Negative refractive index, Perfect Lens and Cesàro convergence

In this letter, we show that the restoration of evanescent wave in perfect lens obeys a new kind of convergence known as Cesaro convergence. Cesaro convergence allows us to extend the domain of convergence that is analytically continuing to the complex plane in terms of Riemann zeta function. Therefore, from the properties of Riemann zeta function we show that it is not possible to restore the evanescent wave for all the values of $r_z'$, [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 physicists proof of Riemann Hypothesis.

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