Nonlinear birefringence due to non-resonant, higher-order Kerr effect in isotropic media

The recent interpretation of experiments on the nonlinear nonresonant birefringence induced in a weak probe beam by a high intensity pump beam in air and its constituents has stimulated interest in the nonresonant birefringence due to higher-order Kerr nonlinearities. Here a simple formalism is invoked to determine the non-resonant birefringence for higher-order Kerr coefficients. Some general relations between nonlinear coefficients with arbitrary frequency inputs are also derived for isotropic media. It is shown that the previous linear extrapolations for higher-order birefringence (based on literature values of n(2) and n(4)) are not strictly valid, although the errors introduced in the values of the reported higher-order Kerr coefficients are a few percent. (C) 2011 Optical Society of America