1. Optical Metamaterials
Negative index and perfect lensing
air n =1 = - 1 q
Propagating waves
n=-1
image
plane
Evanescent waves

2. Fish in a Pond
n=1.3
n=-1.3

3. Negative permittivity and permeability
Maxwell’s Equations for plane monochromatic waves
Right-handed triplet
Left-handed triplet
Veselago, 1968
Why negative n?
Energy
Does not depend on the sign! (Right-hand)
Energy and k are in opposite directions
Energy always moves forward  k moves backward

4. Refraction between right and left handnessx
n>0? z
Is not conserved

5. Refraction between right and left handnessx
n<0 z
conserved

6. Negative refraction
Taken from youtube

7. Properties of NIM slab Flat lens d ABCD matrix Interface between
air n =1 = - 1 q
ABCD matrix
Interface between
Propagation of distance d 2d
Imaging with NIM slab

8. Properties of NIM slab Impedance matching for n=-1
air n =1 = - 1 q
Impedance matching for n=-1 2d
No reflection for any K-vector

9. Negative refraction makes a perfect lens
Sir John Pendry
Propagating waves
Object
plane
n=-1
Evanescent waves
air n =1 = - 1 q
image
Negative-index
Metamaterials
Super-resolution
Imaging
Optical Illusion
(e.g., cloaking)

10. Negative refraction makes a perfect lens
Pendry assumed lossless NIM with n=-1
Calculated the transmitted field as a function of k (OTF)
Fresnel coefficients for magnetic field of TM wave
From air to NIM (0=air 1=NIM): , ,
air n =1 = - 1 q
(Impedance matching)

11. Negative refraction makes a perfect lens
Pendry assumed lossless NIM with n=-1
Calculated the transmitted field as a function of k (OTF)
Fresnel coefficients for magnetic field of TM wave
Transmission through the slab , ,
air n =1 = - 1 q
Symmetric
Transmission function

12. Negative refraction makes a perfect lens
Now, what about evanescent waves?
evanescent waves amplification?

13. Negative refraction makes a perfect lens
Before going into discussion… what do we have?
Reflection coefficient goes to infinity ?
Convergence of the geometric series
Sign of evanescent kz
Enhancement for every kx
1. Reflection coefficient
Yes. Reflection coefficient can be infinite (pole in the transfer matrix)! This corresponds to guided mode (like surface plasmon) and can occur even when epsilon and mu different than -1
Example – plasmon dispersion

14. Negative refraction makes a perfect lens
Reflection coefficient goes to infinity ?
Convergence of the geometric series
Sign of evanescent kz
Enhancement for every kx
2. Convergence of the geometric series
Works only if
q<1 Or
q is not real positive (negative or complex)

15. Negative refraction makes a perfect lens
Reflection coefficient goes to infinity ?
Convergence of the geometric series
Sign of evanescent kz
Enhancement for every kx
3. Sign of kz
Not sure? Let’s pick the “-” sign

16. Negative refraction makes a perfect lens
How come?
Changing the sign of kz1 corresponds to r1/r
The sign of kz1 does not matter!

17. Negative refraction makes a perfect lens
Reflection coefficient goes to infinity ?
Convergence of the geometric series
Sign of evanescent kz
Enhancement for every kx
3. Works for every kx
This happens in the limit
Why? Because this “enhancement” is related to the existence of surface waves
For every k?

18. Negative refraction makes a perfect lens
Reflection coefficient goes to infinity ?
Convergence of the geometric series
Sign of evanescent kz
Enhancement for every kx
3. What about the limit
for

19. Evanescent amplification condition
Condition for amplification:

20. Evanescent amplification condition
Condition for amplification:
Deviation from the resonance condition limits resolution

21. Evanescent amplification condition

22. Practical issues Solution – use metallic slab (“poor man’s lens”)
No such material exists in nature
Loss seems inevitable
Dispersion, causality, etc…
Solution – use metallic slab (“poor man’s lens”)
Only negative permittivity
Does not support propagating waves
No impedance matching
Only works for TM through surface plasmons erxcitation

23. Slab of lossless “metal”
Assume lossless metal with
Object
plane
e=-1
image
Take the limit
Seems we get a similar result, but…

24. Slab of lossless “metal”
For
What happens for

25. Evanescent amplification in metal?

26. Metal vs. NIM Single polarization (TM only)
Single plasmon wave-vector at high kx
Impedance mismatch - reflection
Supports evanescent waves only
Metal
NIM

27. Metal with loss
NIM vs. Lossless metal is a nice theoretical discussion
Neither lossless NIM or metal was obtained so far
No NIM for super-resolution
Real metal
Loss can actually help!
Permittivity mismatch too!
D=35nm

28. Super-resolution imaging with silver slab
Zhang (2005) silver superlens (‘poor man’s lens’)
35 nm silver slab 365nm illumination
60/90nm resolution

29. Superlens at mid-infrared
Silicon Carbide – e goes negative between 10.3mm and 12.5mm
Phonon polariton
Near-field microscopy
l/20 resolution

30. Conclusions So far, only metallic super-lens for near-field imaging
Resolution is limited by the loss
NIMs have been demonstrated, without super-resolution
Their unit cell is typically not small enough for high-k
Next lessons:
Realization of NIMs by artificial magnetism
Extraction of their properties
Other metamaterials for super-resolution applications