Transform-limited pulse generation in phase-mismatched optical parametric oscillators

•The relation between the phase-mismatch and pulse characteristics of ultrafast optical parametric oscillators.•In a phase-mismatched optical parametric oscillator, transform-limited femtosecond optical pulses could be generated due to the interplay between the phase-mismatch and the intracavity group-velocity-dispersion effects.•A non-zero phase-mismatch in a nonlinear crystal would introduce a frequency up-chirp or down-chirp in the resonating pulses of optical parametric oscillators.•The sign and magnitude of the phase-mismatch induced frequency-chirp could be controlled by manipulating the wavevector-mismatch of the nonlinear crystal.