PT-symmetric Optical Potential Research Articles

Computing Dirichlet eigenvalues of the Schrödinger operator with a PT-symmetric optical potential

We provide estimates for the eigenvalues of non-self-adjoint Sturm–Liouville operators with Dirichlet boundary conditions for a shift of the special potential 4cos ^{2}x+4iVsin 2x that is a PT-symmetric optical potential, especially when |c|=|sqrt{1-4V^{2}}|<2 or correspondingly 0leq V<sqrt {5}/2. We obtain some useful equations for calculating Dirichlet eigenvalues also for |c|geq 2 or equally Vgeq sqrt{5}/2. We discuss our results by comparing them with the periodic and antiperiodic eigenvalues of the Schrödinger operator. We even approximate complex eigenvalues by the roots of some polynomials derived from some iteration formulas. Moreover, we give a numerical example with error analysis.

Parity-time symmetry in coherent asymmetric double quantum wells

A coherently prepared asymmetric double semiconductor quantum well (QW) is proposed to realize parity-time (PT) symmetry. By appropriately tuning the laser fields and the pertinent QW parameters, PT-symmetric optical potentials are obtained by three different methods. Such a coherent QW system is reconfigurable and controllable, and it can generate new approaches of theoretically and experimentally studying PT-symmetric phenomena.

Butterfly-shaped and dromion-like optical waves in a tapered graded-index waveguide with variable group-velocity dispersion

Butterfly-shaped and dromion-like optical waves in a tapered graded-index waveguide (GRIN) are reported for the first time. The generalized nonlinear Schrödinger equation, which describes wave propagation in GRIN with variable group-velocity dispersion (GVD), nonlinearity, PT symmetric optical potentials, is investigated and analytical solutions for this dynamical system are obtained. The physical effects affecting these waves are explicated in detail. The stability of dromion-like structures is analyzed when the GVD parameter is perturbed. We have observed oscillation structure exhibiting strong interference due to this applied perturbation. For a particular value of the modulation of the GVD parameter, the oscillation structure is transformed into two dromion-like structures. It indicates that the dromion-like structure is unstable, and the coherence intensity is affected by the modified perturbation parameter. We further demonstrate the phenomenon of unbreakable PT symmetry of these novel nonlinear waves for three explicit examples.

Erratum:PT-symmetric optical potentials in a coherent atomic medium [Phys. Rev. A88, 041803(R) (2013)

Erratum:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric optical potentials in a coherent atomic medium [Phys. Rev. A<b>88</b>, 041803(R) (2013)

Spectral singularity in confined PT symmetric optical potential

We present an analytical study for the scattering amplitudes (Reflection $|R|$ and Transmission $|T|$), of the periodic ${\cal{PT}}$ symmetric optical potential $ V(x) = \displaystyle W_0 \left( \cos ^2 x + i V_0 \sin 2x \right) $ confined within the region $0 \leq x \leq L$, embedded in a homogeneous medium having uniform potential $W_0$. The confining length $L$ is considered to be some integral multiple of the period $ \pi $. We give some new and interesting results. Scattering is observed to be normal ($|T| ^2 \leq 1, \ |R|^2 \leq 1$) for $V_0 \leq 0.5 $, when the above potential can be mapped to a Hermitian potential by a similarity transformation. Beyond this point ($ V_0 > 0.5 $) scattering is found to be anomalous ($|T| ^2, \ |R|^2 $ not necessarily $ \leq 1 $). Additionally, in this parameter regime of $V_0$, one observes infinite number of spectral singularities $E_{SS}$ at different values of $V_0$. Furthermore, for $L= 2 n \pi$, the transition point $V_0 = 0.5$ shows unidirectional invisibility with zero reflection when the beam is incident from the absorptive side ($Im [V(x)] < 0$) but finite reflection when the beam is incident from the emissive side ($Im [V(x)] > 0$), transmission being identically unity in both cases. Finally, the scattering coefficients $|R|^2$ and $|T|^2 $ always obey the generalized unitarity relation : $ ||T|^2 - 1| = \sqrt{|R_R|^2 |R_L|^2}$, where subscripts $R$ and $L$ stand for right and left incidence respectively.