  Dual-comb lasers from which asynchronous ultrashort pulses can be
simultaneously generated have recently become an interesting research subject.
They could be an intriguing alternative to the current dual-laser
optical-frequency-comb source with highly sophisticated electronic control
systems. If generated through a common light path traveled by all pulses, the
common-mode noises between the spectral lines of different pulse trains could
be significantly reduced. Therefore, coherent dual-comb generation from a
completely common-path, unidirectional lasing cavity would be an interesting
territory to explore. In this paper, we demonstrate such a dual-comb lasing
scheme based on a nanomaterial saturable absorber with additional pulse
narrowing and broadening mechanisms concurrently introduced into a mode-locked
fiber laser. The interactions between multiple soliton formation mechanisms
result in unusual bifurcation into two-pulse states with quite different
characteristics. Simultaneous oscillation of pulses with four-fold difference
in pulsewidths and tens of Hz repetition rate difference is observed. The
coherence between these spectral-overlapped, picosecond and femtosecond pulses
is further verified by the corresponding asynchronous cross-sampling and
dual-comb spectroscopy measurements.
