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LOCALIZED STATES IN A LINEAR MEDIUM WITH NONLINEAR THIN LAYER
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DOI：10.59277/RomJPhys.2026.71.202.png)
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Abstract
En 中文
A theoretical study of localized states in a linear medium with a thin nonlinear defect layer modeled by a point potential is provided. Analytical expressions for the wave function and localization energy are obtained, generalizing known results for the symmetric delta potential to the case of different permittivities on either side of the defect. It is shown that the condition for the existence of a localized state is the positivity of the nonlinear interaction potential at the defect. The total number of excitations is introduced and analyzed. It is found that this quantity can reach a minimum at a certain critical value of the field amplitude at the defect, which physically corresponds to the surface wave excitation threshold. It is proven that minimization of the number of excitations (power flow) in a symmetric localized state is achieved only with quadratic (Kerr) nonlinearity of the defect. Various models of the nonlinear layer response are investigated, including power-law and saturable nonlinearities. The minimum total number of excitations exists within a certain range of exponents for power-law nonlinearity. The localization energy saturates at high excitation levels for saturable nonlinearity. A relationship between the localization energy and the total number of excitations is obtained using a semiclassical approach. This dependence is a power law with an exponent determined by the type of nonlinearity for power-law nonlinearity. For saturable nonlinearity, the localization energy asymptotically tends to a constant value.
Keywords:
Schr & ouml
dinger equation
exact solution
localized state
delta-function potential
nonlinearity
localization energy
Journal
R
IF:
1.9
Papers:
28
Citations:
0
