Optical properties of Euler–Heisenberg black hole surrounded by perfect fluid dark matter

This work explores the phenomenon of plasma lensing in weak plasma fields around Euler–Heisenberg black holes submerged in perfect fluid dark matter. For both uniform and non-uniform plasma environments, the deflection angle is systematically determined, investigating the impact of different parameters on the deflection angle in each plasma field. We also discuss on the gravitational deflection ring using the deflection angle for uniform and non-uniform plasma. We also investigate the energy collision inside the black hole, offering a thorough investigation of the relationship between energy collision, gravitational deflection, and plasma lensing for Euler–Heisenberg black holes encircled by perfect fluid dark matter. we concluded that the deflection angle in uniform plasma is greater than in non-uniform plasma. Similarly, image magnification from the source is higher in higher plasma concentration. Image is also more magnified in the uniform plasma than in the SIS plasma field. Ring deflection angle in Uniform plasma is also more than SIS plasma field.