The development of small-scale self-focusing in a nonlinear Kerr medium after preliminary self-filtering of a laser beam propagating in free space is studied numerically. It is shown that, under definite conditions, due to self-filtering, filamentation instability (beam splitting into filaments) either occurs at significantly larger values of the B-integral, or does not occur at all. In the latter case, there develops the honeycomb instability revealed in this work. This instability is the formation of a random honeycomb structure in the beam cross-section. It is shown that self-filtering can significantly increase the permissible values of the B-integral, at which the beam quality remains acceptable.

This paper presents a compact dual-band filtering antenna without extra employing of filter structures. The antenna is designed using a planar dual-composite right/left-handed (D-CRLH) transmission line unit cell, where the filtering function is achieved through current cancellation between the D-CRLH resonators. The antenna is designed to function at 3.0 and 5.1 GHz, which can serve different WLAN applications. The antenna is a co-planar waveguide fed with a very compact size of only 30 × 16 mm2. Compared to the conventional patch antenna, the antenna size is only 17% at 3.0 GHz and 31% at 5.1 GHz. Despite the small size, the antenna preserves a good omni-directional radiation pattern at the two resonant frequencies with a measured realized gain of 2 and 2.7 dB, respectively. At the stopband in-between the two resonant bands, the reflection coefficient is almost 0 dB at 4.25 GHz and complete non-radiation is proved with a −11 dB measured realized gain. The different antenna filtering functions are verified by full-wave simulation and measurements.