Effect of Cherenkov radiation on localized-state interaction

Abstract

We study theoretically the interaction of temporal localized states in all fiber cavities and microresonator-based optical frequency comb generators. We show that Cherenkov radiation emitted in the presence of third order dispersion breaks the symmetry of their interaction and greatly enlarges the interaction range thus facilitating the experimental observation of the soliton bound states. Analytical derivation of the reduced equations governing slow time evolution of the positions of two interacting localized states in the Lugiato-Lefever model with third order dispersion term is performed. Numerical solutions of the model equation are in close agreement with analytical predictions.PACS numbers: 42.60. Da, 42.60.Fc, 42.65.Sf, 42.65.Tg, 05.45.Yv Frequency comb generation in microresonators has revolutionized such research disciplines as metrology and spectroscopy [1,2]. This due to the development of laser-based precision spectroscopy, including the optical frequency comb technique [3]. Driven optical microcavities widely used for the generation of optical frequency combs can be modeled by Lugiato-Lefever equation [4] that possesses solutions in the form of localized structures also called cavity solitons (CSs) [5,6]. Localized structures of the Lugiato-Lefever model have been theoretically predicted in [7] and experimentally observed in [8]. In particular, temporal CSs manifest themselves in the form of short optical pulses propagating in the cavity. The experimental evidence of temporal CSs interaction performed in [8] indicated that due to a very fast decay of the their tails, stable CS bound states are hardly observable. It has been also theoretically shown that when periodic perturbations are present [9, 10], radiation of weakly decaying dispersive waves, i.e., so-called Cherenkov radiation emitted by CSs leads to a strong increase of their interaction range [11,12]. Experimental investigation of this radiation induced by the high order dispersion was carried out in [13,14]. Numerical studies on CSs bound states in the presence of high order dispersions have been reported in [15,[17][18][19][20][21][22].In this letter, we provide an analytical description of how two CSs can interact under the action of the Cherenkov radiation induced by high order dispersion. For this purpose, we use the paradigmatic Lugiato-Lefever model with the third order dispersion term. We derive the equations governing the time evolution of the position of two well-separated CSs interacting weakly via their exponentially decaying tails. We demonstrate that the presence of the third order dispersion term breaking the parity symmetry of the model equation leads to a great increase of the CS interaction range and affects strongly the nature of the CSs interaction. We show that the interference between the dispersive waves emitted by two interacting CSs produces an oscillating pattern responsible for the stabilization of the CS bound states. In particular, we show that when two CSs interact, one of them remains almost unaffected by the...

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