Influence of Nonlocality on Transmittance and Reflectance of Hyperbolic Metamaterials

Abstract

<jats:p>In this paper we investigate transmittance and reflectance spectra of multilayer hyperbolic metamaterials in the presence of strong spatial dispersion. Our analysis revealed a number of intriguing optical phenomena, which cannot be predicted with the local response approximation, such as total reflectance for small angles of incidence or multiple transmittance peaks of resonant character (instead of the respective local counterparts, where almost complete transparency is predicted for small angles of incidence and the broad-angle transparency can be observed within a range of larger angles of incidence). We believe that the observed effects may serve as a working principle in a number of new potential applications, such as spatial filtering, biosensing, or beam steering.</jats:p>

Nonlocality-Enabled Magnetic Free Optical Isolation in Hyperbolic Metamaterials

“…At this point, we would like to underline that the observed nonlocal effects do not originate from any unique properties of chosen materials, which are assumed to be non-magnetic, linear, and local, but rather from interactions between plasmonic modes propagating in the considered multilayer structure [ 31 ]. Thus, similar effects may be obtained for different material compositions, i.e., various sets of dielectric and plasmonic material, as indicated in our previous studies [ 28 , 33 ].…”

“…Now, knowing that the plane of incidence is the x–z plane, spatial differentiation may be simplified as follows . Based on above assumptions and Maxwell equations [ 33 ], the problem of wave propagation through an anisotropic structure may be formulated as the following matrix equation: where z’ = z/k o is normalized position, while the characteristic matrix Ω and field vector ψ may be described in the following form: …”

“…For simplicity of interpretation, we assume normalization of wavevector as well as magnetic field and components. Solution of the Equation (9) may be written as which can be also formulated as an eigenvalue problem [ 33 ]: where c = W −1 ψ (0) is a vector of field amplitudes, while W and λ are eigen-vector and eigen-value matrices of characteristic matrix Ω. By applying continuity condition for field components at the interfaces of the anisotropic layer to the Equation (11), we can formulate a matrix equation describing the relationship between field amplitudes at reflection ( ) and transmission ( ) sides of the structure: where L is the thickness of the anisotropic layer and W out and W in are eigen-vector matrices of media surrounding the layer.…”

“…The intensity reflection coefficients (further regarded as reflectance) for TE and TM polarization may be formulated as follows [ 33 ]: …”

Distributed Feedback Laser Based on Tunable Photonic Hypercrystal

“…H 0 e jk x x e jk y y e jk z z , where e +jkz denotes +z direction propagation and k x,y,z are components of the wavevector, the problem of wave propagation in a nonmagnetic biaxial anisotropic medium may be formulated in the form of the matrix equation [44]:…”