Fig. 2: Principle of photonic parallel spaces.
From: Nonlocality-enabled photonic analogies of parallel spaces, wormholes and multiple realities
a The EFCs of an ordinary anisotropic material \({{{\boldsymbol{\varepsilon }}}}\), \({{{\boldsymbol{\mu }}}}\) and free space. b The EFCs of an artificial material with two equal-frequency surfaces (red and blue) shifted along the kx and ky directions, where external propagating photons can only excite the eigenstates with dispersions shifted along the kx and ky directions through red boundary α (BDY α) or blue boundary β (BDY β), respectively. c The eigenstates of the red or blue equal-frequency surface inside the artificial material are confined by the boundary β or boundary α due to the momentum mismatch. d Calculated band structure of artificial material â… (AM â… ) for TE-polarization. The unit cell (inset) consists of an elliptical rod (\(\varepsilon=12\)) with major and minor axes of 0.8a and 0.5a in a host of \(\varepsilon=4\). a is the lattice constant. e The EFCs of the unit cell and supercells at the working frequency \({fa}/c=0.25\) (dashed line in D). f Simulated electric field distributions, Re(\({E}_{z}\)), for a point source illuminating a slab of artificial material â… with α (left panel) or β (right panel) boundaries, respectively. The background is set as the corresponding effective medium \({{{{\boldsymbol{\varepsilon }}}}}_{{{{\boldsymbol{\alpha }}}}}\), \({{{{\boldsymbol{\mu }}}}}_{{{{\boldsymbol{\alpha }}}}}\) or \({{{{\boldsymbol{\varepsilon }}}}}_{{{{\boldsymbol{\beta }}}}}\), \({{{{\boldsymbol{\mu }}}}}_{{{{\boldsymbol{\beta }}}}}\). The source is 10a away from the slabs, and the slab widths are \(w=6a\) and \(w=7a\), respectively. g Simulated electric intensity distributions (\({\left|{E}_{z}\right|}^{2}\)), for a Gaussian beam incident upon the boundaries α (left panel) or β (right panel) of a square sample (100a × 100a) of artificial material â… , at 45°.
