BIG IDEAS ADVANCED: INVISIBILITY To be invisible is a dream as old as human history. Not only does • ExplainAdvanced and demonstrate: Invisibility it have far-reaching applications Bigfor medicalIdea science and the the Rochester Cloak at an military, but opens doorsExplain we don’t and demonstrateeven know are the there yet. The advanced level. To be invisible is a dream as old as human history. Nottechnique only does you’ll it be exploringRochester in Cloakthis activity at an advanced is one of many ways that researchers have tackled the problem of making the visible have far-reaching applications for medical science and the military, level. less so. It turns out that Harry Potter’s invisibility cloak in no longer but opens doors we don’t even know are there yet. Theas magical technique as you might think… WHAT YOU’LL NEED you’ll be exploring in this activity is one of many ways that What You’ll Need ELECTROMAGNETIC RADIATION researchers• have2 Lenses: tackled 50mm the problem diameter, of making the visible less so. • 2 Lenses: 50mm diameter, All visible light is a form of electromagnetic radiation. It falls within It turns out that150mm Harry focalPotter’s length invisi (fbility1) cloak in no longer as 150mm focal length (f1) the , which also includes , magical as •you 2 Lenses:might think… 50mm diameter, • 2 Lenses: 50mm diameter, radio waves, x-rays and light. 50mm focal length (f ) 2 50mm focal length (f2) • 4 Lens holders Electromagnetic waves consist of an electric field and a magnetic Electromagnetic Radiation • 4 Lens holders field. Each of these components is a transverse wave (Act 9), All visible light• 1 isRed a form LASER of electromagnetic pointer radiation. It falls within transverse meaning a• point1 Red on LASERthe wave pointer moves up and down, • A ruler the electromagnetic spectrum, which also includes microwaves,not forwards and backwards.• A ruler The direction of this up-and-down • A sheet of graph paper movement is called the polarization of the wave. radio waves, x-rays and infrared light. • A sheet of graph paper • A long flat surface (table) Electromagnetic waves consist of an electric field andThe a magneticelectric and magnetic fields in an electromagnetic wave are • Masking tape (optional) • A long flat surface (table) field. Each of these components is a transverse wavepolarized (Act 9), perpendicular to one another, as shown in Figure 1. • Double-sided tape • Masking tape (optional) transverse meaning a point on the wave moves up andThe down, polarization not of each is also perpendicular to the direction of (optional) propagation, or the direction• Double in -whichsided tape the wave(optional) itself is moving as a forwards and backwards. The direction of this up-and-down whole. movement is called the polarization of the wave. RELATED PRODUCTS

The electric and magnetic fields in an electromagnetic wave are polarized perpendicular to one another, as shown in Figure 1. The polarization of each is also perpendicular to the direction of propagation, or the direction in which the wave itself is moving as a Invisibility Kit for Muggles whole. Click here to purchase! Figure 1: Electromagnetic Wave

Perfect Invisibility An object can be made invisible by something called a “” or a cloak. In order for something WWW.LASERCLASSROOM.COM to be considered a perfect cloaking device, it needs to meet a certain set of requirements.

Firstly, the perfect cloak should be able to render any object invisible. This means that not only should the object disappear from view, but the background behind the object needs to be visible as if the object were PERFECT INVISIBILITY An object can be made invisible by something called a “cloaking device” or a cloak. In order for something to be considered a perfect cloaking device, it needs to meet a certain set of requirements.

Firstly, the perfect cloak should be able to render any object invisible. This means that not only should the object disappear from view, but the background behind the object needs to be visible as if the object were not there at all. The background must be the same size, color and in the same place as it would be if the cloak and hidden object weren’t there.

Secondly, an observer should not know that the cloak itself is there. This is the more difficult of the two requirements. The cloak itself should be invisible; looking at it should be just the same as looking at a volume of air.

HISTORY OF INVISIBILITY One of the oldest stories about invisibility is the invisibility cap used by the hero Perseus in Greek mythology to slay the monstrous Medusa. This story went on to influence Celtic and Norse mythology, and legend has it that one of King Arthur’s most prized possessions was an invisibility cloak. Even German fairy tales make mention of a Tarnkappe; an invisibility cap owned by a dwarf king.

The fascination extended into the modern age, with H.G. Well’s book The Invisible Man where a scientist obsessed with optics changes his body’s refractive index to that of air. In other words, his body reflected and absorbed no light, and so he was invisible. Other authors were less forthcoming with scientific explanations for their uses of invisibility, leaving the workings of things like Harry Potter’s invisibility cloak and the titular ring from the Lord of the Rings to the realm of imagination.

TRANSFORMATION OPTICS In 2006, two research teams simultaneously published their findings in the prestigious journal Science on a method of invisibility called “”. They had created the first fully functional invisibility cloak which could hide microwaves from detection.

The approach relies on the use of : artificial matter which does not interact with electromagnetic waves the same way natural matter does. Most optical devices interact mainly with the electric field component of an electromagnetic (EM) wave, which causes familiar optical phenomena such as refraction. These metamaterials, on the other hand, interact with both the electric and magnetic fields. We thus call transformation optics full field cloaking, because it hides the entire EM-wave.

One of the advantages of the method of transformation optics is that one can engineer various types of metamaterials that each interact uniquely with EM-radiation and thereby produce different effects at each wavelength. While visible light has not yet been cloaked using this method, it may very well be on the horizon. Another strength of this method of cloaking is that it is omnidirectional - it doesn’t matter from which direction you look at the cloaked object, it remains hidden.

WWW.LASERCLASSROOM.COM RAY OPTICS CLOAKING Transformation optics method endeavours to cloak the entire electromagnetic wave, which involves considering the electric and magnetic field, along with a host of other properties. This can be quite a complicated procedure, which is why it isn’t yet possible to cloak visible light. The ray optics cloaking is a simplification of the transformation optics process and considers only the direction and power of the EM-wave.

Think of the ray diagrams you draw in class to describe optic systems. The lines representing light waves don’t show us how the electric or magnetic fields behave; instead, we care only about the overall direction of propagation of the wave. Ray optics cloaking seeks to prevent the light from interacting with the object it wishes to cloak in the first place. If the light does not reflect off the object, we won’t see it.

When the ray optics cloaking method was first conceived, there were a number of problems. The magnification of the background was not be perceived to be1, but, slightly larger. The cloak was also unidirectional, i.e. the object would only be cloaked from one specific direction. If you moved even slightly from the perfect line of sight, the object would become visible, or the background so distorted that it becomes obvious that a cloak was present.

PARAXIAL RAY OPTICS CLOAKING In the special case where the incident (or incoming) light rays are parallel to the vertical axis of the lens, paraxial ray optics cloaking can be implemented. This case tends to occur when a background is relatively close to the lens, not giving the light much time to diverge before entering the lens. Paraxial ray optics cloaking has proved the most successful of the ray optics cloaking methods to date, producing results with a magnification of 1 and limited multi-directionality. The Rochester Cloak we’ll be building is an example of paraxial ray optics cloaking.

CONVEX LENSES & FOCAL LENGTHS

Keycauses to the light operation rays entering of the the Rochester lens to refract Cloak towards is knowing the normal the focal perpendicular length of a to convex the surface lens precisely.of the lens at A convex lens is any optically transparent material that is uniformly thicker in the middle than at the any given point, as shown in Figure 2. ends. This shape causes light rays entering the lens to refract towards the normal perpendicular toAll the rays surface entering of athe convex lens atlens any perpendicular given point, to as the shownaxis of in the Figure lens will2. refract and meet at a single Allpoint. rays This entering point ais convexcalled the lens focal perpendicular point of the lens. toThe the distance axis of thebetween lens thewill centerrefract of and the meet lens andat a the singlefocal pointpoint. is This called point the isfocal called length the of focal the lenspoint. of the lens. The distance between the centercentre of the lens and the focal point is called the focal lengthIt is crucial of the to lens. realize that not every convex lens has the same focal length. Thinner convex lenses It is crucial to realise realize that not every convex Figure 2: Focal Length of Refracted Rays typically have longer focal lengths. This is because the thicker the lens usually is, the more it bends the light, so the closer the focal point is to the lens.

WWW.LASERCLASSROOM.COM The Rochester Cloak The Rochester Cloak is the first perfect paraxial ray optics cloak, developed by Professor John Howell and his doctoral student Joseph Choi at the University of Rochester. It uses four converging lenses to redirect light from the background behind a cloaked object in such a way that it never comes in contact with the object, and the viewer sees only the background as it would be if the object were not there.

The Rochester Cloak consists of two pairs of convex lenses, each pair having a different focal length. The lenses are set up in a straight line, with the thicker lenses in the middle and the thinner lenses on the ends.

The thin lenses have focal length f1, and the thick lenses focal length f2.

Figure 3: Ray Optics of a Rochester Cloak causes light rays entering the lens to refract towards the normal perpendicular to the surface of the lens at any given point, as shown in Figure 2.

All rays entering a convex lens perpendicular to the axis of the lens will refract and meet at a single point. This point is called the focal point of the lens. The distance between the center of the lens and the focal point is called the focal length of the lens.

It is crucial to realize that not every convex lens has the same focal length. Thinner convex lenses Figure 2: Focal Length of Refracted Rays typically have longer focal lengths. This is because lens has the same focal length. Thinner convex lenses typically have longer focal lengths. This is the thicker the lens usually is, the more it bends the light, so the closer the focal point is to the lens. because the thicker the lens usually is, the more it bends the light, so the closer the focal point is to the lens. The Rochester Cloak THE ROCHESTER CLOAK The Rochester Cloak is the first perfect paraxial ray optics cloak, developed by Professor John Howell and his doctoralThe Rochester student Cloak Joseph is Choi the firstat the perfect University paraxial of Rochester ray optics. It usescloak, four developed converging by lensesProfessor to redirect John Howell light and his doctoral student Joseph Choi at the University of Rochester. It uses four converging lenses from the background behind a cloaked object in such a way that it never comes in contact with the object, to redirect light from the background behind a cloaked object in such a way that it never comes in andcontact the viewerwith the sees object, only theand background the viewer assees it would only thebe ifbackground the object were as it not would there. be if the object were not there.

The RochesterRochester Cloak Cloak consists consists of oftwo two pairs pairs of convex of convex lenses, lenses, each each pair havingpair having a different a different focal length. focal length.The lensesThe lenses are set are up set in upa straight in a straight line, with line, the with thicker the thicker lenses inlenses the middle in the andmiddle the andthinner the lenses thinner on lenses the ends. on

Thethe ends.thin lenses The thin have lenses focal lengthhave focal f1, and length the thick f1, and lenses the focalthick length lenses f 2focal. length f2.

The optimal distances between the lenses are calculatedFigure 3 : usingRay Optics the offormula a Rochesters Cloak

and ! ! ! ! The optimal distances between the lenses areThe calculated optimal using distances the formula betweens 𝑑𝑑 the= lenses𝑑𝑑 = 𝑓𝑓 are+ 𝑓𝑓 calculated using the formulas: and (𝑓𝑓! + 𝑓𝑓!) and 𝑑𝑑! = 𝑑𝑑! = 𝑓𝑓! + 𝑓𝑓! 𝑑𝑑! = 2𝑓𝑓! Consider the Rochester Cloak illustrated(𝑓𝑓 in! − Figure𝑓𝑓!) 3. Light reflected off or created by the background Consider the entersRochester the Cloakfirst lens illustrated from pointin Figure (1). It4 .is Light refracted reflected inwards off or createdand converges by the background before entering enters the second lens. The( grey𝑓𝑓! + 𝑓𝑓shaded!) area denoted by (3) is completely avoided by the light waves; that is, any the first lens from𝑑𝑑! = point2𝑓𝑓! (1). It is refracted inwards and converges before entering the second lens. The grey an object( placed𝑓𝑓! − 𝑓𝑓!) in the shaded region would not interact with and henceor obstruct light from the shaded area denoted by (3) is completely avoided by the light waves; any object placed in the shaded region Consider the Rochester Cloak illustrated in Figurebackground. 4. Light reflected The grey off shaded or created areas by are the calledbackground cloaked enters regions, and form a donut shaped volume of would not interactinvisibility with oraround obstruct the light central from axis the ofbackground. the lenses. The grey shaded areas are called cloaked the first lens from point (1). It is refracted inwards and converges before entering the second lens. The grey regions, and form a donut shaped volume of invisibility around the central axis of the lenses. shaded area denoted by (3) is completely avoidedFollowing by the the light red waves; light raysany ob throughject placed the systemin the shaded of lenses, region you’ll see that they emerge at (2), where the viewer is standing. This observer will hence see only the background, and no light from the cloaked would not interact with or obstruct light from the background. The grey shaded areas are called cloaked Following theregions red light whatsoever. rays through Any the objectsystem placedof lenses, in theyou’ll cloaked see that regions they emerge becomes at (2), are where therefore the viewer invisible to a regions, and form a donut shaped volume of invisibilityviewer looking around through the central the lenses!.axis of the lenses. is standing. This observer will see only the background, and no light from the cloaked regions whatsoever.

Any object placed in the cloaked regions becomes invisible to a viewer looking through the lenses! Following the red light rays through the system of lenses, you’ll see that they emerge at (2), where the viewer is standing. This observer will see only the background, and no light from the cloakedWWW.LASERCLASSROOM.COM regions whatsoever. Why the Spacing Matters Any object placed in the cloaked regions becomes invisible to a viewer looking through the lenses! It’s important that the spacing between lenses is very precise in order for the Rochester Cloak to work. This is because the device depends entirely on using the lenses’ focal lengths to make sure the light bends Why the Spacing Matters around the cloaked regions. It’s important that the spacing between lenses is very precise in order for the Rochester Cloak to work. This is because the device depends entirely on using the lenses’ focal lengths to make sure the light bends Consider the rays moving between the first two lenses, around the cloaked regions. as shown in Figure 5. The rays moving in from the left pass through the first lens with focal length f1 and Consider the rays moving between the first two lenses, converge to the focal point of the first lens. as shown in Figure 5. The rays moving in from the left pass through the first lens with focal length f1 and Now take a look at the second lens, with focal length converge to the focal point of the first lens. f2 and notice how the rays emerge parallel from this lens. This is only possible if the focal point of f1 is Now take a look at the second lens, with focal length f2 and notice how the rays emerge parallel from this exactly a distance of f2 (the focal length of the second Figure 4: First Two Lenses of Rochester Cloak lens. This is only possible if the focal point of f1 is lens) away from the second lens. For the experiment to work, the lenses must be separated by a distance of f1 + f2. exactly a distance of f2 (the focal length of the second Figure 4: First Two Lenses of Rochester Cloak lens) away from the second lens. For the experiment The Future of Invisibility to work, the lenses must be separated by a distance of f1 + f2.

The Future of Invisibility The optimal distances between the lenses are calculated using the formulas

and 𝑑𝑑! = 𝑑𝑑! = 𝑓𝑓! + 𝑓𝑓!

(𝑓𝑓! + 𝑓𝑓!) 𝑑𝑑! = 2𝑓𝑓! (𝑓𝑓! − 𝑓𝑓!) Consider the Rochester Cloak illustrated in Figure 4. Light reflected off or created by the background enters the first lens from point (1). It is refracted inwards and converges before entering the second lens. The grey shaded area denoted by (3) is completely avoided by the light waves; any object placed in the shaded region would not interact with or obstruct light from the background. The grey shaded areas are called cloaked regions, and form a donut shaped volume of invisibility around the central axis of the lenses.

Following the red light rays through the system of lenses, you’ll see that they emerge at (2), where the viewer is standing. This observer will see only the background, and no light from the cloaked regions whatsoever. Any object placed in the cloaked regions becomes invisible to a viewer looking through the lenses!

Why the Spacing Matters It’s important that the spacing between lenses is very precise in order for the Rochester Cloak to work. This is because the device depends entirely on using the lenses’ focal lengths to make sure the light bends around the cloaked regions.

ConsiderWHY THE the rays SPACING moving between MATTERS the first two lenses, asIt’s shown important in Figure that 5the. The spacing rays moving between in from lenses the isleft very precise in order for the Rochester Cloak to pass through the first lens with focal length f1 and work. This is because the device depends entirely converge to the focal point of the first lens. on using the lenses’ focal lengths to make sure the light bends around the cloaked regions. Now take a look at the second lens, with focal length Consider the rays moving between the first two flenses,2 and notice as shown how the in Figurerays emerge 4. The parallel rays moving from this in lens.from Thisthe leftis only pass possible through if thethe focalfirst pointlens ofwith f1 isfocal length f1 and converge to the focal point of the first exactlylensshown. a distance of f2 (the focal length of the second Figure 4: First Two Lenses of Rochester Cloak lens)Now awaytake afrom look the at secondthe second lens. lens, For the with experiment focal tolength work, f 2the. and lenses noticeNotice must be separated how the raysby a distanceemerge parallelof f1 + f2 from. this lens. This is would only be possible if the focal point of f1 was exactly the is exactly a distance of focal length f2 (the focal length of the second lens) away from the second lens. For the experiment to work, the lenses must be separated The Future of Invisibility by a distance of f1 + f2. Imagine tracing the rays backwards from the second lens. The system would work exactly the same way! This is imperative to the working of the Rochester Cloak.

THE FUTURE OF INVISIBILITY Invisibility has countless possible applications in our current day-to-day. In the field of medical science, invisibility cloaks may could be used by surgeons to see through their own hands as they operate, or into the organs of the patient. With the right cloaking device, Ddoctors could even see unborn babies through their mothers’ stomachs in with perfect clarity and to check them for early defects or diseases, all without any discomfort to the mother.

Using invisibility cloaks to mask obstructions between transmission towers could would allow the exchange of radio waves to continue unhindered, leaving us all with better and more reliable cell phone reception.

The development of metamaterials in the pursuit of invisibility opens doors to creating lenses that are stronger than any we’ve manufactured to date. Scientists may develop lenses that can see microscopic objects, like the inside of a human cell, or even a strand of DNA!

Invisibility cloaks may even be extended to not only cloak electromagnetic waves, but longitudinal waves like sound. It might even dampen the waves produced by an earthquake! The best partexciting aboutaspect of invisibility is that the greatest innovations in the field are still beyond our wildest dreams.

WWW.LASERCLASSROOM.COM ACTIVITY SHEET: BASIC INVISIBILITY

We’re now going to build our own Rochester Cloak! The optimal distances between the lenses are calculated using the formulas CALCULATE DISTANCE BETWEENThe LENSES optimal distances between the lenses are calculated using the formulas

1. Calculate the distance between lenses 1 & 2 and lenses 3 & 4 using the formula: where f and f are focal andlengths. 𝑑𝑑! = 𝑑𝑑! = 𝑓𝑓! + 𝑓𝑓! 1 2 and 𝑑𝑑! = 𝑑𝑑! = 𝑓𝑓! + 𝑓𝑓! 2. Calculate the distance between lenses 2 and 3 using the formula: ! ! where f and f are focal lengths. (𝑓𝑓 + 𝑓𝑓 ) ! ! 1 2 𝑑𝑑! = 2𝑓𝑓! (𝑓𝑓 + 𝑓𝑓 ) (𝑓𝑓! − 𝑓𝑓𝑑𝑑!!) = 2𝑓𝑓! (𝑓𝑓! − 𝑓𝑓!) Consider the Rochester Cloak illustrated in Figure 4. Light reflected off or created by the background enters Consider the Rochester Cloak illustrated in Figure 4. Light reflected off or created by the background enters the first lens from point (1). It is refracted inwards and converges before entering the second lens. The grey BUILD ROCHESTER CLOAK the first lens from point (1). It is refracted inwards and converges before entering the second lens. The grey shaded area denoted by (3) is completely avoided by the light waves; any object placed in the shaded region 1. Place the lenses in the lens holders. Keepshaded track area of whichdenoted lenses by (3) have is completely which their avoided focal bylengths. the light waves; any object placed in the shaded region would not interact with or obstruct light from the background. The grey shaded areas are called cloaked TIP: If you mix them up, the thicker lenswould has thenot interactshorter focalwith or leng obstructth (f2). light from the background. The grey shaded areas are called cloaked regions, and form a donut shaped volume of invisibility around the central axis of the lenses. 2. Stick the sheet of graph paper to the wallregions, on the and edgeend form a donut of the shaped long surface, volume orof propinvisibility it up aroundagainst the central axis of the lenses.

a box. Following the red light rays through the system of lenses, you’ll see that they emerge at (2), where the viewer 3. Place one f lens at the zero mark. ThisFollowing can be either the red closest light rays orf furthestthrough thefrom system the graph of lenses, paper; you’ll it see that they emerge at (2), where the viewer 1 is standing. This observer will see only the background, and no light from the cloaked regions whatsoever. doesn’t matter. You can use a strip of maskingis standing. tape This along observer the surface will see toonly mark the offbackground, measurements and no light from the cloaked regions whatsoever. Any object placed in the cloaked regions becomes invisible to a viewer looking through the lenses! and make sure your lenses are in a straightAny object line. Use placed the in double-sided the cloaked regions tape to becomes secure the invisible lens to a viewer looking through the lenses! holder in place.

Why the Spacing Matters 4. Place one f2 lens distance d1 from the firstWhy lens.the Spacing Note that Matters you measure from the surface of the It’s important that the spacing between lenses is very precise in order for the Rochester Cloak to work. This lenses, not their centrescenters! It’s important that the spacing between lenses is very precise in order for the Rochester Cloak to work. This is because the device depends entirely on using the lenses’ focal lengths to make sure the light bends 5. Place the other f2 lens distance d2 fromis the because second the lens. device Again, depends measure entirely from on the using surface! the lenses’ focal lengths to make sure the light bends around the cloaked regions. 6. Lastly, place the other f lens distance daround from the the cloaked third lens. regions. 1 3

7. Use the LASER pointer toConsider check thatthe rays your moving lenses between are aligned. the first Shine two the lenses, LASER through the Consider the rays moving between the first two lenses, centre of the first lens towardsas shown the in Figuregraph 5paper.. The raysThe movingbeam should in from emergethe left through all four lenses unchanged: no bigger or blurrier. If the asbeam shown is blurry, in Figure adjust 5. The your rays lenses moving until in fromthey theline left up nicely. pass through the first lens with focal length f1 and pass through the first lens with focal length f1 and 8. Stand 2-3 meters from theconverge first lens. to the You focal may point have of tothe crouch first lens to. be on eye-level with the lenses. You should see the graph paper unmagnifiedconverge through to the focalthe lenses. point of the first lens.

9. Have someone move a penNow or take other a look long, at thinthe secondobject lens,between with lensesfocal length 2 and 3. You should see Now take a look at the second lens, with focal length the object disappear towards the top and bottom of the lenses. See if you can find other areas of f2 and notice how the rays emerge parallel from this invisibility! f2 and notice how the rays emerge parallel from this lens. This is only possible if the focal point of f1 is lens. This is only possible if the focal point of f1 is

exactly a distance of f2 (the focal length of the second Figure 4: First Two Lenses of Rochester Cloak exactly a distance of f2 (the focal length of the second Figure 4: First Two Lenses of Rochester Cloak lens) away from the second lens. For the experiment lens) away from the second lens. For the experiment to work, the lenses must be separated by a distance of f1 + f2. to work, the lenses must be separated by a distance of f1 + f2.

The FutureWWW.LASERCLASSROOM.COM of Invisibility The Future of Invisibility