16 Theoretical Foundations of Super-Resolution in Microspherical Nanoscopy
435
or plastics have been used. Super-resolution has been shown to persist under various illumination conditions. This includes transmission and reflection modes with
white light and monochromatic light, scanning confocal mode [33, 45], as well
as structured illumination [57] and imaging mediated by coupling with plasmonic
metasurfaces [43, 44, 100]. These developments should lead to the creation of a new
generation of inexpensive, fast, and very simple optical microscopes with resolution
laying between that of the standard microscopes (∼λ/2) and NSOM or AFM systems
(λ/20).
This consideration suggests that the quantification of the resolution is an important
issue for emerging microspherical nanoscopy. Experimental quantification of resolution was performed at various conditions using different criteria and the results
vary in a broad range, as illustrated in Table 16.1. The application of rigorous resolution criteria allows one to estimate conservatively that the experimental resolution
of nanoplasmonic objects can reach at least ∼λ/6 − λ/7 for virtual imaging through
the microspheres [34, 37, 38]. A similar resolution can be achieved by resonant coupling the FL objects to the localized surface plasmon resonances in the underlying
plasmonic metasurfaces [44, 100–102].
In this chapter, we provided a review of theoretical resolution quantification results
for imaging incoherent point sources based on the exact numerical solution of the
Maxwell equations [74–77, 80, 83]. This accounts for several new, compared to the
standard microscopy, effects: near-to-far-field conversion and excitation of WGMs
in dielectric microspheres [53]. The results are quite intriguing and puzzling because
they predict a lower resolution compared to the experimental values observed in
nanoplasmonic structures. For low-index silica microspheres in air, the nonresonant
and resonant resolutions can be estimated as ∼λ/3 and ∼λ/4, respectively. For highindex (n = 2) microspheres immersed in liquids or dielectric slabs, the resolution
can be improved by the factor determined by the background index for the same
index contrast [53]. This puts the theoretical resolution in the resonant case closer to
the experimentally reported values. However, this resolution still remains somewhat
lower compared to the experiment and that raises a very interesting question about
the fundamental nature of super-resolution in microspherical nanoscopy.
One way to answer this question is to refer to an enhanced fraction of near fields
in nanoplasmonic structures under resonance with LSPRs in metallic nanodisks and
other similar objects. These objects (or illumination provided in near-field zone of
such objects) are fundamentally different from the dipole emission considered in our
theoretical consideration. It is quite possible that the super-resolution of such objects
is influenced by the increased near fields under resonance with the LSPRs spectral
peaks in nanoplasmonic arrays. One fact which points toward this hypothesis is an
experimental observation that the super-resolution imaging of FL nanospheres at
the top of nanoplasmonic arrays becomes possible only for extremely small gaps
and periods of such arrays [44, 101, 102]. Another fact which strongly supports
this interpretation is a preliminary observation that the resonance between the FL
band of dielectric nanospheres and LSPRs in underlying nanoplasmonic arrays is
indeed required for super-resolution imaging of such objects [102]. However, these
experiments are in their beginning stage and more work is required to prove the
435
or plastics have been used. Super-resolution has been shown to persist under various illumination conditions. This includes transmission and reflection modes with
white light and monochromatic light, scanning confocal mode [33, 45], as well
as structured illumination [57] and imaging mediated by coupling with plasmonic
metasurfaces [43, 44, 100]. These developments should lead to the creation of a new
generation of inexpensive, fast, and very simple optical microscopes with resolution
laying between that of the standard microscopes (∼λ/2) and NSOM or AFM systems
(λ/20).
This consideration suggests that the quantification of the resolution is an important
issue for emerging microspherical nanoscopy. Experimental quantification of resolution was performed at various conditions using different criteria and the results
vary in a broad range, as illustrated in Table 16.1. The application of rigorous resolution criteria allows one to estimate conservatively that the experimental resolution
of nanoplasmonic objects can reach at least ∼λ/6 − λ/7 for virtual imaging through
the microspheres [34, 37, 38]. A similar resolution can be achieved by resonant coupling the FL objects to the localized surface plasmon resonances in the underlying
plasmonic metasurfaces [44, 100–102].
In this chapter, we provided a review of theoretical resolution quantification results
for imaging incoherent point sources based on the exact numerical solution of the
Maxwell equations [74–77, 80, 83]. This accounts for several new, compared to the
standard microscopy, effects: near-to-far-field conversion and excitation of WGMs
in dielectric microspheres [53]. The results are quite intriguing and puzzling because
they predict a lower resolution compared to the experimental values observed in
nanoplasmonic structures. For low-index silica microspheres in air, the nonresonant
and resonant resolutions can be estimated as ∼λ/3 and ∼λ/4, respectively. For highindex (n = 2) microspheres immersed in liquids or dielectric slabs, the resolution
can be improved by the factor determined by the background index for the same
index contrast [53]. This puts the theoretical resolution in the resonant case closer to
the experimentally reported values. However, this resolution still remains somewhat
lower compared to the experiment and that raises a very interesting question about
the fundamental nature of super-resolution in microspherical nanoscopy.
One way to answer this question is to refer to an enhanced fraction of near fields
in nanoplasmonic structures under resonance with LSPRs in metallic nanodisks and
other similar objects. These objects (or illumination provided in near-field zone of
such objects) are fundamentally different from the dipole emission considered in our
theoretical consideration. It is quite possible that the super-resolution of such objects
is influenced by the increased near fields under resonance with the LSPRs spectral
peaks in nanoplasmonic arrays. One fact which points toward this hypothesis is an
experimental observation that the super-resolution imaging of FL nanospheres at
the top of nanoplasmonic arrays becomes possible only for extremely small gaps
and periods of such arrays [44, 101, 102]. Another fact which strongly supports
this interpretation is a preliminary observation that the resonance between the FL
band of dielectric nanospheres and LSPRs in underlying nanoplasmonic arrays is
indeed required for super-resolution imaging of such objects [102]. However, these
experiments are in their beginning stage and more work is required to prove the