Resonances hidden between grid points in thick optical coatings, seen and suppressed from the complex plane

A coating optimized on a wavelength grid can meet its sampled target while hiding narrow transmission peaks between grid points. We detect these peaks from the transmission phase at complex wavelengths spaced like the grid, and check the detection with an independent count of the poles. Each unwanted resonance then adds one merit-function term at its moving real maximum. Numerical tests show that this penalty reduces hidden peaks without resolving their widths on the optimization grid. A confinement model explains why the risk increases with optical thickness and why a finer grid raises the estimated threshold only logarithmically. Reducing transmission peaks, however, does not necessarily reduce internal field enhancement.