Upper bounds on broadband absorption

We address the question of the optimal broadband absorption of waves in an open, dissipative system. We develop a general framework for absorption induced by multiple overlapping resonances, based on quasi-normal modes and radiative and non-radiative decay rates. Upper bounds on broadband absorption in a slab of thickness $d$ take the simple form: $A= 1-\exp(-F \alpha d)$, where $\alpha$ is the absorption coefficient and $F$ the path enhancement factor. We apply these results to sunlight absorption in photovoltaics and answer the long-standing debate on the best light-trapping strategy in solar cells. For angle-independent absorption, we derive the isotropic scattering upper bound $F = 4 n^2$ ($n$ the refractive index), extending the well-know Yablonovitch limit beyond the ray optics and weak absorption regimes. For angle-restricted illumination, we show that $F$ can be further increased up to $8 \pi n^2 / \sqrt{3}$ using multi-resonant absorption induced by periodical patterning. These results have a general scope in the field of wave physics and open new opportunities to maximize absorption, detection, and attenuation of electromagnetic or mechanical waves in ultrathin devices.