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Engineering light-matter interactions using non-Hermiticity, particularly through spectral degeneracies known as exceptional points (EPs), is an emerging field with potential applications in areas such as cavity quantum electrodynamics, spectral filtering, sensing, and thermal imaging. However, tuning and stabilizing a system to a discrete EP in parameter space is a challenging task. Here, we circumvent this challenge by operating a waveguide-coupled resonator on a surface of EPs, known as an exceptional surface (ES). We achieve this by terminating only one end of the waveguide with a tuneable symmetric reflector to induce a nonreciprocal coupling between the frequency-degenerate clockwise and counterclockwise resonator modes. By operating the system at critical coupling on the ES, we demonstrate chiral and degenerate perfect absorption with squared-Lorentzian lineshape. We expect our approach to be useful for studying quantum processes at EPs and to serve as a bridge between non-Hermitian physics and other fields that rely on radiation engineering.

 

The linear response of non-Hermitian resonant systems demonstrates various intriguing features such as the emergence of non-Lorentzian lineshapes. Recently, we have developed a systematic theory to understand the scattering lineshapes in such systems and, in doing so, established the connection with the input/output scattering channels. Here, we follow up on that work by presenting a different, more transparent derivation of the resolvent operator associated with a non-Hermitian system under general conditions and highlight the connection with the structure of the underlying eigenspace decomposition. Finally, we also present a simple solution to the problem of self-orthogonality associated with the left and right Jordan canonical vectors and show how the left basis can be constructed in a systematic fashion. Our work provides a unifying mathematical framework for studying non-Hermitian systems such as those implemented using dielectric cavities, metamaterials, and plasmonic resonators.

 

Abstract Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonality of their eigenmodes, and the presence of exceptional points (EPs). Here, we derive a closed form series expansion of the resolvent associated with an arbitrary non-Hermitian system in terms of the ordinary and generalized eigenfunctions of the underlying Hamiltonian. This in turn reveals an interesting and previously overlooked feature of non-Hermitian systems, namely that their lineshape scaling is dictated by how the input (excitation) and output (collection) profiles are chosen. In particular, we demonstrate that a configuration with an EP of order M can exhibit a Lorentzian response or a super-Lorentzian response of order M s with M s  = 2, 3, …,  M , depending on the choice of input and output channels. 

We demonstrate an exceptional surface in a waveguide-coupled resonator by establishing unidirectional coupling between its frequency-degenerate counterpropagating modes. When operated on the ES, the system exhibits chiral perfect absorption with quartic lineshape. 

We develop a linear theory for non-Hermitian optical systems having exceptional points. In contrast to previous studies, our analysis results in an exact expression for the resolvent operator without the need to use perturbation expansions. 

Abstract Optical resonators are structures that utilize wave interference and feedback to confine light in all three dimensions. Depending on the feedback mechanism, resonators can support either standing- or traveling-wave modes. Over the years, the distinction between these two different types of modes has become so prevalent that nowadays it is one of the main characteristics for classifying optical resonators. Here, we show that an intermediate link between these two rather different groups exists. In particular, we introduce a new class of photonic resonators that supports a hybrid optical mode, i.e. at one location along the resonator the electromagnetic fields associated with the mode feature a purely standing-wave pattern, while at a different location, the fields of the same mode represent a pure traveling wave. The proposed concept is general and can be implemented using chip-scale photonics as well as free-space optics. Moreover, it can be extended to other wave phenomena such as microwaves and acoustics. 

We introduce a new class of photonic resonators with resonant modes that feature hybrid standing-travelling waves.