hv
photonics
Article
Lithographically Fabricated Magnifying Maxwell
Fisheye Lenses
Vera Smolyaninova 1, *, Christopher Jensen 1 , William Zimmerman 1 , Anthony Johnson 1 ,
David Schaefer 1 and Igor Smolyaninov 2
1
2
*
Department of Physics, Astronomy and Geosciences, Towson University, 8000 York Rd., Towson, MD 21252,
USA; [email protected] (C.J.); [email protected] (W.Z.);
[email protected] (A.J.); [email protected] (D.S.)
Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA;
[email protected]
Correspondence: [email protected]; Tel.: +1-410-704-2608
Received: 11 February 2016; Accepted: 3 March 2016; Published: 8 March 2016
Abstract: Recently suggested magnifying Maxwell fisheye lenses, which are made of two half-lenses
of different radii, have been fabricated and characterized. The lens action is based on control of
polarization-dependent effective refractive index in a lithographically formed tapered waveguide.
We have studied wavelength and polarization dependent performance of the lenses, and their
potential applications in waveguide mode sorting.
Keywords: metamaterials; transformation optics; microscopy; waveguide; mode sorting
1. Introduction
Transformation optics (TO) has recently become a useful methodology for the design of unusual
optical devices, such as novel metamaterial lenses and invisibility cloaks. Unfortunately, typical
TO designs require metamaterials with low-loss, broadband performance, which appear difficult
to develop. These difficulties are especially severe in the visible frequency range where good
magnetic performance is limited. On the other hand, very recently we have demonstrated that many
transformation optics and metamaterial-based devices requiring anisotropic dielectric permittivity and
magnetic permeability may be emulated by specially designed tapered waveguides [1]. This approach
leads to low-loss broadband performance in the visible frequency range, which is difficult to achieve
by other means. We have applied this technique to broadband electromagnetic cloaking in the visible
range [1] and successfully extended it to birefrigent TO devices, which perform useful and different
functions for mutually orthogonal polarization states of light [2]. Therefore, such use of tapered
waveguides belongs to the broadly-defined transformation optics approach. In this paper we have
applied this approach to lithographically fabricated magnifying Maxwell fisheye lenses, which were
originally introduced in a microdroplet form [3].
2. Materials and Methods
Unlike the earlier microdroplet design, which is difficult to fabricate and control, our current
design is based on lithographically defined metal/dielectric waveguides. Adiabatic variations of the
waveguide shape enable control of the effective refractive indices experienced by the transverse electric
(TE) and transverse magnetic (TM) modes propagating inside the waveguides, as shown in Figure 1a.
They are defined as neff = kω/c for each polarization, where the k vector at a given frequency ω is
calculated via the boundary conditions at two interfaces as follows:
ˆ
k1
ik2
´
εm
ε
˙ˆ
ik2
k3 ´
ε
Photonics 2016, 3, 8; doi:10.3390/photonics3010008
˙
ˆ
e
´ik2 d
“
k1
ik2
`
εm
ε
˙ˆ
ik2
k3 `
ε
˙
eik2 d
(1)
www.mdpi.com/journal/photonics
Photonics 2016, 3, 8
2 of 7
Photonics 2016, 3, 8
2 of 7
for the TM, and
k1  ik 2 k3  ik 2 eik2d  k1  ik 2 k3  ik 2 eik2d
(2)
for the TM, and
2 d “ pk ` ik q pk ` ik q eik 2 d
pk1 ´modes,
e´ikvertical
ik2 q pk3where
´ ik2 q the
(2)
for the TE polarized guided
of2 the wavevector ki are defined
2
3
1 components
as:
for the TE polarized guided modes, where the vertical components of the wavevector ki are defined as:
1/ 2

 2  1{ 2

k1 ˆ k 2   m ω 22 ˙
k1 “ k2 ´ ε m c2 
c
(3)
(3)
1/ 2
2
2
1{2
k 2 ˆω 22   k ˙
k2 “  c2 ε ´ k2 
c
1/ 2
ˆ 2 2 2˙1{2
k3   k2 ω 2 
k3 “ k ´ c2

c 
(4)
(4)
(5)
(5)
in
in metal,
metal, dielectric,
dielectric, and
and air,
air, respectively.
respectively. As
As illustrated
illustrated in
in Figure
Figure 1a,
1a, effective
effective birefringence
birefringence for
for the
the
lowest
guided
TM
and
TE
modes
appears
to
be
very
strong
at
waveguide
thickness
d
<
0.4
µm,
and
lowest guided TM and TE modes appears to be very strong at waveguide thickness d < 0.4 μm, and
both
bothpolarizations
polarizationsdemonstrate
demonstratestrong
strongindex
indexdependence
dependenceon
onthe
thewaveguide
waveguidethickness.
thickness. This
This behavior
behavior
may
maybe
beused
usedin
in building
building non-trivial
non-trivialbirefringent
birefringentTO
TOdevices
devicesififaawaveguide
waveguidethickness
thicknessas
asaafunction
functionof
of
spatial
coordinates
d(r)
may
be
controlled
lithographically
with
enough
precision.
spatial coordinates d(r) may be controlled lithographically with enough precision.
Figure1.1.(a)
(a)Effective
Effectiverefractive
refractiveindex
index
plotted
a function
of thickness
a tapered
waveguide
for
Figure
plotted
as as
a function
of thickness
of aof
tapered
waveguide
for TM
TM
and
TE
polarizations.
The
waveguide
geometry
is
shown
in
the
inset.
(b)
Atomic
Force
and TE polarizations. The waveguide geometry is shown in the inset. (b) Atomic Force Microscope
Microscope
image of a lithographically
defined
individual
magnifying
fisheye
lens
made of
(AFM)
image(AFM)
of a lithographically
defined individual
magnifying
fisheye
lens made
of two
half-lenses
two
half-lenses
radii. (c)
Corresponding
distribution
of theindex.
effective
refractive
of
different
radii. of
(c)different
Corresponding
spatial
distributionspatial
of the effective
refractive
(d) COMSOL
index. (d) COMSOL
Multiphysics
simulation
the fisheye lens
magnification.
The insets
Multiphysics
simulation
of the fisheye
lens imageofmagnification.
Theimage
insets illustrate
ray propagation
illustrate
ray propagation
in the original
the magnifying fisheye lenses.
in
the original
and the magnifying
fisheyeand
lenses.
We have developed a lithography technique which enables such d(r) shape control of the
We have developed a lithography technique which enables such d(r) shape control of the dielectric
dielectric photoresist on gold film substrate, as illustrated in Figure 1b. Shieply S1811 photoresist
photoresist on gold film substrate, as illustrated in Figure 1b. Shieply S1811 photoresist having
having refractive index n ~ 1.5 was used for device fabrication. In traditional lithographic
refractive index n ~ 1.5 was used for device fabrication. In traditional lithographic applications for
applications for the best results of pattern transfer the profile of resist should be rectangular or even
the best results of pattern transfer the profile of resist should be rectangular or even with overhang.
with overhang. Our purpose is different. We want to create a more gradual edge profile. This can be
Our purpose is different. We want to create a more gradual edge profile. This can be done by
done by disregarding typical precautions employed to make the edges sharp. Instead of contact
disregarding typical precautions employed to make the edges sharp. Instead of contact printing (when
Photonics 2016, 3, 8
3 of 7
mask is touching the substrate), we used soft contact mode (with the gap between the mask and the
substrate). This allows for the gradient of exposure due to the diffraction at the edges, which leads to a
gradual change of thickness of the developed photoresist. Different degrees of separation between
the mask and the substrate produced progressively softer photoresist profile. Further variations of
the profile were achieved by use of underexposure and underdevelopment, which produce much
softer photoresist edges. This technique has been used previously to fabricate such TO-based devices
as a modified Luneburg lens [2]. However, no image magnification has been demonstrated in these
experiments. On the other hand, as was noted in [3], it is relatively straightforward to incorporate
image magnification into such TO lens designs as Eaton and Maxwell fisheye lenses.
The refractive index distribution in a Maxwell fisheye lens is defined as
ˆ
n “ 2n1
r2
1` 2
R
˙´1
(6)
at r < R, where 2n1 is the refractive index at the center of the lens, and R is the scale factor. A reflective
surface is assumed to be placed at r = R, so that n < 1 values of the refractive index do not need to be
used. In our experiments the role of such reflective surface is played by the lens edge. On the other
hand, an inverted Eaton lens [4] is defined as n = n1 for r < R, and
ˆ
n “ n1
˙1{2
2R
´1
r
(7)
for r > R. Since the refractive index distribution in the fisheye lens is obtained via the stereographic
projection of a sphere onto a plane [5,6], points near the lens edge correspond to points located near
the equator of the sphere. Therefore, these points are imaged into points located near the opposite lens
edge, as shown in the inset in Figure 1d. The inverted Eaton lens has similar imaging properties.
As demonstrated in [3], both refractive index distributions may be emulated with a suitable d(r)
profile of a thin dielectric placed on top of a metal film, which is also evident from Figure 1a. As shown
in Figure 1c,d, two halves of either Maxwell fisheye or inverted Eaton lens having different values
of parameter R may be brought together to achieve image magnification. The image magnification
in this case is M = R1 /R2 . Our numerical simulations in the case of M = 2 are presented. Since the
sides of the lens play no role in imaging, the overall shape of the imaging device can be altered to
smooth the sharp corners, resulting in the magnifying fisheye lens shape shown in Figure 1b, which
was fabricated using the lithographic technique described above.
3. Results
Experimental images in Figure 2 demonstrate measured performance of the designed magnifying
fisheye lenses. In these experiments a near-field scanning optical microscope (NSOM) fiber tip was
brought in close proximity to the arrays of lithographically formed TO devices and used as an
illumination source. As expected from the numerical simulations, an image of the NSOM tip was easy
to observe at the opposite edge of the lens. Angular and polarization testing of individual lenses in the
array agrees well with theoretical modelling presented in Figure 1c,d. As illustrated by Figure 1a, the
same d(r) profile produces a different refractive index distribution for TM and TE polarized light.
Photonics 2016, 3, 8
4 of 7
Photonics 2016, 3, 8
4 of 7
Photonics 2016, 3, 8
4 of 7
Figure
testing of
of angular
(a,b) and
Figure 2.
2. Experimental
Experimental testing
angular (a,b)
and polarization
polarization (c)
(c) performance
performance of
of the
the magnifying
magnifying
fisheye
488 nm.
nm. The
The scale
scale bar
bar length
length is
is 55 μm
µm in
in all
all images.
images.
fisheye lenses
lenses at
at λ
λ=
= 488
Image
and magnification
of thenear
fabricated
magnifying
Maxwell
fisheye
lenses
Due
to resolution
near zero effective
refractive index
the device
edge, a fisheye
lens
for TM
lightmay
will
be
evaluated
based
on
images
of
lens
testing
presented
in
Figure
3.
Experimental
testing
of
operate as a spatial (directional) filter for TE light [2]. We should note that while the NSOM fibertwo
tip
fisheyeunpolarized
lenses having
M = response
R1/R2 ratio
is shown
these images.
image
emits
light,different
polarization
of the
image in
produced
by a TOThe
device
canresolution
be clearly
appears toFigure
be close
to diffraction-limited
(~ 0.6λ
488
nm),
while
image
magnification
close tolight.
the
2. Experimental
of angular
(a,b)
and
polarization
(c)
performance
of the magnifying
separated
into
the
TM
and TEtesting
contributions
withat
respect
to the
plane
of incidence
of theissource
fisheye
lenses
at
λ
=
488
nm.
The
scale
bar
length
is
5
μm
in
all
images.
design
values
M
=
2
and
M
=
3,
respectively.
We
should
also
note
a
very
broad
(almost
180°)
angular
Polarization behavior of lenses in Figure 2 demonstrates excellent agreement with theory.
rangeImage
of theresolution
magnifying
fisheye
lens operation.
and
magnification
of the fabricated magnifying Maxwell fisheye lenses may be
Image resolution and magnification of the fabricated magnifying Maxwell fisheye lenses may
evaluated based on images of lens testing presented in Figure 3. Experimental testing of two fisheye
be evaluated based on images of lens testing presented in Figure 3. Experimental testing of two
lensesfisheye
havinglenses
different
M =different
R1 /R2 ratio
is1/R
shown
in these images. The image resolution appears to be
having
M = R
2 ratio is shown in these images. The image resolution
close appears
to diffraction-limited
(~
0.6λ
at
488
nm),
while
image
is close to the
design
values
to be close to diffraction-limited (~ 0.6λ at 488
nm), magnification
while image magnification
is close
to the
˝
M = 2design
and M
= 3, respectively.
should also
note
a very
180
) angular
values
M = 2 and M = We
3, respectively.
We
should
alsobroad
note a (almost
very broad
(almost
180°) range
angularof the
magnifying
lens operation.
range offisheye
the magnifying
fisheye lens operation.
Figure 3. Experimental testing of image magnification at λ = 488 nm of two fisheye lenses with
different M = R1/R2 ratio: (a,b) Original magnified images obtained at different source positions. The
location of image and source are indicated by the arrows. (c) Digital overlap of the images in (a) and
(b) indicates that image magnification is close to the design value M = 2. (d,e) Similar original images
Figure
3. Experimental
testing
of image
magnification
λ = nm
488 of
nmtwo
of fisheye
two fisheye
lenses
Figure
3. Experimental
testing
of image
magnification
at λat= 488
lenses
withwith
different
and (f) the digital overlap image obtained with a different magnifying lens designed for M = 3.
M
=
R
1/R2Original
ratio:
(a,b)
Original
magnified
images
obtained
at
different
source
positions.
The of
M = Rdifferent
/R
ratio:
(a,b)
magnified
images
obtained
at
different
source
positions.
The
location
1
2
of image
source by
arethe
indicated
by(c)
theDigital
arrows.overlap
(c) Digital
of the
(a) indicates
and
imagelocation
and source
are and
indicated
arrows.
of overlap
the images
inimages
(a) andin(b)
The (b)
projected
broadband
performance
the magnifying
fisheye lenses
has been
indicates that
image magnification
closeof
to the
value M = Maxwell
2. (d,e) Similar
that image
magnification
is close to the isdesign
valuedesign
M = 2.
(d,e) Similar
original original
imagesimages
and (f) the
verified inand
the
λ
=
488–633
nm
range.
Examples
of
such
testing
at
515
nm
and
633
nm
are
presented
(f) the digital overlap image obtained with a different magnifying lens designed for M = 3.
digital overlap image obtained with a different magnifying lens designed for M = 3.
in Figure 4 (compare these images with Figure 2a,b obtained at 488 nm). This experimental result
The projected
broadband
of the magnifying
Maxwell
fisheye lenses
has been [1].
may be understood
similar
to theperformance
broadband cloaking
performance
demonstrated
in Reference
verified
in
the
λ
=
488–633
nm
range.
Examples
of
such
testing
at
515
nm
and
633
nm
are
presented
In all cases the effective refractive index of the tapered waveguide scales as d/λ at small d. Thus, light
in Figure 4 (compare these images with Figure 2a,b obtained at 488 nm). This experimental result
may be understood similar to the broadband cloaking performance demonstrated in Reference [1].
In all cases the effective refractive index of the tapered waveguide scales as d/λ at small d. Thus, light
Photonics 2016, 3, 8
5 of 7
The projected broadband performance of the magnifying Maxwell fisheye lenses has been verified
in the λ = 488–633 nm range. Examples of such testing at 515 nm and 633 nm are presented in
Figure 4 (compare these images with Figure 2a,b obtained at 488 nm). This experimental result may
be
understood similar to the broadband cloaking performance demonstrated in Reference [1]. In
all
Photonics 2016, 3, 8
5 of 7
Photonics
2016,
3, 8
5 ofat7
cases
the
effective
refractive index of the tapered waveguide scales as d/λ at small d. Thus, light
these
wavelengths
(488
nm,
515
at these
wavelengths
(488
nm,
515nm
nmand
and633
633nm)
nm)perceives
perceivesthe
thewaveguide
waveguideedge
edge as
as having
having similar
similar
at these wavelengths
(488
nm, 515index
nm and
633wavelengths.
nm) perceives
the
waveguide
edge(see
as having
similar
distribution
of
effective
refractive
at
all
We
have
also
verified
Figure
distribution of effective refractive index at all wavelengths. We have also verified (see Figure 5)
5) that
that
distribution
of
effective
refractive
index
at
all
wavelengths.
We
have
also
verified
(see
Figure
5) that
the
the same
same lens
lens used
used in
in reverse
reverse direction
direction may
may be
be utilized
utilized to
to achieve
achieve image
image reduction.
reduction. This
This fact
fact is
is not
not
the same
lens
used
ingeometry
reverse direction
may
be
utilizedtogether”
to achieve
image
reduction.
This factfisheye
is not
trivial
since
the
lens
is
obtained
by
“gluing
two
halves
of
the
Maxwell
trivial since the lens geometry is obtained by “gluing together” two halves of the Maxwell fisheye
trivial since the
lens geometry
is obtained
by “gluing
two halves
the Maxwell
lenses
different
radii, which
which
fromtogether”
the ray
ray optics
optics
point of
ofofview
view
may lead
leadfisheye
to ray
ray
lenses having
having considerably
considerably different
radii,
from
the
point
may
to
lenses
having
considerably
different
radii,
which
from
the
ray
optics
point
of
view
may
lead
to
ray
scattering
such
anan
arrangement
of the
magnifying
fisheye
lens lens
may may
find
scattering by
bythe
thelens
lensedges.
edges.Potentially,
Potentially,
such
arrangement
of the
magnifying
fisheye
scattering
by
the
lens
edges.
Potentially,
such
an
arrangement
of
the
magnifying
fisheye
lens
may
lithographic
applications.
find lithographic
applications.
find lithographic applications.
Figure 4. Experimental verification of broadband performance of the magnifying Maxwell fisheye
Figure
broadband
performance
of the
magnifying
Maxwell
fisheye
lens.
Figure 4.
4. Experimental
Experimentalverification
verificationofof
broadband
performance
of the
magnifying
Maxwell
fisheye
lens. (a,b) Images taken at λ = 515 nm. (c,d) Images taken at λ = 633 nm. The scale bar length is 5 μm
(a,b)
Images
taken
at
λ
=
515
nm.
(c,d)
Images
taken
at
λ
=
633
nm.
The
scale
bar
length
is
5
µm
in
lens. (a,b) Images taken at λ = 515 nm. (c,d) Images taken at λ = 633 nm. The scale bar length is 5 μm
in
all
images.
all
images.
in all
images.
Figure 5. Operation of the magnifying Maxwell fisheye lens in reverse direction, which leads to
Figure 5. Operation of the magnifying Maxwell fisheye lens in reverse direction, which leads to
Figure
5. Operation
of the magnifying
Maxwell
fisheye
lensfisheye
in reverse
which using
leads
image reduction.
(a) COMSOL
Multiphysics
simulation
of the
lens direction,
image reduction
image reduction. (a) COMSOL Multiphysics simulation of the fisheye lens image reduction using
to
image index
reduction.
(a) COMSOL
Multiphysics
simulation of
the fisheye
image reduction
refractive
distribution
corresponding
to the experimental
variation
of thelens
waveguide
thickness.
refractive
index distribution
corresponding
to the experimental
variationvariation
of the waveguide
thickness.
using
refractive
index
distribution
corresponding
to the fisheye
experimental
of the
waveguide
(b,c) Experimental
testing
of angular
performance of
lens used in reverse
direction.
λ=
(b,c)
Experimental
testing
of
angular
performance
of
the
fisheye
lens
used
in
reverse
direction.
λ=
thickness.
(b,c)
Experimental
testing
of
angular
performance
of
the
fisheye
lens
used
in
reverse
488 nm. Image reduction factor M = 1/2 is observed. The scale bar length is 5 μm in all images.
488 nm. Image
reduction
factor
M = 1/2 isfactor
observed.
Theisscale
bar length
5 μmbar
in length
all images.
direction.
λ = 488
nm. Image
reduction
M = 1/2
observed.
Theisscale
is 5 µm in
all images.
4. Discussion
4. Discussion
Since the developed lithographic Maxwell fisheye lenses are based on tapered waveguide
4. Discussion
Since the developed lithographic Maxwell fisheye lenses are based on tapered waveguide
geometry, their high magnification and very compact design are highly suitable in waveguide mode
geometry, their high magnification and very compact design are highly suitable in waveguide mode
Since
the developed
lithographic
Maxwell
fisheye
are based
tapered
waveguide
sorting
applications.
Compact
and efficient
mode
sorterslenses
are required
in on
on-chip
mode-division
sorting applications. Compact and efficient mode sorters are required in on-chip mode-division
geometry,
their[7]high
and very compact
designMultiphysics
are highly suitable
in waveguide
mode
multiplexing
andmagnification
sensing [8] applications.
COMSOL
simulations
of a Maxwell
multiplexing [7] and sensing [8] applications. COMSOL Multiphysics simulations of a Maxwell
sorting
applications.
Compact
and efficient
mode
sortersthe
aresignal
required
in in
on-chip
mode-division
fisheye-based
mode sorter
are presented
in Figure
6, where
is sent
through
a multimode
fisheye-based mode sorter are presented in Figure 6, where the signal is sent in through a multimode
waveguide from the left and out-coupled through three single mode output waveguides to the right.
waveguide from the left and out-coupled through three single mode output waveguides to the right.
These simulations demonstrate excellent mode-sorting performance of a magnifying Maxwell
These simulations demonstrate excellent mode-sorting performance of a magnifying Maxwell
fisheye lens, having spatial dimensions of only a few micrometers (the spatial dimensions are chosen
fisheye lens, having spatial dimensions of only a few micrometers (the spatial dimensions are chosen
to match experimentally fabricated lens shown in Figure 1). As demonstrated by Figure 6a,
to match experimentally fabricated lens shown in Figure 1). As demonstrated by Figure 6a,
symmetric excitation of the multimode input waveguide leads to the output power being channeled
Photonics 2016, 3, 8
6 of 7
multiplexing [7] and sensing [8] applications. COMSOL Multiphysics simulations of a Maxwell
fisheye-based mode sorter are presented in Figure 6, where the signal is sent in through a multimode
waveguide from the left and out-coupled through three single mode output waveguides to the right.
These simulations demonstrate excellent mode-sorting performance of a magnifying Maxwell fisheye
lens, having spatial dimensions of only a few micrometers (the spatial dimensions are chosen to match
experimentally fabricated lens shown in Figure 1). As demonstrated by Figure 6a, symmetric excitation
of the multimode input waveguide leads to the output power being channeled primarily into the
Photonics 2016, 3, 8
6 of 7
central single mode output waveguide. On the other hand, asymmetric excitation of the multimode
waveguide
leads to propagation
of higher
spatial modes,
whichspatial
are channeled
preferentially
into the
of the multimode
waveguide leads
to propagation
of higher
modes, which
are channeled
side
single
mode
waveguides,
as
shown
in
Figure
6b.
preferentially into the side single mode waveguides, as shown in Figure 6b.
Figure 6. COMSOL Multiphysics simulations of a Maxwell fisheye-based mode sorter. (a) Symmetric
Figure 6. COMSOL Multiphysics simulations of a Maxwell fisheye-based mode sorter. (a) Symmetric
excitation of the multimode input waveguide leads to the output power being channeled into the
excitation of the multimode input waveguide leads to the output power being channeled into the
central single mode output waveguide. (b) Asymmetric excitation of the multimode waveguide
central single mode output waveguide. (b) Asymmetric excitation of the multimode waveguide leads
leads to propagation of higher spatial modes, which are channeled preferentially into the side single
to propagation of higher spatial modes, which are channeled preferentially into the side single mode
mode waveguides. The spatial dimensions of the magnifying Maxwell fisheye lens in these
waveguides. The spatial dimensions of the magnifying Maxwell fisheye lens in these simulations are
simulations are the same as in Figure 1.
the same as in Figure 1.
Additional applications of the magnifying Maxwell fisheye lenses may include microscopy and
Additional
applications
of the
magnifyingasMaxwell
fisheyenonlinear
lenses may
include microscopy
and
spatially
resolved
fluorescence
spectroscopy,
well as various
spectroscopy
techniques,
which require
considerable
local
field enhancement.
spatially
resolved
fluorescence
spectroscopy,
as well as various nonlinear spectroscopy techniques,
which require considerable local field enhancement.
5. Conclusions
5. Conclusions
In conclusion, we have reported the first experimental realization of TO-based birefringent
lithographically
Maxwell
fisheye lenses,
which operate
over a very
broad
In conclusion,fabricated
we havemagnifying
reported the
first experimental
realization
of TO-based
birefringent
angular
range.
The
lens
action
is
based
on
control
of
polarization-dependent
effective
refractive
lithographically fabricated magnifying Maxwell fisheye lenses, which operate over a very broad
index range.
in a tapered
We have
studied
wavelength and polarization
dependent
angular
The lenswaveguide.
action is based
on control
of polarization-dependent
effective
refractive
performance
of the
lenses. TheWe
fabricated
TO designs
are broadband,
which was
verified in
the 488–
index
in a tapered
waveguide.
have studied
wavelength
and polarization
dependent
performance
wavelength
range. Our
together
with other
related
[9–11]
opens
up annm
of 633
the nm
lenses.
The fabricated
TOtechnique
designs are
broadband,
which
was results
verified
in the
488–633
additional
degree
of
freedom
in
optical
design
and
considerably
improves
our
ability
to
manipulate
wavelength range. Our technique together with other related results [9–11] opens up an additional
light on submicrometer scale. In particular, it enables extremely compact and efficient waveguide
degree of freedom in optical design and considerably improves our ability to manipulate light on
mode sorters, which are required in on-chip mode-division multiplexing and sensing applications.
submicrometer scale. In particular, it enables extremely compact and efficient waveguide mode
Another potentially interesting application of the magnifying Maxwell fisheye lenses would be
sorters, which are required in on-chip mode-division multiplexing and sensing applications. Another
verification of the recently proposed perfect imaging without negative refraction [6], which is
potentially interesting application of the magnifying Maxwell fisheye lenses would be verification of
currently under debate. Our experiments already demonstrated that the image resolution of the
thefabricated
recently proposed
perfecttoimaging
negative refraction
[6], which
is currently
debate.
lenses appears
be closewithout
to the diffraction
limit. Further
studies
of imageunder
resolution
Our
experiments
demonstrated that the image resolution of the fabricated lenses appears to be
would
be highlyalready
interesting.
close to the diffraction limit. Further studies of image resolution would be highly interesting.
Acknowledgments: This research was supported by the National Science Foundation (NSF) grant
DMR-1104676. We This
are grateful
Jeff Klupt
for experimental
help.Science Foundation (NSF) grant DMR-1104676.
Acknowledgments:
researchtowas
supported
by the National
We are grateful to Jeff Klupt for experimental help.
Author Contributions: V.S., I.S. and D.S. conceived and designed the experiments; C.J., W.Z. and A.J.
performed the experiments; V.S. and I.S. analyzed the data and wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Smolyaninov, I.I.; Smolyaninova, V.N.; Kildishev, A.V.; Shalaev, V.M. Anisotropic metamaterials
Photonics 2016, 3, 8
7 of 7
Author Contributions: V.S., I.S. and D.S. conceived and designed the experiments; C.J., W.Z. and A.J. performed
the experiments; V.S. and I.S. analyzed the data and wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Smolyaninov, I.I.; Smolyaninova, V.N.; Kildishev, A.V.; Shalaev, V.M. Anisotropic metamaterials emulated by
tapered waveguides: Application to electromagnetic cloaking. Phys. Rev. Lett. 2009, 102, 213901. [CrossRef]
[PubMed]
Smolyaninova, V.N.; Ermer, H.K.; Piazza, A.; Schaefer, D.; Smolyaninov, I.I. Experimental demonstration of
birefrigent transformation optics devices. Phys. Rev. B 2013, 87, 075406. [CrossRef]
Smolyaninova, V.N.; Smolyaninov, I.I.; Kildishev, A.V.; Shalaev, V.M. Maxwell fish-eye and Eaton lenses
emulated by microdroplets. Opt. Lett. 2010, 35, 3396–3398. [CrossRef] [PubMed]
Lock, J.A. Scattering of an electromagnetic plane wave by a Luneburg lens. Wave theory. JOSA A 2008, 25,
2980. [CrossRef] [PubMed]
Minano, J.C. Perfect imaging in a homogeneous three-dimensional region. Opt. Express 2006, 14, 9627–9635.
[CrossRef] [PubMed]
Leonhardt, U. Perfect imaging without negative refraction. New J. Phys. 2009, 11, 093040. [CrossRef]
Martínez-Garaot, S.; Tseng, S.-Y.; Muga, J.G. Compact and high conversion efficiency mode-sorting
asymmetric Y junction using shortcuts to adiabaticity. Opt. Lett. 2014, 39, 2306–2309. [CrossRef] [PubMed]
Racz, G.Z.; Bamiedakis, N.; Penty, R. Mode-selective optical sensing using asymmetric waveguide junctions.
Sens. Actuators A 2015, 233, 91–97. [CrossRef]
Mitchell-Thomas, R.C.; Quevedo-Teruel, O.; McManus, T.M.; Horsley, S.A.R.; Hao, Y. Lenses on curved
surfaces. Opt. Lett. 2014, 39, 3551–3554. [CrossRef] [PubMed]
Sheng, C.; Liu, H.; Wang, Y.; Zhu, S.N.; Genov, D.A. Trapping light by mimicking gravitational lensing.
Nat. Photonics 2013, 7, 902–906. [CrossRef]
Šarbort, M.; Tyc, T. Spherical media and geodesic lenses in geometrical optics. J. Opt. 2012, 14, 075705.
[CrossRef]
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons by Attribution
(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).