Light extraction from light emitting diodes and/or phosphors has been an increasingly studied topic over the last twenty plus years (see Figure 1). More recently, it has been shown that there is an absolute limit to the amount of electromagnetic radiation that can transmit from one medium to another across an interface defined by differing refractive indices.^[1-4] This limit has been established using both thermodynamic arguments^[1-3] and classical electromagnetic theory.^[4] In this talk, we will briefly derive the limits of transmittance of light through an interface and discuss what implications there are for the overall extraction efficiency of a simple system.

Finite-difference time-domain (FDTD) simulations were performed to verify the transmittance limit. The results of the simulations will be presented for several different interface types, such as smooth, pseudo-random roughness, photonic crystal lattices, micro-sphere arrays, etc. It was found that regardless of the interface type, all of the simulations confirm the transmittance limit.

Finally, we will show that despite the relatively low transmittance limits, extraction efficiencies of 100% are theoretically possible, but only because of scattering and cavity effects, not through an increase of the so-called first-pass transmittance. We use a simple two-interface system and numerical simulations based on geometrical optics to demonstrate the effects of transmittance and other important factors on the overall forward extraction efficiency.

[1] J. Muschaweck and C. Wiesmann, Adv. Opt. Technol., 2, 291 (2013).

[2] A. Lenef, J. F. Kelso, and A. Piquette, Opt. Lett., 39, 3058 (2014).

[3] A. Lenef, A. Piquette, and J. Kelso, ECS J. Solid State Sci. Technol., 7, R3211 (2018).

[4] K. C. Mishra and A. Piquette, ECS J. Solid State Sci. Technol., 7, R3016 (2018).