Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field
Introduction
Many condensed matter properties are determined by surface properties. Very often, surface waves, which are electromagnetic eigenmodes of the surface, play a key role. Let us mention a few examples. It has been demonstrated [1] that the lifetime of a molecule varies dramatically when a metallic surface is brought at a distance smaller than a micron. This effect is due to the resonant excitation of surface plasmons. The van der Waals force between a molecule and an interface is proportional to , where is the dielectric constant of the medium. There is therefore a resonance for the particular frequency such that . This condition coincides with a branch of the dispersion relation of a surface wave. It can be viewed as a resonant excitation of surface charge oscillations. It was shown in [2] that the van der Waals force between a molecule and a surface can become repulsive depending on the relative position of the molecule and the surface resonances. Enhanced scattering due to the resonant excitation of surface charges has also been demonstrated for SiC in the infrared: a tip brought close to a surface generates a very strong scattering signal for some particular frequencies corresponding to the excitation of surface waves [3]. Both experiments can be understood by replacing the interface by an image whose amplitude is very large owing to the excitation of a resonance of the surface charges. Surface enhanced Raman scattering (SERS) is partially due to the enhancement of the electromagnetic field at the interface due to the excitation of a surface wave. The resonance of the electromagnetic (EM) field at an interface is also responsible for the enhanced transmission of a metallic film with a periodic array of holes [4], [5]. The resonance of the EM field associated with the surface mode is responsible for the so-called “perfect lens” effect [6]. A key feature of all the above examples is that they involve the interaction of a surface and an object in the near field of the structure. As it will be explained in detail in Section 2, surface waves are evanescent waves whose amplitude decreases away from the interface on a wavelength scale. In the far field, the influence of such modes is therefore negligible. In the near field on the contrary, their role is essential.
We will see in Section 3 that surface waves can be excited by thermal fluctuations inside a body. The role of surface waves in the modification of the density of EM states at the interface has a strong influence on the thermally emitted fields. Their intensity is many orders of magnitude larger in the near field than in the far field [7]. In addition, they are quasi-monochromatic in the vicinity of the surface. This entails that their coherence properties are extremely different from those of the blackbody radiation [8]. There have been recently several experiments that have probed these thermal fields in the near-field regime: heating of trapped atoms [9], realization of a spatially partially coherent thermal source [10]. After reviewing these experiments, we will show how an EM approach with random fluctuating thermal sources can be used to describe and analyse these effects. It is based on the fluctuation–dissipation theorem. We will see that the knowledge of the electromagnetic energy density gives access to a fundamental concept: the local density of EM states. In Section 4, we study the EM coherence properties near a material supporting surface waves and held at a temperature T. We will see that the emitted field has very peculiar spatial coherent properties in the near field. Indeed, the field can be spatially coherent over a length larger than several tens of wavelength. We then use this property to design coherent thermal sources. In Sections 5 Coherence properties of planar thermal sources in the near-field, 6 Spatially partially coherent thermal sources in the far field we show that the radiative heat transfer is enhanced by several orders of magnitude in the near field when two material supporting surface waves are put face to face. We will consider three cases: two nanoparticles face to face, a nanoparticle near a plane interface and two semi-infinite half-spaces separated by a narrow gap. In the last section, we will analyse the role played by the surface waves in the Casimir force, i.e. in the force of interaction between two semi-infinite bodies. We will see that this force is dominated in the near field by the interaction between surface waves. Finally, we review the work done to analyse the contribution of fluctuating electromagnetic fields to the friction forces.
Section snippets
Introduction to surface electromagnetic waves
In this section, we give a brief introduction to the main properties of electromagnetic surface waves. This particular type of waves exists at the interface between two different media. An electromagnetic surface wave propagates along the interface and decreases exponentially in the perpendicular direction. Surface waves due to a coupling between the electromagnetic field and a resonant polarization oscillation in the material are called surface polaritons. From a microscopic point of view, the
Fluctuation–dissipation theorem: cross-spectral density
In this section, we introduce the tools and methods that are useful to derive the field radiated by a body in thermal equilibrium at temperature T both in the near field and in the far field. Whereas the phenomenological theory of radiometry based on geometrical optics describes correctly the field emitted in the far field, it fails to predict the behaviour of the emitted radiation in the near field. Indeed, geometrical optics does not include evanescent waves. A new framework to describe
Electromagnetic energy density and local density of states (LDOS)
In this section, we will study how the electromagnetic energy density is modified by the presence of material media. We shall first examine the amount of electromagnetic energy emitted by a half-space at temperature T. It will be shown that the density of energy is dramatically different in the near field and in the far field when surface waves are excited. The second point that we address is the general problem of the definition of the local density of electromagnetic states. Whereas it is
Coherence properties of planar thermal sources in the near-field
In this section, we examine the second-order coherence properties of the fields due to thermal excitation in the presence of surface waves. We have shown that the density of energy is completely dominated by the contribution of surface waves in the near field. We shall see that they are also responsible for a deep modification of coherence properties. In what follows, we restrict ourselves to second-order coherence properties.
Radiative heat transfer in the near field
We have shown previously that the density of electromagnetic energy increases in the near field due to the contribution of surface waves. We now address the question of heat transfer between bodies separated by distances smaller than the wavelength. In that case, contributions of the surface waves to the radiative heat transfer are expected. This topic has already a long history. Anomalous radiative heat transfer was observed in the 1960s. Cravalho et al. [77] and Boehm and Tien [78] studied
Concluding remarks
Many years after the discovery of surface polaritons, new discoveries and effects are still being reported. A major reason is the development of near-field techniques that allows us to probe the properties of surfaces with a nanometric resolution and motivates further work. Although thermal excitation of surface waves had been studied in the past, their major role in many phenomena has been realized only recently. It has been shown that heat transfer is dramatically enhanced in the near field
Acknowledgements
The authors are very grateful to Carsten Henkel and Lukas Novotny for many fruitful discussions.
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