I understand that most animals that look blue don't have blue pigment but instead have microscopic structures that scatter blue light. I was wondering if it would be possible for an organism to evolve photosynthesis that instead of using photosynthetic pigments uses microscopic structures that trap light. If so under what circumstances would photosynthesis through light absorbing structures be easier to evolve than photosynthesis through photosynthetic pigments and what would such structures look like?
I understand that most animals that look blue don't have blue pigment but instead have microscopic structures that scatter blue light.
Right, but this has nothing to do with photosynthesis.
If so under what circumstances would photosynthesis through light absorbing structures be easier to evolve than photosynthesis through photosynthetic pigments and what would such structures look like?
A photosynthetic pigment is nothing more than a molecule that absorbs light and convert its electromagnetic energy into chemical energy. In other words, it's exactly a "light absorbing structure"
What you're looking for can be found in the Oriental hornet, particularly its pigmentation. The pigments of vespa orientalis are not just for show, but also serve to turn light into energy. The wasp uses this solar energy to help it fly or dig its burrow, which is why they are most active during midday. Pigments in the oriental hornet's cuticle absorb solar energy that is turned into electrical energy. The banded sections have multiple layers that get successively thinner and sandwhich the pigments. The brown cuticle has about 30 layers while the yellow layer roughly 15.
Scientists have found that the outer brown layer is covered in grooves that act almost like gratings that help trap light, allowing the rays to funnel inward for better absorption. The outer yellow layer is covered in oval-shaped bumps that increase effective surface area for absorption. Both of these areas exhibit antireflection and light-trapping properties, enhancing the absorption of light in the cuticle. The enzymatic activity in these regions has been shown to decrease when the hornet is exposed to light, allowing it to conserve energy.
As has bene pointed out, a pigment is simply a molecule that absorbs or reflects light of a given wavelength. A photosynthetic pigment is more than that - instead of just heating up the molecule absorbing it, light energy absorbed is transferred to an electron that can be passed along to ultimately participate in a chemical reaction and generate ATP. This is a high hurdle for evolution and only a few such pigments are known to exist.
The OP asks for a microscopic structure. I picture something bigger than a protein or molecule. The structure could be something like the Crookes radiometer, pictured above. These are a type of heat engine, turning electromagnetic energy into heat and from there into kinetic energy.
Movement with black-body absorption When a radiant energy source is directed at a Crookes radiometer, the radiometer becomes a heat engine. The operation of a heat engine is based on a difference in temperature that is converted to a mechanical output. In this case, the black side of the vane becomes hotter than the other side, as radiant energy from a light source warms the black side by black-body absorption faster than the silver or white side.
The mill will turn with any frequency that can heat the black side, and will turn in reverse if ambient surroundings are cooler than it is - propelled now by blackbody radiation from the black side.
WB stack has bandied about the idea of using kinetic energy (e.g. wind) to generate ATP. In the scenario here, heat energy is turned into kinetic energy which could be used to generate ATP - which is nice because heat works on every molecular scale and you don't need to gear down captured energy as you would with wind. Nanoscale heat engines exist and operate on the scale of the protein mechanisms that make ATP.
A nanoscale heat engine is probably even a higher hurdle for evolution. Less high for intelligent design!