Reconstruction and Synthesis of Arbitrary Optical Intensity Patterns in Extremely Multimode Waveguide Cavities via Physics-Informed Optimized Modal Superposition

Multimode dielectric waveguide cavities support hundreds to thousands of guided modes whose coherent interference governs the intracavity optical field. Accurate full-wave modeling of such structures is computationally demanding because the entire cavity must be discretized with subwavelength resolution. Here, we present a physics-informed reduced-order semi-analytical approach that analytically incorporates mode-dependent Fabry–Perot (FP) cavity physics into a finite-difference eigenmode (FDE) formulation, eliminating numerical discretization along the propagation direction and enabling efficient modeling of large multimode waveguide cavities. To represent experimental excitation conditions, the framework further incorporates Gaussian beam mode-overlap theory to provide a physics-informed initial estimate of the excited cavity modes for the subsequent inverse optimization. The three-dimensional waveguide cavity is first reduced to an equivalent two-dimensional problem using an effective-index approach. The vertical and lateral eigenmodes are computed using a finite-difference eigenmode solver, while the analytical FP formulation describes longitudinal propagation and multiple facet reflections for each guided mode. The physics-informed inverse optimization is then applied to recover the complex modal excitation coefficients from experimentally measured near-field intensity profiles at the input facet. The proposed method is validated against finite-element eigenmode analysis, full-wave cavity simulations, and experiments based on Si₃N₄ waveguides, showing close agreement. The recovered modal coefficients are subsequently used to reconstruct and predict the intracavity optical field throughout the cavity. Finally, the proposed framework is applied to synthesize arbitrary intracavity optical field distributions. As a proof of concept, the letters U, N, and C are generated within the cavity through coherent superposition of the guided modes.