Photons must pass within the photon sphere to complete a full loop around a black hole, as demonstrated by strong-field gravitational lensing and general relativistic orbit analyses.
The retrieved papers consistently define the photon sphere as the region containing unstable circular null geodesics, which act as the threshold for strong deflection lensing where light rays can orbit or loop around the black hole. None of the papers refute this relationship; rather, they rely on it to study black hole shadows and lensing.