# Arbitrary Cherenkov emission angle

## Description

Cherenkov radiation, also known as Vavilov–Cherenkov radiation,[a] is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. The characteristic blue glow of an underwater nuclear reactor is due to Cherenkov radiation. It is named after Soviet scientist Pavel Alekseyevich Cherenkov, the 1958 Nobel Prize winner who was the first to detect it experimentally. A theory of this effect was later developed within the framework of Einstein’s special relativity theory by Igor Tamm and Ilya Frank, who also shared the Nobel Prize. Cherenkov radiation had been theoretically predicted by the English polymath Oliver Heaviside in papers published in 1888–89.

Cherenkov radiation can also radiate in an arbitrary direction using a properly engineered one dimensional metamaterials . The latter is designed to introduce a gradient of phase retardation along the trajectory of the fast travelling particle ( d\phi/dx ), reversing or steering Cherenkov emission at arbitrary angles given by the generalized relation shown here.

Related formulas## Variables

θ | Cherenkov emission angle (deg) |

n | refractive index of the medium (dimensionless) |

β | ratio between the speed of the particle and the speed of light (dimensionless) |

k_{0} | free-space wavenumber (°*m^{-1}) |

dϕ | gradient of phase retardation along the trajectory of the fast travelling particle (deg) |

dx | tavel distance (m) |