (you're using lasers for this...) or it falls back onto you.
Does this mean you can't use it in your story? Not at all. Most scifi readers either don't know enough about the science to realize these problems, or they're more like me where I'm in it for the story and don't worry about the little things.
However, to give you an idea about how issues like this can be resolved. You can adopt Larry Niven's solution: the General Products hull, which is basically impervious to everything other than visible light, antimatter, and gravity. Designed as a single molecule with "strengthened inner bonds," it's simply the best built armor in the universe. Can such a material exist? Not that we know — but that doesn't stop anyone from enjoying his stories.