An infrared study of the pancake vortex state in La$_{2-x}$Sr$_{x}$CuO$_{4}$ across the phase diagram

We report on a doping dependent study of the far-infrared interlayer response in the high-temperature superconductor La$_{2-x}$Sr$_{x}$CuO$_{4}$ (La214). A magnetic field up to 8 Tesla applied perpendicular to the CuO$_{2}$ planes is found to increasingly suppress the Josephson plasma resonance (JPR) with decreased doping. By 6 Tesla at a temperature of 8 Kelvin, the c-axis reflectivity is identical to that of the normal state in the most underdoped samples, suggesting the sample is in a two dimensional superconducting state. This behavior is in contrast to fields parallel to the CuO$_{2}$ planes, where only a small suppression of the JPR is seen up to 17 Tesla. Vortex wandering and static spin density waves are considered as possible mechanisms for plane decoupling.