J. Eur. Opt. Society-Rapid Publ. 22, 2( 2026) 19
Figure 9. The deduced values involve:( a) refractive index variation with k,( b) variation of( n 2 � 1) �1 with( hv) 2 to estimate E 0 and E d,( c) the relation between( n 2 � 1) �1 and( 1 / k 2) for obtaining S 0 and k 0, and( d) k 2 dependence of n 2 to calculate e L and N m for Bi 2-x Mn x O 3 thin films for different Mn concentrations.
Figure 10. Dielectric constant( a) and dielectric loss( b) vs wavelength, and loss tangent( c) and quality factor( d) vs hv Bi 2-x Mn x O 3 thin films.
respectively. The rise in e 1 with increasing Mn content indicates enhanced dielectric polarization, likely due to the introduction of additional dipoles that strengthen the material’ s dielectric response. Similarly, e 2 exhibits an increase with higher Mn concentrations, suggesting a greater contribution from energy dissipation mechanisms. The loss tangent( tand) can be expressed by the following relation [ 48 ]:
Tan ðdÞ ¼ e 2 e 1
: ð16Þ
Figure 10c illustrates the dependence of the loss tangent( Tan d) on photon energy for the investigated thin films. A decrease in Tan d was observed with increasing Mn content, attributed to alterations in the electronic energy levels