of 8
Controlling the sign of chromatic dispersion in
diffractive optics with dielectric metasurfaces
E
HSAN
A
RBABI
,
1
A
MIR
A
RBABI
,
1,2
S
EYEDEH
M
AHSA
K
AMALI
,
1
Y
U
H
ORIE
,
1
AND
A
NDREI
F
ARAON
1,
*
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125, USA
2
Department of Electrical and Computer Engineering, University of Massachusetts Amherst, 151 Holdsworth Way, Amherst, Massachusetts 01003, USA
*Corresponding author: faraon@caltech.edu
Received 22 February 2017; revised 3 May 2017; accepted 5 May 2017 (Doc. ID 287279); published 7 June 2017
Diffraction gratings disperse light in a rainbow of colors with the opposite order than refractive prisms, a phenomenon
known as negative dispersion. While refractive dispersion can be controlled via material refractive index, diffractive
dispersion is fundamentally an interference effect dictated by geometry. Here we show that this fundamental property
can be altered using dielectric metasurfaces, and we experimentally demonstrate diffractive gratings and focusing
mirrors with positive, zero, and hyper-negative dispersion. These optical elements are implemented using a reflective
metasurface composed of dielectric nano-posts that provide simultaneous control over phase and its wavelength
derivative. In addition, as a first practical application, we demonstrate a focusing mirror that exhibits a five-fold
reduction in chromatic dispersion, and thus an almost three-times increase in operation bandwidth compared with
a regular diffractive element. This concept challenges the generally accepted dispersive properties of diffractive optical
devices and extends their applications and functionalities.
© 2017 Optical Society of America
OCIS codes:
(260.2030) Dispersion; (050.6624) Subwavelength structures; (050.1965) Diffractive lenses; (220.1000) Aberration
compensation.
https://doi.org/10.1364/OPTICA.4.000625
1. INTRODUCTION
Most optical materials have positive (normal) dispersion, which
means that the refractive index decreases at longer wavelengths.
As a consequence, blue light is deflected more than red light by
dielectric prisms [Fig.
1(a)
]. The reason diffraction gratings are
said to have negative dispersion is that they disperse light similar
to hypothetical refractive prisms made of a material with negative
(anomalous) dispersion [Fig.
1(b)
]. For diffractive devices,
dispersion is not related to material properties, and it refers to
the derivative of a certain device parameter with respect to
wavelength. For example, the angular dispersion of a grating that
deflects normally incident light by a positive angle
θ
is given by
d
θ
d
λ

tan

θ

λ
(see [
1
] and
Supplement 1
, Section S2).
Similarly, the wavelength dependence of the focal length (
f
)
of a diffractive lens is given by
d
f
d
λ

f
λ
[
1
,
2
]. Here we
refer to diffractive devices that follow these fundamental chro-
matic dispersion relations as
regular.
Achieving new regimes of
dispersion control in diffractive optics is important both at the
fundamental level and for numerous
practical applications. Several
distinct regimes can be differentia
ted as follows. Diffractive devices
are dispersionless when the derivative is zero [i.e.,
d
θ
d
λ

0
,
d
f
d
λ

0
shown schematically in Fig.
1(c)
], have positive
dispersion when the derivative has opposite sign compared with
a regular diffractive device of the same kind (i.e.,
d
θ
d
λ
<
0
,
d
f
d
λ
>
0
) as shown in Fig.
1(d)
, and are hyper-dispersive when
the derivative has a larger absolute value than a regular device
(i.e.,
j
d
θ
d
λ
j
>
j
tan

θ

λ
j
,
j
d
f
d
λ
j
>
j
f
λ
j
), as seen in
Fig.
1(e)
. Here we show that these regimes can be achieved in
diffractive devices based on optical metasurfaces.
Metasurfaces have attracted great interest in the recent years
[
3
12
] because they enable precise control of optical wavefronts
and are easy to fabricate with conventional microfabrication tech-
nology in a flat, thin, and lightweight form factor. Various con-
ventional devices, such as gratings, lenses, holograms, and planar
filter arrays [
7
9
,
13
26
], as well as novel devices [
27
,
28
] have
been demonstrated using metasurfaces. These optical elements
are composed of large numbers of scatterers, or meta-atoms placed
on a two-dimensional lattice to locally shape optical wavefronts.
Similar to other diffractive devices, metasurfaces that locally
change the propagation direction (e.g., lenses, beam deflectors,
holograms) have negative chromatic dispersion [
1
,
2
,
29
,
30
].
This is because most of these devices are divided in Fresnel zones
whose boundaries are designed for a specific wavelength [
30
,
31
].
This chromatic dispersion is an important limiting factor in many
applications, and its control is of great interest. Metasurfaces with
zero and positive dispersion would be useful for making achro-
matic singlet and doublet lenses, and the larger-than-regular
dispersion of hyper-dispersive metasurface gratings would enable
high resolution spectrometers. We emphasize that the devices
with zero chromatic dispersion discussed here are fundamentally
different from the multiwavelength metasurface gratings and
lenses recently reported [
30
40
]. Multiwavelength devices have
2334-2536/17/060625-08 Journal © 2017 Optical Society of America
Research Article
Vol. 4, No. 6 / June 2017 /
Optica
625
several diffraction orders, which result in lenses (gratings) with the
same focal length (deflection angle) at a few discrete wavelengths.
However, at each of these focal distances (deflection angles), the
multi-wavelength lenses (gratings) exhibit the regular negative
diffractive chromatic dispersion (see [
30
,
31
],
Supplement 1
,
Section S3, and Fig. S1). At will control of chromatic dispersion,
adds a new functionality to metasurfaces not available in conven-
tional diffractive or refractive devices.
2. THEORY
Here we argue that simultaneously controlling the phase imparted
by the meta-atoms composing the metasurface (
φ
) and its deriva-
tive with respect to frequency
ω
(
φ
0

φ
∕∂
ω
, which we refer to
as chromatic phase dispersion or dispersion for brevity) makes
it possible to dramatically alter the fundamental chromatic
dispersion of diffractive components. This, in effect, is equivalent
to simultaneously controlling the
effective refractive index
and
chromatic dispersion
of the meta-atoms. We have used this con-
cept to demonstrate metasurface focusing mirrors with zero
dispersion [
41
] in near IR. More recently, the same structure
as the one used in Ref. [
41
] (with titanium dioxide replacing
α
:Si
) was used to demonstrate achromatic reflecting mirrors in
the visible [
42
]. Using the concept introduced in [
41
], here
we experimentally show metasurface gratings and focusing mir-
rors that have positive, zero, and hyper-chromatic dispersions.
We also demonstrate an achromatic focusing mirror with a highly
diminished focal length chromatic dispersion, resulting in an
almost three-times increase in its operation bandwidth.
First, we consider the case of devices with zero chromatic
dispersion. In general for truly frequency independent operation,
a device should impart a constant delay for different frequencies
(i.e., demonstrate a true time delay behavior), similar to a refrac-
tive device made of a non-dispersive material [
1
]. Therefore, the
phase profile will be proportional to the frequency:
φ

x;y
;
ω

ω
T

x;y

;
(1)
where
ω

2
π
c
λ
is the angular frequency (
λ
, wavelength;
c
,
speed of light) and
T

x;y

determines the function of the device
(for instance,
T

x;y

x
sin
θ
0
c
for a grating that deflects
light by angle
θ
0
;
T

x;y

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
x
2

y
2

f
2
p
c
for a spherical-
aberration-free lens with a focal distance
f
). Since the
phase profile is a linear function of
ω
, it can be realized using
a metasurface composed of meta-atoms that control the phase
φ

x;y
;
ω
0

T

x;y

ω
0
and its dispersion
φ
0

φ

x;y
;
ω

ω

T

x;y

. The bandwidth of dispersionless operation corre-
sponds to the frequency interval over which the phase locally im-
posed by the meta-atoms is linear with frequency
ω
. For gratings
or lenses, a large device size results in a large
j
T

x;y
j
, which
means that the meta-atoms should impart a large phase
dispersion. Since the phase values at the center wavelength
λ
0

2
π
c
ω
0
can be wrapped into the
0
2
π
interval, the meta-atoms
only need to cover a rectangular region in the
phase-dispersion
plane bounded by
φ

0
and
2
π
lines, and
φ
0

0
and
φ
0
max
lines, where
φ
0
max
is the maximum required dispersion that is re-
lated to the device size (see
Supplement 1
, Section S5, and
Fig. S2). The required phase-dispersion coverage means that,
to implement devices with various phase profiles, for each specific
value of the phase, we need various meta-atoms providing that
specific phase but with different dispersion values.
Considering the simple case of a flat dispersionless lens
(or focusing mirror) with radius
R
, we can get some intuition
to the relations found for phase and dispersion. Dispersionless
operation over a certain bandwidth
Δ
ω
means that the device
should be able to focus a transform limited pulse with bandwidth
Δ
ω
and carrier frequency
ω
0
to a single spot located at focal
length
f
[Fig.
2(a)
]. To implement this device, part of the
pulse hitting the lens at a distance
r
from its center needs to ex-
perience a pulse delay (i.e., group delay
t
g

φ
∕∂
ω
) smaller by

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
2

f
2
p
f

c
than part of the pulse hitting the lens at
its center. This ensures that parts of the pulse hitting the lens
at different locations arrive at the focus at the same time.
Also, the carrier delay (i.e., phase delay
t
p

φ

ω
0

ω
0
) should
(a)
(b)
(c)
(d)
(e)
Fig. 1.
Schematic illustrations of different dispersion regimes. (a) Positive chromatic dispersion in refractive prisms and lenses made of materials with
normal dispersion. (b) Regular (negative) dispersion in typical diffractive and metasurface gratings and lenses. (c) Schematic illustration of ze
ro, (d)
positive, and (e) hyper-dispersion in dispersion-controlled metasurfaces. Only three wavelengths are shown here, but the dispersions are valid fo
r any other
wavelength in the bandwidth. The diffractive devices are shown in transmission mode for ease of illustration, while the actual devices fabricated in
this
paper are designed to operate in reflection mode.
Research Article
Vol. 4, No. 6 / June 2017 /
Optica
626
also be adjusted so that all parts of the pulse interfere construc-
tively at the focus. Thus, to implement this phase delay and group
delay behavior, the lens needs to be composed of elements, ideally
with sub-wavelength size, that can provide the required phase de-
lay and group delay at different locations. For a focusing mirror,
these elements can take the form of sub-wavelength one-sided
resonators, where the group delay is related to the quality factor
Q
of the resonator (see
Supplement 1
, Section S7), and the phase
delay depends on the resonance frequency. We note that larger
group delays are required for lenses with larger radius, which
means that elements with higher quality factors are needed. If
the resonators are single mode, the
Q
imposes an upper bound
on the maximum bandwidth
Δ
ω
of the pulse that needs to be
focused. The operation bandwidth can be expanded by using one-
sided resonators with multiple resonances that partially overlap.
As we will show later in the paper, these resonators can be imple-
mented using silicon nano-posts backed by a reflective mirror.
To realize metasurface devices with non-zero dispersion of a
certain parameter
ξ

ω

, phase profiles of the following form
are needed:
φ

x;y
;
ω

ω
T

x;y;
ξ

ω

:
(2)
For instance, the parameter
ξ

ω

can be the deflection angle of a
diffraction grating
θ

ω

or the focal length of a diffractive lens
f

ω

. As we show in
Supplement 1
, Section S4, to independently
control the parameter
ξ

ω

and its chromatic dispersion
ξ
∕∂
ω
at
ω

ω
0
, we need to control the phase dispersion at this
frequency in addition to the phase. The required dispersion
for a certain parameter value
ξ
0

ξ

ω
0

, and a certain dispersion
ξ
∕∂
ω
j
ω

ω
0
, is given by
φ

x;y
;
ω

ω




ω

ω
0

T

x;y;
ξ
0

ξ
∕∂
ω
j
ω

ω
0
ω
0
T

x;y;
ξ

ξ




ξ

ξ
0
:
(3)
This dispersion relation is valid over a bandwidth where a linear
approximation of
ξ

ω

is valid. One can also use Fermat
s prin-
ciple to get similar results to Eq. (
3
) for the local phase gradient
and its frequency derivative (see
Supplement 1
, Section S6).
We note that discussing these types of devices in terms of
phase
φ

ω

and phase dispersion
φ
∕∂
ω
, which we mainly
use in this paper, is equivalent to using the terminology of phase
delay (
t
p

φ

ω
0

ω
0
) and group delay (
t
g

φ
∕∂
ω
). The zero
dispersion case discussed above corresponds to a case where
the phase and group delays are equal. Figures
2(b)
and
2(c)
show
the required phase and group delays for blazed gratings and
focusing mirrors with various types of dispersion, demonstrating
the equality of phase and group delays in the dispersionless case.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Fig. 2.
Required phase and group delays and simulation results of dispersion-engineered metasurfaces based on hypothetical meta-atoms.
(a) Schematics of focusing of a light pulse to the focal distance of a flat lens. The
E
versus
t
graphs show schematically the portions of the pulse passing
through the center and at a point at a distance
r
away from center both before the lens and when arriving at focus. The portions passing through different
parts of the lens should acquire equal group delays and should arrive at the focal point in phase for dispersionless operation. (b) Required values of g
roup
delay for gratings with various types of chromatic dispersion. The dashed line shows the required phase delay for all devices, which also coincides wi
th the
required group delay for the dispersionless gratings. The gratings are
90
μ
m
wide and have a deflection angle of 10 deg in their center wavelength of
1520 nm. (c) Required values of group delay for aspherical focusing mirrors with various types of chromatic dispersion. The dashed line shows the
required phase delay for all devices. The mirrors are 240
μ
m in diameter and have a focal distance of 650
μ
m at their center wavelength of
1520 nm. (d) Simulated deflection angles for gratings with regular, zero, positive, and hyper-dispersions. The gratings are 150
μ
m wide and have
a 10 deg deflection angle at 1520 nm. (e) Simulated focal distances for metasurface focusing mirrors with different types of dispersion. The mirrors
are 500
μ
m in diameter and have a focal distance of 850
μ
m at 1520 nm. All gratings and focusing mirrors are designed using hypothetical meta-atoms
that provide independent control over phase and dispersion (see
Supplement 1
, Section S1 for details). (f) Intensity in the axial plane for the focusing
mirrors with regular negative, (g) zero, (h) positive, and (i) hyper-dispersions plotted at three wavelengths (see Fig. S3 for other wavelengths).
Research Article
Vol. 4, No. 6 / June 2017 /
Optica
627
In microwave photonics, the idea of using sets of separate optical
cavities for independent control of the phase delay of the optical
carrier and group delay of the modulated RF signal has previously
been proposed [
43
] to achieve dispersionless beam steering and
resemble a true time delay system over a narrow bandwidth.
For all other types of chromatic dispersion, the phase and group
delays are drastically different, as shown in Figs.
2(b)
and
2(c)
.
Assuming hypothetical meta-atoms that provide independ-
ent control of phase and dispersion up to a dispersion of
150 Rad
μ
m
(to adhere to the commonly used convention,
we report the dispersion in terms of wavelength) at the center
wavelength of 1520 nm, we have designed and simulated four
gratings with different chromatic dispersions (see
Supplement 1
,
Section S1 for details). The simulated deflection angles as func-
tions of wavelength are plotted in Fig.
2(d)
. All gratings are
150
μ
m wide and have a deflection angle of 10 deg at their center
wavelength of 1520 nm. The positive dispersion grating exhibits a
dispersion equal in absolute value to the negative dispersion of a
regular grating with the same deflection angle but with an oppo-
site sign. The hyper-dispersive design is three times more disper-
sive than the regular grating, and the dispersionless beam deflector
shows almost no change in its deflection angle. Besides gratings,
we have also designed focusing mirrors exhibiting regular, zero,
positive, and hyper-dispersions. The focusing mirrors have a
diameter of 500
μ
m and a focal distance of 850
μ
mat
1520 nm. Hypothetical meta-atoms with a maximum dispersion
of
200 Rad
μ
m
are required to implement these focusing mir-
ror designs. The simulated focal distances of the four designs are
plotted in Fig.
2(e)
. The axial plane intensity distributions at three
wavelengths are plotted in Figs.
2(f)
2(i)
(for intensity plots at
other wavelengths, see Fig. S3). To relate to our previous
discussion of dispersionless focusing mirrors depicted in Fig.
2(a)
,
a focusing mirror with a diameter of 500
μ
m and a focal distance
of 850
μ
m would require meta-atoms with group delay of
24
λ
0
c
(corresponding to a
36.5
μ
m
propagation in free
space, or a
10.7
μ
m
propagation in bulk silicon), with
λ
0

1520 nm
. To implement this device, we used hypothetical
meta-atoms with maximum dispersion of
100Rad
μ
m
, which
corresponds to a group delay of
24
λ
0
c
. The hypothetical meta-
atoms exhibit this almost linear dispersion over the operation
bandwidth of 1450 to 1590 nm.
3. METASURFACE DESIGN
An example of meta-atoms capable of providing
0
2
π
phase
coverage and different dispersions is shown in Fig.
3(a)
. The
meta-atoms, composed of a square cross-section amorphous
silicon (
α
-Si) nano-post on a low refractive index silicon dioxide
(
SiO
2
) spacer layer on an aluminum reflector, play the role of the
multi-mode one-sided resonators mentioned in Section
2
[Fig.
2(a)
]. They are located on a periodic square lattice [Fig.
3(a)
,
middle]. The simulated dispersion versus phase plot for the meta-
atoms at the wavelength of
λ
0

1520 nm
is depicted in Fig.
3(b)
and shows a partial coverage up to the dispersion value of
100 Rad
μ
m
. The nano-posts exhibit several resonances,
which enable high dispersion values over the 1450 nm to
1590 nm wavelength range. The meta-atoms are 725 nm tall,
the
SiO
2
layer is 325 nm thick, the lattice constant is 740 nm,
and the nano-post side length is varied from 74 to 666 nm at
1.5 nm steps. Simulated reflection amplitude and phase for the
periodic lattice are plotted in Figs.
3(c)
and
3(d)
, respectively.
The reflection amplitude over the bandwidth of interest is close
to 1 for all nano-post side lengths. The operation of the nano-post
meta-atoms is best intuitively understood as truncated multi-mode
waveguides with many resonances in the bandwidth of interest
[
28
,
44
]. By going through the nano-post twice, light can obtain
larger phase shifts compared with the transmissive operation mode
of the metasurface (i.e., without the metallic reflector). The met-
allic reflector keeps the reflection amplitude high for all sizes,
which makes the use of high quality factor resonances possible.
As discussed in Section
2
, high quality factor resonances are nec-
essary for achieving large dispersion values, because, as we have
shown in
Supplement 1
, Section S7, dispersion is given by
φ
0
Q
λ
0
, where
Q
is the quality factor of the resonance.
Using the dispersion-phase parameters provided by this meta-
surface, we designed four gratings operating in various dispersion
regimes. The gratings are
90
μ
m
wide and have a 10 deg
deflection angle at 1520 nm. They are designed to operate in
the 1450
1590 nm wavelength range and have regular negative,
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 3.
High dispersion silicon meta-atoms. (a) A meta-atom com-
posed of a square cross-section amorphous silicon nano-post on a silicon
dioxide layer on a metallic reflector. Top and side views of the meta-
atoms arranged on a square lattice are also shown. (b) Simulated
dispersion versus phase plot for the meta-atom shown in (a) at
λ
0

1520 nm
. (c) Simulated reflection amplitude and (d) phase as a
function of the nano-post side length and wavelength. The reflection
amplitude and phase along the dashed lines are plotted on the right.
(e) and (f) Scanning electron micrographs of the fabricated nano-posts
and devices.
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Vol. 4, No. 6 / June 2017 /
Optica
628
zero, positive, and hyper (3-times-larger negative) dispersion.
Since the phase of the meta-atoms does not follow a linear fre-
quency dependence over this wavelength interval [Fig.
3(d)
,
top right], we calculate the desired phase profile of the devices
at 8 wavelengths in the range (1450
1590 nm at 20 nm steps)
and form an
8
×
1
complex reflection coefficient vector at each
point on the metasurface. Using Figs.
3(c)
and
3(d)
, a similar
complex reflection coefficient vector is calculated for each
meta-atom. Then, at each lattice site of the metasurface, we place
a meta-atom whose reflection vector has the shortest weighted
Euclidean distance to the desired reflection vector at that site.
The weights allow for emphasizing different parts of the operation
bandwidth and can be chosen based on the optical spectrum of
interest or other considerations. Here, we used an inverted
Gaussian weight (
exp

λ
λ
0

2
2
σ
2

,
σ

300 nm
), which val-
ues wavelengths farther away from the center wavelength of
λ
0

1520 nm
. The same design method is used for the other
devices discussed in the paper. The designed devices were
fabricated using standard semiconductor fabrication techniques
as described in
Supplement 1
, Section S1. Figures
3(e)
and
3(f)
show scanning electron micrographs of the nano-posts, and some
of the devices fabricated using the proposed reflective meta-atoms.
Figure S5 shows the chosen post side lengths and the required as
well as the achieved phase and group delays for the gratings with
different dispersions. Required phases and the values provided by
the chosen nano-posts are plotted at three wavelengths for each
grating in Fig. S6.
4. EXPERIMENTAL RESULTS
Figures
4(a)
and
4(b)
show the simulated and measured deflection
angles for gratings, respectively. The measured values are calcu-
lated by finding the center of mass of the deflected beam 3 mm
away from the grating surface (see
Supplement 1
, Section S1, and
Fig. S8 for more details). As expected, the zero dispersion
grating shows an apochromatic behavior resulting in a reduced
dispersion, the positive grating shows positive dispersion in the
1490
1550 nm
bandwidth, and the hyper-dispersive one shows
an enhanced dispersion in the measurement bandwidth. This can
also be viewed from the grating momentum point of view: a regu-
lar grating has a constant momentum set by its period, resulting
in a constant transverse wave-vector. In contrast, the momentum
of the hyper-dispersive grating increases with wavelength, while
that of the zero and positive gratings decreases with it. This means
that the effective period of the non-regular gratings changes
with wavelength, resulting in the desired chromatic dispersion.
Figures
4(e)
4(h)
show good agreement between simulated in-
tensities of these gratings versus wavelength and transverse
wave-vector (see
Supplement 1
, Section S1 for details) and the
measured beam deflection (black stars). The change in the grating
pitch with wavelength is more clear in Fig. S6, where the required
and achieved phases are plotted for three wavelengths. The green
line is the theoretical expectation of the maximum intensity
trajectory. Measured deflection efficiencies of the gratings, defined
as the power deflected by the gratings to the desired order, divided
by the power reflected from a plain aluminum reflector (see
Supplement 1
, Section S1, and Fig. S8 for more details), are plot-
ted in Figs.
4(c)
and
4(d)
for TE and TM illuminations, respec-
tively. A similar difference in the efficiency of the gratings for
TE and TM illuminations has also been observed in previous
works [
16
,
28
].
As another example for diffractive devices with controlled
chromatic dispersion, four spherical-aberration-free focusing
mirrors with different chromatic dispersions were designed, fab-
ricated, and measured using the same reflective dielectric meta-
atoms. The mirrors are 240
μ
m in diameter and are designed to
have a focal distance of 650
μ
m at 1520 nm. Figure S7 shows the
chosen post side lengths and the required as well as the achieved
phase and group delays for the focusing mirrors with different
dispersions. Figures
5(a)
and
5(b)
show simulated and measured
focal distances for the four focusing mirrors (see Figs. S9, S10, and
S11 for detailed simulation and measurement results). The pos-
itive dispersion mirror is designed with dispersion twice as large as
a regular mirror with the same focal distance, and the hyper-
dispersive mirror has a negative dispersion 3 1/2 times larger than
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Fig. 4.
Simulation and measurement results of gratings in different dispersion regimes. (a) Simulated deflection angles for gratings with different
dispersions, designed using the proposed reflective meta-atoms. (b) Measured deflection angles for the same gratings. (c) Measured deflection eff
iciency
for the gratings under TE and (d) TM illumination. (e)
(h) Comparison between FDTD simulation results showing the intensity distribution of the
diffracted wave as a function of normalized transverse wave-vector (
k
x
k
0
,
k
0

2
π
λ
0
, and
λ
0

1520 nm
) and wavelength for different gratings, and
the measured peak intensity positions plotted with black stars. All simulations here are performed with TE illumination. The green lines show the
theoretically expected maximum intensity trajectories.
Research Article
Vol. 4, No. 6 / June 2017 /
Optica
629