Polarization optics analogy of quantum wavefunctions in graphene

Abstract

Detailed similarities between polarization states of light and ballistic charge carriers in graphene are derived. Based on these, the optical equivalent of quantum wavefunctions, Dirac equation, and the effect of an electrostatic potential are found, and the quantum analog of the refractive index of light and of the optical composition law of reflection coefficients are obtained. The differences between the behavior of quantum wavefunctions in graphene and electromagnetic fields, due to the chiral symmetry of ballistic charge carriers that cannot be mimicked in classical polarization optics, are also evidenced.

Influence of light polarization on the analogy between ballistic nanostructures and the electromagnetic field

“…Note that equivalent optical-graphene structures in a limited range of parameters were also found in [34], where the energy and incidence angles of electrons could be tuned to obtain the same transmission as for a given optical structure normally illuminated with TE waves. An additional tunable parameter, i.e., the polarization angle α, generalizes previous results [33,34] and allows the design and even implementation of analogous opticalgraphene structures with the same transmission/reflection in wider ranges of parameters.…”

“…The spinorial wavefunction in graphene has been put into correspondence with polarized states of light [33], without finding similar boundary conditions, and with the TE electromagnetic field [34], without finding a set of analogous parameters. The reason is that, except for normal incidence, when R 0, expression (14) describes a square modulus of a complex number, with no counterpart in nonabsorbing and nonamplifying optical media, irrespective of light polarization [see Eqs.…”

“…Although in graphene the wavefunction has two components, it is still scalar, so that the search of a set of graphenelight analogies for an arbitrary linearly polarized radiation would lead to nonunique results, as for Schrödinger electrons. Moreover, since the physics of graphene and polarized light is totally different, in the sense that the TE and TM components of light propagate independently, while quantum chirality links the two components of the spinorial wavefunction in graphene [33], a set of graphene-light analogous parameters, even if found, could not be directly used to design optical structures with the same R value as in ballistic graphene structures. In addition, there is no physical ground for a direct link between α and the polar angle of the spinor wavefunction in graphene, for example.…”

Guided modes in a triple-well graphene waveguide: analogy of five-layer optical waveguide

“…Many optics-like phenomena have been explored in graphene, such as negative refraction [7], collimation [8], Goos-Hänchen effect [9,10], Bragg reflection [11], and subwavelength optics [12]. The propagation of chiral fermions in different electrostatic potentials in graphene has also been mimicked with that of electromagnetic fields in optical structures [13,14].…”

Kane-like electrons in type II/III heterostructures versus Dirac-like electrons in graphene

“…Similar to the situation in Ref. 3, in our case this additional parameter is required by the difference in the dispersion relations in graphene and Kane-type heterostructures.A second problem is to find an InP/GaAsSb/InP hetero ission coefficient through a finite-width GaAsSb layer as that through a region with potential energy2 V in graphene sandwiched between identical semi-infinite regions with potential energies 1 . More precisely, the transmission coefficient through such a layer with thickness L is given by V impose an additional condition for the propagation of charge carriers in graphene and semiconductor heterostructures in order to obtain the same l T in both cases: , where s L , g L are the respective widths of layer 2 in semiconductor and graphene.…”