On the wavelength dependence of the refractive index of photons

Photon mass and negative index of refraction

“…where photon rest-mass is assumed to be wavelengthdependent [1][2][3]. Relation (3) coincides, except the minus sign, with the approximate formula (6) of Ref.…”

“…From formula (3), it is obvious that the involved subradical quantity must be non-negative so that one has [2,3]: m 0 (l)ph/cl (see, in addition, Ref. [4] (3) indicates that refractive index takes on negative values so that the quantum foam [1][2][3] through which light propagates behaves as a left-handed medium. Characterization of the above foam as a lefthanded medium is only a mathematical model to extrapolate it, in a suitable way, to real situations within the context of optical materials with negative refractive index.…”

“…In particular, a lot of theoretical work is needed in order to understand the physics underlying optical materials with negative index of refraction because a number of questions appear as open problems in the field in question. One of these problems can be related to certain aspects of non-zero photon rest-mass [1][2][3]. In fact, we will analyze in the following the implications of this mass on negative refractive index.…”

Estimation of the photon rest-mass from gravitational interaction

“…[1] and, on the other hand, Refs. [2][3][4]. Within the above context, we can say that a primary objective is to find an upper bound for the photon rest-mass given that this mass does depend on wavelength (consider previous references).…”

“…Nevertheless, in order to get a crude estimation for m o ðlÞ; we may set a % 0 so that, by using relationship (2) with the corresponding values of the involved parameters, it follows:…”