Casimir force between $\delta-\delta^{\prime}$ mirrors transparent at high frequencies

We investigate, in the context of a real massless scalar field in $1+1$ dimensions, models of partially reflecting mirrors simulated by Dirac $\ensuremath{\delta}\ensuremath{-}{\ensuremath{\delta}}^{\ensuremath{'}}$ point interactions. In the literature, these models do not exhibit full transparency at high frequencies. In order to provide a more realistic feature for these models, we propose a modified $\ensuremath{\delta}\ensuremath{-}{\ensuremath{\delta}}^{\ensuremath{'}}$ point interaction that enables full transparency in the limit of high frequencies. Taking this modified $\ensuremath{\delta}\ensuremath{-}{\ensuremath{\delta}}^{\ensuremath{'}}$ model into account, we investigate the Casimir force, comparing our results with those found in the literature.