Superconducting plasma edge along the \boldmath $c$ axis in La$_{2-x}$Ba$_x$CuO$_4$\unboldmath

The optical properties of La$_{2-x}$Ba$_x$CuO$_4$ (LBCO) have been measured for a number of temperatures over a wide frequency range along the poorly-conducting $c$ axis for the $x=0.095$, $0.125$ and $0.155$ Ba concentrations. In slightly underdoped LBCO ($x=0.095$, $T_c\simeq 32$~K), a sharp plasma edge is observed in the reflectance at low frequency below $T_c$; this plasma edge is associated with Josephson coupling of the copper-oxygen planes and the formation of a bulk three-dimensional superconducting state. A plasma edge is also observed in the more heavily-doped material ($x=0.155$, $T_c\simeq 32$~K) below $T_c$ at higher frequency; however, it is significantly broader in character. Interestingly, for the $x=1/8$ doping, static charge and spin stripe order develop at 54 and 42~K, respectively; the superconducting transition is strongly suppressed ($T_c\simeq 3$~K) and the plasma edge is not observed. The failure to observe a plasma edge for this doping is consistent with the recently proposed view that the layers are decoupled due to the formation of spin stripes, blocking the formation of a coherent three-dimensional superconducting state.