Fig. 2: Design of ultra-wideband mode multiplexer based on multi-layer optical diffraction network.

a End-to-end inverse design framework for ultra-wideband mode multiplexer. \(O_{\lambda^c}\) and \(T_{\lambda^c}\) represent the generated and target modes light fields of wavelength λ at the c-th mode channel on the output plane. The symbols \(U^{k}_{\lambda^{c}_{min}} < /Emphasis > < /Subscript > \), \(U^{k}_{\lambda^{c}_{r}} < /Emphasis > < /Subscript > \), \(U^{k}_{\lambda^{c}_{max}} < /Emphasis > < /Subscript > \) denote the forward optical field at the minimum, reference, and maximum wavelengths, respectively, of the c-th mode channel. Similarly, \(U^{\prime k}_{\lambda^{c}_{min}} < /Emphasis > < /Subscript > \), \(U^{\prime k}_{\lambda^{c}_{r}} < /Emphasis > < /Subscript > \), \(U^{\prime k}_{\lambda^{c}_{max}} < /Emphasis > < /Subscript > \) denote the corresponding backward optical field. b Simulated phase distributions of ultra-wideband four linearly polarized (LP)-mode multiplexer. c Simulated wavelength-dependent average mode purity, maximum mode crosstalk, average insertion loss (IL) and mode dependent loss (MDL).