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We provide a new analysis technique to measure the effect of the isotropicpolarization rotation, induced by e.g. the isotropic cosmic birefringence fromaxion-like particles and a miscalibration of CMB polarization angle, via modecoupling in the cosmic microwave background (CMB). Several secondary effectssuch as gravitational lensing and CMB optical-depth anisotropies lead to modecoupling in observed CMB anisotropies, i.e., non-zero off-diagonal elements inthe observed CMB covariance. To derive the mode coupling, however, we usuallyassume no parity violation in the observed CMB anisotropies. We first derive anew contribution to the CMB mode coupling arising from parity violation inobserved CMB. Since the isotropic polarization rotation leads to parityviolation in the observed CMB anisotropies, we then discuss the use of the newmode coupling for constraining the isotropic polarization angle. We find thatconstraints on the isotropic polarization angle by measuring the newmode-coupling contribution are comparable to that using the $EB$ cross-powerspectrum in future high-sensitivity polarization experiments such as CMB-S4 andLiteBIRD. Thus, this technique can be used to cross-check results obtained bythe use of the $EB$ cross-power spectrum.

CMB Mode Coupling with Isotropic Polarization Rotation