Here in the experiment, the width of the rectangular waveguide is changed. It influences the effective path of light, refractive index for both Transverse Electric and Transverse Magnetic polarizations at the same time.
TE and TM polarizations are mainly distributed in the central and right regions of the waveguide, respectively.
The detuning of TE and TM polarizations is proportional to the difference in their respective effective refractive indices. The evolution direction for the Hamiltonian parameters is determined by the detuning of double-coupled waveguides.
The hamiltonian can be written as
Hamiltonian describes the dynamic behavior of light as it propagates through the double-coupled waveguide system. It characterizes the system's energy and the interactions between modes within the waveguides, including factors like polarization, loss, and coupling strength.
https://www.nature.com/articles/s41377-025-01762-9#Sec3
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