Fig. 1: Principle of symmetrical dispersion-engineering for microcomb generation.

a Dispersion profile with single perturbation at mode \(\mu =-1\) is divided into even and odd components. The purple dashed lines indicate the additional phase shift induced by the second perturbation at mode \(\mu =+1\), which cancels out the odd component of the dispersion. b Microresonator with both inner and outer sidewall Bragg gratings enables the spontaneous formation of platicon microcomb in normal-dispersion regime. Inset: transmission spectrum where two selected mode splittings are independently controlled by the two sets of gratings with different numbers of periods. c Evolution of comb spectra with increased frequency detuning. The color gradient represents the optical power on a logarithmic scale. d Dispersion profiles and phase-matching condition for FWM. The cold- and hot-cavity resonances are marked by blue triangles and orange circles, respectively. The phase-matching conditions are marked by orange dashed lines (perfect) and the yellow thick lines (within a range of \(\pm \kappa /2\)). \({\delta }_{{SPM}}\) and \({\delta }_{{XPM}}\) are the phase shifts caused by Kerr nonlinearity with a relation of \({\delta }_{{XPM}}=2{\delta }_{{SPM}}\), while the local dispersion alterations have been included in both cold- and hot-cavity dispersion profiles. A: asymmetric dispersion engineering with a single dispersion alteration positioned at mode \(\mu =-1\). S: symmetric dispersion engineering with two dispersion alterations positioned at modes \(\mu =\pm 1\).