Expanding on our prior efforts to search for Lorentz invariance violation (LIV) using the linear optical polarimetry of extragalactic objects, we propose a new method that combines linear and circular polarization measurements. While existing work has focused on the tendency of LIV to reduce the linear polarization degree, this new method additionally takes into account the coupling between photon helicities induced by some models. This coupling can generate circular polarization as light propagates, even if there is no circular polarization at the source. Combining significant detections of linear polarization of light from extragalactic objects with the absence of the detection of circular polarization in most measurements results in significantly tighter constraints regarding LIV. The analysis was carried out in the framework of the Standard-Model Extension (SME), an effective field theory framework to describe the low-energy effects of an underlying fundamental quantum gravity theory. We evaluate the performance of our method by deriving constraints on the mass dimension $d=4$ CPT-even SME coefficients from a small set of archival circular and linear optical polarimetry constraints and compare them to similar constraints derived in previous works with far larger sample sizes and based on linear polarimetry only. The new method yielded constraints that are an order of magnitude tighter even for our modest sample size of 21 objects. Based on the demonstrated gain in constraining power from scarce circular data, we advocate for the need for future extragalactic circular polarization surveys.
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