Negative frequencies in the scattering properties of parity–time symmetry and anti-parity–time symmetry

We present the scattering properties of parity–time (PT)-symmetric and anti-parity–time (APT)-symmetric systems embedded in a new electronic waveguide. The set-up is built around imaginary resistors and positive or negative other components. These combinations give rise to a real spectrum in breakable and unbreakable PT symmetries. When it exists, the transition marks the passage from real to complex eigenvalues whereas in the APT symmetry, the eigenvalues pass from pure imaginary to complex eigenvalues. The frequencies of cells in PT-symmetric configurations must have the same sign whereas in APT-symmetric configurations, the frequencies must have opposite signs. The electrical line presented can drive negative frequencies and gives the possibility to demonstrate the existence of a mirror behaviour in scattering properties of the PT symmetry. We derive the condition of appearance of the coherent perfect absorber and laser, unidirectional invisibility from one or both sides of the system. In APT symmetry, only the coherent perfect absorber exists in the two configurations of waveguides used. The respect of the law of conservation depends on the nature of the eigenspectrum peculiar to each type of the dimer.