Figure 1

(Color online) (a) Schematic of the optical waveguiding structure composed by a slab waveguide $S$ and by two identical channel waveguides $W_1$ and $W_2$. (b) Typical behavior of refractive index profile $n\left(x,y\right)$ of the structure used in numerical simulations. (c) and (d) represent the quantum-mechanical analog of the light transfer dynamics describing the decay of two degenerate bound states $|1⟩$ and $|2⟩$ into a common continuum of states $|k⟩$ limited from below. In (c) the energy of the bound states is below the continuum, leading to two-photon Rabi oscillations via the continuum. In (d) the bound states are embedded in the continuum, and a trapped state may exist as discussed in Sec. 4.Reuse & Permissions

Figure 2

(Color online) Optical analog of two-photon Rabi oscillations via a continuum. The plots show the behavior of numerically computed fractional light powers trapped in the channels waveguides $W_1$ and $W_2$ versus propagation distance $z$ in the ${\beta }_0<{\beta }_S$ regime $\left(\Delta n_S=0.01,\Delta n_g=0.009\right)$. In (a)–(c) the two-photon Rabi oscillations are shown for $d_1=d_2=8\mu \text{m}$ and for increasing values of the horizontal waveguide displacement $s$: $s=\left(\text{a}\right)0$, (b) 4, and (c) $8\mu \text{m}$. In (d) an example of detuned two-photon Rabi oscillations is shown for $d_1=7\mu \text{m}$, $d_2=9\mu \text{m}$, and for $s=4\mu \text{m}$. The values of other parameters are given in the text.Reuse & Permissions

Figure 3

(Color online) Optical analog of population trapping in the guiding structure of Fig. 1a in the ${\beta }_0>{\beta }_S$ regime $\left(\Delta n_S=0.005,\Delta n_g=0.009\right)$. The figures show the behavior of numerically computed fractional light powers trapped in the channel waveguides $W_1$ (solid curves) and $W_2$ (dotted curves) versus propagation distance $z$. In (a) $d_1=8\mu \text{m}$ and waveguide $W_2$ is very far from the slab waveguide; note that the decay law ${\left|c_1\left(z\right)\right|}^2$ is almost exponential according to the Markovian approximation. In (b)–(g) $d_1=d_2=8\mu \text{m}$ and the behavior of ${\left|c_1\left(z\right)\right|}^2$ and ${\left|c_2\left(z\right)\right|}^2$ is shown at increasing values of horizontal displacement $s$: $s=\left(\text{b}\right)0$, (c) 6, (d) 9, (e) 12.2, (f) 18, and (g) $24.4\mu \text{m}$. Note the incomplete decay in (b), (e), and (g), which is related to the existence of a trapped state. (h) shows the existence of an unbalanced trapped state for $s=0$, $d_1=8\mu \text{m}$, and $d_2=7\mu \text{m}$. In (b), (e), (g), and (h) the insets show the transverse profile of the field intensity ${\left|\psi \right|}^2$ at the $z=6\text{cm}$ output plane.Reuse & Permissions

Figure 4

(Color online) Adiabatic transfer of light between two weakly curved channel waveguides $W_1$ and $W_2$ via a slab waveguide. (a) $s=0$ and $\delta =25\text{mm}$; (b) $s=12.2\mu \text{m}$ and $\delta =25\text{mm}$; (c) $s=24.4\mu \text{m}$ and $\delta =25\text{mm}$; (d) $s=7\mu \text{m}$ and $\delta =25\text{mm}$; (e) $s=0$ and $\delta =0$; (f) $s=0$ and $\delta =-25\text{mm}$. The values of other parameters are given in the text.Reuse & Permissions