  We present a fast active microrheology technique exploring the phase response
of a microscopic probe particle trapped in a linear viscoelastic fluid using
optical tweezers under an external perturbation. Thus, we experimentally
determine the cumulative response of the probe to an entire repertoire of
sinusoidal excitations simultaneously by applying a spatial square pulse as an
excitation to the trapped probe. The square pulse naturally contains the
fundamental sinusoidal frequency component and higher odd harmonics, so that we
measure the phase response of the probe over a very wide frequency band in a
single shot. We then determine the responses to individual harmonics using a
lock-in algorithm, and compare the phase shifts to those obtained theoretically
by solving the equation of motion of the probe particle confined in a harmonic
potential in the fluid in the presence of a sinusoidal perturbation. We go on
to relate the phase response of the probe to the complex shear modulus
$G^{*}(\omega)$, and proceed to verify our technique in a mixture of
polyacrylamide and water, which we compare with known values in literature and
obtain very good agreement. Our method ensures that any drifts in time are
almost entirely ruled out from the data, with the added advantage of high speed
and ease of use.
