  We experimentally demonstrate that the next-nearest-neighbor(NNN)coupling in
an array of waveguides can naturally be negative. To do so, dielectric zig-zag
shaped waveguide arrays are fabricated with direct laser writing (DLW). By
changing the angle of the zig-zag shape it is possible to tune between positive
and negative ratios of nearest and next-nearest-neighbor coupling, which also
allows to reduce the impact of the NNN-coupling to zero at the correct
respective angle. We describe how the correct higher order coupling constants
in tight-binding models can be derived, based on non-orthogonal coupled mode
theory. We confirm the existence of negative NNN-couplings experimentally and
show the improved accuracy of this refined tight-binding model. The negative
NNN-coupling has a noticeable impact especially when higher order coupling
terms can no longer be neglected. Our results are also of importance for other
discrete systems in which the tight-binding model is often used.
