Effect of Cherenkov radiation on the interaction of temporal dissipative solitons in a driven cavity with high order dispersion

Driven optical cavities widely used for generation of optical frequency combs are known to support the so-called temporal cavity solitons (CSs) manifesting themselves in the form of short optical pulses propagating along the cavity. A formation of temporal CSs in a standard silica fiber cavity [1] and in a continuous-wave driven nonlinear optical microresonators [2] were recently studied experimentally. In particular, the experimental investigation of the temporal CSs interaction performed in [1] indicates that due to a very fast decay of the CS tail stable soliton bound states (BS) are hardly observable. Here we demonstrate theoretically that the interaction of bright and dark temporal CSs is strongly modified in the presence of even very small high order chromatic dispersion terms. We show that the appearance of weakly decaying dispersive waves (sometimes referred to as a Cherenkov radiation, see Fig. 1) emitted by CSs leads to a strong enhancement of their interaction at large distances and, hence, strongly facilitates experimental observation of the BS. We present an analytical theory of the CSs interaction [3] and show that for the CSs interaction the Newton's 3rd Law is violated in the presence of third order dispersion. We consider dynamics of CSs in a driven optical cavity described by the well-known Lugiato-Lefever equation with high order dispersion terms. We derive the equations governing the slow time evolution of the coordinates of two well separated solitons interacting weakly via their exponentially decaying tails. We show that the interference between solitons and the Cherenkov radiation produces an oscillating pattern responsible for the formation of a large number of stable BS with large CSs separations (see Fig. 2). Furthermore, we demonstrate that the soliton interaction is very asymmetric: while one of the two solitons remains almost unaffected by the interaction force, another one is strongly modified by the interaction. Finally, we discuss the effect of forth and higher order dispersions on the CSs interaction and the influence of the high order dispersion on the interaction of dark CSs.