For a perfectly conducting cylinder, the M and E polarizations correspond to Dirichlet and Neumann scalar fields:
Can be used to compute the interaction between a cylinder and a plate:
"Casimir Interaction between a Plate and a Cylinder,"
T. Emig, R.L. Jaffe, M. Kardar & Scardicchio, Phys. Rev. Lett. 96, 080403 (2006)
Limiting force for a thin wire (R >> H ):
due to long wave-length charge fluctuations along the length of the cylinder.
Unexpected non-monotonicity due to three-body effects:
"Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders,"
Rahi, Rodriguez, Emig, Jaffe, Johnson, & Kardar, Phys. Rev. A 77, 030101(R) (2008)