Regularization of the spectral singularity in $\mathcal{P}\mathcal{T}$-symmetric systems by all order nonlinearities: Nonreciprocity and optical isolation

Abstract

Spectral singularities are ubiquitous with PT-symmetry leading to infinite transmission and reflection coefficients. Such infinities imply the divergence of the fields in the medium thereby breaking the very assumption of the linearity of the medium used to obtain such singularities. We identify saturable nonlinearity retaining contributions from all orders of the field to limit the infinite growth and regularize the spectral singularity. We present explicit numerical results to demonstrate regularization. The all order nonlinear PT-symmetric device is shown to exhibit very effective isolation or optical diode action, since transmission through such a system is nonreciprocal. In contrast, a linear system or a system with Kerr nonlinearity is known to have only reciprocal transmission. Further we demonstrate optical bistability for such a system with high contrast.

5 pages, 5 figures

References in corpus (7)

• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• PT-Symmetric Talbot Effects
• Invisibility and PT-symmetry
• PT-Symmetric Wave Chaos
• Bypassing the bandwidth theorem with PT symmetry

Cited by in corpus (28)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• On the optical nonreciprocity and slow light propagation in coupled spinning optomechanical resonators
• PT-symmetry breaking in multilayers with resonant loss and gain locks light propagation direction
• Exceptional points and spectral singularities in active epsilon-near-zero plasmonic waveguides
• Nonreciprocal Transmission in Nonlinear PT-Symmetric Metamaterials Using Epsilon-near-Zero Media Doped with Defects
• Optical lattices with exceptional points in the continuum
• Lasing Threshold Condition for Oblique TE and TM Modes, Spectral Singularities, and Coherent Perfect Absorption
• Generalized Unitarity and Reciprocity Relations for PT-symmetric Scattering Potentials
• Asymmetric lasing at spectral singularities
• Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials
• Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
• The New Phase due to Symmetry Protected Piecewise Berry Phases; Enhanced Pumping and Non-reciprocity in Trimer Lattices
• Broadband and Wide-Angle Nonreciprocity with a Nonhermitian Metamaterial
• Perturbative Unidirectional Invisibility
• Nonlinear Spectral Singularities and Laser Output Intensity
• High-order spectral singularity
• Kerr Nonlinearity Induced Nonreciprocity in dissipatively coupled resonators
• Cavity controlled spectral singularity
• Unidirectional Reflection and Invisibility in Nonlinear Media with an Incoherent Nonlinearity
• Solving scattering problems in the half-line using methods developed for scattering in the full line
• Scattering Theory and $\mathcal{P}\mathcal{T}$-Symmetry
• Spectral Singularities, Threshold Gain, and Output Intensity for a Slab Laser with Mirrors
• Quantum noise induced nonreciprocity for single photon transport in parity-time symmetric systems
• Spectral singularity enhances transverse spin
• Heat transport through an open coupled scalar field theory hosting stability-to-instability transition
• Consequences of nonreciprocity in reflection from a truncated spatial Kramers-Kronig medium
• Spectral singularities and threshold gain of a slab laser under illumination of a focused Gaussian beam