Conical diffraction modulation in fractional dimensions with a PT-symmetric potential

This study analyzes conical diffraction in space-fractional parity-time (PT) symmetry, which arises in a fractional Schrödinger equation with a periodic PT-symmetric potential. The peculiar characteristics of the corresponding Floquet Bloch modes are also examined in detail. We find that the band structure in such a model is different from that in regular PT symmetry, especially the critical point, which becomes symmetric linear for the one-dimensional case, and cone-like for the two-dimensional case. During propagation, the linear band structure has peculiar properties, including splitting or diffraction-free propagation, preferential propagation, and unidirectional propagation. Whether the cone-like band structure leads to cone diffraction or nondiffracting propagation depends on which Floquet Bloch modes are excited by the input. Our results may have potential application in light modulation in PT symmetry and provide a new platform to study other exciting topics related to conical diffraction.