What is the role of via fencing in preventing substrate mode propagation in a thick PCB at millimeter wave?

The role of via fencing in preventing substrate mode propagation in a thick PCB at millimeter-wave frequencies is to create an electromagnetic barrier that confines the fields to the desired transmission line mode and suppresses parasitic parallel-plate and surface wave modes that would otherwise radiate, couple to adjacent circuits, and cause resonances. At mmW frequencies, the substrate thickness relative to the wavelength becomes large enough that higher-order modes can propagate. The substrate modes include: the parallel-plate mode (TEM and higher-order modes between two ground planes or between a ground plane and the top surface; the first higher-order mode's cutoff frequency is: f_c = c / (2h x sqrt(Dk)), where h is the substrate thickness; for h = 0.5 mm and Dk = 3.0: f_c = 173 GHz, above which the mode propagates), and surface waves (TE and TM modes guided by the dielectric-air interface; for a grounded dielectric slab: the first surface wave mode has no cutoff for TM0, but its power content increases with frequency and substrate thickness). Via fencing suppresses these modes by: placing rows of grounded vias along both sides of a transmission line or around a circuit, creating a waveguide-like structure that has a cutoff frequency above the operating frequency for the parasitic modes (the cutoff is determined by the via-to-via spacing: f_cutoff approximately c / (2s x sqrt(Dk)), where s is the via pitch; for effective suppression at 77 GHz: s < c / (2 x 77e9 x sqrt(3)) = 1.12 mm; typical via pitch for 77 GHz is 0.5-0.8 mm).