Phase-locked arrays of antiguides: analytical theory

By employing a variational technique on the eigenvalue equation for finite arrays of antiguides we obtain accurate analytical expressions for key parameters characterizing the resonant array modes: the radiation loss at resonance, α_RR, and the propagation constant at resonance. The previously empirical finding that α_RR is equal to the radiation loss of a single antiguide divided by the number of array elements is found to be a good approximation only for large element/interelement width ratios (⩾3) and for, high-index-step (Δn⩾0.05) devices. By using an expansion, the radiation loss versus index-step curve is well approximated near resonance by a parabola, which gives curve halfwidths at half intensity only 10 to 15% less than numerically calculated values. An extremely accurate approximation formula is obtained for the resonant-mode propagation constant over large ranges in index-step variation around the resonance point. The obtained formulae are discussed in light of device design