On-chip integration fundamentally changes the way in which information is processed. The exploding communication capacity requires a high degree of integration of optical devices in a limited footprint. These requirements have pushed the minimization of optical chips almost to their physical limits. One potential way to break this limitation is to increase the number of functionalities in a module, for which the most critical issue is to expand the degree of freedom of information processing. Here, we propose a degree of freedom of information processing based on the basic mode vectors in the anti-parity-time-symmetry system. Based on our principle, adjacent whispering-gallery modes in a ring cavity are remarkably distinguished in their sensitivity to the signal intensity. What is more, the desired modes are labeled by individual resonance frequencies. This principle is demonstrated experimentally based on the wavelength-selective nonlinear excitation in microring resonators with the nonlinear material ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. In addition, the combination of this proposed degree of freedom and the signal-direction-dependent function is experimentally demonstrated. This research provides a degree of freedom for designing multifunction devices, which will fundamentally expand the capacity of on-chip information processing.

• Received 3 June 2020
• Revised 24 August 2020
• Accepted 21 September 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.044050