“…The fantasy of periodic structures may be seen in antennas, antenna feeds, electromagnetic filters, phase shifters, polarizers, photonic crystals for optical power dividers, multiplexers, switches, photonic band gap structures for solid-state lasers [1][2][3][4][5][6][7][8][9][10], etc. and even in the vacuum electronic devices, such as, linear/particle accelerators [11,12], backward-wave oscillators (BWOs) [13], magnetrons [14], coupledcavity and helix travelling-wave tubes (TWTs) [15][16][17][18][19], cyclotron masers [20,21], gyrotron sources [21][22][23][24] and amplifiers [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], etc..…”