Measuring Tiny Forces with Light

Photons have no mass, but they have momentum. This allows researchers to use light to push matter around. Scientists at the Physical Measurement Laboratory (PML) at the National Institute of Standards and Technology (NIST) have taken advantage of this property to develop devices that can create and measure minute forces, an area traditionally underserved by the metrology community.

A prototype for the chip-sized small-force meter. The cantilever is near the intersection of the two rectangles in the center of the glass cylinder.

The official SI unit of force is the newton. One newton is equivalent to about the weight of an average-sized apple. The experiments the group is working on can measure forces that are tiny fractions of a newton — from micronewtons (10^-6, millionths of a newton) all the way down to 15 femtonewtons (10^-15, a million billionth of a newton) at the level of atomic interactions.

The PML team is currently developing two types of force-measurement devices that use laser light to reliably create small forces. The first is a chip-sized sensor that can use micro- to milliwatt-power light. The second is a tabletop device designed for laser light of about 1 watt, but which could potentially be developed for light of tens of kilowatts of power.

Eventual commercial applications could include sensors that use laser light as a built-in reference, allowing scientists to ensure their devices really are measuring force correctly. But the potential applications go beyond force into inexpensive field-portable balances for near-instant measurement of masses of a milligram or less, and into compact laser power meters that make their measurements in real time.

A Chip-Sized Balance

The smaller of the two types of force meter being developed is a chip-sized sensor made of fused quartz. It consists of a small cantilever less than 1 cm in length. The bigger the force, the more the cantilever moves. A built-in interferometer acts as a motion sensor. Physically pushing the cantilever is one way to apply a force for measurement. But researchers also need to gauge the sensitivity of their sensor. The best way to measure sensitivity is to apply a well-known force to the cantilever and see how it is interpreted by the interferometer.

To manipulate the cantilever with light, it was fitted with a highly reflective, gold-coated surface that can reflect light shining on it from an optical fiber. When this light hits the gold surface, it transfers its momentum to the cantilever, which begins to vibrate.

They found that if laser light is reflected off the surface, there's a relatively straightforward way to calculate what the force should be based on the laser power. The higher the power, the more photons there are, and the larger the force that's generated. Furthermore, since the cantilever's resonant frequency changes almost instantly if a mass is placed on it, the mechanism could also be used as a very sensitive balance; particularly for objects that are extremely valuable or dangerous. For example, it could be used as a field-portable disposable tool for measuring samples of hazardous materials.

Unlike the current “gold standard” method of measuring laser power — a cryogenic radiometer — a chip-based laser power meter like this can be used at room temperature and in real time.

The Force of a Single Photon

But even at the lowest laser powers used so far — just millionths of a watt — the light still contains an enormous number of photons. A force measurement device capable of single-photon detection could be developed. The reason is that integers don't have uncertainty; if you count individual photons, and you know how much force each photon produces, then you can calculate the force.

The proposed scheme would require measuring mere zeptonewtons of force (10^-21), which translates to 100 million photons per second. Before that's possible, the team has to determine how to cool the single-photon force sensors down to just fractions of a degree above absolute zero, which requires a cryostat. But a typical cryostat creates too many vibrations for such precise measurements — a factor of 10,000 more than they could accept.

While they prepare to test their prototype in a new, less shaky cryostat design, they've turned the vibration issue into a potential solution for a different problem. The force sensors could be used as accelerometers, which enable measurement of how much vibration the cryostats are creating.

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