Around M-dwarfs, red-edge was expected to be shifted to a longer wavelength, since planets on the exoplanets use abundant IR radiation for photosynthesis.Researchers at the Astrobiology Center (ABC) of National Institutes of Natural Science (NINS) in Japan and their colleagues have proposed and alternative prediction that red-edge could be observed as on the Earth even on exoplanets around M-dwarfs in the online journal on August 8th, 2017.
On the Earth, red-edge appears between red and infrared (IR) wavelengths, since red-light is absorbed for photosynthesis while IR radiation is reflected.
Five excitation wavelength phytoplankton and photosynthesis analyzer for differential analysis of the photosynthetic performance of mixed algae populations and determination of the functional absorption cross section (σ).
The action spectrum of photosynthesis is a graph showing the rate of photosynthesis for each wavelength of light. The rate of photosynthesis will not be the same for every wavelength of light. The rate of photosynthesis is the least with green-yellow light (525 nm-625 nm). Red-orange light (625nm-700nm) shows a good rate of photosynthesis however the best rate of photosynthesis is seen with violet-blue light (400nm-525nm).
As we can see, there is a close relationship between the action spectrum and absorption spectrum of photosynthesis. There are many different types of photosynthetic pigments which will absorb light best at different wavelengths. However the most abundant photosynthetic pigment in plants is chlorophyll and therefore the rate of photosynthesis will be the greatest at wavelengths of light best absorbed by chlorophyll (400nm-525nm corresponding to violet-blue light). Very little light is absorbed by chlorophyll at wavelengths of light between 525nm and 625 (green-yellow light) so the rate of photosynthesis will be the least within this range. However, there are other pigments that are able to absorb green-yellow light such as carotene. Even though these are present in small amounts they allow a low rate of photosynthesis to occur at wavelengths of light that chlorophyll cannot absorb.
LED lighting can be designed to optimize the amount of useable light per space. It is easy to manipulate to allow only the light omitted from the fixture to be in the wavelength that stimulates photosynthesis. This equates to 400 to 700 nanometers which delivers the greatest yield per watt or amount of energy consumed.
Yes, it's not an easy topic.
Visible light has wavelengths from 400nm (violet-blue) to 700nm (red), and chlorophyll can absorb at all these wavelengths (just not so efficiently at green wavelengths, which is why plants appear green). Other pigments used by photosynthetic organisms often absorb optimally at the wavelengths that chlorophyll is not so efficient at using, but they will also tend to have a broad spectrum.
Energy transfer through the antenna complex is not as simple as the transfer of photons, as you rightly suggest. Unfortunately, it is also not as simple as the transfer of electrons. It happens by a process called radiationless energy transfer, whereby an excited electron drops back to its ground state and the released energy is immediately absorbed by an electron in the next molecule, without any photon being emitted. Transfers are very fast (picoseconds) and the molecules have to be within a certain distance of each other (Wikipedia suggests less than 10nm).
I've only given a very brief overview so please re-post if you have more questions, and maybe some other people on this site will have more to add. However, this whole area is at the very borderline of biology and physics, so if you can find a site called 'askaphysicist', you might get a more thorough answer!