Sure! I think it's quite doable to do theoretical work. There's plenty of solvers available (at least somewhat open source ones) that you can use to mess around with 2D and 3D structures (though, of course, larger structures will take a much longer time to solve). If you're interested in the numerical parts, I'd even highly recommend making your own solver and such! (We can chat in more detail about that if you're interested).
More classical optics setups with some decent lasers can be found off-the-shelf (though I'd have to look for consumer-type kits since the toys we have in the lab are a little more than my budget could personally handle ;). Either way, this is the best way to start since much of the subject really is based on doing experiments with light polarization, interferometry, etc., that forms the base of much of the work here (and many of the means of measurement). This is what this paper does, essentially, with the huge structures they've created (except with microwaves, which require some specialized equipment to measure).
Now, if you're interested in doing experimental work with photonic crystals, this question becomes a bit more difficult since it's essentially required that you have a foundry and some amount of cash to blow (as almost everything is fabricated and would require scanning electron microscopes and such to verify). You can also ship off parts to places like TSMC (which would likely form the basis of a somewhat expensive hobby), which I think deal with some small-scale manufacturing, but the time turnaround is pretty large as is the cost.
Would you mind going deeper into the suggestion to write your own solver?
I have an idea for making microwave metamaterials, fairly cheaply, but don’t have the physics background to write the solver for the material structuring.
I have a heavy math background though, eg, dealing with convex optimization in the context of economics.
Sure! If you already have a good math background, essentially the only thing left is to do a "bit" of numerical computing. Steven Johnson at MIT has a good course starting this (with Julia! Which is awesome and I highly recommend) [0] and, for further information, it's worth looking at some books (of which there are plenty, as far as I can tell. I studied out of Chew's Waves and Fields in Inhomogeneous Media, but this book is quite out of date and not particularly pedagogically good).
Overall, the mathematics itself is not difficult (essentially, everyone is using some simple preconditioned CG method for solving the linear problems, along with some [sometimes smart, sometimes not] meshing), but generating robust solvers is, almost universally, still an open problem. Depending on what you'd like to simulate and such, you're going to have to make use of the different properties of the operators you're working with to get really good results. We can email and I can say a little more given more details of your project/potentially guide you in a slightly better direction.
More classical optics setups with some decent lasers can be found off-the-shelf (though I'd have to look for consumer-type kits since the toys we have in the lab are a little more than my budget could personally handle ;). Either way, this is the best way to start since much of the subject really is based on doing experiments with light polarization, interferometry, etc., that forms the base of much of the work here (and many of the means of measurement). This is what this paper does, essentially, with the huge structures they've created (except with microwaves, which require some specialized equipment to measure).
Now, if you're interested in doing experimental work with photonic crystals, this question becomes a bit more difficult since it's essentially required that you have a foundry and some amount of cash to blow (as almost everything is fabricated and would require scanning electron microscopes and such to verify). You can also ship off parts to places like TSMC (which would likely form the basis of a somewhat expensive hobby), which I think deal with some small-scale manufacturing, but the time turnaround is pretty large as is the cost.