Download Negative Refraction Makes Light Run Backwards in Time

Negative Refraction Makes Light Run Backwards in Time
J.B. Pendry
The Blackett Laboratory
Imperial College
London SW7 2BZ
UK
How familiar and safe is the concept of a refractive index: wine glasses sparkle, deep
pools appear shallow, camera lenses focus sharp images. ‘Ah yes, light bends towards
the surface normal - Snell's law’ and we move on to more interesting topics. My
complacency was recently given a jolt by Sheldon Schultz and David Smith of UCSD
who reported at the recent American Physical Society meeting in Minneapolis that they
had made a material with negative refractive index.
What on earth does that mean? Take Snell’s law: light is no longer bent towards the
normal but is bent up to and past the normal so that sin θ is negative. A moment’s
thought shows that a plane slab of this material focuses light. In fact there is a double
focussing effect if the material is thick enough. Check figure 1 which is drawn to obey
Snell’s law for a refractive index n = −1 .
Figure 1. A negative refractive index medium bends to a negative angle with the
surface normal. Light formerly diverging from a point source, is set in reverse
and converges back to a point. Released from the medium the light reaches a
focus for a second time.
One interpretation is to say that time runs backwards inside a negative-n material forcing
light to reverse its trajectory whilst it resides in the medium. This explains the double
focus effect as light having reversed back through the focal point emerges into a normal
system and goes forward through the focus a second time.
This and other odd effects, such as a negative Doppler effect and Cerenkov radiation
that appears in a direction opposite to the velocity of the charged particle, were
described in an old paper by Veselago [1]. He realised that the key to negative-n is a
medium in which both the dielectric constant, ε , and the magnetic permeability, µ , are
negative. Then a close scrutiny of Maxwell’s equations forces us to choose the minus
sign in the conventional formula for the refractive index,
n = ± εµ
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Negative Refraction Makes Light Run Backwards in Time
Materials with negative− ε exist: at optical frequencies most metals have this property,
and my own group in collaboration with Tony Holden, Will Stewart and Dave Robbins
at Marconi have made artificial negative dielectrics in the GHz band [2,3]. The sticking
point is the absence of negative−µ. This last obstacle was removed when Mike Wiltshire
(Marconi) and I showed how to make a negative−µ material active in the GHz band [4].
The trick we used was to recognise that electrical currents moving in circles fake the
effect of a magnet. So a structure comprising a set of conducting rings will be
magnetically active, and by tuning the parameters we were able to show theoretically
that negative−µ can be achieved over a relative broad band of GHz frequencies. Our
structure is shown in figure 2.
Figure 2. Top: the basic building block for negative−µ is a copper ring etched
onto a printed circuit board. The double ring structure has capacitance as well as
inductance. Below: an extended view of a single layer of the structure. Stacking
together many layers produces the negative−µ structure.
Schultz and Smith quickly realised that here was the missing ingredient needed for
negative refractive index, and constructed a model similar to the one shown above. To
this they added a set of thin wires, the ingredients of the negative− ε structure, and
measured the properties. As it happens there is a very clear signature: a material with
negative−µ/positive− ε expels radiation and will not transmit incident waves. Similarly
positive−µ/negative− ε structures also have low transmittance. However making both ε
and µ negative will result in a transparent medium. Here are Schultz and Smith’s
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Negative Refraction Makes Light Run Backwards in Time
measurements shown in figure 3 which demonstrate convincingly that they have
achieved the elusive negative-n result.
Transmission coefficient (dB)
0
positive ε
-10
-20
-30
-40
negative ε
-50
5.0
6.0
Frequency (GHz)
7.0
Figure 3. Schultz and Smith’s microwave transmission test of negative refractive
index. The green curve shows the response of a split ring structure which
exhibits negative−µ in a band around 5GHz and hence has very low transmission.
Adding negative− ε results in the red curve where the situation is reversed: in
this case both ε and µ are negative in the 5GHz band and transmission is
restored.
And what next for these magical materials: deep pools whose contents float in mid air;
cameras with flat lenses? Have I been drinking too much sparkling wine?
[1]
[2]
Soviet Physics USPEKHI 10, 509 (1968).
VG Veselago
Phys. Rev. Lett. 76 4773-6 (1996).
JB Pendry, AJ Holden, WJ Stewart, I Youngs
[3]
Phys. Rev. Lett., 76 2480 (1996).
DF Sievenpiper ME Sickmiller and E Yablonovitch
[4]
IEEE transactions on microwave theory and techniques 47, 2075-84 (1999).
JB Pendry, AJ Holden, DJ Robbins, and WJ Stewart
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