Tailoring light to create invariant modal spectra through complex channels

Light's spatial degree of freedom is emerging as a potential resource for a myriad of applications, in both classical and quantum domains, including secure communication, sensing, and imaging. However, it has been repeatedly shown that a complex medium that can include the atmosphere, optical fiber, turbid media, etc., can perturb the spatial amplitude, phase, and polarization of the structured light fields, leading to a degradation in their performance. A promising solution to this is the use of invariant modes, to which the medium appears transparent. While the creation and robustness of these modes have been experimentally demonstrated, they are difficult to implement in many important applications due to large channel matrices, a susceptibility to numerical artifacts, non-physical solutions, and unreliable performance. In this work, we leverage the modal description of paraxial light beams and outline a procedure for determining a set of modes, each with an invariant modal spectrum. Such modes can be used in place of the eigenmodes of a channel, are free from the numerical restrictions that plague calculating true eigenmodes, are consistently realizable, and require a much smaller channel matrix to compute. Using atmospheric turbulence and Laguerre-Gaussian (LG) modes as the underlying basis as an illustrative example, we find robust modes for various turbulence strengths with a basis of only 231 modes, one order of magnitude smaller than previous approaches. These modes consistently show a fidelity of above 80% after propagating through the complex channel, a significant improvement over sending the individual LG/orbital angular momentum modes themselves, and reveal an invariant modal spectrum through the channel. Our approach will work for any complex medium and modal basis, paving the way for the effective implementation of the eigenmode approach in real-world situations.