A new class of out-gap discrete solitons in binary waveguide arrays

We analytically and numerically investigate beyond-band discrete solitons, which present a completely new class of stable localized out-gap solitons with detunings being located beyond the two bands of the linear plane waves in a periodic binary waveguide array. Each of the even and odd components of these discrete solitons does not change its sign across the transverse direction of the binary waveguide array. The even and odd components of these newly found discrete solitons can be approximately presented by two hyperbolic secant functions with the only difference in their peaks. This approximation is especially good in the low-intensity regime in which the detuning of these solitons can asymptotically reach the two limits of a linear spectrum. These distinguishing features altogether make the newly found discrete solitons different from all other classes of discrete solitons investigated earlier in binary waveguide arrays. Two transformation rules for constructing even and odd components of these discrete solitons are also found for various combinations of signs of the propagation mismatch σ and nonlinear coefficient γ.