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Introduction
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The decomposition of fields into eigenmodes is a well established technique to solve various problems within physical sciences. The most prominent example is the Schrödinger’s equation within the field of quantum mechanics, where energy spectra of atoms are determined via the eigenvalue spectra and associated wavefunctions of the Hamiltonian operator. Indeed, electron orbits are eigenmodes of the energy, angular momentum, and spin operators [@cohen-tannoudji1977] and as such they deliver fundamental insights into the physics of atoms. Within classical mechanics, modes of vibration of music instruments give, for example, their resonant frequencies while their spectrum is associated with the shape of the instrument [@Kac:1966p9889]. In the optical domain, mode decomposition is used in order to describe light propagation within waveguides [@Sudbo:1993p9727], photonic crystals [@Bienstman:2001p9890], optical cavities [@Reithmaier:1997p9888], laser resonators 