I did a spectra analysis of the beam of my violet laser pointer with my CD-R, when pointing to the wall, non fluorescet white plastic or any white or other color surface that don't fluorescence, and seen a mystery dim boardband emission in the spectrum, in additional to the 405nm laser line itself, that starts in the red and ends in the blue (Similar to the one that exists in the spectrum of violet, NUV and UVA LEDs).
What is this emission (Laser shouldn't emit any boardband emission by themselves)?

Most "white" things wouldn't be "white enough" without the use what is called "brighteners". They are used as part of wll paint mixes, white plastic, as part of paper, fabrics,... E.g. any paper without these would be brownish color, they are virtually everywhere...
The brighteners are nothing else than phosphors, which convert some of the near UV and UV to visible, the exact spectrum depend on the use an "natural" color of the material to be treated. So I would guess the mystery broadband spectrum is cominbg from these brighteners and not from the laser...

So you would have to first pass the laser beam through the CD and only then let it strike something wihite...

I tryed to see the spectrum of the laser itself, by pointing it to the CD-R so that the reflection of the light from the laser itself will be visible (But not such that the reflecting beam pointing to my eyes directly, and still seen the dim continuous background. I see this dim background with non fluorescencing white paints on the wall and plastic (Where the beam looks purple). With fluorescent plastic and paper, the beam is bright bluish white, and the background is very bright while the laser violet line is almost completely invisible.