tl;dr: The technique only works at low pressure, and works on a small pressure difference between top and bottom, so it's really only for extremely thin and lightweight "microflyers" and is not extendable to large spacecraft.
The video links to the open access paper in science Controlled levitation of nanostructured thin films for sun-powered near-space flight and there's a long PDF with more information and six videos in the paper's Supplementary Materials.
Let's look at the paper's summary:
In summary, this work demonstrated an approach to photophoretic levitation of macroscopic structures that does not require a temperature gradient within the object, offering a path to the development of affordable photophoretic microflyers for the mesosphere. We developed a theoretical model for thin disks, which showed agreement with the experiments done using low-cost fabrication methods. The levitation tests were successful at pressures of ~10 Pa and incident light intensity of 0.5Wcm2. We also presented a method to trap and control the hovering of the thin microflyers. Last, photophoretic levitation through Δα-force showed consistent upward lift force direction regardless of the direction of incoming light.
Our experimentally validated model predicts that the same approach can be used in the near space at altitudes between 50 and 100 km. Such microflyers can use sunlight or a laser beam from any direction to stay levitated for extended periods of time, allowing, for example, the mapping of wind flows at these high altitudes by tracking the location of these flyers using a radar or lidar. There is a large opportunity to further increase the force by increasing the difference in accommodation coefficients and reducing the infrared emissivity. Such improvements will allow the microflyers to carry payloads of up to 10 mg, which can consist of thin substrate or smart dust sensors for weather and climate applications, such as measuring temperature, pressure, or carbon dioxide levels.
- The demonstraton offers "a path to the development of affordable photophoretic microflyers for the mesosphere".
- These "microflyers can use sunlight or a laser beam from any direction to stay levitated for extended periods of time, allowing, for example, the mapping of wind flows at these high altitudes by tracking the location of these flyers using a radar or lidar."
How does it work? What is the principle?
Cropped from Figure 1.
A thin, low mass disk absorbs sunlight or laser light and gets pretty warm or hot in a very low density part of the atmosphere where cooling is less efficient. As air molecules collide with the hot surfaces they scatter with a higher velocity on average.
If the details of the shapes of the microstructures or nanostructures each side differ, they can enhance the scattering of air molecules on one side compare to the other in a certain way; they frustrate the molecules from recoiling with a perpendicular velocity component on one side; the molecules are more likely to scatter left-right on one side than the other due to squiggly-looking nanostructures on one suruface.
On a micrscopic scale, pressure is just the sum of all the zillions of little impulses that a surface experiences by all the little molecules hitting it. If the sum of all the normal components on one side is lower than the other, then there is a pressure difference.
Integrate that over the surface and you've got lift!
note: this works when the mean free path of the molecules is long enough that they scatter away from the nanostructured surface before interacting with other molecules. Currently the technique will not work at sea level; you have to get these up into a low pressure part of the atmosphere some other way.
How much lift is there?
The lift is the pressure difference times the area. The pressure difference is a small fraction of the total atmospheric pressure, which the paper's abstract mentions is in the 10 to 30 Pa regime, the pressure difference will be a small fraction of that. The pressure at Earth's surface for comparison is 100,000 Pa.
So we're talking a 100,000th to a millionth of 15 psi. Tiny.
The question asks:
How powerful would a laser need to be to make this sort of propulsion at a distance of e.g. 80 km feasible, and how large a craft could realistically be bought up to that altitude?
I'll go along with @Uwe's assessment that a "large craft" will not ever be levitated by this particular mechanism.
This is strictly for mesospheric photophoretic microflyers.