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We report a fully stabilized self-referenced all-solid-state-laser frequency comb based on a home-built Kerr-lens mode-locked Yb:CaYAlO4 oscillator, which delivers ultrafast pulses with a pulse duration of 54 fs and an average power of 1.5 W. Free running carrier-envelope phase offset frequency (fceo) is observed with a signal to noise ratio of 40 dB at 100 kHz resolution bandwidth, which is phase-locked to a microwave frequency synthesizer with a residual phase jitter of 370 mrad [1 Hz–1 MHz] and with a standard frequency deviation of 0.8 mHz at 1-s gate time within 3-h, corresponding to the relative frequency instability of 2.9 × 10−18 at 1-s average time. It is the lowest phase noise and the highest frequency stability of fceo obtained in a watt-level all-solid-state bulk laser frequency comb to the best of our knowledge. A 13th repetition rate is simultaneously phase-locked to the same microwave standard with a frequency instability level of 10−12 at 1 s average time. Such fully stabilized power scaling Yb: CaYAlO4 laser frequency combs have great potential for applications in broadband dual comb spectroscopy as well as high loss cases such as long-distance time and frequency transfer. [ABSTRACT FROM AUTHOR]