8 Controlling Thermal Radiation with Surface Waves
301
Polder and van Hove a few years later [99]. The experimental observation at ambient
temperature remained difficult and some inconclusive results were reported [127].
A significant heat flux increase results from this tunneling. In presence of resonant surface modes such as surface polaritons, the radiative heat exchange can
even surpass by several orders of magnitude the Stefan-Boltzmann law as first predicted in Refs. [84, 85]. These results have been experimentally confirmed [52,
60, 87, 90, 107, 113] and have opened new possibilities for the development of
innovative technologies for nanoscale thermal management, near-field energy conversion (thermophotovoltaic conversion devices [8, 37, 67, 86], heating assisted
data storage [23], plasmon assisted nanophotolithography [116]) or IR sensing and
spectroscopy [56]. In what follows we will first introduce an appropriate theoretical
framework to describe the radiative heat transfer between arbitrary media out of thermal equilibrium. Next we will establish a link between this theory and the Landauer
theory of charge transport used in mesoscopic physics of electron transport. From
this new formulation we will then derive the fundamental limits for heat exchanges
both in far and near-field. Finally, we will present different practical applications
of the near-field heat transfer theory for innovative technologies for nanoscale thermal management and near-field energy conversion. In this review, we focus on the
heat transfer between two parallel flat surfaces with local dielectric constants. The
effect of non-locality is discussed in Ref. [25], the effect of roughness is addressed
in Refs. [13, 47, 76]. Heat transfer between a nanoparticle and a surface is analyzed
in Refs. [14, 26, 35]. Two review papers have been recently published [38, 123].
8.2.1 Heat Flux Exchanged Between Two Planar Media
Equipped with the correlation function for the source currents in Eq. (8.1) and
the linear relations in Eqs. (8.3) and (8.4) we can now determine the correlation
functions of the electromagnetic fields between the bodies ∪ ˜
E f
i (r, ω) ˜
E f
j (r ≈ , ω ≈ )∼,
∪ ˜
H f
i (r, ω) ˜
H f
j (r ≈ , ω ≈ )∼, and ∪ ˜
E f
i (r, ω) ˜
H f
j (r ≈ , ω ≈ )∼ in terms of Green’s functions and
the bodies temperatures. Hence, if we know the classical electromagnetic Green
functions G E and G H for a given geometry, we can evaluate the correlation functions
of the fields allowing for determining heat fluxes. Although some purely quantum
mechanical approaches exist [1, 55, 72], fluctuational electrodynamics has the advantage of being conceptually simple while giving the correct results for the correlation
functions of the fields.
Now we want to determine the heat flux between two semi-infinite media (see
Fig. 8.14) which are at local thermal equilibrium and have the temperatures T 1 and
T 2 . We assume that both media are separated by a vacuum gap of thickness d. In
order to determine the heat flux, we first consider T 2 = 0, so that we consider only
fluctuating currents j f
1 in medium 1. The fluctuating fields E f
1 and H f
1 inside the
vacuum gap generated by the fluctuating sources in medium 1 can be expressed in
terms of the relations (8.3) and (8.4). From these expressions one can determine the
301
Polder and van Hove a few years later [99]. The experimental observation at ambient
temperature remained difficult and some inconclusive results were reported [127].
A significant heat flux increase results from this tunneling. In presence of resonant surface modes such as surface polaritons, the radiative heat exchange can
even surpass by several orders of magnitude the Stefan-Boltzmann law as first predicted in Refs. [84, 85]. These results have been experimentally confirmed [52,
60, 87, 90, 107, 113] and have opened new possibilities for the development of
innovative technologies for nanoscale thermal management, near-field energy conversion (thermophotovoltaic conversion devices [8, 37, 67, 86], heating assisted
data storage [23], plasmon assisted nanophotolithography [116]) or IR sensing and
spectroscopy [56]. In what follows we will first introduce an appropriate theoretical
framework to describe the radiative heat transfer between arbitrary media out of thermal equilibrium. Next we will establish a link between this theory and the Landauer
theory of charge transport used in mesoscopic physics of electron transport. From
this new formulation we will then derive the fundamental limits for heat exchanges
both in far and near-field. Finally, we will present different practical applications
of the near-field heat transfer theory for innovative technologies for nanoscale thermal management and near-field energy conversion. In this review, we focus on the
heat transfer between two parallel flat surfaces with local dielectric constants. The
effect of non-locality is discussed in Ref. [25], the effect of roughness is addressed
in Refs. [13, 47, 76]. Heat transfer between a nanoparticle and a surface is analyzed
in Refs. [14, 26, 35]. Two review papers have been recently published [38, 123].
8.2.1 Heat Flux Exchanged Between Two Planar Media
Equipped with the correlation function for the source currents in Eq. (8.1) and
the linear relations in Eqs. (8.3) and (8.4) we can now determine the correlation
functions of the electromagnetic fields between the bodies ∪ ˜
E f
i (r, ω) ˜
E f
j (r ≈ , ω ≈ )∼,
∪ ˜
H f
i (r, ω) ˜
H f
j (r ≈ , ω ≈ )∼, and ∪ ˜
E f
i (r, ω) ˜
H f
j (r ≈ , ω ≈ )∼ in terms of Green’s functions and
the bodies temperatures. Hence, if we know the classical electromagnetic Green
functions G E and G H for a given geometry, we can evaluate the correlation functions
of the fields allowing for determining heat fluxes. Although some purely quantum
mechanical approaches exist [1, 55, 72], fluctuational electrodynamics has the advantage of being conceptually simple while giving the correct results for the correlation
functions of the fields.
Now we want to determine the heat flux between two semi-infinite media (see
Fig. 8.14) which are at local thermal equilibrium and have the temperatures T 1 and
T 2 . We assume that both media are separated by a vacuum gap of thickness d. In
order to determine the heat flux, we first consider T 2 = 0, so that we consider only
fluctuating currents j f
1 in medium 1. The fluctuating fields E f
1 and H f
1 inside the
vacuum gap generated by the fluctuating sources in medium 1 can be expressed in
terms of the relations (8.3) and (8.4). From these expressions one can determine the