RESUMO
Lenses with a tunable focus are highly desirable but remain a challenge. Here, we demonstrate a microwave varifocal meta-lens based on the Alvarez lens principle, consisting of two mechanically movable tri-layer metasurface phase plates with reversed cubic spatial profiles. The manufactured multilayer Alvarez meta-lens enables microwave beam collimation/focusing at frequencies centered at 7.5 GHz, and shows one octave focal length tunability when transversely translating the phase plates by 8 cm. The measurements reveal a gain enhancement up to 15 dB, 3-dB beam width down to 3.5∘, and relatively broad 3-dB bandwidth of 3 GHz. These advantageous characteristics, along with its simplicity, compactness, and lightweightness, make the demonstrated flat Alvarez meta-lens suitable for deployment in many microwave systems.
RESUMO
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of vacancy particles are considered. In one set all vacancies are of one-cell size. In the other set the sizes of vacancy particles match the separation between atoms. Explicit expressions are obtained for the Gibbs free energy and the distribution of spaces between atoms at thermal equilibrium. Applications to various types of interaction potentials are discussed, including long-range potentials that give rise to phase transitions. Extensions to hard rod systems are straightforward and are shown to agree with existing results for lattice models and their continuum limits.
