  Dissipative Kerr soliton microcombs in microresonators has enabled
fundamental advances in chip scale precision metrology, communication,
spectroscopy, and parallel signal processing. Here we demonstrate polarization
diverse soliton transitions and deterministic switching dynamics of a self
stabilized microcomb in a strongly coupled dispersion-managed microresonator
driven with a single pump laser. The switching dynamics are induced by the
differential thermorefractivity between coupled transverse magnetic and
transverse electric supermodes during the forward backward pump detunings. The
achieved large soliton existence range and deterministic transitions benefit
from the switching dynamics, leading to the cross polarized soliton microcomb
formation when driven in the transverse magnetic supermode of the single
resonator. Resultantly the pump laser always exists at the effective blue
detuning of the transverse magnetic resonance, fundamentally mitigating the
thermal destabilization barrier and improving accessibility of the soliton
formation regime. Subsequently and secondly, we demonstrate two distinct
polarization diverse soliton formation routes arising from chaotic or
periodically modulated waveforms via pump power selection. The generated self
stabilized supermode microcomb features an extraordinarily large soliton
existence range, a variety of soliton state transitions with well defined pump
laser tuning, high pump microcomb conversion efficiency, and low repetition
rate phase noise.
