Characteristic scaling parameters for tunneling in strong time-dependent electric fields

Tunneling through a single driven barrier is studied where the ac potential on either side of the barrier is of the general form ${\mathrm{V}}_{\mathrm{ac}}$(z,t)=(a-|${\mathrm{Ax}}^{\mathrm{l},\mathrm{r}}$z+b-|${\mathrm{Ax}}^{\mathrm{l},\mathrm{r}}$)cos ωt (l,r: left,right). Analytic expressions for the transmission and reflection amplitudes are obtained in the δ-barrier limit. The ${\mathrm{\omega }}^{\mathrm{-}1}$ characteristic scaling behavior of the Tien-Gordon theory is recovered in the special case of vanishing ac fields, a-|${\mathrm{Ax}}^{\mathrm{l},\mathrm{r}}$=0, while an ${\mathrm{\omega }}^{\mathrm{-}2}$ scaling is found for finite ac fields, a-|${\mathrm{Ax}}^{\mathrm{l},\mathrm{r}}$≠0, which is not contained in the Tien-Gordon theory. An analogy with the Fabry-Perot interferometer is used to extend the theory to multiple barriers. Implications for experiments are discussed.