Why is making a laser that shines light over the full spectrum, i.e. a 'white laser', so difficult? Why is it that, while there are red, green, and blue laser out there, I can't seem to find lasers that shine light over the full spectrum of colors"white lasers"? How hard is to make one? Is it possible?
 A: World's first white laser demonstrated
Scientists Finally Created a White Laser—and It Could Light Your Home
White lasers already exist years ago, but they depends of the combination of colors.
Since 2015 scientist developed pure white color lares. But, not depends only of the spectrum, they have a lot of variants (like lens).
The white laser is currently in proof of concept form and several hurdles need to be overcome before the technology is practical. According to the studies, the biggest of these is making it run off a battery. In its present form, the material runs off a separate laser, which pumps electrons into the semiconductor.
A monolithic white laser
A: It is certainly possible to build laser systems that produce light with the types of extremely broad bandwidth that are required to make white light: as an example, titanium-sapphire lasers have a bandwidth spanning just short of an octave, with a span that's comparable in range to that of the visible spectrum.
Looking at the  bandwidths of the various gain media in use, it seems that only dye lasers are able to cover the full span of the visible; this is likely due to the fact that there are many laser dyes out there, but then again it's conceivable that you could use multiple different dyes as concurrent gain media.


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Alternatively, you could combine three different gain media, either inside the same cavity or with three parallel cavities, and use them to make a light source with a three-band spectrum that looks visually white to the human eye.
Basically, though, your question isn't particularly well-posed, because "white light" can mean many different things in many different contexts.

*

*It can mean, for example, any light that looks visually white to the human eye. This is a very lax requirement, and indeed you could combine three different existing lasers $-$ the red, green and blue lasers you've already found $-$, combine them using dichroic mirrors, and you're done.

*However, most often, the term "white light" refers to light with a near-constant spectral distribution spanning all of the visible part of the spectrum. As discussed above, this is in principle possible but not all that easy.

*Further to that, though, when we say "white light", we normally mean an incoherent mixture of the entire visible spectrum.

Generally speaking, if you have a laser with a large bandwidth, then with enough engineering you can probably arrange things so that it lases evenly across all its bandwidth without inducing additional coherence between the different frequencies, giving you that third case, but that's mostly a pointless exercise: if you have a bandwidth that's that large, and you want your device to lase across all of its spectrum, then you're almost certainly building a pulsed laser that relies on coherent emission in all the different frequencies. (If you wanted incoherent mixtures, you'd just get a white-light lamp of the myriad of non-laser types available.)
If you do build such a broadband pulsed laser, then the pulses quite often do look white. (On the other hand, extremely-broadband lasers tend to work in the infrared, and you only bleed into the visible by using Raman-based supercontinuum generation in gas-filled hollow-core fibers used for spectral broadening. But then again, if that bothers you, then you probably shouldn't be calling green-light laser pointers "green lasers", as they're actually frequency-doubled IR lasers.) It is extremely unusual for such lasers to be termed "white-light lasers", though, because we care about their pulses and the duration of those pulses, together with the central carrier frequency, much more than we do about their visual aspects.
And this brings me to the core reason why people don't make white-light lasers much: because there is basically no point. If you want white light, then an incoherent source works just as well, and you're better off working with that. There are reasons for making broadband lasers, but you'll see them marketed under those reasons rather than their visual aspect.
