Abstract
Long-range interactions between dark vectorial temporal cavity solitons are induced by the formation of patterns via spontaneous symmetry breaking of orthogonally polarized fields in ring resonators. Turing patterns of alternating polarizations form between adjacent solitons, pushing them apart so that a random distribution of solitons along the cavity length spontaneously reaches equal equilibrium distances, the soliton crystal, without any mode crossing or external modulation. Enhancement of the frequency comb is achieved through the spontaneous formation of regularly spaced soliton crystals, 'self-crystallization', with greater power and spacing of the spectral lines for increasing soliton numbers. Partial self-crystallization is also achievable in long cavities, allowing one to build crystal sections with controllable numbers of cavity solitons separated by intervals of pattern solutions of, again, controllable length.
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