I was doing some thinking about light and how it behaves and trying to figure out what the smallest we could focus a beam of photons would be. In my research, I think the answer would be something related to the frequency of the light, but i'm not sure.

 

basically i was wondering if it would be possible to focus a beam of light into a singularity of sorts, and if any odd things might happen at that point depending on energy levels, frequency, etc.

Yes, the minimum spot size is related to the wavelength or frequency, and also the the focal length of the lens and the original size of the beam. Strongly converging/diverging beams can be focused to a smaller spot, but over a shorter distance than the opposite case.

 

http://en.wikipedia.org/wiki/Gaussian_beam#Beam_width_or_spot_size

Don't forget the perfect lens;

 

http://prl.aps.org/abstract/PRL/v85/i18/p3966_1

Could you explain how negative refractive indices are achieved?

Could you explain how negative refractive indices are achieved?

you do it with photonic crystals, particularly three dimensional ones. The basic principle is that there are lots of tiny holes and chambers etched within a block of material, so that when you find the refractive index, it is negative. You can even do it for larger structures. I think the first negative refractive index materials were made for microwaves (much simpler as the wavelength of light is longer and the structures larger.