Inside the Wavelength: Seeing Really Small Objects with Light - Professor Sir John Pendry

Inside the Wavelength
seeing really small objects with light

JB Pendry
The Blackett Laboratory, Imperial College London
email: j.pendry@imperial.ac.uk

collaborators:

Stefan Maier
Ortwin Hess
Alexandre Aubry
Dang Yuan Lei
Antonio I. Fernandez-Dominguez
Wei Hsiung Wee
Yu Luo

Focussing light
exp (ik0 x sin θ + ik0 z cos θ − iωt )

θ

Galileo by Leoni - 1624 lens, n. L. lens lentil, from the similarity in form. A piece
of glass with two curved surfaces

Focussing light: wavelength limits the resolution
Contributions of the far field to the image ….

exp (ik0 x sin θ + ik0 z cos θ − iωt )

θ

….. are limited by the free space wavelength:
θ = 90° gives maximum value of k x = k0 = ω c0 = 2π λ 0 − the shortest
wavelength component of the 2D image. Hence resolution is no better than,
2π 2πc
Δ≈ = = λ0
k0 ω

Negative Refractive Index and Focussing

A negative refractive index medium bends light to a negative angle relative to
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.

Limitations to a Conventional Lens (2)
Contributions of the near field to the image …..
come from large values of k x responsible for the finest details in the source.
Forget about ray diagrams because,
k z = +i k x − ω2c −2 ,
2
ω2c0 2 < k x
− 2

and ‘near field’ light decays exponentially with distance from the source. i.e.
the near field is confined to the immediate vicinity of the source. Unless we
can make an amplifier it is inevitable that the finest detail is lost from the
image.

Attempting the impossible:
near-field amplifier
of source a lens for the near field,
a negative story

Near field superlensing experiment:
Nicholas Fang, Hyesog Lee, Cheng Sun and Xiang Zhan, UCB

Left: the objects to be imaged are
inscribed onto the chrome. Left is an
array of 60nm wide slots of 120nm
pitch. The image is recorded in the
photoresist placed on another side of
silver superlens.
Below: Atomic force microscopy of a
developed image. This clearly shows a
superlens imaging of a 60 nm object
(λ/6).

Imaging by a Silver Superlens.
Nicholas Fang, Hyesog Lee, Cheng Sun, Xiang Zhang, Science 534 308 (2005)

(A) FIB image of the object. The linewidth of the ‘‘NANO’’ object was 40 nm.
(B) AFM of the developed image on photoresist with a 35-nm-thick silver superlens.
(C) AFM of the developed image on photoresist when the layer of silver was replaced by PMMA spacer
as a control experiment.
(D) blue line: averaged cross section of letter ‘‘A’’ line width 89nm
red line: control experiment line width 321nm.

Limitations of the Veselago Lens

• Surface roughness

• Losses in the metamaterial from which the lens is manufactured

Currently the main limitation is surface roughness, but ultimately
we need to reduce losses either by introducing amplification, or
find a better material than silver.

Smoothing the superlens
Chaturvedi et at, Appl. Phys. Lett., 96, 043102, (2010)
Left: a chromium grating imaged using a 15nm thick silver superlens showing
resolution of to λ/12. Right: simulation of resolution.

A surfactant (germanium in this case) deployed during growth of the silver
film, results in a much smoother surface and resolution is increased to λ/12.

Negative refractive index metamaterials

Diagram (left) and scanning electron microscope image (right) of a ‘fishnet’
structure fabricated by the Xiang group at Berkeley California. The structure
consists of alternating layers of 30nm silver and 50nm magnesium fluoride.

Compensating for loss in metamaterials
Shumin Xiao et al., Nature Letters, 466, 735 (2010)

The fabrication process into which gain is introduced by the Shalaev group.
Left: one-quarter of the structure with an alumina spacer. Middle: after etching
the alumina, the structure has air or solvent as the spacer with alumina pillars
as support. Right: finally the gain material (an organic dye shown in pink) is
introduced into the structure.

Harvesting light – enhancing non linearity
What is ‘harvesting’?
A lens gathers beams of light from points in an object and brings them to a
focus at the corresponding points in the image.
In contrast a light harvester concentrates all the beams at a single point.
Harvesters can be used for:
• Making very intense concentrations of light, forcing photons to
interactwith one another
• Detecting molecules with high sensitivity – ideally sensing a single
molecule
• Enhancing the efficiency of solar cells
• Improving the efficiency of lasers
Light harvesters suffer from the same wavelength restrictions as lenses, but we
can use the same tricks of negative refraction to improve their performance

Harvesting light – non linear mixing
Incident radiation at ω1,ω1 interacts non linearly to produce ω1 + ω1 and
ω1 − ω1. The process is enhanced by harvesting energy to the site of the non-
linear material.

Strategy for broadband Harvesting of Light
• Start with a ‘mother system’ that collects light, is broad band, and is
sufficiently simple to be solved analytically, but may not have the desired
geometry.
• Make a coordinate transformation to a desirable geometry.
• Use ‘transformation optics’ to calculate the properties of the transformed
system. The daughter structure inherits the mother’s analytical solution.
• A whole family of structures is now possible containing the same analytic
genes but of sometimes wildly different shapes and sizes.

Constructing a broadband absorber
Resonant systems, such as silver spheres, enhance the absorption of radiation
hence greatly improving the sensitivity to adsorbed molecules; but absorption
by a single resonance is narrow band and therefore of limited use.
• start with a dipole exciting an infinite system – most infinite systems have
a broadband continuum
• invert about the origin to convert to a finite system excited by a plane
wave. The spectrum is unchanged and remains broadband.

a metallic slab of finite thickness has
a broadband spectrum

a Zoo of Structures
continuous spectrum
discrete
spectrum

continuous spectrum

continuous spectrum

the properties of each
of these structures can
be found analytically

Inversion About the Origin
z ' = 1 z , ! ( z ) " ! ( z ')
This conformal transformation maps a semi ! slab into a cylinder

spectra of the slab and the cylinder are identical in the electrostatic limit
linear momentum, q, maps into angular momentum, m.

An inversion maps a dipole
into a uniform electric field

Studying a dipole interacting with a flat surface tells us how a cylinder responds
to a plane wave. (We assume the diameter to be sub-wavelength). The
absorption cross section comprises a sharp resonance at !sp in both cases.

Inversion about the origin, z ' = 1 z , converts a slab
to a cylindrical crescent
The dipole source is transformed into a uniform electric field

Left: a thin slab of metal supports surface plasmons that couple to a dipole source,
transporting its energy to infinity. Th e spectrum is continuous and broadband
therefore the process is effective over a wide range of frequencies.
Right: the transformed material now comprises a cylinder with cross section in the
form of a crescent. The dipole source is transformed into a uniform electric field.

Inversion about the origin, z ' = 1 z , converts a cavity
to a pair of kissing cylinders
The dipole source is transformed into a uniform electric field

Left: a cavity supports surface plasmons that couple to a dipole source,
transporting its energy to infinity. The spectrum is continuous.
Right: the transformed material now comprises two kissing cylinders. The dipole
source is transformed into a uniform electric field.

Broadband field enhancement in singular structures
(Alexandre Aubry, Dang Yuan Lei, Antonio I. Fernandez-Dominguez, et al.)

Calculated E x normalized to the incoming field (E -field along x ). The left and
right panels display the field in the crescent and in the two kissing cylinders
respectively. The metal is silver and ω = 0.9ωsp . The scale is restricted to
−10+5 to +10+5 but note that the field magnitude is far larger around the
structural singularities.

Field enhancement versus angle – crescent

Blue curve: E x at the surface of the crescent, plotted as a function of θ , for
ω = 0.75ωsp and ε = −7.058 + 0.213i taken from Johnson and Christy.
Red curve: ε = −7.058 + 2 × 0.213i i.e. more loss. Both curves are normalised
to the incoming field amplitude E0. The crescent is defined by the ratio of
diameters r = 0.5

The transformation z ' = a exp ( 2π z d ) converts
periodic cavities into a wedge

a a
The transformation z ' = +
exp ( 2π z d ) − 1 2
converts periodic cavities into 2 embedded cylinders

Raman signal enhancement for inclusions

a
The transformation z ' = converts
exp ( 2π z d ) − 1
periodic dipoles into 2 separated cylinders
In this case the spectrum is finite, not continuous

Absorption cross section: non-touching cylinders

Absorption cross section normalised to the physical cross section, D0 , as a
function of separation between the cylinders, ! .

Extension of Harvesting Theory
from Cylinders to Spheres

Analytic theory in the electrostatic limit is exact for touching cylinders.
For spheres theory approximates to the cylindrical solution near the touching
point.

Spheres as Light Harvesting Devices
Theory by Antonio Fernandez-Dominguez

Electric field enhancement at various photon frequencies for touching spheres.
Enhancement is an order of magnitude greater than for touching cylinders
because energy is compressed in 2 directions.

Leveraging Nanoscale Plasmonic Modes to Achieve
Reproducible Enhancement of Light
Ryan T. Hill, Jack J. Mock, Yaroslav Urzhumov, David S. Sebba, Steven Oldenburg, Shiuan-Yeh Chen,
Anne A. Lazarides, Ashutosh Chilkoti, and David R. Smith. NanoLetters 10 4150 (2010).

A: Gold nanoparticle near a gold. B: Localized NP-film field enhancement
using SERRS from MGITC molecules adsorbed on the surface of the NP and
within the NP-film gaps, which were created by a single molecular layer of
PAH (0.6nm layer thickness).

Measured distance dependence of SERRS
from MGITC molecules in the NP-film gaps with varying spacer distances.

Benefits of Broadband Harvesting

• Multi - frequency systems benefit from enhancement of all
frequencies.
• e.g. one system can enhance detection of a wide range of
molecules
• e.g. if we are amplifying a weak signal at one frequency
using a pump of another frequency, both are enhanced.

What can go wrong?
The theory predicts spectacular enhancements in the harvested fields, even
when realistic values of the silver permittivity are included. Harvesting is
much less sensitive to resistive losses than is perfect imaging.
Enhancements in field strength of 10 4 are predicted, implying an enhancement
of the SERS signal of 1016 . Several factors will prevent this ideal from being
attained:
• radiative losses
• non locality of ε
• problems in nm scale precision manufacture
Nevertheless substantial effects can be expected

Conclusions

Sub wavelength resolution in both imaging systems and harvesting devices
requires control of the near field via a resonant system.
This can be achieved through negative refraction, ε < 0, μ < 0, as in the
Veselago lens or in a limited form in plasmonic systems, ε < 0 .
We outlined a design strategy in which a simple easily solved mother system
gave rise to a series of daughters of increasing geometric complexity, but
possessing the same spectral properties.
The tool of choice manipulating the geometry was transformation optics
Currently the chief limitation in performance is the perfection of manufacture
of sub nanoscale structures.

Radiative Losses
In the electrostatic approximation there ar e no radiative losses. This is a valid
assumption provided that the cylinders are small compared to the wavelength.
In practice this means:
D ( diameter ) < 200nm
Their effect is to damp the resonant harvesting states and steal energy from the
light harvesting mechanism.
In the electrostatic limit the harvesting cross section σ a ∝ D 2 reflecting the
scale invariance of an electrostatic system.
However computer simulations using COMSOL show this scaling breaking
down as radiative corrections kick in and σ a falling dramatically.

Calculating radiative corrections analytically

(a) Two semi-infinite metal slabs support
surface plasmons that couple to a dipole
source, transporting its energy to infinity.

A fictional absorbing particle superimposed
on the emitting dipole chosen to account for
the radiative damping in the transformed
geometry.

(b) The transformed material consists of two
kissing cylinders. The dipole source is
transformed into a uniform electric field, and
the radiative losses are approximated by lossy
material outside the large sphere.

The effect of radiative loss on enhancement

Electric field along the x- direction
normalized by the incident electric field
E0, for D = 100 nm and D =�200 nm
for % = 0.9 %sp.

The analytical prediction for the effect
of radiative loss (red) is compared to
the numerical result (green) and to the
electrostatic case where there is no
radiative loss (blue).

Inside the Wavelength: Seeing Really Small Objects with Light - Professor Sir John Pendry

More Related Content

What's hot

Viewers also liked

Similar to Inside the Wavelength: Seeing Really Small Objects with Light - Professor Sir John Pendry

More from The Air Force Office of Scientific Research

Recently uploaded

Inside the Wavelength: Seeing Really Small Objects with Light - Professor Sir John Pendry