Introduction to Nanophotonics

Introduction to Nanophotonics

Logan LiuMicro and Nanotechnology Lab

Department of Electrical & Computer EngineeringUniversity of Illinois

What is Nanophotonics?This area of nanoscience, called nanophotonics, is defined as “the science and engineering of light matter interactions that take place on wavelength and subwavelength scales where the physical, chemical or structural nature of natural or artificial nanostructured matter controls the interactions”

-‐‐National Academy of Science

Early Examples of Nanophotonics

Nanophotonics in Mother Nature

Foundation of Nanophotonics

• Photon-Electron Interaction and Similarity

“There’s Plenty of Room at the Bottom” (Feynman, 1961)

Foundation of NanophotonicsBasic Equations describing propagation of photons in dielectrics has some similarities to propagation of electrons in crystals

Similarities between Photons and Electrons

Wavelength of Light,

Wavelength of Electrons,

Foundation of NanophotonicsMaxwell’s Equations for Light

1 DHc t

1 BEc t

Eigenvalue Wave Equation:

Describes the allowed frequencies of light

Schrodinger’s Eigenvalue Equation for Electrons:2

2( )4 [ ( )] ( ) ( )2

h

V r r E rm

Describes allowed Energies of Electrons

1 2

1 2

[ ( )] ( )[ ( )] ( )

E r E rH r H r

2

0( ) ( )E r k E r For plane wave

Foundation of NanophotonicsFree Space Solutions:

triktrik eeEE ..0Photon Plane Wave:

Electron Plane Wave: triktrik eec ..

Interaction Potential in a Medium:Propagation of Light affected by the Dielectric Medium (refractive index)

Propagation of Electrons affected by Coulomb Potential

Foundation of NanophotonicsPhoton tunneling through classically

forbidden zones. E and B fields decay exponentially. k-vector imaginary.

Electron Wavefunction decays exponentially in forbidden zones

Foundation of NanophotonicsConfinement of Light results in field variations similar to the confinement of Electron in a

Potential Well. For Light, the analogue of a Potential Well is a region of high refractive-index bounded by a region of lower refractive-index.

Microscale Confinement of Light Nanoscale Confinement of Electrons

Foundation of Nanophotonics• Free space propagation of both electrons and photons can

be described by Plane Waves.• Momentum for both electrons and photons, p = (h/2π)k• For Photons, k = (2π/λ) while for Electrons, k = (2π/h)mv• For Photons, Energy E = pc =(h/2π)kc while for Electrons,

Near Field OpticsIn Far-Field Microscopy,

NAsolution

222.1Re

This can be overcome with Near-Field Techniques by having nanoscale apertures or by using aperture-less techniques which enhance light interaction over nanoscale dimensions with the use of nanoscale tips, nanospheres etc. The idea of using sub-wavelength aperture to improve optical resolution was first proposed by Synge in a letter to Einstein in 1928. These ideas were implemented into optics much later in 1972 [Ash and Nicholls]

Near-field light decays over a distance of 50 nm from aperture.

Schematic set-ups for Near-Field Scanning Optical Microscope (NSOM)

Tapered Optical-Fiber

Aperture-less Technique: Near-Field around Nano-Tip

Near-Field OpticsPSTM SNOM

Tip illuminates the sample;Scattered light is collected

Tip collects the evanescent light created by laser illuminating the sample from the back

Near Field Optics

2 2 1/2

2 2 1/2

2 2 ( )

2 2 ( )2

2

( , ) ( , 0) (1)

For far field only need to integrate over / , i.e.

( , ) ( , 0) (2)

x x

x x

i x i Zx x

i x i ZCx x

C

f x z Z d e F z e

k c

f x z Z d e F z e

, T hen E qn. (1 ) is recap tured by Zz

frequency spatial one with),()0,( KKEzF xox

2 2

"

2 ( )22 2

"22" "

"

Then taking at aperture, ( , ) ( )

Now far field: ( , ) {

sin(( ) ) ( , 0)

xx

x

i Zi xCx

C

i x x xx x

x x

xf x z rect

f x z Z d e e

wd e F z e

2 "2

} (3)x

(Paesler, <Near-field Optics>)

Near Field OpticsContinued from the previous page

Notes: Eqn. (4) fulfills all our notions about far-field microscope and its inabilityto carry information beyond certain spatial frequency

Eqn. (5) integral doesn’t vanish for , such that high-frequency elements still contribute to the signal arriving at z=Z (far field).

Eqn. (4) collapses to (5) when w (aperture width) is large, i.e.

In the near-field, evanescent terms must be taken into account, due to the convolution of the tip and the sample.

2 22 2.(1) ( , ) for / 0, for / (4)

i Kx i K ZoEqn f x z Z E e e K C

K C

2 22 2 2 ( )22 2 2

sin( ).(3) ( , ) (5)xx i Zi xi K xCo x

C x

K wEqn f x z Z E e d e eK

CK /

)()sin( KK

wKx

x

x

Quantum confinementQuantum-confined materials refer to structures which are constrained to nanoscale lengths in one, two or all three dimensions. The length along which there is Quantum confinement must be small than de Broglie wavelength of electrons for thermal energies in the medium.

de Broglie Wavelength,Thermal Energy, E =

For T = 10 K, the calculated λ in GaAs is 162 nm for Electrons and 62 nm for HolesFor effective Quantum-confinement, one or more dimensions must be less than 10 nm. Structures which are Quantum-confined show strong effect on their Optical Properties. Artificially created structures with Quantum-confinement on one, two or three dimensions are called, Quantum Wells, Quantum Wires and Quantum Dots respectively.

Quantum Confinement

Z

Nanoscale Confinement in 1-Dimension results in a “Quantum Well”

At 300 K, The band gap of GaAs is 1.43 eV while it is 1.79 eV for AlxGa1-xAs (x=0.3). Thus the electrons and holes in GaAs are confined in a 1-D potential well of length L in the Z-direction.

Quantization of energy into discrete levels has applications for fabrication of new solid-state lasers. Two or more Quantum wells side-by-side give rise to Multiple Quantum Wells (MQM) structure.

Motion is confined only in the Z-direction. For electrons and holes moving in the Z-direction in low bandgap material, their motion can be described by Particle in a Box. If the depth of Potential Well is V, for energies E<V, we can write,

e

yx

eCkkn m

kkhLm

hnEEyx 2

222

2

22

,, 8)(

8 n = 1, 2, 3,…..

Quantum Confinement

2222 yxD ppmE

e

y

zexeCknn m

khLmhn

LmhnEE

y 2

22

2

222

2

221

,, 88821

Due to 1-D confinement, the number of continuous energy states in the 2-D phase space satisfy

Quantum Well: 1D Confinement

Quantum Wire: 2D Confinement

2D confinement in X and Z directions. For wires (e.g. of InP, CdSe). with rectangular cross-section, we can write:

Quantum Dot: 3D ConfinementFor a cubical box with the discrete energy levels are given by:

)(8 2

23

2

22

2

21

2

,, 321

zyxeCnnn L

nLn

Ln

mhEE

Quantum Confinement

Size Dependence of Optical PropertiesIn general, confinement produces a blue shift of the band-gap. Location of discrete energy levels depends on the size and nature of confinement.

Increase of Oscillator StrengthsThis implies increase of optical transition probability. This happens anytime the energy levels are squeezed into a narrow range, resulting in an increase of energy density. The oscillator strengths increase as the confinement increases from Bulk to Quantum Well to Quantum Wire to Quantum Dot.

Computational Nanophotonics• Analytical approach hampered by over-simplifying

assumptions– Perfect conductivity, zero thickness materials,

semi-infinite structures, …• Frequency vs. Time domain?• Computational resources becoming less constraining

– Very complex problems being tackled• Finite Difference Time Domain (FDTD)• Frequency Domain Integral-differential

Computational Nanophotonics

• Numerical integration of Ampere/Faraday

• Impulse excitation• Numerical integration to get steady

state• Relate time series to frequency domain

via F.T.• Some problems with highly dispersive

media (convolutional response)• No big things to invert but lots of

memory• Sophisticated variable mesh

• Time harmonic excitation (steady state)

• Boundary value problem based on integro-differential equation

• Big things to invert (stability/accuracy issues possible)

• Relate to time domain by F.T.

Time Domain Frequency Domain

Finite Difference Time Domain (FDTD)

t0 1/2 1

E(1)E(0) H(1/2)

zkjinHkjinH

ykjinHkjinH

kjitkjinEkjinE

yy

zz

xx

),,,(),,,(

),,,(),,,(),,(

),,,(),,,1(

21

21

21

21

21

21

21

21

Yee Cell – Space/Time

Static State Computation

dB

20 10 0 -1030 -20

4dB

9 dB

30 dB

(, )

0112

2

2

1)/(0,)( aE

Solve Laplace equation

Charge density

)0(Singularity near the sharp tip

0)(0)(

21

21

HHEE

Electrostatic Approximation Finite Element Simulation

020 zz EkE

0)( 20 zz HkH

zz EEHn 02

zz HHEn 02

Solve Harmonic Wave Equation

For Plane Wave

Low-reflecting Boundary Condition

(b)

0

16

xy

z|E|/|E0| at 785 nm

PlasmonicsTransverse EM wave coupled to a plasmon (wave of charges on a metal/dielectric interface) = SPP

(surface plasmon polariton)

Polariton – any coupled oscillation of photons and dipoles in a medium

Note: the wave has to have the component of E transverse to the surface (be TM-polarized).

10 µm

1 µm1 µm1 µm

Plasmonics Research

Details in Prof. Nick Fang’s Lecture

Metamaterials

Hormann et al, Optics Express (2007)

Details in Prof. Nick Fang’s Lecture

Photonic CrystalThe most striking similarity is the Band-Gap within the spectra of Electron and Photon Energies

Solution of Schroedinger’s equation in a 3D periodic coulomb potential for electron crystal forbids propagation of free electrons with energies within the Energy Band-Gap.

Likewise, diffraction of light within a Photonic Crystal is forbidden for a range of frequencies which gives the concept of Photonic Band-Gap. The forbidden range of frequencies depends on the direction of light with respect to the photonic crystal lattice. However, for a sufficiently refractive-index contrast (ratio n1/n2), there exists a Band-Gap which is omni-directional.

Photonic Crystal

All-Optical Processor

Molecular Nanophotonics


Photosynthetic Solar Cell Molecular Nano Antenna


)cos(0 tEE ex

rr 0

0

)cos(0 trr vib

ttErr

tE vibexvibexex )(cos)(cos21)cos( 00

000

)cos()cos()cos( 000

00 ttErr

tEE vibexex

Excitation electric field Nuclear displacement Polarizonbility

Dipole moment

Anti-Stokes line Stokes line

r r

Coupled Spring Model

Rayleigh Scattering

ωex ωvib

Nanophotonic Interaction

10-30

10-28

10-26

10-24

10-22

10-20

10-18

10-16

10-14

Opt

ical

Cro

ss S

ectio

n [c

m2 ]

RayleighScattering

Fluorescence

Raman scattering

Resonance Raman

SERS

SERRS Geometrical cross-section of a single biomolecule

FTIR

10-30

10-28

10-26

10-24

10-22

10-20

10-18

10-16

10-14

Opt

ical

Cro

ss S

ectio

n [c

m2 ]

RayleighScattering

Fluorescence

Raman scattering

Resonance Raman

SERS


FTIR

12 orders of magnitude

10-30

10-28

10-26

10-24

10-22

10-20

10-18

10-16

10-14

Opt

ical

Cro

ss S

ectio

n [c

m2 ]

RayleighScattering

Fluorescence

Raman scattering

Resonance Raman

SERS


FTIR

10-30

10-28

10-26

10-24

10-22

10-20

10-18

10-16

10-14

Opt

ical

Cro

ss S

ectio

n [c

m2 ]

RayleighScattering

Fluorescence

Raman scattering

Resonance Raman

SERS


FTIR

12 orders of magnitude

Electromagnetic Enhancement Chemical Enhancement

500 1000 1500

0

50

100

150

Inte

nsity

[a.u

]

Raman Shift [cm-1]

A C G T

hωinc hωinc±hωvib

hω

EFermi

hω’

HOMO

LUMO

Raman Spectra of DNA Bases Optical Cross Section

Nanophotonic Field Enhancement

Cresyl blue SERS spectra. Adapted from Stöckle et al., Chem. Phys. Lett. 2000, 318, 131.

Hybrid Nanophotonics• Inorganic-organic hybrid structures

Fabrication of Nanophotonics

Nanophotonic BioimagingNanoparticles are also used for bioimaging by non-optical techniques like Magnetic Resonance Imaging (MRI), Radioactive Nanoparticles as tracers to detect drug pathways or imaging by Positron Emission Tomography (PET), and Ultrasonic Imaging. For MRI, the magnetic nanoparticles could be made of

oxide particles which are coated with some biocompatible polymer.Newer Nanoparticle Heterostructures have been investigated which offer the possibility of imaging by several techniques simultaneously. An example is Magnetic Quantum Dot.

Nanophotonic BioimagingDual-Functional Nanoprobes for Dual-Modality Animal Imaging

Photoacoustic T2 MRI T1 MRI

Fluorescence

Bouchard and Liu et al, PNAS 2009

Nanophotonic Energy Conversion

E0e-jωt

Conduction Electron

Metal lattice

NPNPmedium

medium

NPmedium

mediumNP

tplasmonplasmon

E

Ei

tEtjQ

Im2

38

23

81Re

)()(

220

220

8/0200 cEI

NPNPmedium

mediumNP

caIT

Im

23

3

2

0

20

3

2 QaT NP

Temperature Increase due to Photothermal Conversion

Electron-Lattice Collision(Electron-Phonon Relaxation)

Joule Heat due to Plasmon Current

Light Intensity

NRL 1, 84-90 (2006)

At steady state

PRET

Chemical/Biomolecules

Nanophotonics Therapy

H. Atwater, Scientific American 2007

Nanophotonic Molecular Manipulation

Lee et al, Nano Letter (2009)

50 nm

Steady State 57 οC52 οC

47 οC

42 οC

37 οC

32 οC

27 οC

0 50 100 150

30

40

50

60

Tem

pera

ture

( C

)

Distance (nm)

Steady state 0 ns 1 ns 3 ns 32 ns

Nanophotonic Fluidic Manipulation

Liu et al, Nature Materials (2006)

Optofluidic Molecular Manipulation

Optical Pre-Concentration of DNA

Biomolecule concentrating

Photothermal Nanofilm

Microfluidic Channel

Light Ilumination

Nanophotonic Particle Manipulation

StirrerRotorConveyer

Liu et al. Manuscript in preparation

Nanophotonics Market

Research Trends

Introduction to Nanophotonics

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