Ferroelectric relaxors are complex materials with distinct properties. The understanding of their dielectric susceptibility, which strongly depends on both temperature and probing frequency, has been a challenge to researchers for many years. Here we report a macroscopic and phenomenological approach based on statistical modeling to investigate how the dielectric response of a relaxor depends on temperature. Employing the MaxwellBoltzmann distribution and considering temperature dependent dipolar orientational polarizability, we propose a minimum statistical model and specific equations to understand and fit numerical and experimental dielectric responses versus temperature. We show that the proposed formula can successfully fit the dielectric response of typical relaxors, including Ba(Zr,Ti)O 3 , 0.87Pb(Zn 1/3 Nb 2/3 ) 0.87 O 3 -0.13PbTiO 3 , 0.95Pb(Mg 1/3 Nb 2/3 )O 3 -0.05Pb(Zr 0.53 Ti 0.47 )O 3 , and Bi-based compounds, which demonstrate the general applicability of this approach.
Spatial shaping of light beams has led to numerous new applications in fields such as imaging, optical communication, and micromanipulation. However, structured radiation is less well explored beyond visible optics, where methods for shaping fields are more limited. Binary amplitude filters are often used in these regimes and one such example is a photon sieve consisting of an arrangement of pinholes, the positioning of which can tightly focus incident radiation. Here, we describe a method to design generalized photon sieves: arrays of pinholes that generate arbitrary structured complex fields at their foci. We experimentally demonstrate this approach by the production of Airy and Bessel beams, and Laguerre-Gaussian and Hermite-Gaussian modes. We quantify the beam fidelity and photon sieve efficiency, and also demonstrate control over additional unwanted diffraction orders and the incorporation of aberration correction. The fact that these photon sieves are robust and simple to construct will be useful for the shaping of short-or long-wavelength radiation and eases the fabrication challenges set by more intricately patterned binary amplitude masks.
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