# Reflectivity and transmissivity greater than 1

In plasmonics, it is often seen that reflection coefficient and transmission coefficient are greater than 1. How is energy conservation valid in such cases?

• Your title says "Negative" and your question says "greater than 1". These sound like opposite concepts. Can you please clarify? Jul 25, 2016 at 12:20
• @MartinKochanski Thanks for pointing that out. It was an oversight. Jul 25, 2016 at 12:24
• I assume transmissivity is a property and transmission coefficient is a number that should be $\leq$1? I ask because it might be that you are confusing terms. Jul 25, 2016 at 12:43
• Please provide reference to an article that makes such a claim; the paper should describe the process. Jul 25, 2016 at 12:50
• A laser amplifier has a transmission coefficient greater than 1 (aka gain), for some range of wavelengths. It also needs to be pumped (energy put in) to amplify the beam. Jul 25, 2016 at 12:55

In the book "Plasmonics and Plasmonic Metamaterials: Analysis and Applications" edited by G. Shvets, Igor Tsukerman, we read in section 2.1:

In other words - they clearly state that the enhanced reflectivity is a result of the presence of a inverted dye - that is, a dye with a population inversion, meaning that it can be subject to stimulated emission.

In other words - Jon Custer's hunch was correct. There is no violation of the conservation of energy. The energy is coming from the pumped medium.

Perhaps an easy analogy is a mouse trap. Imagine dropping a large ball on a mouse trap. As the trap closes, the ball gets "kicked" by the closing spring, and shoots away with more speed than it came in. No violation of the conservation of energy: the energy of the spring was released by the impact of the ball, and sent the ball on its way. Somebody had to set the trap before dropping the ball - the equivalent of pumping the dye.