Power-conserving coupled-mode theory for high-index-contrast multiwaveguide systems from the field continuous at the interfaces

Conventional electric-field-based coupled-mode expansions can become inaccurate at high index contrast because superpositions of isolated modes do not satisfy the interface conditions of the coupled structure. We avoid this mismatch by expanding the interface-continuous electric field for TE polarization or magnetic field for TM polarization and deriving the partner field from the remaining curl equation. For arbitrary numbers of waveguides and guided modes, the resulting first-order equations have Hermitian weight and coupling matrices and conserve power exactly. A checkable overlap condition makes the weight matrix positive definite, giving real propagation constants and power-orthogonal supermodes. The magnetic-field formulation further supplies exact self-coupling coefficients and an integral-identity proof of Hermitian symmetry. Against exact slab solutions, it remains within 1.5 % for symmetric TM couplers through an index contrast of 4, where the electric-field formulation reaches 20\%; for TE polarization, the ranking reverses. For two- and three-core fibers with core and cladding indices of 2.8 and 2.4, calibrated finite-element and finite-difference tests reproduce the hybrid supermodes within 0.08 %, whereas near-cutoff accuracy is limited by the omission of radiation modes. The principal result is therefore the guaranteed conservation structure rather than uniformly superior propagation-constant accuracy.