Phase-locked arrays of antiguides: analytical theory II

By employing a variational technique on the eigenvalue equation for finite arrays of antiguides we obtain accurate analytical expressions for key parameters characterizing the adjacent array modes: the edge radiation loss, the loss caused by interelement losses, and the effective index. The upper adjacent mode at its maximum-loss point is found to be well approximated by the sum of two Bloch waves of wavenumbers ±π/[(N-1)Λ], where N is the element number, and Λ is the array period. The intermodal discrimination, Δα, between the adjacent mode and the resonant mode (at the adjacent-mode maximum-loss point) is found to be well approximated (<10% error) by α_RR, the resonant-mode loss at resonance. Accurate analytical expressions are also derived for the two-dimensional optical-mode confinement factor Γ, and the dispersion between the resonant and adjacent modes. The obtained analytical formulas are discussed in light of device design, and general design rules are presented