  Dual-comb spectroscopy typically requires the utilization of two independent
and phase-locked femtosecond lasers, resulting in a complex and expensive
system that hinders its industrial applications. Single-cavity dual-comb lasers
are considered as one of the primary solution to simplify the system. However,
controlling the crucial parameter of difference in repetition rates remains
challenging. In this study, we present a dual-comb mode-locked Yb:CALGO laser
based on a cavity-shared configuration with separated end mirrors. We employ
two pairs of end mirrors and two thin-film polarizers angled at 45 degrees to
the cavity axis, leading to separating the cross-polarized laser modes. We
achieve simultaneous operation of two combs at approximately 1040 nm with pulse
durations of around 400 fs and an average power exceeding 1 W. The repetition
rates are approximately 59 MHz and their difference can be easily tuned from
zero up to the MHz range. By effectively canceling out common mode noises, we
observe minimal fluctuation in the repetition rate difference with a standard
deviation of about 1.9 Hz over ten minutes, while experiencing fluctuations in
repetition rates as large as 90 Hz. We demonstrate the capabilities of this
system by utilizing the free-running dual-comb setup for asynchronous optical
sampling on a saturable absorber and measuring etalon transmission spectrum.
This system allows for simple and independent control of the repetition rates
and their difference during operation, facilitating the selection of optimal
repetition rate difference and implementation of phase-locking loops. This
advancement paves the way for the development of simple yet high-performance
dual-comb laser sources.
