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A. V. Maslov and V. N. Astratov
LSPRs in the underlying array [44] rather than due to collective bandstructure coupling effects. A particularly attractive feature of the latter mechanism is that it does
not require post-imaging processing for reconstructing the super-resolved images.
Most of this chapter (Sects. 16.2, 16.3, and 16.4) is devoted to the theoretical models
of the observed super-resolution and the remaining part (Sect. 16.5) reviews several experimental results related to a combination of microspherical nanoscopy with
nanoplasmonics and plasmonic metasurfaces.
16.1.2 Theoretical Modeling
The ability to see deeply subwavelength features through dielectric microspheres
naturally prompted a search for its physical explanation. It was suggested that the
observed super-resolution is related to the ability of microspheres to form photonic
nanojets [29]. If the width of photonic nanojets is strongly subwavelength, then the
image produced by a point source can also be subwavelength. The sharp focusing as the origin of super-resolution was also used in several subsequent studies
[58–68]. However, the quantitative analysis reveals some problems with this analogy, including the fact that the width of photonic nanojets is not significantly smaller
than the wavelength [69–73]. When the nanojet maximum is away from the surface,
the nanojet width is ∼λ/2. When the nanojet maximum is on the surface, it becomes
narrow and its width can be as small as λ/(2n), where n is the refractive index of the
microsphere. Thus, for typical SiO 2 microspheres with index n = 1.46, the width
becomes ∼λ/3 which is significantly larger than the experimental resolution values.
Another issue is that the focusing of light and imaging are two different problems. It
was also suggested that the super-resolution can be related to the transformation of
the evanescent waves to propagating at the curved surface of the microsphere [74].
If this mechanism works, then the microsphere can perform as a near-field probe
similar to that in NSOM.
With the lack of a simple physical explanation of the super-resolution in microspherical nanoscopy, some efforts have been undertaken to model it. The imaging
of a point source near a microsphere was addressed using the multipole expansion
based on spherical harmonics [75]. The theoretical results for a microsphere with
D = 4.74 µm, n = 1.46 showed that one cannot reach sub-100 nm resolution using
the standard two-point resolution criterion. Slightly higher resolution, but still below
the values claimed in the experiments, was achieved using microsphere resonances
(the second radial order resonance was considered). The imaging of dipoles near
microspheres was also studied using finite element method (FEM) [76]. The resolution and magnification were studied for various refractive indices of the microsphere
and the substrate as well as for the different dipole orientations. The resolution of
dipoles was found to be in the range 0.24λ − 0.3λ. It was also suggested that since
small metal nanostructures can emit as some effective dipoles located in their centers,
then the center-to-center separation of 0.24λ between the metal nanostructures can
correspond to a much smaller edge-to-edge distance which was perhaps observed
A. V. Maslov and V. N. Astratov
LSPRs in the underlying array [44] rather than due to collective bandstructure coupling effects. A particularly attractive feature of the latter mechanism is that it does
not require post-imaging processing for reconstructing the super-resolved images.
Most of this chapter (Sects. 16.2, 16.3, and 16.4) is devoted to the theoretical models
of the observed super-resolution and the remaining part (Sect. 16.5) reviews several experimental results related to a combination of microspherical nanoscopy with
nanoplasmonics and plasmonic metasurfaces.
16.1.2 Theoretical Modeling
The ability to see deeply subwavelength features through dielectric microspheres
naturally prompted a search for its physical explanation. It was suggested that the
observed super-resolution is related to the ability of microspheres to form photonic
nanojets [29]. If the width of photonic nanojets is strongly subwavelength, then the
image produced by a point source can also be subwavelength. The sharp focusing as the origin of super-resolution was also used in several subsequent studies
[58–68]. However, the quantitative analysis reveals some problems with this analogy, including the fact that the width of photonic nanojets is not significantly smaller
than the wavelength [69–73]. When the nanojet maximum is away from the surface,
the nanojet width is ∼λ/2. When the nanojet maximum is on the surface, it becomes
narrow and its width can be as small as λ/(2n), where n is the refractive index of the
microsphere. Thus, for typical SiO 2 microspheres with index n = 1.46, the width
becomes ∼λ/3 which is significantly larger than the experimental resolution values.
Another issue is that the focusing of light and imaging are two different problems. It
was also suggested that the super-resolution can be related to the transformation of
the evanescent waves to propagating at the curved surface of the microsphere [74].
If this mechanism works, then the microsphere can perform as a near-field probe
similar to that in NSOM.
With the lack of a simple physical explanation of the super-resolution in microspherical nanoscopy, some efforts have been undertaken to model it. The imaging
of a point source near a microsphere was addressed using the multipole expansion
based on spherical harmonics [75]. The theoretical results for a microsphere with
D = 4.74 µm, n = 1.46 showed that one cannot reach sub-100 nm resolution using
the standard two-point resolution criterion. Slightly higher resolution, but still below
the values claimed in the experiments, was achieved using microsphere resonances
(the second radial order resonance was considered). The imaging of dipoles near
microspheres was also studied using finite element method (FEM) [76]. The resolution and magnification were studied for various refractive indices of the microsphere
and the substrate as well as for the different dipole orientations. The resolution of
dipoles was found to be in the range 0.24λ − 0.3λ. It was also suggested that since
small metal nanostructures can emit as some effective dipoles located in their centers,
then the center-to-center separation of 0.24λ between the metal nanostructures can
correspond to a much smaller edge-to-edge distance which was perhaps observed