Separating the real and imaginary components, ε ε ^ ^ ( ω ω ) = ε ε 1 ( ω ω ) + i ε ε 2 ( ω ω ) = [ ε ε ∞ ∞ + ∑ ∑ j s j ( ω ω 0 , j 2 − − ω ω 2 ) ( ω ω 0 , j 2 − − ω ω 2 ) 2 + ( Γ Γ j ω ω ) 2 ] + i [ ∑ ∑ j s j ( Γ Γ j ω ω ) ( ω ω 0 , j 2 − − ω ω 2 ) 2 + ( Γ Γ j ω ω ) 2 ]