  We present the first design and analysis of a solid-state Mamyshev
oscillator. We utilize the phase-mismatched cascaded quadratic nonlinear
process in periodically poled lithium niobite waveguide to generate substantial
spectral broadening for Mamyshev modelocking. The extensive spectral broadening
bridges the two narrowband gain media in the two arms of the same cavity,
leading to a broadband mode-locking not attainable with either gain medium
alone. Two pulses are coupled out of the cavity and each of the output pulses
carries a pulse energy of 25.3 nJ at a repetition rate of 100 MHz. The 10-dB
bandwidth of 2.1 THz supports a transform limited pulse duration of 322 fs,
more than 5 times shorter than what can be achieved with either gain medium
alone. Finally, effects of group velocity mismatch, group velocity dispersion,
and nonlinear saturation on the performance of Mamyshev mode-locking are
numerically discussed in detail.
