Reflection and refraction of directrons at the interface

Reflection and refraction are ubiquitous phenomena with extensive applications, yet minimizing energy loss and information distortion during these processes remains a significant challenge. This study examines the behavior of structurally stable solitons, known as directrons, in nematic liquid crystals interacting with an interface where the director field orientation changes, despite identical physical properties, external potentials, and boundary anchoring in the two regions. During reflection and refraction, the directrons maintain nearly constant structure and velocity, ensuring energy conservation and information integrity. Microscopic analyses of the director field and macroscopic evaluations of effective potential are employed to elucidate the dependence of reflection and refraction probabilities on the directron's incident angle and the orientation difference across the interface. The findings provide valuable insights into the dynamics of solitary waves in structured liquid crystal systems, offering significant implications for the development of tunable photonic devices, reconfigurable optical systems, and nanoscale material engineering.