Fig. 1: General concept of polariton dispersion management and optical modeling of polariton filters.

a Sketch of cavity-based transmission filter between light source and detector, with a variable angle of incidence θ. b–d Transfer matrix simulation of the angular dispersion of an uncoupled or weakly coupled cavity with intracavity refractive index \(n\approx 1.45\) (b), a strongly coupled cavity with Rabi-splitting \(\hslash{\Omega }_{{\rm{R}}}\approx 0.2\,{\rm{eV}}\), negative detuning \(\delta \approx -0.2\,{\rm{eV}}\) (c), and an ultra-strongly coupled cavity with \(n\approx 1.85\), \(\hslash {\Omega }_{{\rm{R}}}\approx 1\,{\rm{eV}}\) and positive detuning of \(\delta \approx 0.2\,{\rm{eV}}\) (d). Strong coupling leads to formation of upper and lower polariton branches (UPB/LPB) which avoid the crossing point of cavity photon (dashed line) and material exciton (solid blue line). In each panel, the transmitted modes are indicated as solid red lines. While the uncoupled cavity shows a characteristic and large angular dependence, strong coupling can dramatically reduce this dependence; under ultra-strong coupling conditions in particular, the angular dispersion can be almost negligible. e Transfer matrix simulation of angle-resolved transmission of a metal-dielectric-metal weakly coupled (Weak) cavity (left) and a strongly coupled (SC) cavity (right). Angular dispersion leads to a significant blueshift and polarization splitting of the narrowband transmission for the weak cavity. For the SC cavity, the resonance is further narrowed and shows almost no blueshift and polarization splitting at large angles. Lines represent a coupled-oscillator model of polariton modes (red lines) as well as the bare exciton (green dashed) and cavity (white dashed) resonances. f Simulated transmission of a distributed Bragg reflector (DBR, left) and a blue-shifted strongly coupled DBR cavity (right). For the latter, the DBR sidebands couple to the excitonic resonance, leading to an angle-independent stopband between 400 nm and 500 nm.