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Multi-dimensional laser mode combs (mode hyper-combs)

Laser frequency combs, as most lasers, are one-dimensional. Here we present a realization of d-dimensional laser mode lattices (mode hyper-combs) with unique properties. They are constructed from regular 1-dimensional combs by multi-frequency modulation in active mode-locking (AML). The hyper-comb, with near neighbor mode interaction and noise functioning as temperature, is mapped to interacting magnetic spin-lattices in the spherical-model, which is one of the few statistical-mechanics systems soluble in all dimensions. The important result is that such systems have, in d>2 dimensions, a phase-transition to a global mode-phase-ordered hyper-comb. It changes the nature of AML lasers, giving ultimately short and robust pulses which can capture very broad frequency bandwidths. Additionally, the hyper-combs can serve as a rare physical realization of the spherical-model in any dimension.