Coherent Perfect Absorbers: Time-Reversed Lasers

We show that an arbitrary body or aggregate can be made perfectly absorbing at discrete frequencies if a precise amount of dissipation is added under specific conditions of coherent monochromatic illumination. This effect arises from the interaction of optical absorption and wave interference and corresponds to moving a zero of the elastic $S$ matrix onto the real wave vector axis. It is thus the time-reversed process of lasing at threshold. The effect is demonstrated in a simple Si slab geometry illuminated in the 500–900 nm range. Coherent perfect absorbers act as linear, absorptive interferometers, which may be useful as detectors, transducers, and switches.

Figure 1

Motion of exact $S$-matrix zeros (blue crosses) and poles (blue triangles) in the complex-$k$ plane, as dissipation increases from zero, for a two-channel resonator of length $a$ and uniform index $n$. In the external region, $n_0=1$. For $n\approx 3+0.05i$, the fourth zero from the left touches the real axis, yielding a CPA zero. Also shown are the zeros (red circles) and poles (red squares) predicted from Eq. (6). Inset: Schematic of system; each input is a single-mode fiber.

Figure 2

Complex refractive indices leading to perfect absorption for the device of Fig. 1, for $ka=664.7$. Only parity-even solutions are shown (blue circles). The green curve shows the refractive index of Si, $n(k)$. Inset: Parity-even solutions (hollow blue circles) and parity-odd solutions (filled red circles) in the region $3.55<\mathrm{Re}(n)<3.62$; the green cross shows the index of Si at $ka=664.7$, $a=100\mu \mathrm{m}$ (i.e., $\lambda =945.3\mathrm{nm}$).

Figure 3

Semilog plot of normalized output intensities $|s{|}^2$ vs the wavelength $\lambda =2\pi /k$, for a $100\mu \mathrm{m}$ Si slab. Solid lines show ${log}_{10}(|s{|}^2)$ for a parity-even (blue) or parity-odd (red) eigenmode. The dashed line shows $2(|r{|}^2+|t{|}^2)$, the total output intensity when the two input beams are incoherent. Inset: Upper and lower bounds for $|s{|}^2$ over a wide range of $\lambda$. The gray area shows the actual bounds, and the solid black line show the approximate lower bound from Eq. (10).

Figure 4

Plot of output intensities $|s{|}^2$, as a function of wavelength, for a distributed feedback CPA consisting of 20 Si slabs of width 188.5 nm, separated by ${\mathrm{SiO}}_2$ slabs of width 266 nm. The refractive index of ${\mathrm{SiO}}_2$ ($n=1.46$) is real to a good approximation in this wavelength range, so absorption occurs only in the Si. A large ($\sim 99\%$) absorption contrast can be observed at 956 nm near the photonic band gap. Inset: The intensity of the two eigenmodes, as a function of $x$, close to the edge of the system, at 956 nm.