Robust topological edge states from one-dimensional diatomic chain photonic crystals

The Su–Schrieffer–Heeger (SSH) model can occur in a one-dimensional (1D) diatomic chain photonic crystal (PC) in which a unit cell includes two same slabs (atoms). With different intervals of the two slabs, the two combined 1D PCs can support topological edge states in all photonic boundary bandgaps. These topological edge states come from the inversion of topological phase of the bands through the band folding effect. When the sum of the two atom intervals in the two different 1D PCs equals to the unit cell length, these edge state frequencies keep invariant.

A Diatomic Chain with A Mass Impurity

A classic diatomic chain with one mass impurity is studied using the recurrence relations method. The momentum autocorrelation function of the impurity results from contributions of two pairs of resonant poles and three branch cuts. The pole contribution is given by cosine function(s) and the cut contribution is the acoustic and optical branches. The acoustic and optical branches are given by expansions of even-order Bessel function. The expansion coefficients are integrals of elliptic functions in the real axis in a complex plane for the acoustic branch and along a contour parallel to the imaginary axis for the optical branch, respectively. An integral 22 22 1 2 0 d / ( r sin )( r sin ) 1 1 ϕ θ − θ− θ ∫ (r2 2 >r1 2 >1) is evaluated.