Unidirectional emission from a P T -symmetric annular microcavity

The introduction of a scattering center to microdisk lasers has been considered as an effective way to tailor their far-field emissions. However, this approach is practically limited by its nearby modes with higher quality ($Q$) factors and worse directionalities. In this research, by applying the simple concept of parity-time ($\mathcal{P}\mathcal{T}$) symmetry, we demonstrate that the resonances with well-designed directionalities can be selectively excited in optical microcavities. Taking the annular microcavities as examples, the unidirectional laser emissions and single-mode operations have been realized simultaneously by breaking the $\mathcal{P}\mathcal{T}$ symmetry. More interestingly, we find that the $\mathcal{P}\mathcal{T}$-symmetric modulations on the imaginary parts of the refractive index in a circular microdisk can affect the internal ray dynamics and thus generate highly directional laser emission. This research can boost both the fundamental studies and the practical applications of $\mathcal{P}\mathcal{T}$-symmetric systems.