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Temporal coupled-mode theory (TCMT) provides a simple yet powerful platformto model and analyze electromagnetic resonator systems. Nevertheless,restrictive assumptions and lack of rigorous connection to Maxwell's equationslimit the TCMT formulation's generality and robustness. Herein, we present theBlack-box Coupled-Mode Theory (BBCMT), a general ab initio CMT frameworkdeveloped from Maxwell's equations and quasinormal mode (QNM) theory to modelthe electromagnetic interactions of dispersive, lossy, and open resonators.BBCMT development is enabled by employing Poynting's and conjugated reciprocitytheorems to rigorously normalize QNMs and calculate their expansioncoefficients. Our novel QNM analysis approach allows the definition of aresonator Hamiltonian matrix to characterize the modes' electromagneticinteractions, energy storage, and absorption. Uniquely, the BBCMT framework cancapture a resonator's non-resonant scattering and absorption by treating theresonator scattered fields as a perturbation to those of a backgroundstructure, which can be flexibly chosen considering the desiredaccuracy-simplicity trade-off. BBCMT modeling complexity can be furtheradjusted by treating user-defined subcomponents of a resonator system asblack-boxes described only by their input-output transfer characteristics.Beyond the BBCMT formulation, we present two lemmas to reverse-engineer themodeling parameters from calculated or measured far-field spectra. Moreover, weintroduce the signal flow graphs from control theory to illustrate, interpret,and solve the BBCMT equations. To evince BBCMT's validity and generality, wecompare the BBCMT and TCMT predictions for two plasmonic nanoresonator systemsto finite-difference time-domain simulations and find BBCMT results to be amuch better match. BBCMT reduces to TCMT or cavity perturbation theory undercertain constraints and approximations.

Black-Box Coupled-Mode Theory: An Ab Initio Framework to Model Electromagnetic Interactions of Open, Lossy, and Dispersive Resonators