Coherent scattering from semi-infinite non-Hermitian potentials

Abstract

When two identical (coherent) beams are injected at a semi-infinite non-Hermitian medium from left and right, we show that both reflection $(r_L,r_R)$ and transmission $(t_L,t_R)$ amplitudes are non-reciprocal. In a parametric domain, there exists Spectral Singularity (SS) at a real energy $E=E_{\ast }$ and the determinant of the time-reversed two port S-matrix i.e., $|\det (S)|=|t_L{t}_R-r_L{r}_R|$ vanishes sharply at $E=E_{\ast }$ displaying the phenomenon of Coherent Perfect Absorption (CPA). In the complimentary parametric domain, the potential becomes either left or right reflectionless at $E=E_z$. But we rule out the existence of Invisibility despite $r_R(E_i)=0$ and $t_R(E_i)=1$ in these new models. We present two simple exactly solvable models where the expressions for $E_{\ast }$, $E_z$, $E_i$ and the parametric conditions on the potential have been obtained in explicit and simple forms. Earlier, the novel phenomena of SS and CPA have been found to occur only in the scattering complex potentials which are spatially localized (vanish asymptotically) and having $t_L=t_R$.

Six pages, 3 figures, no table, language improved

References in corpus (7)

• Coherent Perfect Absorbers: Time-reversed Lasers
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Invisibility and PT-symmetry
• Phase transition through the splitting of self-dual spectral singularity in optical potentials
• Soliton dynamics in symmetric and non-symmetric complex potentials
• Asymmetric scattering by non-hermitian potentials
• Coherent perfect absorption with and without lasing in complex potentials

Cited by in corpus (5)

• A universal form of complex potentials with spectral singularities
• Spectral singularities and tunable slab lasers with 2D material coating
• Three types of discrete energy eigenvalues in complex PT-symmetric scattering potentials
• Solving scattering problems in the half-line using methods developed for scattering in the full line
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states