**Parabolic cylinder**

Due to translation invariance, the M and E polarizations decouple to Dirichlet and Neumann scalar fields:

"Casimir force at a knife’s edge,"

Graham, Shpunt, Emig, Jaffe, & Kardar, Phys. Rev. D

81, 061701(R) (2010)

The interaction energy between a parabolic cylinder and a mirror at a separation

H:

The limitH >> Rcorresponds to aknife edge, where the interaction as a function of tilt angle is