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Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

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Page 1: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Page 2: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Near-field radiative heat transfer :application to energy conversion

Jean-Jacques Greffet

Ecole Centrale Paris, CNRS.

Page 3: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Collaborators

• Rémi Carminati, O. Chapuis, K. Joulain, F. Marquier, J.P. Mulet, M. Laroche, S. Volz

• C. Henkel ( Potsdam)

• A. Shchegrov ( Rochester)

• Y. Chen, S. Collin, F.Pardo, J.L. Pelouard ( LPN, Marcoussis)

• Y. de Wilde, F. Formanek, P.A. Lemoine ( ESPCI)

Page 4: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Density of energy above a SiC surface at temperature T

Temperature T

z

Page 5: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

20x103

15

10

5

0500x10

124003002001000

ω ( )Hz

1.0

0.8

0.6

0.4

0.2

0.0

=100 z μm

=1 z μm

= 100 z nm

15

10

5

0

T=300 K

z

Density of energy near a SiC-vacuum interface

PRL, 85 p 1548 (2000)

Page 6: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

20x103

15

10

5

0500x10

124003002001000

ω ( )Hz

1.0

0.8

0.6

0.4

0.2

0.0

=100 z μm

=1 z μm

= 100 z nm

15

10

5

0

T=300 K

z

Density of energy near a SiC-vacuum interface

PRL, 85 p 1548 (2000)

Page 7: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

20x103

15

10

5

0500x10

124003002001000

ω ( )Hz

1.0

0.8

0.6

0.4

0.2

0.0

=100 z μm

=1 z μm

= 100 z nm

15

10

5

0

T=300 K

z

Density of energy near a SiC-vacuum interface

PRL, 85 p 1548 (2000)

Page 8: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

T=300 K

z

Density of energy near a Glass-vacuum interface

Page 9: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

What is the physical mechanism responsible for this huge enhancement ?

The density of energy is the product of

- the density of states, - the energy h- the Bose Einstein distribution.

The density of states can diverge due to the presence of surface waves :Surface phonon-polaritons.

Page 10: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

-+ + + + + +-- - -

Page 11: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

+

++

+

+

+-

--

-

---

Page 12: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Dispersion relation of a surface phonon-polariton

It is seen that the number of modes diverges for a particular frequency. This happens only close to the surface.

PRB, 55 p 10105 (1997)

Page 13: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Derivation of the thermal emission of a hot body

i) A volume element below the interface contains currents due to the random thermal motion of charges.

ii) Each volume element is equivalent to a dipolar antenna that emits radiation.

iii) The mean field is null.

E(r,ω)=iμ0ω

t G (r,r',ω)⋅ j(r' )d3r'

V∫∫∫

j(r' )d3r'

j(r' ) =0 ⇒ E(r' ) =0

PRL, 82 p 1660 (1999)

Page 14: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

iv) Derivation of the intensity

E(r,ω)2

=μ0ω

2 t G (r,r' ,ω)⋅ j(r' )d3r'

V∫∫∫

2

v) The only quantity needed is the correlation function of the random current. This is given by the fluctuation-dissipation theorem.

jn(r) j

m

* (r' ) = ωπε

0Im(ε)δ

m,nδ(r−r' )

exphωkT[ ]−1

PRL, 82 p 1660 (1999)

Page 15: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Advantages of the electromagnetic approach

-It is valid in the near field

- It yields the value of the emissivity

- It yields physical insight in Kirchhoff law.

Page 16: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Direct proof of the coherence of thermal radiation in the near field.

Application to the measurement of the EM LDOS

Page 17: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Direct experimental evidence of the spatial coherence of thermal radiation in near field

de Wilde et al. to be published in Nature

Page 18: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Direct experimental evidence of the spatial coherence of thermal radiation in near field

de Wilde et al. to be published in Nature

Page 19: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Fabrication of a coherent source

of infrared radiation :Infrared antenna

Page 20: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

The thermally emitted fields may be spatially coherent along the interface !

PRL 82, 1660 (1999)

T=300 K

z

M P

Page 21: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Fabricating an infrared antenna with a microstructured semiconductor.

Thermal currents radiates surface waves

A grating ruled on the surface scatters the surface wave. The scattered wavevector is related to the surface wave wavevector by the relationship :

ksw +

2πd

= 2πλ

sinθs

Page 22: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Image of the SiC grating taken with an atomic force microscope.

Nature 416, p 61 (2002)

Page 23: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

The emission pattern looks like an antenna emission pattern. The angular width is a signature of the spatial coherence.

Emission pattern of a SiC grating

Green line : theory (300K)Red line : measurement(800K).

Nature 416, p 61 (2002)

Page 24: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Comparison between theory and measurements

Nature 416, p 61 (2002)

Page 25: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Thermal emission by a tungsten grating

Opt.Lett. 30 p 2623 (2005)

Angular width : 14 mrad

Page 26: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Emission mediated by surface waves

1. Excitation of a surface wave.

2. Scattering by a grating.

Re Ksp( ) + p2π

a=

λsin θ( )

Page 27: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

• Coherent thermal emission

T

Source : current thermal fluctuations

Greffet et al., Nature (London) 416, 61 (2002), Marquier et al. PRB 69, 155412 (2004)

Emission mediated by surface waves

Page 28: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

The interface as an antenna (1)

• What is an antenna ?i) Increases the emitted power.ii) Modifies the emission pattern.

•How does it work ?

Antenna = Intermediate resonator between the source and vacuum :

i) More energy is extracted from the source because the LDOS is enhanced (Purcell effect)ii) The resonator is a secondary source.

Page 29: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

The interface as an antenna (2)

Example of antenna: a guitar

Source :the string

Resonator

Optical analog : microcavity

Page 30: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

The interface as an antenna (3)

Source : current fluctuations

T

Resonator : the interface+ the grating

i) The output is increased because the LDOS is increased (Purcell effect)

ii) The angular pattern of the antenna depends on the decay length of the SPP.

Page 31: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Electromagnetic heat transfer in the near field

Page 32: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Application to radiative heat transfer between two half-spaces

Temperature T1

Temperature T2>T1.

d

h =lim

T1→ T

2

Φ(T

1,T

2)

T1−T

2

Poynting vector yields the radiative enregy flux.

Page 33: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Radiative heat transfer coefficient, T=300 K.

d

Page 34: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Monochromatic radiative heat transfer coefficient, d=10 nm, T=300K.

d

Microscale Thermophysical Engineering 6, p 209 (2002)

Page 35: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Au GaN

Kittel et al. , PRL 95 p 224301 (2005)

Experimental data

Page 36: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Implications of near-field heat transfer for thermophotovoltaics

Page 37: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

thermal source

T= 2000 K

TPV cell

T= 300 K

d << rad

thermal source

T= 2000 K

TPV cell

T= 300 K

PV cell

T= 300 K

Photovoltaics Thermophotovoltaics Near-fieldthermophotovoltaics

T= 6000K

Page 38: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

potential improvement on the output electric power and efficiency

of near-field thermophotovoltaic devices :

necessity of a quantitative model

thermal sourceT= 2000 K

TPV cell

T= 300 K

d << rad

PR (

W.m

-2 )

d (m)

400

enhanced radiative power transfer

Why near field ?

Page 39: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Near-field I-V characteristic of a TPV cell

z

I = Io eeV / kT −1( ) − Iph

enhanced radiative power (Mulet 2002, Whale 2002, Chen 2003)

Io ∝1

τ

modification of the electron-hole pairs lifetime (Baldasaro 2001)

hot source

T= 2000 K

TPV cell

T= 300 K

d << rad

Page 40: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Near-field radiative power transfer

ω (rad.s-1)

PR(W

. m

-2.

Hz-1

)

d = 10 μmW

T= 2000 K

GaSb cell

T= 300 K

d

ω (rad.s-1)

PR(W

. m

-2.

Hz-1

)

d = 30 nm(near field)

(far field)

1.10-10

3.5.10-10

evanescent waves contribution in the near fieldenhancement by a factor 3

Page 41: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Near-field effects on the radiative power transfer

d = 30 nm

d = 10 μm

ω (rad.s-1)

PR(W

. m

-2.

Hz-1

)ω (rad.s-1)

PR(W

. m

-2.

Hz-1

)

Drude Metal

T= 2000 K

GaSb cell

T= 300 K

d(far field)

(near field)

9.10-12

6.10-10

evanescent waves contribution in the near fieldenhancement by two orders of magnitudemonochromaticity degraded by the presence of the TPV converter

Page 42: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Enhanced radiative transfer and photogeneration current in the near field

d (m)

PR (

W.m

-2 )

tungsten source quasi-monochromatic source

PR (

W.m

-2 )

d (m)

d (m)d (m)

I ph (

A.m

-2 )

I ph (

A.m

-2 )

PR T1,T2( ) = dω0

∫ PR T1,T2,ω( )

Iph = dωEG = 0.7eV

∫PR T1,T2,ω( )

h ω

50

40

400

1000

Page 43: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Near-field electron-hole pairs lifetime

ΓΓn

=1+2π

nωo /cIm Tr G

env

E

r,r,ωo( ) ⎛

⎝ ⎜

⎠ ⎟

⎣ ⎢

⎦ ⎥

hot source

d << rad vacuum

GaSb

z

for both sources : near-field effect on the radiative recombination lifetime of electron-hole pairs negligible

Page 44: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Near-field output electric power

output electric power enhanced by at least one order of magnitude

tungsten source quasi-monochromatic source

d (m)

50

far field :3.104 W/m2

near field :15.105 W/m2

Pe

l (W

. m

- 2)

d (m)

near field : 2.5.106 W/m2

far field : 1.4.103 W/m2

3000

Pe

l (W

. m

- 2)

BB 2000 KBB 2000 K

Page 45: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Near-field TPV converter efficiency

η =Pel

Pradη (%

)

d (m) d (m)

η (%

)

near field : 27%

far field : 21 %

near field : 35%

significant increase of the efficiency

far field : 8 %

tungsten source quasi-monochromatic source

BB 2000 K BB 2000 K

Page 46: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Summary

20x103

15

10

5

0500x10

124003002001000

ω ( )Hz

1.0

0.8

0.6

0.4

0.2

0.0

=100 z μm

=1 z μm

= 100 z nm

15

10

5

0

?

Page 47: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Heat transfer between two nanoparticles

Page 48: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Heat transfer between two nanoparticles

PRL 94, 85901, (2005)

QuickTime™ et undécompresseur BMP

sont requis pour visionner cette image.

Page 49: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2CPRL 94, 85901, 2005

Page 50: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Radiative heat transfer between a small sphere and an interface

d

Appl.Phys.Lett, 78, 2931 (2001)

Page 51: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

10-6

10-4

10-2

100

102

10-8 10-7 10-6 10-5 10-4

d in m

Far field value

Power absorbed by a SiC sphere as a function of the distance.

Diameter = 10 nm, SiC substrate.

Appl.Phys.Lett, 78, 2931 (2001)

Page 52: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Emission mediated by surface plasmons

QW luminescenceA. SchererNature Materials 3, p 601 (2004)

Page 53: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Conclusions

* The existence of surface modes of electromagnetic waves modifies drastically the emission. * Radiative heat transfer can be increased by four orders of magnitude between two plates.* Radiative heat transfer can be very local. * Radiative heat transfer is almost monochromatic at nanoscale.* Radiation emitted by a thermal source is temporally coherent (monochromatic)close to an interface that supports a surface wave.* Radiation emitted by a thermal source is spatially coherent (narrow emitted beams).* Highly directional infrared thermal antennas can be designed.

Page 54: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Dispersion relation of the surface-phonon polariton

Nature 416, p 61 (2002)

Page 55: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Introduction

Measurement of the coherence length

Page 56: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Comparison of calculated and measured emissivity

Calculation with optical dataat 300 K

Calculation with optical dataat 800 K

Phys.Rev.B (2004)

Page 57: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Application to local heating.

The peak power deposited per unit volume is 100 MWm-3.

A SiC sphere (a=5 nm) is located at a distance 100 nm above a SiC surface.

Contours line are in log scale.

The power decreases as R-6.

R

T=300 K

-0.8

-0.6

-0.4

-0.2

0.0

1.00.80.60.40.20.0

lateral distance in μm

7

5.5

5

4

3.5

3.5

2.5

7 6.5

6

6

5.5

5

4.5

4.5

4.5

4

4

3.5

3

3

3

2.5

2.5

2

Appl.Phys.Lett, 78, 2931 (2001)

Page 58: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Thermal emission by photonic crystals

PRL 96, 123903 (2006)

Page 59: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

2D photonic crystal

PRL 96, 123903 (2006)

Page 60: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Thermal emission assisted by surface waves

Transmission

Absorptionby the crystal

Absorption by the truncated crystal

Page 61: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

(a) slab, (b) photonic crystal,(c) truncated PC, (d) amplitude of the surface wave

Page 62: Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques Greffet Ecole Centrale Paris, CNRS.

Laboratoire EM2C

Design of an isotropic source