336
I. I. Smolyaninov and V. N. Smolyaninova
thickness. If the lithographically-defined waveguide thickness d(r) is well controlled
as a function of the radial coordinate r, this behavior may be used to build non-trivial
birefringent transformation optics devices.
As illustrated in Fig. 13.20b, we were able to develop novel lithography techniques
which provide the required precise shape control d(r) of the dielectric photoresist on
a gold film substrate. We have used Shieply S1811 photoresist with refractive index n
~ 1.5 for our device fabrication. Since we wanted to create a gradual edge profile, we
have disregarded the typical procedures, which are employed to make the photoresist
edges sharp. Instead of contact printing, we have used the soft contact lithographic
mode in which a gap is left between the mask and the substrate. Due to diffraction
effects, this gap provided a gradient of UV light exposure at the mask edges. This
gradient in turn has led to a gradual change of the developed photoresist thickness.
During the experiments we have tried different degrees of separation between the
mask and the substrate, which produced progressively softer photoresist profile.
Underexposure and underdevelopment were also used to provide further variations
of sharpness of the waveguide profile edge.
Note that these techniques were also used previously to fabricate such TO-based
devices as a modified Luneburg lenses [28] (while, no image magnification has been
demonstrated in these experiments). However, as noted in [18], the transformation
optics designs of the Eaton and Maxwell fisheye lenses allow straightforward modification to incorporate image magnification.
Equation (13.9) defines the refractive index distribution in a Maxwell fisheye lens,
while an inverted Eaton lens is defined by (13.10). The refractive index distribution
in the fisheye lens is obtained via the stereographic projection of a sphere onto a
plane [16]. Therefore, points near the lens edge correspond to points located near
the equator of the sphere. As a result, as shown in the inset in Fig. 13.20d, these
points are imaged into points located near the opposite edges of the lens. The imaging properties of the inverted Eaton lens are similar. As illustrated in Fig. 13.20c, d,
two halves of either Maxwell fisheye or inverted Eaton lens may be brought together,
so that the difference in their R parameter will lead to increased magnification. The
image magnification in these cases may be defined as M = R 1 /R 2 . We have performed numerical simulations of image magnification in the case of M = 2, which
are presented in Fig. 13.20d. The sides of the lens appear not to play much role in
the imaging properties of the resulting structure. Therefore, the overall shape of the
lens may be altered to smooth the sharp corners. The resulting magnifying fisheye
lens shape is shown in Fig. 13.20b. Such lenses were fabricated using the lithographic technique described above, which is illustrated in the experimental images
in Fig. 13.21. In these experiments a near-field scanning optical microscope (NSOM)
fiber tip was scanned in close proximity to the lithographically formed magnifying
lenses. The point of the tip was used as an illumination source. Similar to the numerical simulations, an image of the NSOM tip was observed near the opposite edge of
the lens. The studied angular and polarization performance of the individual lenses
in the array agreed well with the theoretical prediction presented in Fig. 13.20c, d.
We should also point out [28] that a fisheye lens for TM light will operate as a
spatial filter for TE light due to near zero effective refractive index near the device
I. I. Smolyaninov and V. N. Smolyaninova
thickness. If the lithographically-defined waveguide thickness d(r) is well controlled
as a function of the radial coordinate r, this behavior may be used to build non-trivial
birefringent transformation optics devices.
As illustrated in Fig. 13.20b, we were able to develop novel lithography techniques
which provide the required precise shape control d(r) of the dielectric photoresist on
a gold film substrate. We have used Shieply S1811 photoresist with refractive index n
~ 1.5 for our device fabrication. Since we wanted to create a gradual edge profile, we
have disregarded the typical procedures, which are employed to make the photoresist
edges sharp. Instead of contact printing, we have used the soft contact lithographic
mode in which a gap is left between the mask and the substrate. Due to diffraction
effects, this gap provided a gradient of UV light exposure at the mask edges. This
gradient in turn has led to a gradual change of the developed photoresist thickness.
During the experiments we have tried different degrees of separation between the
mask and the substrate, which produced progressively softer photoresist profile.
Underexposure and underdevelopment were also used to provide further variations
of sharpness of the waveguide profile edge.
Note that these techniques were also used previously to fabricate such TO-based
devices as a modified Luneburg lenses [28] (while, no image magnification has been
demonstrated in these experiments). However, as noted in [18], the transformation
optics designs of the Eaton and Maxwell fisheye lenses allow straightforward modification to incorporate image magnification.
Equation (13.9) defines the refractive index distribution in a Maxwell fisheye lens,
while an inverted Eaton lens is defined by (13.10). The refractive index distribution
in the fisheye lens is obtained via the stereographic projection of a sphere onto a
plane [16]. Therefore, points near the lens edge correspond to points located near
the equator of the sphere. As a result, as shown in the inset in Fig. 13.20d, these
points are imaged into points located near the opposite edges of the lens. The imaging properties of the inverted Eaton lens are similar. As illustrated in Fig. 13.20c, d,
two halves of either Maxwell fisheye or inverted Eaton lens may be brought together,
so that the difference in their R parameter will lead to increased magnification. The
image magnification in these cases may be defined as M = R 1 /R 2 . We have performed numerical simulations of image magnification in the case of M = 2, which
are presented in Fig. 13.20d. The sides of the lens appear not to play much role in
the imaging properties of the resulting structure. Therefore, the overall shape of the
lens may be altered to smooth the sharp corners. The resulting magnifying fisheye
lens shape is shown in Fig. 13.20b. Such lenses were fabricated using the lithographic technique described above, which is illustrated in the experimental images
in Fig. 13.21. In these experiments a near-field scanning optical microscope (NSOM)
fiber tip was scanned in close proximity to the lithographically formed magnifying
lenses. The point of the tip was used as an illumination source. Similar to the numerical simulations, an image of the NSOM tip was observed near the opposite edge of
the lens. The studied angular and polarization performance of the individual lenses
in the array agreed well with the theoretical prediction presented in Fig. 13.20c, d.
We should also point out [28] that a fisheye lens for TM light will operate as a
spatial filter for TE light due to near zero effective refractive index near the device