I think I might have a solution to the problem of deflecting macroscopic light beams through large angles under electronic control at submicrosecond time scales, using a plano-convex lens and a plano-concave lens, which translate relative to each other — or, rather, an array of each, like the surface of a lenticular 3-D image. Then you can get large light deflections out of submicron movements.
One of the problems I’ve frequently confronted — in, for example, Bokeh pointcasting, Photodiode camera, and CCD oscilloscope — is how to rapidly change the direction of light beams, such as laser beams, under the control of some kind of control system, such as an electronic circuit. This is a standard problem, and Michelson and Morley’s 19th-century solution to it — a prismatic mirror spinning on an air bearing — led to new measurements of the speed of light and is used today in, among other things, supermarket scanners and laser printers. (I think it also led to the modern dentist’s drill.). However, the spinning mirror has a lot of momentum, so while the movement is very predictable, it is not very controllable.
Modern laser light shows confront this problem with “laser galvos”, descendants of the old instrument for measuring small currents — a galvanometer connected to a mirror rather than a needle. These are used in pairs, one for X deflection and one for Y deflection. Galvos for laser shows are rated in “kpps”, thousands of points per second, and a few tens of kpps is typical.
Contrast this with the electron gun in a CRT. High-end mass-market CRT computer monitors in the early 2000s supported 1200 scan lines at a 72 Hz refresh rate, meaning that even with magnetic deflection, they could scan the electron beam across the screen in a sawtooth-wave pattern at 86 kHz. Analog oscilloscopes, using electrostatic deflection, routinely managed 20 MHz vertical deflections with 3 dB attenuation; high-end ones could reach 100 MHz. To look at it a certain way, that’s 200 000 kpps.
The limitation on galvos is that mirrors have mass, which makes it harder to move them. If you try to make them smaller so that they have less mass, you suffer from divergence problems, where focusing the laser beam onto a smaller mirror narrows the beam waist and induces beam spreading through diffraction.
This is a serious problem: light can change direction in femtoseconds, and it’s easy to switch electricity in nanoseconds, but changing the direction of light with electricity takes microseconds. Isn’t there any way to get that number down to hundreds of nanoseconds or better, without suffering milliradians of divergence?
Well, there are lots of things that might work, like Kerr cells and dynamic LCD holography and ultrasonic gratings and whatnot, but I think I’ve found a good one.
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A meniscus lens is concave on one side and convex on the other; it can be designed concave, convex, or neutral, so that collimated on-axis light entering the convex side comes out still collimated on the concave side. The exiting light is brighter and does not cover all of the lens; this effect gets stronger as the lens gets thicker, reaching a singularity when the lens thickness is the focal length of the convex side and, in the geometric-optics approximation, the light would come out in an infinitely thin pencil.
Take a neutral meniscus lens that is thick enough to be sliced along a flat plane parallel to its curved surfaces without interrupting either surface, and slice it in this way, dividing it into a plano-convex lens and a plano-concave lens. Separate the two halves by just enough air or oil to equal the delay of the glass removed. Aside from the stray light reflections at the new surfaces, this compound lens still behaves precisely as before, leaving collimated light collimated, but making it brighter.
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However, if we slide the two halves relative to each other, retaining flat-surface parallelism and distance, the collimated light exiting will change direction. If we slide the plano-concave half up, for example, the light passing through the center of the plano-convex lens, previously not deflected at all, now finds itself exiting just below the center of the plano-concave half, and so is refracted slightly down. The light a little above it enters the plano-convex lens and is refracted down, but exits through the center of the plano-concave lens, continuing its trajectory parallel to the other beam.
The beam remaining collimated depends on the deflection being linear with off-axis distance, and this linearity is not perfect. I think it’s pretty good over ±30°, though, especially if the lens system is thick enough.
Consider the case where instead of one lens we have many, like two layers of that lenticular plastic covering that covers those 3-D parallax Jesus cards, except that the lenslets on one of them are concave:
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This exhibits the same direction-changing behavior over the same angle with the same displacement as the single lens, but can handle a great deal more light.
You could fabricate this with little hexagonal lenslets in two dimensions, so that you can slide the two sheets relative to each other in two dimensions and deflect light on two axes, or you could fabricate it as two prismatic solids with complicated profiles amounting to many concatenated “cylindrical” lenses, like the typical 3-D lenticular parallax Jesus cards, and get only one dimension of displacement.
The speed of sound in glass is commonly about 4500 m/s though it varies from 4000–6000 m/s for different glasses. Suppose you have a 100-mm-wide sheet of these lens things and you give it a shove on one edge, parallel to its surface, say with a piezoelectric actuator. That shove produces a sound wave that bounces back and forth through the glass about ten times before the whole thing has settled, in about 220 μs, using the above estimate of its speed of sound.
This sounds dismayingly slow, but I don’t think the picture is that bleak. It’s true that you have latency in the tens of microseconds, but it’s very consistent, predictable latency. You can inverse-filter for the phase delay. XXX what about variation across the sheet while it’s strained? Just turn the laser off except at key moments?
You might also be able to improve the situation with some acoustic impedance matching: some kind of matched resistance on the other side of the glass sheet that absorbs the shock and keeps it from bouncing back. That doesn’t save you the initial 22-μs latency, but it means you don’t have to contend with reflection.
This doesn’t depend on the thickness of the sheet, as long as it’s stiff enough not to buckle.
If you make the lenslets smaller than the wavelength of the light in question, they won’t work at all. I think the variation in phase delay needs to be about half a wavelength from the center of the lenslet to its edge. That makes me think you should be able to make them on the order of 100 μm wide for visible light, even for fairly shallow curvatures.
That means that the relative movements between the lenslet sheets to get light deflections can be on the order of 1 μm.
Is it possible to deal with the acoustic delay somehow?
Will the light coming out of each lenslet have a different phase delay from the light coming out of the other lenslets? Does this mean that each individual beamlet will diffract on its own, giving a uselessly large divergence?