The cavity resonance mode of Bi$_{\mathrm{2}}$Sr$_{\mathrm{2}}$CaCu$_{\mathrm{2}}$O$_{\mathrm{8}}$ mesa terahertz sources as probed by scanning laser thermal microscopy*

Stacked Intrinsic Josephson Junctions (IJJs) in the extremely anisotropic high-$T_{c}$ superconductor Bi$_{\mathrm{2}}$Sr$_{\mathrm{2}}$CaCu$_{\mathrm{2}}$O$_{\mathrm{8\thinspace }}$are a promising solid-state source of coherent terahertz radiation in the so-called ``THz gap'' range. In these devices, a geometric resonant mode of a stack of IJJs of typical dimensions 300 x 60 x 1 microns$^{\mathrm{3}}$ acts to synchronize the individual junctions, resulting in coherent far-field THz emission. This resonance can be probed by scanning thermal laser microscopy, in which a modulated optical laser beam is rastered across the top surface of a stack. The resulting thermal perturbation to the stack's cavity mode can thus be mapped via the resulting \textit{xy}-dependent modulation of the stack's electrical resistance. Here we discuss the experimentally measured scanning laser pattern of such a THz cavity mode, and the implications of its symmetry for the mechanism of IJJ synchronization in these devices.