  Optical resonators enable the generation, manipulation, and storage of
electromagnetic waves. They are widely used in technology and fundamental
research, in telecommunications, lasers and nonlinear optics, ultra-sensitive
measurements in cavity optomechanics, and the study of light-matter
interactions in the context of cavity QED. The physics underlying their
operation is determined by the constructive interference of electromagnetic
waves at specific frequencies, giving rise to the resonance spectrum. This
mechanism causes the limitations and trade-offs of resonator design, such as
the difficulty of confining waves larger than the resonator and 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, such as the largest resonant wavelength, the
free spectral range, the linewidth, and the quality factor. We confirm the
existence of these modes experimentally in an integrated waveguide cavity with
mode converters coupling two transverse modes into one supermode. The resonance
signature of the cascaded-mode resonator is a spectrum resulting from the
coherent superposition of the coupled transverse modes. We also demonstrate a
transverse mode-independent transmission through the resonator and show that
its engineered spectral properties agree with theoretical predictions.
Cascaded-mode resonators introduce properties not found in traditional
resonators and provide a mechanism to overcome the existing trade-offs in the
design of resonators in various application areas.
