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A perfect vortex beam has been attracting tremendous attention due to the fact that its ring radius is independent of the topological charge. Taking advantage of the superposition principle of phase in Fourier space, we proposed to generate perfect vortex beam using propagation-phase-based dielectric metasurface, which exhibits production efficiency larger than 83.5%. Due to the sensitivity of propagation phase to the polarization of incident beam, two sets of phase profiles can be imposed on a single dielectric metasurface, enabling the simultaneous generation of dual perfect vortex beams. Based on this property, convenient control to the radius and/or topological charge of perfect vortex beam is achieved by switching the incident polarization between two orthogonal polarizations, without redesigning metasurface or changing optical path. What’s more important, the crosstalk of these two channels is low, less than 4%. Thus, the propagation-phase method of producing perfect vortex beam will find significant applications in optical communication, particle trapping, particle manipulation and holographic display.

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Although the inverse Doppler effect has been observed experimentally at optical frequencies in photonic crystal with negative effective refractive index, its explanation is based on phenomenological theory rather than a strict theory. Elucidating the physical mechanism underlying the inverse Doppler shift is necessary. In this article, the primary electrical field component in the photonic crystal that leads to negative refraction was extracted, and the phase evolution of the entire process when light travels through a moving photonic crystal was investigated using static and dynamic finite different time domain methods. The analysis demonstrates the validity of the use of np (the effective refractive index of the photonic crystal in the light path) in these calculations, and reveals the origin of the inverse Doppler effect in photonic crystals.

The negative Goos-Hänchen shift (GHS) on a two-dimensional photonic crystal with an effective negative refractive index is investigated by simulation and experiment. The measured refractive index of the fabricated photonic crystal is nearly -0.44. The difference between the Goos-Hänchen shift of the transverse electric wave G_TE and that of the transverse magnetic wave G_TM (DGHS) in the height direction of a silicon rod is measured at three incident angles. The result shows that DGHS is always smaller than -G_TM, thus G_TE<0; therefore, the negative GHS does occur on the surface of the photonic crystal with a negative refractive index.