  The emerging concept of extremely-large holographic multiple-input
multiple-output (HMIMO), beneficial from compactly and densely packed
cost-efficient radiating meta-atoms, has been demonstrated for enhanced degrees
of freedom even in pure line-of-sight conditions, enabling tremendous
multiplexing gain for the next-generation communication systems. Most of the
reported works focus on energy and spectrum efficiency, path loss analyses, and
channel modeling. The extension to secure communications remains unexplored. In
this paper, we theoretically characterize the secrecy capacity of the HMIMO
network with multiple legitimate users and one eavesdropper while taking into
consideration artificial noise and max-min fairness. We formulate the power
allocation (PA) problem and address it by following successive convex
approximation and Taylor expansion. We further study the effect of fixed PA
coefficients, imperfect channel state information, inter-element spacing, and
the number of Eve's antennas on the sum secrecy rate. Simulation results show
that significant performance gain with more than 100\% increment in the high
signal-to-noise ratio (SNR) regime for the two-user case is obtained by
exploiting adaptive/flexible PA compared to the case with fixed PA
coefficients.
