On occasion, a scientific idea comes along that is so simple and elegant that one wonders that it hadn’t been done before! Such is the case with the results of an article published online in Nature Photonics in December, which demonstrates that it is possible to make a microscopic optical wing that can “fly” on beams of light!
How is this possible? Light carries momentum, and can transfer that momentum to objects that it scatters off of. For flight, it serves the role of the force of wind, and an appropriately shaped optical wing can direct that force of light to provide lift.
Scientists have been aware that light carries its own “kick” in the form of momentum since James Clerk Maxwell first correctly suggested that light is an electromagnetic wave. In fact, Maxwell himself evidently was the first to demonstrate this in terms of the electromagnetic theory in his 1873 book A Treatise on Electricity and Magnetism (§792-793):
Hence in a medium in which waves are propagated there is a pressure in the direction normal to the waves, and numerically equal to the energy in unit of volume.
Thus, if in strong sunlight the energy of the light which falls on one square foot is 83-4 foot pounds per second, the mean energy in one cubic foot of sunlight is about 0-0000000882 of a foot pound, and the mean pressure on a square foot is 0.0000000882 of a pound weight. A flat body exposed to sunlight would experience this pressure on its illuminated side only, and would therefore be repelled from the side on which the light falls. It is probable that a much greater energy of radiation might be obtained by means of the concentrated rays of the electric lamp. Such rays falling on a thin metallic disk, delicately suspended in a vacuum, might perhaps produce an observable mechanical effect.
Obviously, this is a tiny amount of pressure: by Maxwell’s calculation, a square foot of the Earth experiences a tenth of a millionth of a pound of force from sunlight!
This isn’t a lot of pressure, but given enough time — and the frictionless environment of space — it can have a big effect. In 2007, observations of a pair of asteroids in the solar system confirmed the existence of the YORP effect, in which sunlight altered the rotational properties of the orbiting bodies.
Eros, one of the asteroids for which the YORP effect was confirmed. Image by NASA, via Reuters.
In essence, an irregularly-shaped asteroid can absorb sunlight shining upon it and reradiate it as infrared radiation. For an irregularly shaped asteroid, this process of absorption and reradiation is nonuniform — it happens differently at different places on the asteroid. Because the radiation has momentum, it provides an imbalance of torque on the asteroid, and can consequently alter the spinning of the object.
The momentum of light also has practical and surprising uses. In 1986, a group of researchers at Bell Laboratories demonstrated* that a single focused beam of light can be used to trap microscopic particles in the beam’s focus, including living cells. The technique is called optical tweezing, and is now a standard technique for manipulation of microscopic objects.
What is surprising about optical tweezing is that the microscopic particles can experience a force in a direction perpendicular to, or even opposite to, the overall direction of the light flow. This is schematically illustrated below.
The particle experiences what is known as a gradient force; it is attracted to the region where the light intensity is highest, namely the focal point of the lens.
The idea of a gradient force is perhaps counterintuitive; one might naturally predict that the light would push the particles away from the focal region. We can understand the effect by a simple geometrical optics model, illustrated below.
Figure illustrating gradient forces. Adapted from article by Neuman and Block**.
Suppose a light beam is illuminating a transparent spherical particle from above, and the light intensity increases as one moves to the right. Let us consider the ray on the right first. Due to refraction at the two surfaces of the particle, it ends up bending to the left when it exits. Because momentum is conserved, however, the particle must experience a force to the right. Similarly, the ray on the left generates a force on the particle that pushes it to the left. If the intensities of the light rays are equal, these two forces balance out and the particle doesn’t move left or right. If the light ray on the right is brighter than that on the left, i.e. there is a gradient of light intensity, the particle will experience a net force to the right, into the brighter part of the light. This is the gradient force.
We have seen that a spherical microscopic particle can be moved in surprising ways if it is placed in a nonuniform beam of light. The idea of the optical wing, however, is in a sense the opposite strategy: an irregularly-shaped particle can be moved in surprising ways in a uniform beam of light, much like a wing generates lift in a uniform flow of air.
It’s probably worth saying a few words about the physics of flight. A plane generates lift (the force that “lifts” the plane into the air) through a rather complicated process that is often misleadingly attributed entirely to Bernoulli’s force. In short, a plane flies because air is diverted downward as it passes over/under the wing. The downward push of the air is compensated by an upward push on the airplane. The angle that the wing takes with respect to the oncoming air greatly effect the lift, and is referred to as the angle of attack.
Illustration of lift on a wing. From the ALLSTAR Network website.
The idea of a wing that generates its lift from light was developed by researchers at the Rochester Institute of Technology. They began by performing computer simulations to study the forces produced on a semi-cylindrical rod of glass; the shape is illustrated below.
They indeed found that, in general, the cylindrical rod has two angles of attack for which it experiences stable optical lift! This lift occurs for a reason analogous to that of an aircraft wing: the illuminating light is deflected downwards by the asymmetric rod, therefore resulting in an upward force on the rod.
To verify their predictions, experiments were done with glass rods 0.014 mm long submerged in water. Instead of illuminating the rod from the side, and having it fly up or down, they illuminated it from below, and had the rod “fly” to the side. They found the rods could be stably “flown” sideways; a top-down time lapse photo of such an event is shown below.
Time lapse photo of stable optical lift. Taken from RIT press release.
Perhaps the most important distinction between the optical lift described here and the gradient force described earlier is that optical lift can be achieved in a uniform beam of light. This means that many rods can be lifted and “flown” simultaneously, side by side. In contrast, the gradient force is generally only effective in the immediate vicinity of an optical focus, and very few particles can be trapped together at the same time.
So what can be done with such optical lift? In their article, the authors suggest that an array of microrods could be attached to a solar sail, and manipulation of the position of the rods could be used to control the direction of propulsion of the spacecraft.
I actually had a chance to chat with first author Grover A. Swartzlander, Jr., at the October 2010 Frontiers in Optics meeting in Rochester about his results. (We’ve actually collaborated on a project in the past.) He speculated that an array of microrods might also be used to improve the energy-gathering efficiency of solar panels; the microrods could possibly be designed to use the force of sunlight itself to orient themselves to optimal positions for light collection. The lift force also opens the door for new types of microscopic machines that could be powered entirely by light.
These preliminary results are impressive, and will doubtless lead to more investigations concerning the nature of optical forces on particles. As I noted in the introduction, it is such a simple and elegant idea that it is remarkable that nobody seems to have thought of it earlier!
* A. Ashkin, J.M. Dziedzic, J.E. Bjorkholm and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11 (1986), 288. (A. Ashkin actually began work to study the trapping of particles by light in the early 1970s; this paper represents the first demonstration of the use of a single light beam to trap particles.)
** K.C. Neuman and S.M. Block, “Optical trapping,” Rev. Sci. Inst. 75 (2004), 2787.
Swartzlander, G., Peterson, T., Artusio-Glimpse, A., & Raisanen, A. (2010). Stable optical lift Nature Photonics, 5 (1), 48-51 DOI: 10.1038/NPHOTON.2010.266