**Corrugated Surfaces **

Normal force

A common method
for dealing with non-flat geometries is the **Proximity Force
Approximation**, which in effect assumes an effective Casimir interactions
between locally parallel pairs on points on the two surfaces, and sums over
all such pairs.

"Probing the Strong Boundary Shape Dependence of the Casimir Force,"

Emig, Hanke, Golestanian, & Kardar, Phys. Rev. Lett.

87, 260402 (2001)

Büscher & Emig, Phys. Rev. A

69, 062101 (2004) ("reduced distance" limit)"Nonperturbative approach to Casimir interactions in periodic geometries,"

"Demonstration of the Nontrivial Boundary Dependence of the Casimir Force,"

A. Roy and U. Mohideen, Phys. Rev. Lett. 82, 4380 (1999)

"Measurement of the Casimir Force between a Gold Sphere and a Silicon Surface with Nanoscale Trench Arrays,"

H.B. Chan, Y. Bao,

et. al, Phys. Rev. Lett.101, 030401 (2008)

Lateral force

A sideways
force to "align" the two plates at *b=λ/2*

"Mechanical Response of Vacuum," Golestanian, & Kardar, Phys. Rev. Lett.

78, 3421 (1997)

"Demonstration of the Lateral Casimir Force,"

F. Chen, U. Mohideen,

et. al, Phys. Rev. Lett.88, 101801 (2002)

Manipulating the critical Casimir force with chemically patterned surfaces:

"Critical Casimir forces in colloidal suspensions on chemically patterned surfaces,"

F. Soyka, O. Zvyagolskaya, C. Hertlein, L. Helden, & C. Bechinger, Phys. Rev. Lett., in press (2008) (movie)