Description
Optical frequency combs generated in driven passive cavities are generally associated with cavity solitons, arising from the balance of gain and loss and of Kerr nonlinearity and anomalous quadratic dispersion [1]. Their formation is successfully described by the Lugiato–Lefever equation (LLE) [2]. Cavity solitons often organize into soliton crystals (SCs), ordered arrays of closely spaced cavity solitons filling the cavity [1]. SC formation is commonly attributed to strong oscillatory soliton tails induced by mechanisms such as avoided mode crossings or higher-order dispersion [3]. However, in the absence of these mechanisms the oscillatory tails are strongly damped, becoming pronounced only within a small region of parameter space [4]. Under these conditions, SC formation would therefore be expected to be challenging.
However, we show that SCs can form over a wide region of the parameter space of the standard LLE. Combining dynamical simulations and stability analysis of its solutions, we find that when multiple cavity solitons coexist, their mutual repulsion drives them toward an equally spaced arrangement, leading to a perfect soliton crystal. As the pump power increases, the relaxation time toward an equispaced configuration tends to infinity, allowing non-equispaced soliton arrangements to persist as imperfect crystals. For a fixed number of solitons, we investigate the stability of the corresponding perfect crystal as the inter-soliton distance is varied. Below a critical separation, the crystal becomes unstable through the merger of neighbouring solitons, reducing the crystal order.
Our results provide new insight into soliton-crystals and explain their formation in systems such as fiber cavities and microresonators with weak mode crossings.
[1] Pasquazi et al., Physics Reports 729, 1–81 (2018).
[2] Coen et al., Opt. Lett. 38, 1790–1792 (2013).
[3] Wang et al., Optica 4, 855–863 (2017).
[4] Parra-Rivas et al., Eur. Phys. J. D 71, 198 (2017).
| I am the presenting author | Yes |
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