Resonators with tailored optical path by cascaded-mode conversions.

Optical resonators enable the generation, manipulation, and storage of electromagnetic waves. The physics underlying their operation is determined by the interference of electromagnetic waves, giving rise to the resonance spectrum. This mechanism causes the limitations and trade-offs of resonator design, such as the fixed relationship between free spectral range, modal linewidth, and the resonator's refractive index and size. Here, we introduce a new class of optical resonators, generating resonances by designing the optical path through transverse mode coupling in a cascaded process created by mode-converting mirrors. The generalized round-trip phase condition leads to resonator characteristics that are markedly different from Fabry-Perot resonators and can be tailored over a wide range. We confirm the existence of these modes experimentally in an integrated waveguide cavity with mode converters coupling transverse modes into one supermode. We also demonstrate a transverse mode-independent transmission and show that its engineered spectral properties agree with theoretical predictions.