J. Eur. Opt. Society-Rapid Publ. 22, 2( 2026) 21
Figure 12. Plotting of( a) the optical conductivity and( b) the electrical susceptibility vs wavelength for Bi 2-x Mn x O 3 thin films.
Figure 13. The variation of the linear( a) and the non-linear susceptibility( b) and non-linear refractive index with k for Bi 2-x Mn x O 3 thin films.
v ð3Þ ¼ E 4
d
ð6:82 10 �15 Þðe: s: u: Þ; ð22Þ
E 0 n 2 ¼ 12pvðÞ 3: ð23Þ n 0
Figures 13a – 13c depict the wavelength-dependent behavior of the nonlinear refractive index( n 2), linear susceptibility( v 1), and nonlinear susceptibility( v 3) for Bi 2-x Mn x O 3 thin films, respectively. These parameters consistently increase with higher Mn content, reflecting changes in polarizability and electronic structure induced by Mn incorporation [ 55 ]. The enhanced optical properties of these films are highly beneficial for various applications. Precise control over nonlinear optical characteristics facilitates efficient frequency conversion and optical limiting, critical for advanced photonic and optoelectronic systems.
A comprehensive understanding of these modifications is essential for the rational design and development of nextgeneration materials tailored for cutting-edge optical technologies [ 2, 56 ].
Figure 14 exhibits the variation of the nonlinear absorption coefficient( b c) and the energy for the Bi 2-x Mn x O 3 thin films. The maximum value of b c shifts towards a lower energy photon as the concentration of Mn rises. Doping Mn can establish additional energy levels inside the band gap. Because electrons can be excited from these confined states into the conduction band, these mid-gap states can help absorb lower-energy photons. Since additional photon energies are now resonant with these states, the nonlinear absorption coefficient increases at lower energy. Twophoton absorption and saturable absorption are two of the optical processes that affect the nonlinear absorption coefficient. The density of states varies with increasing Mn content, changing the way these processes take place.