Backward lasing yields a perfect absorber

It is well known that an amplifying medium embedded in an optical cavity, i.e., a laser oscillator, can emit coherent electromagnetic radiation when the gain coefficient of photons in the medium reaches a threshold value that balances the light leakage out of the cavity [1]. The emitted radiation escapes from the cavity in the form of outgoing monochromatic waves, usually along preferred spatial directions [see Fig. 1(a)]. The frequency ω0 and spatial pattern of the emitted waves are those of the electromagnetic mode sustained by the leaky cavity, which experiences the largest amplification in the gain medium. A less familiar process is the time-reversed counterpart of a laser: by replacing the gain with absorption, the same optical system supports a purely incoming radiation pattern with complete absorption and zero reflection [see Fig. 1(b)]. Such an optical system, referred to as a coherent perfect absorber (CPA), has been theoretically proposed in an article appearing in Physical Review Letters by Yidong Chong, Li Ge, Hui Cao, and Douglas Stone at Yale University in the US [2]. In this device, even small single-pass absorption can lead to perfect overall absorption, and optical media that normally do not absorb radiation well at certain frequencies, can be made to do so. When light hits a material, three things can happen: light can be reflected, as by a mirror; it can be transmitted, as with window glass; or it can be absorbed and turned, for example, into heat. The time-reverse of the lasing process ensures that a coherent light shining on a dissipative medium at a specific wavelength and with appropriate spatial pattern is neither reflected nor transmitted, rather it is fully absorbed. This kind of coherent perfect absorption extends and explains in an elegant way previous known methods of absorption enhancement in integrated optical devices [3, 4]. As compared to other perfect optical absorbers, such as those based on engineered metamaterials [5], the CPA principle proposed by Chong et al.[2] works for any kind of absorbing medium, is not based on resonant material absorption, and does not require material nanostructuring. Perfect absorption of photons by a dissipative optical medium as proposed by the authors is reminiscent of the problem of perfect absorbing potentials for matter waves investigated in computational quantum physics, for example, in reactive scattering calculations or other molecular collision studies [6–9]. Perfect absorption of optical and matter waves share a similar mathematical description, involving the search for poles and zeros of the underlying scattering matrix, which relates the incoming and outgoing electromagnetic wave modes. Just as in a laser at the onset of oscillation, coherent perfect absorption provides a clear physical signature of certain spectral singularities that arise in the underlying nonHermitian Hamiltonian [10, 11]. However, the picture of coherent perfect absorption as time-reversed laser oscillation provides a simple and elegant explanation of the underlying physics that does not require any advanced knowledge of scattering or spectral theory. In a dielectric optical cavity filled by a gain medium, the spatial profile of the lasing mode is found as an eigenfunction of the Helmholtz equation for the complex electric field amplitude E, which in the simplest one-dimensional spatial case reads