Fig. 1. Schematic of the system consisting of two coupled whispering-gallery microcavities. We have not explicitly drawn the taper in the figure.

Fig. 2. Spectrum of two coupled cavities, which has a splitting similar to EIT. The parameters are w1=w2=10  GHz, κ1/2=1  MHz, κ2/2=0.1  MHz, κex=κ1/2, and μ=0, 0.2, 0.5  MHz. The corresponding eigenvalues as well as the roots of P(w)=0 are as follows: for μ=0, λ1=10,000−i, λ2=10,000−0.1i, r1=10,000, r2=10,000−0.1i; for μ=0.2 MHz, λ1=10,000−0.15i, λ2=10,000−0.95i, r1=9999.81−0.05i, r2=10,000.19−0.05i; for μ=0.5  MHz, λ1=9999.78−0.55i, λ2=10,000.22−0.55i, r1=9999.50−0.05i, r2=10,000.50−0.05i.

Fig. 3. Re(Δλ) denotes the real splitting between the eigenvalues, Re(Δr) denotes the real splitting between the roots of P(w)=0, and ΔW denotes the splitting in the spectrum. ΔW agrees with Re(Δr). When μ is large, Re(Δλ)≈Re(Δr). The parameters are the same as in Fig. 2.

Fig. 4. Transmission rate in case w1≠w2. There is a large discrepancy between the eigenvalues of the system and the valleys in the spectrum. The parameters are w1=10,000  MHz, w2=10,000.1  MHz, κ1/2=1  MHz, κ2/2=0.1  MHz, and μ=0.3  MHz.

Fig. 5. Transmission rate for different Δμ. There is an EP-like splitting in the spectrum, though the system is not at an EP. The parameters are w1=w2=10  GHz, κ1/2=κ2/2=κex/2=1  MHz, μ0=1  MHz, and μ=μ0+Δμ with Δμ=0, 0.1, 0.2  MHz. The inset shows the approximately linear relation between Δμ and the square of the splitting width (ΔW2). The dashed line is ΔW2=8Δμ, which is a relation that stands approximately for small Δμ, as shown in Eq. (10).