price of a laser is roughly based on the power
power is roughly a metric of how thick a piece of wood it can cut
to cut wood you don't want lower than 10w and ideally 20w+ unlikely to be in the £300 range
lower priced lasers engrave they don't tend to cut...
I have a 5w NEJE - doesn't cut, great at engraving
I also have a 20w XTool D1 Pro - does both and will happily cut through 10-12mm of oak
The jigsaws above are 5.5mm walnut / cherry
I have no issue cutting 12mm+ of ply - but it can be a bit erratic as glue is often not evenly applied when made...
The laser either follows a vector (mathematical curves) - and you really need that for cutting... or it can burn a bitmap (photo image) which it tends to do for engraving... burning happens where the laser is in one place for too long - so cutting can make that happen as it is concentrated and has to go through the wood, so the fringe casualty is burning - engraving should not burn and there are options usually to use a pump to blow fresh air onto the nozzle to reduce burning, but it doesn't eradicate it...
There is a lot of good material on youtube, perhaps worth watching?
This is an example of 10mm quarter sawn oak I cut on the laser to make a doll's cradle - not insubstantial! As you can see - I sanded down the edges afterwards
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