Coherence properties of lambertian and non-lambertian sources*

Carter, W. H.; Wolf, Emil

doi:10.1364/josa.65.001067

Cited by 138 publications

(57 citation statements)

References 7 publications

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“…In fact, a semi-infinite medium of lossy glass is a good approximation of a planar blackbody radiator, and the solid curve in Fig. 1 strongly resembles the sin͑kr͒͞kr shape of the cross-spectral density in the source plane of a Lambertian source, previously obtained in the scalar approximation [1]. Note that, although not shown here for brevity, we have observed this behavior for the three diagonal elements W jj of the cross-spectral density tensor.…”

Section: Rémi Carminati and Jean-jacques Greffetsupporting

confidence: 80%

“…Nevertheless, since the development of optical coherence theory, it has been known that the field emitted by thermal sources may exhibit a certain degree of temporal and spatial coherence. For example, it was shown that light across a planar quasihomogeneous Lambertian source, at a given wavelength l, is spatially correlated over a distance on the order of l͞2 [1]. This result was found to be in agreement with known spatial correlation properties of free blackbody radiation [2].…”

Section: Rémi Carminati and Jean-jacques Greffetmentioning

confidence: 69%

“…In deriving this result, the nonradiating near-field part of the emitted light was ignored [1], because it plays no role in the far-field properties of emission from planar sources. Nevertheless, recent interest in microscale and nanoscale radiative transfers [3], together with the development of local-probe thermal microscopy [4] and the observation of coherent thermal emission from doped silicon and silicon carbide (SiC) gratings [5,6], has raised new challenges.…”

Section: Rémi Carminati and Jean-jacques Greffetmentioning

confidence: 99%

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Near-Field Effects in Spatial Coherence of Thermal Sources

1999

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Section: Rémi Carminati and Jean-jacques Greffetsupporting

confidence: 80%

Section: Rémi Carminati and Jean-jacques Greffetmentioning

confidence: 69%

Section: Rémi Carminati and Jean-jacques Greffetmentioning

confidence: 99%

See 1 more Smart Citation

Near-Field Effects in Spatial Coherence of Thermal Sources

1999

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“…In other words, the scattered field from different sample points is considered to be spatially uncorrelated. This approach is supported by the early theory of coherence stating that the field emitted by an incoherent source at a given wavelength λ is spatially uncorrelated on length scales larger than λ=2 (measured from the surface of the scatterer) [3]. As a consequence, correlations on length scales smaller than λ=2 are inaccessible in standard light scattering, and the signal recorded in the far field is incoherent.…”

mentioning

confidence: 88%

Theory of Spatial Coherence in Near-Field Raman Scattering

et al. 2014

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A theoretical study describing the coherence properties of near-field Raman scattering in two-and onedimensional systems is presented. The model is applied to the Raman modes of pristine graphene and graphene edges. Our analysis is based on the tip-enhanced Raman scheme, in which a sharp metal tip located near the sample surface acts as a broadband optical antenna that transfers the information contained in the spatially correlated (but nonpropagating) near field to the far field. The dependence of the scattered signal on the tip-sample separation is explored, and the theory predicts that the signal enhancement depends on the particular symmetry of a vibrational mode. The model can be applied to extract the correlation length L c of optical phonons from experimentally recorded near-field Raman measurements. The coherence properties of optical phonons have been broadly explored in the time and frequency domains, and the spatially resolved approach presented here provides a complementary methodology for the study of local material properties at the nanoscale. Raman scattering in crystals is usually treated in the literature as a spatially incoherent process [1,2]. In other words, the scattered field from different sample points is considered to be spatially uncorrelated. This approach is supported by the early theory of coherence stating that the field emitted by an incoherent source at a given wavelength λ is spatially uncorrelated on length scales larger than λ=2 (measured from the surface of the scatterer) [3]. As a consequence, correlations on length scales smaller than λ=2 are inaccessible in standard light scattering, and the signal recorded in the far field is incoherent. With the advent of near-field optics and nanoscience in general, studies of thermal emitters revealed correlation lengths much shorter than λ [4][5][6][7][8]. Here, we show that similar effects underlie near-field Raman scattering and that correlation lengths much smaller than λ=2 can be extracted from measured data. Thus, near-field Raman scattering must take into account subwavelength correlations and associated interference effects.The coherence of lattice vibrations is of particular importance for graphene-based electronics since the scattering of optical phonons provides the main channel for relaxation of charge carriers and heat dissipation in this material system [9][10][11][12][13][14]. In this work, we derive a theory for near-field Raman scattering in one-and two-dimensional systems and apply the theory to pristine graphene and graphene edges. Our analysis is based on the tip-enhanced Raman scattering (TERS) scheme, in which a sharp metal tip is located near the sample at distances much smaller than λ. The tip acts as a broadband optical antenna, transferring the information contained in the spatially correlated (but non propagating) near field to the far field. We analyze the dependence of the scattered signal on the tip-sample separation distance and show that different vibrational modes (with distinct symmetries and dimensiona...

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“…Because a Lambertian source is almost fully incoherent, its coherence function µ L ( ρ 0d ) is expected to be very narrow, on the order of a wavelength [8]. We may therefore adopt the following approximations, valid to first order in ρ 0d :…”

Section: Obm Theorymentioning

confidence: 99%

Fast volumetric phase-gradient imaging in thick samples

Giese¹,

Ford²,

Mertz³

2014

Opt. Express

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Oblique back-illumination microscopy (OBM) provides high resolution, sub-surface phase-gradient images from arbitrarily thick samples. We present an image formation theory for OBM and demonstrate that OBM lends itself to volumetric imaging because of its capacity for optical sectioning. In particular, OBM can provide extended depth of field (EDOF) images from single exposures, by rapidly scanning the focal plane with an electrically tunable lens. These EDOF images can be further enhanced by deconvolution. We corroborate our theory with experimental volumetric images obtained from transparent bead samples and mouse cortical brain slices.

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Coherence properties of lambertian and non-lambertian sources*

Cited by 138 publications

References 7 publications

Near-Field Effects in Spatial Coherence of Thermal Sources

Near-Field Effects in Spatial Coherence of Thermal Sources

Theory of Spatial Coherence in Near-Field Raman Scattering

Fast volumetric phase-gradient imaging in thick samples

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