8 the anomalous skin effect assuming that the wave length does not exceed the skin penetration depth δ > v$_{F}$ /ω . In the normal state the current contains the gyrotropic part which is odd function of the wave vector and the fre- quency. It presents a sort of displacement current orig- inating of band splitting in noncentrosymmetric metal. In the superconducting state there is an additional part of the gyrotropy current proportional to magnetic field. The change of the gyrotropy conductivity in the super- conducting state was found. As an example the Kerr rotation for the polarized light reflected from the sur- face of noncentrosymmetric metal with cubic symmetry is calculated. For Δ˜ n in the superconducting state we obtain Finally, for the Kerr angle in the same frequency interval as for the normal state we have One of the authors (V. P. M.) is indebted to E. Kats and L. Falkovsky for the numerous helpful discussions of natural optical activity and technical problems related to its calculation. Acknowledgments VII. CONCLUSION Δ˜ n$_{s}$ = − 2 α 3 π [ ¯ hω γ$_{0}$k$_{F}$ ( 1 + O (Δ $^{2}$/ε2 $_{F}$) ) − γ$_{0}$k$_{F}$ ¯ hω O (Δ $^{2}$/ε2 $_{F}$) ] . (85) θ$_{s}$ = − 2 αω 3 πω 2 $_{p}$τ [ ¯ hω γ$_{0}$k$_{F}$ ( 1 + O (Δ $^{2}$/ε2 $_{F}$) ) − γ$_{0}$k$_{F}$ ¯ hω O (Δ $^{2}$/ε2 $_{F}$) ] . (86) The financial support of another author (Y. Y.) by the Global COE program (G10) from Japan Society for the Promotion of Science is gratefully acknowledged. We have presented here the derivation of the current response to the electromagnetic field with finite frequency and wave vector in noncentrosymmetric metal. The ob- tained general formula valid both in the normal and in the superconducting state was applied to the calculation of observable physical properties in the frequency interval smaller than the band splitting ¯ hω < γ$_{0}$k$_{F}$ . The latter in its turn was supposed to be smaller than the Fermi energy γ$_{0}$k$_{F}$ < ε$_{F}$ . The calculations was performed in the clean case ωτ > 1, that is, in particular, important to neglect the vortex corrections. We did not discuss 14 L. S. Levitov, Yu. V. Nazarov, and G. M. Eliashberg, Pis’ma Zh. Eksp. Teor. Fiz. 41 , 365 (1985) [JETP Lett. 41 , 445 (1985)]. 15 Chi-Ken Lu and Sungkit Yip, Phys. Rev. B 77 , 054515 (2008). 16 E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics, Butterworth-Heinemann, Oxford (1995). 17 V. P. Mineev and M. Sigrist ”Introduction to Super- conductivity in Metals without Inversion Center”, arXiv: 0994.2962. 1 E. Bauer, G. Hilscher, H. Michor, Ch. Paul, E. W. Scheidt, A. Gribanov, Yu. Seropegin, H. No¨el, M. Sigrist, and P. Rogl, Phys. Rev. Lett. 92 , 027003 (2004). 2 T. Akazawa, H. Hidaka, T. Fujiwara, T. C. Kobayashi, E. Yamamoto, Y. Haga, R. Settai, and Y. Onuki, J. Phys.: Condens. Matter 16 , L29 (2004). 3 N. Kimura, K. Ito, K. Saitoh, Y. Umeda, H. Aoki, T. Terashima, Phys. Rev. Lett. 95 , 247004 (2005). 4 I. Sugitani, Y. Okuda, H. Shishido, T. Yamada, A. Thamizhavel, E. Yamamoto, T. D. Matsuda, Y. Haga, T. Takeuchi, R. Settai, and Y. Onuki, J. Phys. Soc. Jpn. 75 , 043703 (2006). 18 K. V. Samokhin and V. P. Mineev, Phys. Rev. B 77 , 104520 (2008). 19 The electromagnetic response theory for the general case of two conducting bands has been developed by L. A. Falkovsky and A. A. Varlamov, Eur. Phys. J. B 56 , 281 (2007). 5 G. Amano, S. Akutagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, J. Phys. Soc. Jpn 73 , 530 (2004). 6 K. Togano, P. Badica, Y. Nakamori, S. Orimo, H. Takeya, and K. Hirata, Phys. Rev. Lett. 93 , 247004 (2004); P. Bad- ica, T. Kondo, and K. Togano, J. Phys. Soc. Jpn. 74 , 1014 (2005). 20 The estimation of neglected terms shows that they yield small corrections of the order of γ 0 k$_{F}$ /ε$_{F}$ to the main terms determining the gyrotropy current. 21 We shall not write here the expression for the total density of current (6) in the band representation. This is out of scope of the present paper. It should be mentioned, how- ever, that in the normal state it obeys the usual prop- erty of absence of diamagnetic responce to the e-m field j ( ω = 0 , q = 0) = 0. 7 G. Schuck, S. M. Kazakov, K. Rogacki, N. D. Zhigadlo, and J. Karpinski, Phys. Rev. B 73, 144506 (2006). 8 V. P. Mineev and K. V. Samokhin, Phys. Rev. B 72 , 212504 (2005). 9 K. V. Samokhin, Phys. Rev. B 76 , 094516 (2007). 10 V.P.Mineev and K.V.Samokhin, Phys. Rev. B 78 , 144503 (2008). 11 L. D. Landau and E. M. Lifshitz, Electrodynamics of con- tinuous media, Pergamon Press, Oxford, 1984. 12 B. Arfi, L. P. Gor’kov, Phys. Rev. B 46 , 9163 (1992). 13 L. S. Levitov, Yu. V. Nazarov, and G. M. Eliashberg, Zh. Eksp. Teor. Fiz. 88 , 229 (1985) [Sov. Phys. JETP 61 , 133 (1985)]. 22 H. S. Bennett and E.A.Stern, Phys. Rev. 137 , A 448 (1965). 23 The calculation done by K. V. Samokhin, E. S. Zijlstra, and S. K. Bose, Phys. Rev. B 69 , 094514 (2004) (see also Erratum 70 , 069902(E) (2004)) for CeP t 3 Si gives rise even larger value of the band splitting.