Modem illumination of monotone polygons

For monotone orthogonal polygons with n vertices we show that for k=1 and for even k, every such polygon can be illuminated with ⌈n−22k+4⌉k-modems, while for odd k≥3, ⌈n−22k+6⌉k-modems are always sufficient. Further, by presenting according examples of monotone orthogonal polygons, we show that both bounds are tight.