Orthogonality plays a fundamental role in various mathematical theorems and in physics. The orthogonal eigenfunctions that represent the intrinsic motions of various physical systems can also be regarded as transverse wave modes in a straight waveguide. Because of their orthogonality, these modes propagate independently, without mutual interference. When the wall separation fluctuates, the former mode orthogonality is destroyed because of the change in the Euclidean space of the system. Here, we experimentally demonstrate the extraordinary single-mode transparency that arises as a result of the intense mode interference induced by orthogonality breaking in a waveguide with a varying cross section. A mode diagram is also introduced to illuminate these mode interactions. In particular, measurements of the transverse field distributions indicate that a three-mode interaction leads to a single high-order mode that penetrates through the lower-mode bandgaps when the wall period is carefully selected. The observation of Bessel-like transverse distributions is promising for applications in wave-control engineering.