422
A. V. Maslov and V. N. Astratov
be resolved if the plane of focus is below x/λ ≈ −7. The in-phase source cannot
be resolved at all for the given parameters. The out-of-phase sources clearly create
images with the best resolution. In fact, the resolution persists if one moves the
out-of-phase sources significantly closer but the emission intensity reduces quite
drastically and the peak-to-peak distance will not be equal to the distance between
the sources. The coherent emission is likely to be present when imaging plasmonic
structures.
16.5 Beyond Solid Immersion Lens: Plasmonic
Contributions
Previous analysis in this Chapter is based on exact numerical solution of the Maxwell
equations and the textbook definition of resolution introduced for incoherent point
sources. Perhaps not surprisingly, we showed that the classical resolution in MN
is reasonably well described by the SIL concept. It should be noted that the SIL
concept has been introduced in the beginning of the 1990s for hemispherical and
superspherical lens shapes which have the advantage of collecting the light from
the object in half of the space with index n >1, meaning that θ approaching π/2
in the Abbe’s limit λ/(2n sin θ). These lenses are represented by hemispheres and
truncated spheres, respectively, and they have a flat base which should be closely
attached to the substrate to provide the optical near-field coupling conditions with
the object located on this substrate. Similar concept can be applied for imaging by
dielectric microspheres. Due to their compact size, however, they have much smaller
near-field coupling region with the substrate. At first glance, it can be viewed as a
disadvantage of microspheres due to the resulting field of view being limited by a
quarter of their diameters. However, the smallness of the contact region simplifies
the minimization of the object-to-lens distance enabling better near-field coupling.
Also, the spheres can be translated along the substrate by a variety of techniques, and
the corresponding super-resolved images can be stitched increasing the field of view.
Another potential concern regarding the resolution comparison of MN with hemispherical and superspherical SILs is related to spherical aberrations of microspheres.
However, for mesoscale spheres, the problem of imaging can be solved exactly using
numerical methods which means that the images are calculated taking into account
all aberrations.
The results of resolution quantification for microspheres obtained by numerical
solution of the Maxwell equations are found to be in a reasonable agreement with
the SIL model. The classical resolution of mesoscale silica spheres with n ∼ 1.5 was
found to be close to ∼λ/3. The resolution of high-index (n ∼ 2) liquid-immersed
or slab-embedded microspheres with the same index contrast as silica in air can
be increased up to ∼λ/5.6 in the case of imaging performed under resonance with
WGMs. The nonresonant resolution is slightly lower, but it is still rather close to
the estimations (∼λ/4) based on the SIL model. Coherent imaging under oblique
A. V. Maslov and V. N. Astratov
be resolved if the plane of focus is below x/λ ≈ −7. The in-phase source cannot
be resolved at all for the given parameters. The out-of-phase sources clearly create
images with the best resolution. In fact, the resolution persists if one moves the
out-of-phase sources significantly closer but the emission intensity reduces quite
drastically and the peak-to-peak distance will not be equal to the distance between
the sources. The coherent emission is likely to be present when imaging plasmonic
structures.
16.5 Beyond Solid Immersion Lens: Plasmonic
Contributions
Previous analysis in this Chapter is based on exact numerical solution of the Maxwell
equations and the textbook definition of resolution introduced for incoherent point
sources. Perhaps not surprisingly, we showed that the classical resolution in MN
is reasonably well described by the SIL concept. It should be noted that the SIL
concept has been introduced in the beginning of the 1990s for hemispherical and
superspherical lens shapes which have the advantage of collecting the light from
the object in half of the space with index n >1, meaning that θ approaching π/2
in the Abbe’s limit λ/(2n sin θ). These lenses are represented by hemispheres and
truncated spheres, respectively, and they have a flat base which should be closely
attached to the substrate to provide the optical near-field coupling conditions with
the object located on this substrate. Similar concept can be applied for imaging by
dielectric microspheres. Due to their compact size, however, they have much smaller
near-field coupling region with the substrate. At first glance, it can be viewed as a
disadvantage of microspheres due to the resulting field of view being limited by a
quarter of their diameters. However, the smallness of the contact region simplifies
the minimization of the object-to-lens distance enabling better near-field coupling.
Also, the spheres can be translated along the substrate by a variety of techniques, and
the corresponding super-resolved images can be stitched increasing the field of view.
Another potential concern regarding the resolution comparison of MN with hemispherical and superspherical SILs is related to spherical aberrations of microspheres.
However, for mesoscale spheres, the problem of imaging can be solved exactly using
numerical methods which means that the images are calculated taking into account
all aberrations.
The results of resolution quantification for microspheres obtained by numerical
solution of the Maxwell equations are found to be in a reasonable agreement with
the SIL model. The classical resolution of mesoscale silica spheres with n ∼ 1.5 was
found to be close to ∼λ/3. The resolution of high-index (n ∼ 2) liquid-immersed
or slab-embedded microspheres with the same index contrast as silica in air can
be increased up to ∼λ/5.6 in the case of imaging performed under resonance with
WGMs. The nonresonant resolution is slightly lower, but it is still rather close to
the estimations (∼λ/4) based on the SIL model. Coherent imaging under oblique