Light extraction from luminescent light sources and application to monolithic ceramic phosphors

Abstract

An extension of a theorem for light extraction [Adv. Opt. Technol.2, 291 (2013)] from a higher index luminescent body (LED or phosphor) through an extracting surface into a lower index output medium is derived. The result is valid for both geometric and diffractive surface structures. Using this bound and radiation transport calculations, we show that extraction from LEDs or phosphors requires a combination of cavity effects to enhance radiance behind the extracting surface and scattering or diffraction to couple trapped total-internal-reflection modes to propagating modes. The treatment applies to macroscopic luminescent sources whose thickness exceeds the longitudinal coherence length of the luminescent radiation.

Thermodynamics of Light Extraction from Luminescent Materials

“…As discussed in Ref. 6, efficient light extraction from a luminescent body also requires cavity enhancement effects to boost the internal radiance (or more generally the electromagnetic field strength) inside the luminescent body. A simple example is just placing a mirror on the back side of the luminescent body, such that the backward directed radiation is redirected toward the forward emitting direction.…”

“…6. Referring to Figure 6, the radiance L 1 ( 1 ) is incident on extraction surface at angle θ 1 , assumed to be spatially homogeneous on the scale of area A.…”

“…11, except that the angular distribution of the input radiance is included. Following 5 and, 6 the extraction efficiency of the extraction surface in Eq. 12 can be maximized if two conditions are met: 1) if the extraction surface has a hypothetical hemispherical transmission function τ 12 ( 1 ) that takes either values of zero or one; i.e., it is a binary function of angle; and 2) if those regions in 1 whereL 1 ( 1 ) takes on the largest values for τ 12 ( 1 ) = 1, and τ 12 ( 1 ) = 0 in the rest of the space.…”

“…In particular, several authors [5][6][7] have pointed out, in various degrees of generality, that surface structures (including nano-optic structures) have strong limits for transmission of radiation. These limits depend on the ratio of the refractive indexes of the output medium n 1 < n 2 , the refractive index of the input medium and, more generally, on the ratios of the combined angular-area phase spaces, orétendues.…”

“…As in Ref. 6, the results are derived using simple thermodynamic arguments that are independent of whether a particular surface is effectively in the geometric optic regime or relies on wave-optic effects, and therefore apply to the variety of photonic and geometric optic structures that have appeared in the literature. [8][9][10][11][12][13] This includes 2D nanostructures, for example, to restrict the angular emission cone by selective reflection and transmission from ceramic phosphor converters.…”