Flexible and fast estimation method of far-field patterns for digital-coding metasurfaces.We propose a flexible and fast estimation method to calculate the far-field patterns of digital-coding metasurfaces (DCMs) by performing chirp Z-transform (CZT), called the DCM-CZT method.  Because of the expression form of convolution, CZT can be accelerated by fast Fourier transform.  Compared with the traditional discrete Fourier transform (DFT) method, the DCM-CZT method can accurately estimate the far-field patterns with arbitrary element periods.  More importantly, the DCM-CZT method can calculate partial far-field patterns for some specific orientations, instead of the global far-field patterns like DFT does.  We show that the DCM-CZT method can efficiently improve the partial space-resolution to avoid the calculation error caused by the fence effect under acceptable computing time.  Results show that the far-field patterns calculated by the DCM-CZT method have good agreements with full-wave simulations and experimental measurements.  We believe that the DCM-CZT method has potential applications in wireless communications and radar detections.
CZT
Compared with the traditional discrete Fourier transform (DFT) method, the DCM-CZT method can accurately estimate the far-field patterns with arbitrary element periods.  More importantly, the DCM-CZT method can calculate partial far-field patterns for some specific orientations, instead of the global far-field patterns like DFT does.  However, the results of main-lobes calculated by the DFT method have obvious deviations when the element period is about 0.2 wavelengths. 
DFT