The geometry-tuned Casimir cell

Why the library suggests it

Same gold, same air: change only the shape of the lower surface, and watch the force move by more than an order of magnitude.

Shape, not material

Same metal, same air, same room temperature: gold facing gold. Change only the shape of the lower surface and the Casimir force changes by more than a factor of twenty, and the way it falls off with distance changes too. Choose a surface, move the gap, and read the multiplier against a plain flat plate of the same metal.

Lower surface

A flat plateA single pillar, 300 nanometres across the radiusA pillar with a hole down the middleA dense array of pillars

Gap between the sphere and the surface

Gap between the sphere and the surface

85

• A single pillar, 300 nanometres across the radius
• Force multiplier against the gap

Multiplier against a flat plate of the same metal:

0.12×

Multiplier against a single isolated pillar:

1.00×

Share of the force carried by the supporting plate below:

60.1%

How the multiplier runs as the gap opens:

Falls away faster than the flat-plate case, until the supporting plate below takes over

What this surface does: A single 300-nanometre pillar cuts the force by roughly a factor of ten. As the gap opens, the supporting plate below takes over the interaction — its share runs from well under one per cent at ten nanometres to above ninety per cent at three hundred.

Read the two multipliers carefully, because they have different baselines. The array's near-threefold gain is measured against a single isolated pillar, never against a flat surface — against a flat plate the array is still below one.

Fabricated dimensions

Sphere radius:

33,100 nm

Pillar radius:

300 nm

Pillar height:

120 nm

Scope: the proximity-force approximation with the ideal plate pressure. The measurement itself used Lifshitz theory with the gold's own measured optical data and a roughness correction, and reports agreement with these sharp-edged shapes to within about a factor of three. The lesson is the one the authors draw: the magnitude and the distance law are both set by geometry alone, with the material held fixed.

The source sheet: Shelden and colleagues, Casimir force control enabled by 3D nanostructures, 2025

Jeremy Munday's group measured a single 300-nanometre gold pillar cutting the force by roughly a factor of ten, a pillar with a hole through it bending the force-versus-distance curve the other way, and a dense pillar array standing nearly three times an isolated pillar — still below the plain plate — all in ordinary air at room temperature (Casimir Force Control Enabled by 3D Nanostructures, 2025). The reason shape rather than energy is the right handle was worked out long before: inside a rectangular cavity the vacuum can push outward on one pair of faces while pulling inward on another at the same time, which is why an energy-only account of a Casimir cycle gives the wrong answer (Unusual properties of conductive rectangular cavities in the zero point electromagnetic field, 1999). Fabrizio Pinto built the apparatus and the calibration procedure for driving something with that force rather than merely measuring it (Membrane actuation by Casimir force manipulation, 2008).

The experiment or build

Take a sphere-and-plate Casimir rig — the standard instrument in the field — and fabricate a plate carrying a library of patterns: bare, single pillar, holed pillar, arrays at several pitches. Measure the force against separation for each. Then close the loop: drive a membrane with the patterned surface and read its resonance. The settling measurement is the force per unit area at a fixed separation, plotted against pattern geometry, with the electrostatic calibration published alongside it — because the calibration is where this measurement is won or lost. Harold White's group found something else while doing exactly this kind of modelling, which is the subject of a later card (Worldline numerics applied to custom Casimir geometry, 2021).