Related papers: Symmetry-Protected Scattering in Non-Hermitian Lin…
Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is…
Asymmetric transmission of circularly polarized waves is a well-established property of lossy, anisotropic, two-dimensionally chiral patterns. Here we show that asymmetric transmission can be observed for oblique incidence onto any lossy…
Parity-time ($\mathcal{PT}$) symmetry plays an important role both in non-Hermitian and topological systems. In non-Hermitian systems $\mathcal{PT}$ symmetry can lead to an entirely real energy spectrum, while in topological systems…
In this work we study the scattering and transfer matrices for electric fields defined with respect to an angular spectrum of plane waves. For these matrices, we derive the constraints that are enforced by conservation of energy,…
In this paper we survey some recent results concerning scattering and non-scattering in the context of the linear Helmholtz equation and inhomogeneities of nontrivial contrast. We examine isotropic as well as anisotropic media. Part of the…
The optical theorem relates the total scattering cross-section of a given structure with its forward scattering, but does not impose any restrictions on other directions. Strong backward-forward asymmetry in scattering could be achieved by…
We highlight the conceptual issues that arise when one applies the quasi-Hermitian framework to analyze scattering from localized non-Hermitian potentials, in particular complex square-wells or delta-functions. When treated in the framework…
The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are…
Parity-time ($\mathcal{PT}$) symmetry, originally conceived for non-Hermitian open quantum systems, has opened an excitingly new avenue for the coherent control of light. By tailoring optical gain and loss in integrated photonic structures,…
Symmetry properties associated with neutrino propagation with or without a background of other particles, including neutrinos, is reviewed. The utility of symmetries is illustrated with examples chosen from the see-saw mechanism and both…
Non-Hermitian (NH) Hamiltonians have become an important asset for the effective description of various physical systems that are subject to dissipation. Motivated by recent experimental progress on realizing the NH counterparts of gapless…
Quasi-bound states in an open system do in general not form an orthogonal and complete basis. It is, however, expected that the non-orthogonality is weak in the case of well-confined states except close to a so-called exceptional point in…
In this thesis we address a series of new problems in non-hermitian optical scattering with increasing degrees of complexity. We develop the theory of reflectionless scattering modes, introducing a novel and broad class of impedance-matched…
In the past decade, the concept of parity-time ($\mathcal{PT}$) symmetry, originally introduced in non-Hermitian extensions of quantum mechanical theories, has come into thinking of photonics, providing a fertile ground for studying,…
The analysis of symmetries is extremely useful across science. In Physics, symmetries are used to derive conservation laws and selection rules for transitions in interacting systems. In the early days of nonlinear optics (NLO), symmetries…
Hourglass dispersion is generally believed to be solely protected by nonsymmorphic symmetries, because these symmetries can introduce high-dimensional projective representations. Here, based on symmetry arguments, we propose that the…
A non-Hermitian region connected to semi-infinite Hermitian lattices acts either as a source or as a sink and the probability current is not conserved in a scattering typically. Even a $\mathcal{P}\mathcal{T}$-symmetric region that contains…
We discuss Hamiltonian symmetries and invariants for quantum systems driven by non-Hermitian Hamiltonians. For time-independent Hermitian Hamiltonians, a unitary or antiunitary transformation $AHA^\dagger$ that leaves the Hamiltonian $H$…
The spectral singularity have been extensively studied over the last one and half decade for different non-Hermitian potentials in non-Hermitian quantum mechanics. The nature of spectral singularities have not been studied for the case of…
We consider transport through a non-Hermitian conductor connected to a pair of Hermitian leads and analyze the underlying non-Hermitian scattering problem. In a typical non-Hermitian system, such as a Hatano--Nelson-type asymmetric hopping…