Energy scalability limits of dissipative solitons

In this study, we apply a thermodynamical approach to elucidate the primary constraints on the energy scaling of dissipative solitons (DS). We rely on the adiabatic theory of strongly chirped DS and define the DS energy scaling in terms of dissipative soliton resonance (DSR). Three main experimentally verifiable signatures identify a transition to DSR: (i) growth of a Lorentzian spike at the centrum of the DS spectrum, which resembles a spectral condensation in Bose-Einstein condensate, (ii) saturation of the spectrum broadening, and (iii) asymptotic DS stretching. We connect the DSR breakup with three critical factors: (i) decoupling of two correlation scales inherent in strongly chirped DS, (ii) resulting rise of the DS entropy with energy, which provokes its disintegration, and (iii) transition to a nonequilibrium phase, which is characterized by negative temperature. The breakup results in multiple stable DS generation. Theoretical results are in good qualitative agreement with the experimental data from a Kerr-lens mode-locked ${\mathrm{Cr}}^{2+}$:ZnS chirped-pulse oscillator (CPO) that paves the way for optimizing high-energy femtosecond pulse generation in solid-state CPO and all-normal-dispersion fiber lasers.