3-D printing glass with continuously varying refractive indices for optics without internal surfaces

Kragen Javier Sitaker, 2016-10-06 (3 minutes)

For the “cloak of invisibility” using optical metamaterials, you don’t actually need a negative refractive index; you just need to be able to precisely grade the refractive index throughout space. The approach they’re taking is to fabricate nanostructures made of resonant components, but this has high dispersion, and so the invisibility fades as you use multiple wavelengths.

As an alternative, you could vary the mix of materials going into a block of glass. More lead oxide in one part, more silicon and aluminum oxides in another. But how can you achieve that? Depositing glass powders and then sintering them will leave you with a part that’s full of voids. Voids are potentially problematic in structural parts (e.g. metal mounting brackets) but totally fatal in optics.

If instead of sintering the powders you fully melt them so that bubbles can rise, the bubbles will mix together the glass that they float through, and to a lesser extent the glass around it, especially if you put it under vacuum to degas it like in resin casting. Also, if the viscosity is too low, you may get convection currents.

Depositing the glass by FDM in air seems like it would hardly be any better.

A possible alternative would be to immerse the workpiece being built in molten lead oxide, using either selective powder deposition or FDM extrusion to deposit a higher-melting glass “underwater”, thus avoiding bubbles; the molten lead oxide would fill any voids. The lead oxide would immediately begin to “flux” or dissolve the higher-melting glass, so tight temporal control of the process is critical. That same process of dissolution or diffusion can continue even below the glass transition, but more slowly, and is crucial to achieving a smooth gradient, but it also limits the strength of the gradient that can be achieved. It may be necessary to bake the finished workpiece in a solid state for some period of time after completion.

(The lowest-melting glass may not be pure lead oxide, but rather some mixture; ideally you’d use the lowest-melting glass for the immersion medium. Above the glass you could use a soft vacuum)

Speaking of gradients, one way to reduce the variability in such a process would be to maintain a vertical temperature gradient in the workpiece being built layer by layer, such that only the surface is above the point of lead oxide, while the layers below are below the glass transition temperature. This won’t prevent diffusion, just slow it down, but it will stop slumping.

Optical systems built in this way, using gradients rather than surfaces, can entirely avoid the problems of stray light from unwanted reflections from the surfaces of lenses, although total internal reflection is still possible, as in a graded-index optical fiber.

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