Cascaded-mode interferometers: Spectral shape and linewidth engineering.

Interferometers are essential tools for measuring and shaping optical fields, widely used in optical metrology, sensing, laser physics, and quantum mechanics. They superimpose waves with a mutual phase delay, modifying light intensity. A frequency-dependent phase delay enables spectral shaping for filtering, routing, wave shaping, or multiplexing. Conventional Mach-Zehnder interferometers generate sinusoidal output intensities, limiting spectral engineering capabilities. Here, we propose a framework that uses interference of multiple transverse modes within a single multimode waveguide to achieve arbitrary spectral shapes in a compact geometry. Designed corrugated gratings couple these modes, enabling energy exchange akin to a beam splitter for easy multimode handling. We theoretically and experimentally demonstrate spectra with independently tunable linewidth and free spectral range, along with distinct spectral shapes for various transverse modes. Our method applies to orthogonal modes of different orders, polarization, and angular momentum, offering potential for sensing, calibration, metrology, and computing.