The quadratic electro-optic effect in the nonconjugated conductive copolymer film of styrene-butadiene-rubber (SBR) has been measured using field-induced birefringence method. Thin films of styrene-butadiene-rubber prepared on various substrates have been characterized using optical absorption spectroscopy and FTIR before and after doping with iodine. The optical absorption spectrum at low doping showed two peaks: one at 4.27 eV and the other at 3.2 eV corresponding to the radical cation and charge-transfer transition, respectively. FTIR data indicated that  vibration bands  and  of polybutadiene decreased upon doping due to transformation of the double-bonds into radical cations. The Kerr coefficients as measured at 633nm and at 1550nm are  and  respectively. These exceptionally large magnitudes have been attributed to the subnanometer-size metallic domains formed upon doping and charge-transfer involving the isolated double-bonds.