Parity time symmetry applications in parity time symmetry

Separating and combining different transverse modes in optical waveguides is one of the research areas in integrated optics. Various passive waveguide coupler designs with different geometrical structure are made for separation of transverse modes. Recently, implementation of PT-symmetry potentials with an anology in optics lead to design of different integrated optical devices. This concept firstly studied in quantum physics. It was stated that potentials satisfying V(x) = V*(-x) condition, could get real eigenvalues like hermitian systems. Thereafter it is noticed that utilizing from similarity between Schrödinger equation and wave equation, PT symmetry can be established provided that the complex refractive index distribution 𝑛(𝐫)=𝑛𝑅(𝐫)+𝑖𝑛𝐼(𝐫) obeys 𝑛(𝐫)=𝑛∗(−𝐫) . In this work, we study the implementation of PT-symmetry in quantum cascade lasers. Taking the advantage of this concept by changing coupling coefficients of transverse modes with modulation of gain and loss parameters, we designed a transverse mode splitter in coupled PT-symmetric quantum cascade lasers. Our design is simulated by finite difference eigenmode solver (FDE) and finite difference beam propagation (FD-BPM) method. First, using FDE solver properties of transverse modes in quantum cascade lasers are determined and proper gain and loss values for separating of transverse modes are calculated. Afterwards,designed coupler with gain and loss medium is simulated by FD-BPM method and at the end of work showed that under appropriate gain and loss values TE0 and TE1 modes can be separated.