We report on a new method to achieve the single-scan polarization-resolved degenerate four-wave mixing (DFWM) spectroscopy in a Rb atomic medium using a vector optical field, in which two pump beams are kept linearly polarized and a vector beam is employed as the probe beam. As the polarization and intensity of the DFWM signal are closely dependent on the polarization state of the probe beam, a vector probe beam with space-variant states of polarization is able to generate a DFWM signal with space-variant states of polarization and intensity across the DFWM image. Accordingly, the polarization-resolved spectra can be retrieved from a single DFWM image. To the best of our knowledge, this is the first time that the single-scan polarization-resolved spectrum detection has been realized experimentally with a vector beam. This work provides a simple but efficient single-scan polarization-resolved spectroscopic method, which would be of great utility for the samples of poor light stability and fast optical processes.

We show that inhomogeneous waveguides of slowly varied parity-time (PT) symmetry support localized optical resonances. The resonance is closely related to the formation of exceptional points separating exact and broken PT phases. Salient features of this kind of non-Hermitian resonance, including the formation of half-vortex flux and the discrete nature, are discussed. This investigation highlights the unprecedented uniqueness of field dynamics in non-Hermitian systems with many potential adaptive applications.