How to build the ultimate optical illusion

I’ve talked about how digital signage is a great way to capture attention – and I’m even starting to think that glasses-free 3D could be a great way to go even further.  However, both of those pale in comparison to creating an optical illusion that appears out of nowhere!

Optical illusions are a great way to capture attention.  Do you remember the “Magic Eye” posters?  I can’t tell you how many people I saw standing and staring at those things.  Research has shown that people linger over optical illusions because our brains hate being tricked.  We have expectations of how something should look – and if it doesn’t look “right,” then we stare at it until our brain can determine what (and why) it is out of order.  It’s the same primal part of our brain that loves magic tricks.  We know the elephant didn’t disappear, but we are delighted when it does.

So, a really cool display would be an optical illusion in which something seems to appear out of thin air – but is there, tangible, so people can touch it and interact.  I have seen really good holographic displays, but while they may draw me in, I can’t grab the product.  A good display uses the hologram to draw attention to the physical product, but the technology just isn’t quite there yet.

However, it could be soon, thanks to metamaterials.

According to John Pendry, how a material affects light falling upon it is dictated in part by its chemical composition, but its internal structure can have an even stronger influence.  Silvered mirrors are highly reflecting, but black-and-white photographs also owe their blackness to silver – billions of nanometer-scale spheres of the metal embedded in the film.  This dramatic difference arises because the silver spheres are much smaller than the wavelength of light.

Metamaterials extend this concept with artificial structures that might be nanometers across for visible light, or as large as a few millimeters for microwave radiation.  Their properties are engineered by manipulating their structure rather than their chemical composition.  The possibilities these materials open up are limited only by our imagination, and not by the nmber of elements in the periodic table.

As a result, metamaterials research has exploded during the past decade.  It has given us optical properties we once thought were impossible, including negative refraction never found in nature, and novel devices such as invisibility cloaks.  However, a clever design tool is required to make the most of metamterials’ potential.  In conventional optics, light travels in a straight line until it hits the boundary between two transparent materials, at which point it abruptly changes direction.  Metamaterials are much more sophisticated.  They can force light to travel along a curved path, thereby opening up the possibility of devices, like an invisibility cloak.  The mathematical tool that tells us what kind ofmetamaterial will bend light along the desired path is known as transformation optics.

A remarkable experiment conducted during a solar eclipse in 1919 showed that the sun acts like a giant lens, bending starlight that passes close to the sun’s disc.  It vindicated Albert Einstein’s prediction in his general theory of relativity that the sun’s gravitational field would distort space.  As far as light is concerned, the warped space near the sun appears to have a large refractive index.  Very helpfully for metamaterials, Einstein produced a formula relating the distortion of space to changes in effective refractive index.  Furthermore, Einstein’s formula is an exact transformation of Maxwell’s equations, which govern all electromagnetic phenomena.

What transformation optics seeks to achieve is to take a ray of light and distort its trajectory in whatever way wanted.  This could be done by distorting space itself using extremely massive objects, but thanks to Einstein’s insight, this is not necessary.  Simply changing the refractive index will have the same effect as far as light is concerned.  Transformation optics can be used to calculate the required refractive indices.  All that is then needed is to construct metamaterials that meet these specifications.

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