Coupledwave

Coupled waves, or coupled-wave systems, describe a situation in which two or more wave modes interact as they propagate, so their evolution is interdependent rather than independent. The coupling causes energy and information to be exchanged between the modes, leading to altered amplitudes, phases, and effective propagation characteristics compared with uncoupled waves.

The phenomenon is commonly modeled with a set of coupled equations for the complex amplitudes of the participating modes. In the simplest two-mode case with constant coupling, the amplitudes exchange energy as they travel, producing periodic power transfer between the modes. The rate of exchange depends on the coupling strength and on the difference in intrinsic propagation properties of the modes. In symmetric situations the exchange can occur with a characteristic beat length, while detuning or loss can modify the transfer efficiency and the oscillation pattern.

Common contexts for coupled waves include optics, where evanescent coupling between nearby waveguides or resonators leads to directional coupling and power transfer; mechanical systems, such as two coupled pendulums or elastic layers; and quantum or acoustic systems where states, modes, or resonances interact through a coupling element. Coupled-wave concepts also appear in seismology, fluid dynamics, and photonic integrated circuits, where controlled coupling enables devices such as couplers, filters, and multiplexers.

Overall, coupled waves describe a broad framework for understanding how interaction between modes shapes wave propagation, with wide-ranging applications in science and engineering.