The intergalactic magnetic field (IGMF) in cosmic voids can be indirectly probed through its effect on electromagnetic cascades initiated by a source of TeV gamma rays, such as blazars, a subclass of active galactic nuclei. Blazars that are sufficiently luminous at TeV energies, "extreme TeV blazars", can produce detectable levels of secondary radiation from inverse Compton scattering of the electrons in the cascade, provided that the IGMF is not too large.

We reveiw recent work in the literature which utilizes this idea to derive constraints on the IGMF for three TeV-detected blazars-1ES 0229+200, 1ES 1218+304, and RGB J0710+591, and we also investigate four other hard-spectrum TeV blazars in the same framework. Through a recently developed detailed 3D particle tracking Monte Carlo simulation code, incorporating all major effects of QED and cosmological expansion, we research effects of major uncertainties such as the spectral properties of the source, uncertainty in the intensity of the UV - far IR extragalactic background light (EBL), under-sampled Very High Energy (VHE; energy > 100 GeV) coverage, past history of gamma-ray emission, source vs. observer geometry, and jet AGN Doppler factor.

The implications of these effects on the recently reported lower limits of the IGMF are thoroughly examined to conclude that presently available data are compatible with a zero IGMF hypothesis.