Giant Goos-Hänchen shifts in non-Hermitian dielectric multilayers incorporated with graphene

Abstract

We theoretically investigate the Goos-Hänchen (GH) shifts of optical beam in a defective photonic crystal composed of dielectric multilayers and graphene. The system is non-Hermitian and possesses exceptional points (EPs) as the scattering matrix becomes defective at the zero points of reflection. The reflective wave at EPs experiences an abrupt phase change and there the eigenvalues of scattering matrix coalesce. The GH shifts are extremely large near EPs in parametric space composed of dielectric refractive index and incident angle. The positive and negative maxima of GH shifts could be as high as 10 times of the incident wavelength. The direction of GH shifts switches at EPs and the EPs position can be readily controlled by the chemical potential of graphene. Moreover, the GH shifts should remarkably change as the incident waves impinge on the structure from opposite directions. The study of GH shifts in the graphene incorporated multilayers may find great applications in highly sensitive sensors.

Exceptional Points in Non-Hermitian Photonic Crystals Incorporated With a Defect

“…The designed PCs could also be abbreviated to (AB) N CD(BA) N , where N is the periodic number of Bragg gratings, and here it shows N = 5. In simulations, the incident wavelength was in the range of terahertz band and the transmission matrix method (TMM) was used to derive the reflection coefficient r and transmission coefficient t [18]. Subsequently, the reflectance of light and transmittance can be denoted by R = rr* and T = tt*, respectively.…”

“…where ϕ r/t is the complex phase of the reflection/transmission coefficient. As a transverse magnetic (TM) polarization wave obliquely impinged upon the PC with the incident angle θ, the lateral GH shift of reflected/transmitted light beam was proportional to the slope of the reflection/transmission coefficient complex phase, with respect to the incident angle, that is D ry/ty = −λdϕ r/t /2πdθ [18], where λ is the incident wavelength.…”

“…The PT-symmetry will spontaneously break if the gain and loss surpass some critical value, which is defined as the exceptional point (EP) [8,13]. The eigenvalues and eigenvectors of Hamiltonian degenerate in non-Hermitian systems at the EPs, around which many fascinating optical properties may be induced, consist of sharp changes in the complex phase [18], unidirectional invisibility [19,20], and topological boundary states [21].…”

Coherent Perfect Absorption Laser Points in One-Dimensional Anti-Parity–Time-Symmetric Photonic Crystals

“…With reference to the lattice structure of solid crystals, people put forward the concept of PCs, which provide a new approach to solve the above problem. At the bandgap edge of the PCs, there is large GH shift [66], and the optical field localization of the defect PCs can also induce large GH shift [62].…”

“…The refraction index in each unit cell is real and given by n(z) = n a as 0 < z < d and n(z) = n b as d < z < 2d. Using the transfer matrix method (TMM), we can relate the electromagnetic fields at the two interfaces of a homogeneous medium by [62]…”