In principle there is nothing wrong with your idea. But I think it is not viable by DIY, at least not with the results I guess you'd be expecting, with such a small understanding of the subject (read: Wikipedia is definitely not enough, and if you were to do things seriously the Sun would be the last source you'd be thinking of). First of all, any lasing medium (the object which contains the excited electrons) only amplifies light in a restricted bandwidth, which means that nearly all the power of sunlight would be wasted. There is no such thing as a "simple machine that produces laser", each laser is built to lase light around a narrow range of wavelenghts. Second of all, in order to DIY an efficient laser without using any pre-built component (which here is the case, as I guess there are no pre-built components for "efficient" solar lasers), you need to know the physics and mathematics behind the lasing mechanism, which includes a basic knowledge on the interaction between radiation and light, some more advanced knowledge on the dynamics of the electromagnetic field both in vacuum and in media, and an actual knowledge of how the theory applies to lasers. Last but not least, with no pre-built components you must be able to do some precision measurements. For example, the laser's resonant cavity (roughly speaking, the apparatus that hosts the mirrors) must be finely tuned in order to be able to amplify the signal.
If you are still determined to build the laser I advise you to get a copy of Svelto's "Principles of Lasers" and/or Saleh's "Fundamentals of Photonics". Here theory is explained in some detail, together with applications to specific laser designs.