Thermodynamic Upper Bound on Broadband Light Coupling with Photonic Structures

The coupling between free space radiation and optical media critically influences the performance of optical devices. We show that, for any given photonic structure, the sum of the external coupling rates for all its optical modes are subject to an upper bound dictated by the second law of thermodynamics. Such bound limits how efficient light can be coupled to any photonic structure. As one example of application, we use this upper bound to derive the limit of light absorption in broadband solar absorbers.

Figure 1

Schematic of an optical resonance coupling into free space through the top surface.

Figure 2

(a) Solar absorber structure (with cutout showing the scattering layer pattern). It consists of cladding layers (brown) of thickness 125 nm and $\epsilon =12.5$ surrounding the 5 nm active layer of $\epsilon =2.5$ on both sides. Below the lower cladding layer, a 150 nm thick scattering layer (green) of air patterns is etched into a slab of $\epsilon =12.5$ with 1200 nm periodicity. The air patterns consist of eight rectangles of $200\times 50\mathrm{nm}$ radially separated at equal angles. In between each rectangle an air circle of radius 60 nm is also placed. Together they generate a strongly scattering layer to couple into desirable optical modes that are confined in the active layer. Below the scattering layer we placed a perfectly reflecting substrate. Finally, on top of the top cladding layer we introduce an optimized four layer antireflection (AR) coating. The layers have heights (from top to bottom) of 60, 35, 110, and 50 nm, and epsilons of 1.9, 3.7, 8.3, and 11.5, respectively. (b) The absorption spectrum for single-pass absorption of $\alpha d=0.02$. This is in the parameter regime where material absorption is significant. The peaks are due to optical resonances. The absorption spectrum is above both the single-pass absorption (black dashed line) and the conventional limit [gray (red) dashed line]. (c). The upper limit of light absorption $A$ as the function of $\alpha d$ for absorbers for different $F$ values calculated from Eq. (11). The black curve is for single-pass absorption. Dots are simulated results for the structure. $F=10$ is the conventional limit and $F=200$ is the limit for the structure in (a).