Optical admittance method for light-matter interaction in lossy planar resonators

Advanced optoelectronic simulation models are needed to study and optimize emerging photonic devices such as thin-film solar cells, lasers, and light-emitting diodes (LEDs). In particular, better tools are required for self-consistent modeling of coupled electrical and optical systems. The recently introduced quantized fluctuational electrodynamics (QFED) and the associated interference-exact radiative transfer equations have been developed for this purpose, but their use is in part complicated by the need to calculate the full dyadic Green's functions. To make QFED and the underlying physical quantities more accessible for new device studies, we introduce a directly usable method where Green's functions are obtained through optical admittances. The optical admittances can be solved analytically for piecewise-homogeneous layer structures and selected graded-index profiles, and numerically for arbitrary position-dependent refractive index profiles using well-known techniques. The solutions enable direct construction of the dyadic Green's functions and all the related optical quantities. To give examples of the general applicability of the method, we calculate the local and nonlocal optical densities of states for selected devices, including GaN-based flip-chip LEDs and vertical-cavity surface-emitting lasers. Using only the rather simple framework presented in this paper, one can analyze energy transport in a wide range of planar photonic devices accurately without additional difficulties or inputs from external solvers.

Figure 1

Schematic illustration of the general layer structure modeled using the optical admittance method. The figure also shows ray-optical illustrations of principally right- and left-propagating optical modes $E^{\to },H^{\to }$ and $E^{\leftarrow },H^{\leftarrow }$. The fields generally have components propagating in both forward and backward directions, apart from the final half-spaces where the modes exit the structure.

Figure 2

10-base logarithm of the normalized photon number $\mathcal{N}$ in the different GaN MQW flip-chip for (a) MQW located 300 nm below the top contact with the source in the middle of the lowest QW, (b) MQW located 300 nm below the top contact with the source in the middle of the uppermost QW, (c) MQW located 600 nm below the top contact with the source in the lowest QW, and (d) MQW located 600 nm below the top contact with the source in the uppermost QW. The horizontal dashed lines mark the escape cones of air and GaN, and the vertical dashed lines the position of the MQW and the metal-air interface. The photon energy and wavelength in the calculations are 2.786 eV and 446 nm, respectively.

Figure 3

10-base logarithm of the normalized photon number $\mathcal{N}$ in the structure of Ref. [34] with the source point in the middle of the (a) first, (b) second, and (c) third QW. The photon energy and wavelength in the calculations are 2.96 eV and 420 nm, respectively.

Figure 4

Normalized photon number $\mathcal{N}$ on a linear scale in the light cone of air for a top-emitting GaN LED with different antireflective coatings: (a) 500 nm of graded ITO with the refractive index $N$ varying from 2.19 to 1.17, (b) ungraded ITO with $N=1.17$, and (c) ungraded ITO with $N=2.19$. In (b) and (c) the ITO thickness is a quarter of the wavelength. The emitting QW is at the 0 position, and the different regions are marked in the figures. The photon energy and wavelength in the calculations are 2.786 eV and 446 nm, respectively.