34
R. W. Taylor and V. Sandoghdar
denotes the complex field reflectivity. In this instance, the detected signal depends
sensitively on the displacement h above the surface or index modulations of the
object.
Schemes such as phase contrast, differential interference contrast, reflection interference, or Mirau interference microscopy can all be described with the same underlying physics of (2.1) if one accounts for specific assignments of E r and E s . In the
conventional realizations of these microscopies, the emphasis has been on visualization of edge contours or refractive index modulations in super-wavelength objects
or features. It turns out, however, that interference microscopy can be even more
important for the detection of very small nanoparticles and single molecules, which
is particularly desirable within the context of nanoscience.
Let us take a spheroid with semiaxes a 1 , a 2 , a 3 much smaller than the wavelength of
light as a model nanoparticle. The response of this particle to light can be formulated
as E s ∝ α E r where
α i = 0 V
s − m
m + L i (( s − m )
(2.2)
denotes the complex particle polarizability along the semiaxis a i , and k signifies
the wavenumber [111]. The quantity V is the volume of the particle, and L i is the
depolarization factor along a i . For a sphere, a 1 = a 2 = a 3 and L i = 1/3. Complex
parameters s and m are the dielectric functions of the scatterer and the embedding medium respectively, and 0 is the dielectric constant. The denominator in this
expression can reach a minimum for metals such as silver and gold, thus enhancing their scattering response, but plasmonic enhancements only amount to about one
order of magnitude for realistic materials in the visible domain. Thus, the chief factor
responsible for the magnitude of α i is the particle volume V . The dependence on the
volume results in the scattering field scaling as the third power of the particle dimension, and hence the scattering intensity (I s = |E s |
2 ) drops with the sixth power of
the particle size.
When the particle is sufficiently small, I s becomes much weaker than the crossterm 2E r E s cos φ in (2.1) which is linearly proportional to the scattered field. As a
result, interferometric detection of scattering seems more favorable over dark-field
schemes. Indeed, (2.1) highlights the challenge in dark-field microscopy of detecting
small particles: the difference between the signal of a 50 nm nanoparticle and one
with 5 nm diameter is a factor of one million! We also remark that (2.1) describes
both homodyne and heterodyne detection schemes [112], where the particle field is
amplified by the larger field of the reference E r in the cross-term. We present a more
differentiated discussion on the comparison between the sensitivities of dark-field
and iSCAT detection later in this section.
The first report of iSCAT microscopy and spectroscopy of single nanoparticles
appeared in 2004 [73] using the configuration shown in Fig. 2.3c (see Sect. 2.4 for
an additional historical anecdote). More precisely, a supercontinuum laser beam was
focused on a glass substrate supporting gold nanoparticles (GNPs) as small as 5 nm
covered by immersion oil. This was quite an impressive step toward optical detec-
R. W. Taylor and V. Sandoghdar
denotes the complex field reflectivity. In this instance, the detected signal depends
sensitively on the displacement h above the surface or index modulations of the
object.
Schemes such as phase contrast, differential interference contrast, reflection interference, or Mirau interference microscopy can all be described with the same underlying physics of (2.1) if one accounts for specific assignments of E r and E s . In the
conventional realizations of these microscopies, the emphasis has been on visualization of edge contours or refractive index modulations in super-wavelength objects
or features. It turns out, however, that interference microscopy can be even more
important for the detection of very small nanoparticles and single molecules, which
is particularly desirable within the context of nanoscience.
Let us take a spheroid with semiaxes a 1 , a 2 , a 3 much smaller than the wavelength of
light as a model nanoparticle. The response of this particle to light can be formulated
as E s ∝ α E r where
α i = 0 V
s − m
m + L i (( s − m )
(2.2)
denotes the complex particle polarizability along the semiaxis a i , and k signifies
the wavenumber [111]. The quantity V is the volume of the particle, and L i is the
depolarization factor along a i . For a sphere, a 1 = a 2 = a 3 and L i = 1/3. Complex
parameters s and m are the dielectric functions of the scatterer and the embedding medium respectively, and 0 is the dielectric constant. The denominator in this
expression can reach a minimum for metals such as silver and gold, thus enhancing their scattering response, but plasmonic enhancements only amount to about one
order of magnitude for realistic materials in the visible domain. Thus, the chief factor
responsible for the magnitude of α i is the particle volume V . The dependence on the
volume results in the scattering field scaling as the third power of the particle dimension, and hence the scattering intensity (I s = |E s |
2 ) drops with the sixth power of
the particle size.
When the particle is sufficiently small, I s becomes much weaker than the crossterm 2E r E s cos φ in (2.1) which is linearly proportional to the scattered field. As a
result, interferometric detection of scattering seems more favorable over dark-field
schemes. Indeed, (2.1) highlights the challenge in dark-field microscopy of detecting
small particles: the difference between the signal of a 50 nm nanoparticle and one
with 5 nm diameter is a factor of one million! We also remark that (2.1) describes
both homodyne and heterodyne detection schemes [112], where the particle field is
amplified by the larger field of the reference E r in the cross-term. We present a more
differentiated discussion on the comparison between the sensitivities of dark-field
and iSCAT detection later in this section.
The first report of iSCAT microscopy and spectroscopy of single nanoparticles
appeared in 2004 [73] using the configuration shown in Fig. 2.3c (see Sect. 2.4 for
an additional historical anecdote). More precisely, a supercontinuum laser beam was
focused on a glass substrate supporting gold nanoparticles (GNPs) as small as 5 nm
covered by immersion oil. This was quite an impressive step toward optical detec-