Related papers: Spectral singularities and Bragg scattering in com…
Bloch oscillations (BO) in complex lattices with PT symmetry are theoretically investigated with specific reference to optical BO in photonic lattices with gain/loss regions. Novel dynamical phenomena with no counterpart in ordinary…
Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which…
Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring…
A curious feature of complex scattering potentials v(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an obstruction to the existence of a complete…
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In…
Simple examples of non-Hermitian Hamiltonians with purely real spectra defined in $L^2(R^+)$ having spectral singularities inside the continuous spectrum are given. It is shown that such Hamiltonians may appear by shifting the ndependent…
Spectral singularities are among generic mathematical features of complex scattering potentials. Physically they correspond to scattering states that behave like zero-width resonances. For a simple optical system, we show that a spectral…
Exceptional point and spectral singularity are two types of singularity that are unique to non-Hermitian systems. Here, we report the high-order spectral singularity as a high-order pole of the scattering matrix for a non-Hermitian…
We describe one-dimensional stationary scattering of a two-component wave field by a non-Hermitian matrix potential which features odd-$PT$ symmetry, i.e., symmetry with $(PT)^2=-1$. The scattering is characterized by a $4\times 4$ transfer…
We introduce a new class of $\mathcal{PT}$-symmetric complex crystals which are almost transparent and one-way reflectionless over a broad frequency range around the Bragg frequency, i.e. unidirectionally invisible, regardless of the…
A potential for propagation of a wave in two dimensions is constructed from a random superposition of plane waves around all propagation angles. Surprisingly, despite the lack of periodic structure, sharp Bragg diffraction of the wave is…
We investigate a two-parametric family of one-dimensional non-Hermitian complex potentials with parity-time ($\mathcal{PT}$) symmetry. We find that there exist two distinct types of phase transitions, from an unbroken phase (characterized…
Bragg scattering in sinusoidal PT-symmetric complex crystals of finite thickness is theoretically investigated by the derivation of exact analytical expressions for reflection and transmission coefficients in terms of modified Bessel…
Non-Hermitian systems with parity-time (PT) symmetric complex potentials can exhibit a phase transition when the degree of non-Hermiticity is increased. Two eigenstates coalesce at a transition point, which is known as the exceptional point…
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…
A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission…
We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and…
For complex one-dimensional potentials, we propose the asymmetry of both reflectivity and transmitivity under time-reversal: $R(-k)\ne R(k)$ and $T(-k) \ne T(k)$, unless the potentials are real or PT-symmetric. For complex PT-symmetric…
It is shown that slow Bragg soliton solutions are possible in nonlinear complex parity-time (PT) symmetric periodic structures. Analysis indicates that the PT-symmetric component of the periodic optical refractive index can modify the…
Using techniques of supersymmetric quantum mechanics, scattering properties of Hermitian Hamiltonians, which are related to non-Hermitian ones by similarity transformations, are studied. We have found that the scattering matrix of the…