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For example, for the material system used in Ref. [9], Δβ is numerically found to be negative and small (~-0.015 μm−1 at 1578nm for TE polarization, w1/w2 = 400/400 nm, and gap = 100 nm). The corresponding simulation results are shown in Fig. 6 in Ref. [9]. We already know Δψ is negative for this coupling geometry (“CB” coupler), and therefore both terms in Eqs. (23) are negative and the second term is dominant. The two features that ϕ11 (ring-ring phase) is negative (corresponding CIFS positive) and ϕ11 and ϕ22 are of opposite signs are readily understood from Eqs. (23) and (24).

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D. Marcuse, Theory of Dielectric Optical Waveguides, second edition (Academic, Boston, 1991), Chap. 6.

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