Fig. 1. Schematic diagram for the model of multimode interactions in optical microcavities. All the modes have very narrow linewidths. A mode in one cavity couples to two different optical modes (a) in the same cavity and (b) in two different cavities separately. (c) Resonance frequency tuning of the intermediate cavity to induce state transfer. The tuning domain is divided into three parts labelled I, II, and III.

Fig. 2. Result of FIST between a1 and a2 by linearly tuning the resonance frequency of at. The speed is chosen as 0.08δ2. The inset is the plot of tuning function, and the unit of time t is δ−1.

Fig. 3. Simulation of final population of mode a2 affected by tuning variables. The units d and v are chosen as δ and δ2, respectively. (a) Population P versus tuning range d with v=0.27δ2. All Δ0 are chosen as Δ0=(δ−d)/2. (b) Population P versus tuning speed v with d=2.65δ and Δ0=−0.825δ. (c) Population P versus tuning range d and tuning speed v. The dashed line shows all the points of evolution time with 10δ−1.

Fig. 4. Population change with respect to evolution time via sine tuning function. Lines labeled with a1, a2, and at are the populations of the corresponding modes.

Fig. 5. Simulation of fast FIST from a1 to a2 by using the gradient descent technique. The parameters are the cross points of Fig. 3(c) with d=2.65δ, v=0.27δ2. (a) Result of the optimized population transfer process. (b) Corresponding optimal tuning function of the intermediate mode. The unit of time here is δ−1.

Fig. 6. Nonreciprocal state transfer between modes a1 and a2. (a) Populations of modes a1 and a2 versus tuning speed. The tuning range is d=14δ. (b) Populations of modes a1 and a2 versus tuning range. The tuning speed is v=0.1δ2. (c) Order difference between the populations of a2 and a1, log10[P(a2)]−log10[P(a1)], in the parameter spaces of tuning speed and tuning range.

Fig. 7. All-optical on-chip microcavity structures. (a) One-dimensional microcavity array. (b) Two-dimensional optical microcavity lattice.