Why are there no solid-state blue lasers? Why are there no viable solid state gain media that directly lase in the visible spectrum? With the exception of ruby used in the first laser (red), all of the bulk gain materials like Nd:YAG and related have transitions between 900 and 1500nm.
What are the fundamental physical reasons that gain materials with transitions below 600nm have not been discovered or invented? With the inefficiencies of frequency doubled solid state lasers surely there is motivation to do so.
Note that I am not counting diode lasers, like GaN, which have many restrictions of geometry and power output compared with a bulk crystal like YAG.
 A: Solid state blue lasers exist. Moreover, they exist for a while and there is even a dedicated Wkipedia article (with hopefully helpful references).
The difficulty in creating solid state blue lasers, depends on what type of laser we are talking about.

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*Semiconductor lasers require material that can be both made conducting by doping and has a sufficiently large bandgap - the more studied materials have bandgaps close to infrared spectrum, which si why the first semiconductor lasers were working in this range, gradually evolving towards higher frequencies as better materials were mastered.

*Lasers based on rare earth elements require ions with the corresponding transition incorporated into solid state matrix. So it is again the question of creating a coresponding material, which was not readily available. Note that this is in a sense a step in the direction of gas lasers, exploting the transitions between the levels of isolated itoms, rather than interband transitions, which are truly a hallmark of the solid state.

*Finally, another successful path is using quantum dots - i.e., artificially created atoms, where the spacing between levels is well controlled and can be made sufficiently large. As their integrated into a crystal as its part, pumpng can be achieved by either electrical or optical means.

Update
As discussed in the comments, many high frequency transitions are easily available in gas and die lasers, but not in the solid state lasers, which are confined to read and infra-red spectrum. Indeed, in a crystal it is difficult to have a metastable state that has energy higher than the bandgap: the continuous spectrum in the bands means that there are many possibilities for non-radiative relaxation (e.g., many processes mediated via Coulomb and phonon interactions). This is not the case with atoms/molecules, where a high energy level can be just as long-living as a lower one.
One could further argue that the valence and the conductance bands of a crystal are essentially formed from the higherst occupied and the lowest unoccupied orbitals of the constituting atoms, thus limiting the optical emission from semiconductor crystals to this interval. This is also the reason for the use of the rare earth elements in solid state lasers, since their f-shell remains relatively uncoupled from the conduction and valence bands, formed from s and p orbitals. These material constraints do not exist for the gas lasers, whose working environment is inert gases that could not be integrated into a solid state matrix.
