Theoretical seminar | 13 January 2021

I will present my results as a part of a midterm attestation

Exceptional point (EP) is a singularity in non-Hermitian systems that exhibits exotic functionalities such as high sensitivity to external perturbations and fine selectivity of a laser mode arising due to the abrupt transition in the eigenvalue spectra. To achieve EP, both the real and imaginary parts of two or several eigenfrequencies should coincide. Perturbations that appeared at the fabrication stage usually lift the degeneracy and it impedes the experimental observation of EP. In this work, we reveal that a Kerr-type nonlinearity can compensate for an initial distortion in resonant frequencies hardly avoidable in practice by the example of a pair of coupled ring resonators. Furthermore, we analytically derive the general conditions of EP in the perturbed pair of coupled ring resonators, where both resonators can be perturbed by different scatterers. Several numerical examples are employed to verify the proposed analytical method. The proposed method enables the possibility to engineer the desired responses in such perturbed systems. For example, it is also shown that, by changing the relative position of the scatterers with respect to each other, quite interesting states such as a chiral EP in one resonator or simultaneous chiral EP in both resonators could be observed.
 

The dynamics of nonlinear optical pulses is an interesting scientific problem, important both from the point of view of new frequencies generation and for the optical processing of information encoded by a sequence of optical pulses. It is convenient to use optical solitons as such pulses since they preserve their shape. To use solitons in practice, it is important to be able to control the way they propagate in waveguiding system. In our research, we study the possibility of solitons manipulation by using the Peierls phase in twisted arrays of optical fibers.