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the woman hides holding a mirror in front of her face; introspection path concept
π Science and technology

Invisibility is just around the corner

Kim Pham
Kim Pham
Associate Professor in Mechanics at ENSTA Paris (IP Paris)
Key takeaways
  • In their quest for invisibility, researchers have developed “metamaterials”.
  • These are objects with multiple microscopic details capable of deflecting a wave from its path, thus preventing it from being reflected on a targeted object.
  • The concept of invisibility applies to any type of wave, making an object “invisible” to a wave protects it from its various effects.
  • As such, this concept can have many real-world applications such as making submarines invisible to sonar, protecting ports from sea waves, developing an anti-earthquake city and, perhaps allowing a person to become invisible.

The­o­ret­i­cal­ly, if an object does not reflect a wave, then it is invis­i­ble to it. This applies to all types of waves, whether elec­tro­mag­net­ic – such as vis­i­ble light, for exam­ple – acoustic or seis­mic. How­ev­er, in prac­tice, many tech­ni­cal chal­lenges remain, which still pre­vent us from achiev­ing com­plete invisibility. 

In their quest for invis­i­bil­i­ty – and in the absence of Har­ry Pot­ter mag­ic – researchers have used their knowl­edge of physics to devel­op meta­ma­te­ri­als, which are struc­tures with micro­scop­ic details that can be spec­i­fied by the user depend­ing on the desired appli­ca­tion. The mul­ti­tude of these details have the effect of trap­ping a tar­get wave pass­ing through, mak­ing it either res­onate until it uses up all its ener­gy, or deflect it to avoid reflect­ing off the tar­get object. Thus, ren­der­ing the object invis­i­ble. Kim Pham, lec­tur­er at the Mechan­ics Unit of ENSTA Paris, is work­ing on this sub­ject that spreads out to var­i­ous applications.

#1 Acoustic waves:

Becoming invisible to sonar

Nature has giv­en us an inter­est­ing lead in the form of whales, and more pre­cise­ly one of their hunt­ing tech­niques. To hunt, they some­times release a wall of bub­bles inside which they make sounds. The wall of bub­bles trap acoustic waves with­in it, caus­ing them to res­onate, thus stun­ning fish trapped inside. Where­as, from the out­side, the sound is almost imper­cep­ti­ble. This prin­ci­ple is explained by Min­n­eart res­o­nance, and the effect of the den­si­ty con­trast between air and water. A micro­scop­ic bub­ble can res­onate wave­lengths a hun­dred times greater than itself and relies on the mul­ti­tude of bub­bles. The result is a wall quite sim­i­lar to meta­ma­te­ri­als. As such, this exam­ple offers an insight into how acoustic waves can be con­trolled through the con­cept of invisibility.

Dur­ing the Sec­ond World War, the Ger­mans had already devel­oped a sim­i­lar defence tech­nique for their sub­marines by lin­ing their exter­nal sur­face with ane­choic tiles. Kim Pham, for exam­ple, is work­ing on these tiles to bet­ter under­stand their math­e­mat­i­cal log­ic and improve their effects. Com­posed of mul­ti­ple cav­i­ties, they ren­der the sub­ma­rine unde­tectable to sonar waves, pro­vid­ed that the cav­i­ties are adjust­ed to the right frequency.

Pho­to by Jonathan Coop­er on Unsplash

#2 Maritime ripples:

Protecting ports from waves

Anoth­er use­ful appli­ca­tion is the pro­tec­tion of har­bours from undu­la­to­ry move­ments of the sea, espe­cial­ly from swell. The aim is to calm the sea sur­face of the har­bour. It is tech­nique already exists, using large con­crete blocks, how­ev­er they aren’t very eco­log­i­cal. To rem­e­dy this, Kim Pham and his team are propos­ing a float­ing res­o­nance belt1, which will sur­round the port to be pro­tect­ed. Even if these pro­to­types are made of plex­i­glass, the choice of mate­r­i­al is not yet deci­sive: the impor­tant thing is that it is light and resis­tant. Inside is a small cav­i­ty that allows the waves of the swell to pass through it, becom­ing trapped inside. One there, they res­onate with­in it until they are exhausted.

Above: the res­o­nance belt with a cav­i­ty. The swell does not pass through the belt.
Below: the cav­i­ty of the belt has been closed. The float­ing belt is there­fore just a non-res­o­nant obsta­cle and the swell can pass through it. (Video cour­tesy of Léo-Paul Euvé)

The inno­va­tion is there­fore in the light­ness of the mech­a­nism, which floats. But also, in its ease of instal­la­tion and move­ment. Hence, such con­cepts could be used on a large scale and poten­tial­ly intro­duced as a way to pro­tect against more vio­lent sea waves such as tsunamis.

#3 Seismic waves:

Redirecting earthquakes into the ground

The con­cept of invis­i­bil­i­ty is also applic­a­ble to seis­mic waves. The two main types of seis­mic waves are sur­face waves and vol­ume waves. The first type, sur­face waves, can cause seri­ous dam­age to the Earth­’s sur­face. The sec­ond type, vol­ume waves, prop­a­gate under­ground, so their impact on the sur­face is lim­it­ed. Kim Pham’s team has dis­cov­ered that, if a num­ber of con­di­tions are met, the trees in a for­est can act on sur­face waves (known as Love waves) by trans­form­ing them into vol­ume waves, and thus send­ing them deep into the ground, reduc­ing poten­tial dam­age2. This con­cept uses the same prin­ci­ples as those of meta­ma­te­ri­als. It is the mul­ti­tude of trees in the for­est that allows the wave to be con­trolled and deflect­ed. It has come to be known as metaforest­ing, where main inno­va­tion is the pro­gres­sive decrease in height of each tree in the path of the sur­face wave.

2D rep­re­sen­ta­tion of a “metafor­est” redi­rect­ing a sur­face wave towards the ground, trans­form­ing it into a vol­ume wave.

The more this wave pass­es through the for­est, the more it will be redi­rect­ed towards the ground, to the point of plung­ing into the Earth’s depths, and thus becom­ing a vol­ume wave. This type of dis­cov­ery allows us to imag­ine many use­ful appli­ca­tions, in par­tic­u­lar the devel­op­ment of cities of the future, built with the same prin­ci­ples as these metaforests3 in the con­struc­tion of build­ings. For exam­ple, an anti-earth­quake city could be cre­at­ed, that resem­bles the now famous pro­to­type of the invis­i­bil­i­ty cloak4 pro­posed by Sébastien Guen­neau (a CNRS Researcher at Insti­tut Fresnel).

#4 Light rays:

Making an object invisible

Since vis­i­ble light is made up of elec­tro­mag­net­ic waves, this con­cept could the­o­ret­i­cal­ly make any object invis­i­ble to the naked eye. We per­ceive a vis­i­ble object because light reflects off it – it is the rea­son why we can­not see any­thing in the dark. If the light waves can be deflect­ed, and thus pre­vent­ed from reflect­ing off the object in ques­tion, then it will be invis­i­ble. Based on this prin­ci­ple, the researcher John Pendry suc­ceed­ed in devel­op­ing a pro­to­type invis­i­bil­i­ty cloak (this time for visu­al light waves)5, which earned him the Isaac New­ton Medal from the UK Insti­tute of Physics in 2013.

Rep­re­sen­ta­tion of an elec­tro­mag­net­ic cloak6 that deflects light rays, pre­vent­ing them from reflect­ing off the object (or sub­ject) posi­tioned in the middle.

How­ev­er, the spec­trum of light vis­i­ble waves is between 380 and 780 nanome­tres (nm). There­in lies the tech­ni­cal chal­lenges. First, in the micro­scop­ic scale of the cav­i­ty of the meta­ma­te­r­i­al used for this pur­pose, which must be sub-wave­length – that is, small­er than the tar­get­ed wave, (a few hun­dred nm). Sec­ond, in the diver­si­ty of colours, each hav­ing a spe­cif­ic wave­length rang­ing, for exam­ple, from 780–622 nm for red light and from 455–390 nm for vio­let. Real objects are rarely mono­chrome, so to make it invis­i­ble, a meta­ma­te­r­i­al with diverse cav­i­ties, spe­cif­ic to the wave­length of each of the tar­get­ed colours, must be designed.

Whilst these tech­no­log­i­cal chal­lenges are hur­dles that need to be over­come to the design this type of object, it in no way means that it is not fea­si­ble. On the con­trary, the phe­nom­e­non has already been mod­elled by soft­ware, and some pro­to­types have already been pro­duced. As such, mak­ing objects invis­i­ble is far from being impos­si­ble. In fact, it could be just around the corner!

Interview by Pablo Andres
1Euvé, L.-P. ; Pies­niews­ka, N. ; Mau­rel, A. ; Pham, K. ; Petit­jeans, P. ; Pag­neux, V. Con­trol of the
Swell by an Array of Helmholtz Res­onators. Crys­tals 2021, 11, 520. DOI:
2Mau­rel, A.; Mari­go, J.-J.; Pham, K.; Guen­neau, S. Con­ver­sion of Love waves in a for­est of trees. Phys. Rev. B 98, 134 311 — Pub­lished 26 Octo­ber 2018 DOI: 10.1103/PhysRevB.98.134311
3The META-FORET project : https://​metaforet​.osug​.fr/
4Boris Gralak, Sébastien Guen­neau. Invis­i­bil­ité et trans­parence. Sig­i­la. Revue trans­dis­ci­plinaire fran­co-por­tu­gaise sur le secret, Gris-France, 2020. ffhal-03087320f https://​hal​.archives​-ouvertes​.fr/​h​a​l​-​0​3​0​87320
5Meta­ma­te­ri­als and the Sci­ence of Invis­i­bil­i­ty: New­ton Lec­ture 2013 ; https://​www​.youtube​.com/​w​a​t​c​h​?​v​=​2​Y​2​r​o​W​8Lv0g
6Tsak­makidis, Kos­mas & Hess, Ortwin. (2008). Optics – Watch your back. Nature. 451. 27. 10.1038/451 027 a


Kim Pham

Kim Pham

Associate Professor in Mechanics at ENSTA Paris (IP Paris)

Kim Pham is a graduate of the Ecole Normale Supérieure de Paris-Saclay (2004). He completed his PhD in Solid Mechanics at the University of Paris-Sorbonne (2010). From 2012 to 2021, he was a lecturer at ENSTA Paris (IMSIA/Unit of Mechanics). In 2021, he was accredited to direct research at Institut Polytechnique de Paris and became an associate professor at ENSTA Paris (IMSIA/Unit of Mechanics) in the same year. His main research area is the modelling of wave propagation in metamaterials and metasurfaces. He currently has 21 publications on this subject and received the Jean Mandel 2021 prize for his advances on the effective behaviour of resonant metasurfaces.

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