  Nodal line semimetals have lately aroused much experimental and theoretical
interest, with their gap closing along unconventional trajectories in the 3D
Brillouin zone. These trajectories or nodal lines can close into loops and
trace out intricate knotted or linked configurations with complicated
topologies. In this work, we investigate the semi-classical optical response of
two nodal loops in linked, unlinked and touching configurations, focusing
particularly on the interplay of response anisotropy and non-linearity. We
provide a geometric picture that unifies these aspects and sheds light on the
effects of nodal topology and geometry. Based on a model abstracted from
generic multi nodal loop scenarios, both with or without linkages, our findings
will be applicable for a large class of nodal semimetal materials with multiple
nodal lines or loops.
