c-axis magneto optics and vortex dynamics of underdoped YBCO

c-axis reflectance measurements have been carried out on high quality single crystals of YBa$_{2}$Cu$_{3}$O$_{x }$at two dopings, x = 6.65 and x = 6.75, with magnetic fields oriented both parallel and perpendicular to the CuO$_{2}$ plane. Fields applied parallel to the plane induced several interesting effects at temperatures below the superconducting transition, including a strong suppression of superfluid density and the appearance of a new mode at frequencies below the Josephson plasma resonance (JPR). This mode is field-dependent both in magnitude and position, shifting to higher energies with increasing field. Here it is analyzed within several models of vortex dynamics, including that of Tachiki, Koyama, and Takahashi. Application of fields perpendicular to the plane creates a shift in the JPR frequency, as predicted by the TKT model.