  We present a high sensitivity method allowing the measurement of the non
linear dielectric susceptibility of an insulating material at finite frequency.
It has been developped for the study of dynamic heterogeneities in supercooled
liquids using dielectric spectroscopy at frequencies 0.05 Hz < f < 30000 Hz .
It relies on the measurement of the third harmonics component of the current
flowing out of a capacitor. We first show that standard laboratory electronics
(amplifiers and voltage sources) nonlinearities lead to limits on the third
harmonics measurements that preclude reaching the level needed by our physical
goal, a ratio of the third harmonics to the fundamental signal about 7 orders
of magnitude lower than 1. We show that reaching such a sensitivity needs a
method able to get rid of the nonlinear contributions both of the measuring
device (lock-in amplifier) and of the excitation voltage source. A bridge using
two sources fulfills only the first of these two requirements, but allows to
measure the nonlinearities of the sources. Our final method is based on a
bridge with two plane capacitors characterized by different dielectric layer
thicknesses. It gets rid of the source and amplifier nonlinearities because in
spite of a strong frequency dependence of the capacitors impedance, it is
equilibrated at any frequency. We present the first measurements of the
physical nonlinear response using our method. Two extensions of the method are
suggested.
