Restoration of evanescent waves in lens obeys Cesáro convergence

Abstract

Abstract In this paper, we show that the restoration of the evanescent wave in a perfect lens obeys a new kind of convergence known as Cesàro convergence. Cesàro convergence allows us to extend the domain of convergence to the complex plane in terms of the Riemann zeta function. Therefore, from the Riemann zeta function properties, we show that it is not possible to restore the evanescent wave for all the values of reflection r z ′ , [here r z ′ is complex]. The special value, that is, r z ′  = 1/2 + ib refers to the non-existence of evanescent wave, is the physicist’s proof of the Riemann Hypothesis.