5 Both integrals are determined by the integration over mo- mentum space between the Fermi surfaces of two bands split by the spin-orbital coupling. The phase transition to the superconducting state changes the Fermi distri- bution of the electrons over energies only in the narrow vicinities of the corresponding Fermi surfaces of the or- der of Δ. Hence, the integration in eqs. (46) and (47) leads to the result only slightly different from that is in the normal state. Even at zero temperature the relative magnitude of corrections do not exceed ∼ Δ $^{2}$/ε2 $_{F}$. So, the gyrotropy coefficient λ determined by the integral I 3 lm is practically keeps its normal state value given by eqn. (28) It means that we should work with the doubled even part of eqn. (39). Expanding the integrand in powers of ω after long but straightforward calculations we come to the following formula Hence, the integral (29) can be rewritten as have The coefficient ν acquires nonzero value. However, it is much smaller than that was found in the paper Ref. 15. The estimation made at T = 0 yields To find a relationship of the gyrotropy conductivity with observable optical properties one has to develop electrodynamic theory of noncentrosymmetric metals. J$_{−}$$_{+}$ ( k , ω ) = J$_{+}$$_{−}$ ( − k , − ω ) . (40) I$_{l}$ = ∫ d $^{3}$k (2 π ¯ h ) $_{3}$ˆ k$_{l}$ [ J$_{+}$$_{−}$ ( k , ω ) + J$_{+}$$_{−}$ ( k , − ω )] . (41) λ = i e $^{2}$ω 12 π $^{2}$γ$_{0}$ k$_{F}$ ( 1 + O (Δ $^{2}$/ε2 $_{F}$) ) . (48) ν = e $^{2}$γ$_{0}$ k$_{F}$ ¯ h $^{2}$c O (Δ $^{2}$/ε2 $_{F}$) (49) I$_{l}$ = 2 ∫ d $^{3}$k (2 π ¯ h ) $_{3}$ˆ k$_{l}$ [ n ( ξ$_{+}$ ( k$_{+}$ )) − n ( ξ$_{−}$ ( k$_{−}$ ))] × { 1 ξ$_{+}$ ( k$_{+}$ ) − ξ$_{−}$ ( k$_{−}$ ) + (¯ hω ) 2 ( ξ$_{+}$ ( k$_{+}$ ) − ξ$_{−}$ ( k$_{−}$ )) 3 } − 2Δ 2 ∫ d $^{3}$k (2 π ¯ h ) $_{3}$ˆ k$_{l}$ (¯ hω ) 2 ( ξ$_{+}$ ( k$_{+}$ ) + ξ$_{−}$ ( k$_{−}$ ))( ξ$_{+}$ ( k$_{+}$ ) − ξ$_{−}$ ( k$_{−}$ )) 3 × ( tanh ϵ$_{+}$ ( k$_{+}$ ) 2 T ϵ$_{+}$ ( k$_{+}$ ) − tanh ϵ − ( k − ) 2 T ϵ$_{−}$ ( k$_{−}$ ) ) , (42) n ( ξ ) = 1 2 ( 1 − ξ ϵ tanh ϵ 2 T ) (43) I$_{l}$ ∼ = 2 ∫ d $^{3}$k (2 π ¯ h ) $_{3}$ˆ k$_{l}$ [ n ( ξ$_{+}$ ( k$_{+}$ )) − n ( ξ$_{−}$ ( k$_{−}$ ))] × { 1 ξ$_{+}$ ( k$_{+}$ ) − ξ$_{−}$ ( k$_{−}$ ) + (¯ hω ) 2 ( ξ$_{+}$ ( k$_{+}$ ) − ξ$_{−}$ ( k$_{−}$ )) 3 } (44) rot B = 4 π c j , (50) rot E = − 1 c ∂ B ∂t (51) j = ϵ 4 π ∂ E ∂t + σ E + λ rot E . (52) j g i ( ω, q ) = ie$_{ijl}$ e $^{2}$γ2 0 c ¯ hq$_{m}$ [ I 1 $_{lm}$+(¯ hω ) $^{2}$I3 $_{lm}$] A$_{j}$ ( ω, q ) , (45) where is the distribution function of electrons over energies. At Δ /γ$_{0}$k$_{F}$ ≪ 1 the second integral is obviously much smaller than the first one. So, we come to the expression To derive the light dispersion law we start from the Maxwell equations which has the same form as the corresponding formula for the normal state (23). Expanding the integrand up to the first order in ∂ξ ± ∂ k q we obtain for the current given by eqn. (19): supplied by the density of current expression The first term here corresponds to the dispersionless part of the displacement current. The second one is the con- ductivity current written at infrared frequency region ω > v$_{F}$ /δ, ωτ > 1, where the current is locally related with an electric field, δ is the skin penetration depth. The last one is the gyrotropy current V. OPTICAL PROPERTIES OF NONCENTROSYMMETRIC METAL A. Dispersion law j$_{g}$ = λ rot E . (53) ∇ $^{2}$E = ϵ c 2 ∂ $^{2}$E ∂t 2 + 4 πσ c 2 ∂ E ∂t + 4 πλ c 2 ∂ rot E ∂t . (54) I 1 lm = ∫ d $^{3}$k (2 π ¯ h ) $_{3}$ˆ k$_{l}$ [ − n ( ξ$_{+}$ ) − n ( ξ$_{−}$ ) ( ξ$_{+}$ − ξ$_{−}$ ) 2 ( ∂ξ$_{+}$ ∂k$_{m}$ + ∂ξ$_{−}$ ∂k$_{m}$ ) + 1 ξ$_{+}$ − ξ$_{−}$ ( ∂n ( ξ$_{+}$ ) ∂ξ$_{+}$ ∂ξ$_{+}$ ∂k$_{m}$ + ∂n ξ$_{−}$ ) ∂ξ$_{−}$ ∂ξ$_{−}$ ∂k$_{m}$ )] , (46) I 3 lm = ∫ d $^{3}$k (2 π ¯ h ) $_{3}$ˆ k$_{l}$ [ − 3 n ( ξ$_{+}$ ) − n ( ξ$_{−}$ ) ( ξ$_{+}$ − ξ$_{−}$ ) 4 ( ∂ξ$_{+}$ ∂k$_{m}$ + ∂ξ$_{−}$ ∂k$_{m}$ ) + 1 ( ξ$_{+}$ − ξ$_{−}$ ) 3 ( ∂n ( ξ$_{+}$ ) ∂ξ$_{+}$ ∂ξ$_{+}$ ∂k$_{m}$ + ∂n ξ$_{−}$ ) ∂ξ$_{−}$ ∂ξ$_{−}$ ∂k$_{m}$ )] . (47) As before we discuss the metal with the cubic point sym- metry. Eliminating the magnetic induction, we obtain