Propagation of photons in homogeneous magnetic fields: Index of refraction

The index of refraction associated with the vacuum polarization induced by homogeneous magnetic fields is calculated for two cases: (i) high-energy photons traversing fields weak compared with the critical field, $H_{\mathrm{cr}}=\frac{m^2{c}^3}{e\hslash }\cong 4.41\times {10}^{13}$ G; and (ii) low-energy photons in fields of arbitrary intensity. Some implications for the physical optics of intense magnetic fields are briefly discussed.