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We study theoretically the optics in undoped direct gap semiconductors whichare strongly driven in the THz regime. We calculate the optical sidebandgeneration due to nonlinear mixing of the THz field and the near infraredprobe. Starting with an inversion symmetric microscopic Hamiltonian we includethe THz field nonperturbatively using non-equilibrium Green functiontechniques. We find that a self induced relativistic spin-THz field couplinglocally breaks the inversion symmetry, resulting in the formation of oddsidebands which otherwise are absent.Comment: 8 pages, 6 figure

Spin-dynamic field coupling in strongly terahertz-field-driven semiconductors: Local inversion symmetry breaking