  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.
