Tunneling times in complex potentials

Tunneling times in absorptive media, described by complex potentials, are investigated. A general expression relating relevant tunneling times is extended by introducing a new term τaτa. For both single Dirac δ   potential and rectangular potential τaτa exhibits a maximum for a specific complex potential configuration. The optimal shape of a complex rectangular potential in respect to the maximization of τaτa differs drastically in the short or long wavelength limits.