A. Kenfack-Jiotsa

Non-Hermitian trimers: PT-symmetry versus pseudo-Hermiticity

We study a structure composed of three coupled waveguides with gain and loss, a non-Hermitian trimer. We demonstrate that the mode spectrum can be entirely real if the waveguides are placed in a special order and at certain distances between each other. Such structures generally lack a spatial symmetry, in contrast to parity-time symmetric trimers which are known to feature a real spectrum. We also determine a threshold for wave amplification and analyse the scattering properties of such non-conservative systems embedded into a chain of conservative waveguides.

Effect of Second-Neighbor Inductive Coupling on the Modulational Instability in a Coupled Line of Transmission

In this work, the dynamics of modulated waves in a couple nonlinear LC transmission line is investigated. By employing the standard linear stability analysis, the growth rate of the instability is derived as a function of the wave numbers and system parameters. The regions of modulational instability can then be obtained and the influence of second-neighbor occuring via inductors in a nonlinear transmission line can be studied. As result, we found that the second-neighbor couplings add new maxima of gain; increase the group velocity, and the magnitude of the wave. Therefore, the network becomes more stable to small external perturbations.

Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines

In this work, we investigate the dynamics of modulated waves non-identical coupled nonlinear transmission lines. Traditional methods for avoiding mode mixing in identical coupled nonlinear electrical lines consist of adding the same number of linear inductors in each branch. Adding linear inductors in a single line leads to asymmetric coupled nonlinear electrical transmission lines which propagate the signal and the mode mixing. On one hand, the difference between the two lines induced the fission for only one mode of propagation. This fission is influenced by the amplitude of the signal and the amount of the input energy as well; it also narrows the width of the input pulse soliton, leading to a possible increasing of the bit rate. On the other hand, the dissymmetry of the two lines converts the network into a good amplifier for the ω_ mode which corresponds to the regime admitting low frequencies.

Thresholdless characterization in space and time reflection symmetry electronic dimers

We develop a general mutual inductive M, inductive L, and capacitive C couplings parity time symmetry (MLC PTS) electronic dimer model. We successfully show that the dimers separately coupled with M, L, or ML can be made thresholdless by adding a capacitance C in parallel. Thus, sufficient conditions for thresholdless transitions were determined. The scattering properties of our model reveal the suppression of unidirectional invisibility from the gain input when the Hermitian line coupling exceeds a critical point. Likewise, the scattering system becomes unidirectional PTS. Remarkably, under the thresholdless conditions, lasing modes appear for imaginary values of wavenumbers corresponding to either real or purely imaginary values of the gain/loss modulation. This latter demonstrates the ability to control prohibited waves in the linear regime.

Second-nearest-neighbor Interaction in a Nonlinear Bi-inductance Transmission Line

The objective of this paper is to study the effects of second-neighbors inductive coupling in a nonlinear bi-inductance transmission line. For this purpose, we first derive the equation governing the wave propagation in the network. The condition for which the network can exhibit modulational instability is also determined. As result, one observes that the second-neighbors well influence the line by increasing the bandwidth, the group velocity and the magnitude of the wave. The coefficients of the complex Ginzburg-Landau equation are significantly modified. The exactness of this analytical analysis is confirmed by numerical simulations performed on the exact equation of the network. Results which have been presented in this work can be also applied in the context of molecular or atomic chains.