Youtube video shows what a expander can do for your 445nm laser

If you want to see what a beam expander can do for your higher divergence 445nm laser, watch this to the end

thanks for sharing. though I think someone can better demonstrate the difference. I can personally attest that with a 10X expander I made a NDB7A75 seem like single mode, albiet with a 1.5 inch wide beam, give or take. it's quite a feat considering the terrible divergence of that diode. some focusable lasers like the one I have/had can allow you to clip less of or none of the beam on the expander's sides by defocusing the laser. to fit that narrower waist in the BE's input. Mine is adjustable. you can greatly reduce artifacts as well.

only drawback is power loss, hence the interest in lasers that enter the diode's raw output directly into an expander setup, rather than through a regular lens then an expander. less optical losses

Yes, the video could have been done better, but I haven't found one yet. I've found that you don't need an expander lens if you take the raw output from a laser diode and place a PCX lens at the appropriate distance in front of it, according to the FL. That way, you reduce from three lenses, down to just one, compared to putting a regular beam expander in front of a collimated laser.