Spatial modulation spectroscopy. (a) Principle of the SMS incident light of power is focused near the diffraction limit in the sample plane on which are dispersed NPs. The spatial modulation of the particle induces a modulation of the transmitted light detected with a lock-in amplifier in phase with the sample modulation. (b) Spatial dependence of the transmission change induced by a gold NP at wavelength , detected either at frequency (left) or at frequency (right). (c) Corresponding cross-section of the transmission change at coordinate vs , either at frequency (left) or at frequency (right).
Experimental setup of SMS in the near-UV-visible, near IR range (300–900 nm). The splitter cube is only used for the observation of the sample (see the image of the sample on the top with the incident light spot) before further investigations. The objectives (M1 and M2) are identical and a schematic view is given in the insert on the left side of the figure.
(a) Map of gold, silver and latex NP sample at three different wavelengths , 550, 700 nm by modulating at frequency . (b) Broadband raw extinction spectrum of a gold NP of about 100 nm in diameter. (c) Cross-section of the transmission change along the direction (dotted line in the mapping at ).
(a) Comparison between experimental intensity profiles (black squares) and theoretical intensity profiles (gray lines) along both and directions. The insert displays the mapping of the spot (in the focal plane at ) deduced from transmission measurements using a single gold NP as a probe (see details in the main text). The color scale gives information about the differential transmission at the chopper modulation frequency. (b) Theoretical PSF intensity profiles for different wavelengths before (black lines) and after convolution (color lines) with the pinhole circular image.
(a) Raw extinction spectra of a gold NP deposited on Formvar obtained either from detection at frequency (on the positive or negative peak) or at frequency on the central peak. (b) Spectral calibration curves for [Eqs. (5)]. (c) Absolute extinction cross-sections deduced from the raw spectra (squares); theoretical extinction cross-sections using the Mie theory with Johnson and Christy’s gold dielectric functions for a spherical particle of diameter determined from the TEM analysis in a medium of effective index (bold gray line) or (light gray line). The high magnification image of the particle is shown in the inset.
Spectral dependence of the absolute extinction cross-section of an almost ellipsoidal gold NP deposited on Formvar resin. The two spectra (red circles and blue triangles) correspond to extreme positions of the SPR measured with two orthogonal polarization directions reported on the TEM image (inset). The experimental extinction cross-sections are in good agreement with DDA calculations (—○— and —△—) for a spheroid of large and small axes (deduced from TEM images) of 65 and 58 nm, respectively, in a medium of effective index .
(a) Spectral dependence of the absolute extinction cross-section of an almost spherical silver NP deposited on Formvar resin (black squares). The particle does not show any polarization effects. Its diameter deduced from TEM image (inset), assuming NP sphericity is , in good agreement with the size obtained from a comparison of the experimental cross-section with the Mie theory with Johnson and Christy’s dielectric constants (gray line). (b) Spectral dependence of the absolute cross-section of a small spherical silver NP with an optical diameter deduced from a comparison of the experimental cross-section with the Mie theory by using the Johnson and Christy’s dielectric constants (gray line). The experimental spectrum is recorded with a time constant .
(Right) Experimental mappings (at , 530, and 650 nm), obtained with a latex nanosphere used as a probe, directly correlated with the spatial intensity distribution in the focal plane. (Left) Black squares: normalized intensity profiles along the direction (corresponding to the signal along the white arrow in the mapping); gray lines: theoretical profiles averaged over the latex nanosphere.
Excepted signals ( and ) displayed as a function of , calculated from Eq. (4) with a fixed extinction cross-section , either with theoretical profiles (gray lines) or with experimental ones (squares).
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