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We study coherent wave scattering through waveguides with a step-like surfacedisorder and find distinct enhancements in the reflection coefficients atwell-defined resonance values. Based on detailed numerical and analyticalcalculations, we can unambiguously identify the origin of these reflectionresonances to be higher-order correlations in the surface disorder profilewhich are typically neglected in similar studies of the same system. Aremarkable feature of this new effect is that it relies on the longitudinalcorrelations in the step profile, although individual step heights are randomand thus completely uncorrelated. The corresponding resonances are verypronounced and robust with respect to ensemble averaging, and lead to anenhancement of wave reflection by more than one order of magnitude.

Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder