Matrix analysis of microring coupled-resonator optical waveguides

Area of Science:

• Photonics and Waveguide Optics
• Nonlinear Optics
• Condensed Matter Physics

Background:

• Coupled-resonator optical waveguides (CROWs) are key components in integrated photonics.
• Understanding light propagation dynamics, including nonlinear effects, is crucial for device design.
• Existing models like the tight-binding approach have limitations in complex geometries.

Purpose of the Study:

• To investigate continuous wave and pulse propagation in microring CROWs.
• To develop and apply the coupling matrix formalism for analyzing CROWs.
• To explore nonlinear dispersive characteristics and anomalous dispersion effects.

Main Methods:

• Utilized the coupling matrix formalism to model light propagation.
• Derived the dispersion relation and compared it with the tight-binding model.
• Obtained analytical expressions for pulse propagation in semi-infinite CROWs.
• Analyzed pulse behavior in finite CROWs, considering anomalous dispersion.

Main Results:

• The coupling matrix formalism provides results consistent with the tight-binding model for weak coupling.
• An analytical expression for nonlinear pulse propagation was derived.
• Pulse intensity in CROWs is inversely proportional to inter-resonator coupling.
• Anomalous dispersion enables negative group velocity and apparent superluminal propagation in finite CROWs.

Conclusions:

• The coupling matrix formalism is a versatile and powerful tool for analyzing microring CROWs.
• This method extends beyond the limitations of the tight-binding approach for complex structures.
• The findings offer insights into controlling light propagation and enabling novel functionalities in CROWs.