High performance solarselective absorbers using coated subwavelength gratings.
ABSTRACT Spectral control of the emissivity of surfaces is essential for efficient conversion of solar radiation into heat. We investigated surfaces consisting of subwavelength Vgroove gratings coated with aperiodic metaldielectric stacks. The spectral behavior of the coated gratings was modeled using rigorous coupledwave analysis (RCWA). The proposed absorber coatings combine impedance matching using tapered metallic features with the excellent spectral selectivity of aperiodic metaldielectric stacks. The aspect ratio of the Vgroove can be tailored in order to obtain the desired spectral selectivity over a wide angular range. Coated Vgroove gratings with optimal aspect ratio are predicted to have thermal emissivity below 6% at 720K while absorbing >94% of the incident light. These subwavelength gratings would have the potential to significantly increase the efficiency of concentrated solar thermal systems.
 [Show abstract] [Hide abstract]
ABSTRACT: Plasmonic nanostructures can significantly advance broadband visiblelight absorption, with absorber thicknesses in the subwavelength regime, much thinner than conventional broadband coatings. Such absorbers have inherently very small heat capacity, hence a very rapid response time, and high light powertotemperature sensitivity. Additionally, their surface emissivity can be spectrally tuned to suppress infrared thermal radiation. These capabilities make plasmonic absorbers promising candidates for fast lighttoheat applications, such as radiation sensors. Here we investigate the lighttoheat conversion properties of a metalinsulatormetal broadband plasmonic absorber, fabricated as a freestanding membrane. Using a fast IR camera, we show that the transient response of the absorber has a characteristic time below 13 ms, nearly one order of magnitude lower than a similar membrane coated with a commercial black spray. Concurrently, despite the small thickness, due to the large absorption capability, the achieved absorbed light powertotemperature sensitivity is maintained at the level of a standard black spray. Finally, we show that while black spray has emissivity similar to a black body, the plasmonic absorber features a very low infrared emissivity of almost 0.16, demonstrating its capability as selective coating for applications with operating temperatures up to 400°C, above which the nanostructure starts to deform.Scientific Reports 11/2014; 4:7181. · 5.08 Impact Factor  SourceAvailable from: opticsinfobase.org[Show abstract] [Hide abstract]
ABSTRACT: Triple mechanisms were employed to trap midinfrared (midIR) rays within a semitransparent SiO<sub>2</sub> film sandwiched between gold gratings and a gold substrate. Dimensions of four absorbers were explicitly determined using an LC (inductorcapacitor) circuit model considering the role transition of SiO<sub>2</sub> film. The film behaves as a capacitance and an inductance when the real part of relative electric permittivity for SiO<sub>2</sub> is positive and negative, respectively. At the normal incidence of transverse magnetic waves, every absorptance spectrum of absorbers showed a peak at wavelength λ = 10 μm due to the first mode excitation of magnetic polaritons (MP). At oblique incidence, the Berreman mode led to another peak at λ = 8 μm while its bandwidth was expanded with epsilon near zero mode excited by diffracted waves. The fullwidthathalfmaximum of both peaks exceeded 0.6 μm thanks to the SiO<sub>2</sub> loss. Other minor absorptance peaks in the midIR were caused by variants of the same MP mode.Optics Express 09/2013; 21(18):2077120785. · 3.55 Impact Factor  SourceAvailable from: YuLung Lo[Show abstract] [Hide abstract]
ABSTRACT: The wavelengthselective infrared absorptance of a singlelayered aluminum subwavelength structure (SWS) is optimized using a hybrid numerical scheme comprising the rigorous coupledwave analysis method and a genetic algorithm. The results show that the optimized SWS yields a strong absorptance peak (0.99) and a fullwidthathalfmaximum (FWHM) of 1.42 μm. In addition, it is shown that the absorptance spectrum of the SWS is insensitive to the angle of incidence of the incoming light and the grating period, but shifts toward a longer (shorter) wavelength as the grating thickness or grating ridge width is increased (decreased). The enhanced absorptance is examined by computing the governing equations of the excitations of RayleighWood anomaly, surface plasmon polaritons, cavity resonance, and magnetic polaritons. The magnetic field patterns and Poynting vector distribution within the grating structure are also analyzed to support the physical mechanism using the finitedifference timedomain (FDTD) method. The results indicate that the absorptance peak of the SWS is the result of cavity resonance. Also, for a doublelayered SWS comprising an aluminum grating and a dielectric layer, a widening of the absorptance spectrum occurs. Overall, the results presented in this study show that SWS gratings which can be easily manufactured using microfabrication technology provide a simple and versatile solution for such applications in tailoring the spectral absorptance used for infrared detection, energy harvesting, and so on.Journal of Lightwave Technology 08/2013; 31(15):24822490. · 2.56 Impact Factor
Page 1
High performance solarselective absorbers
using coated subwavelength gratings
Nicholas P. Sergeant,1 Mukul Agrawal,2 and Peter Peumans1*
1Dept. of Electrical Engineering, Stanford University, Stanford, CA 94305 USA
2Applied Materials Inc., Santa Clara, CA 95054, USA
*ppeumans@stanford.edu
Abstract: Spectral control of the emissivity of surfaces is essential for
efficient conversion of solar radiation into heat. We investigated surfaces
consisting of subwavelength Vgroove gratings coated with aperiodic
metaldielectric stacks. The spectral behavior of the coated gratings was
modeled using rigorous coupledwave analysis (RCWA). The proposed
absorber coatings combine impedance matching using tapered metallic
features with the excellent spectral selectivity of aperiodic metaldielectric
stacks. The aspect ratio of the Vgroove can be tailored in order to obtain
the desired spectral selectivity over a wide angular range. Coated Vgroove
gratings with optimal aspect ratio are predicted to have thermal emissivity
below 6% at 720K while absorbing >94% of the incident light. These sub
wavelength gratings would have the potential to significantly increase the
efficiency of concentrated solar thermal systems.
©2010 Optical Society of America
OCIS codes: (350.6050) Solar energy; (310.4165) Multilayer design; (310.1620) Interference
coatings; (350.4328) Nanophotonics and photonic crystals; (310.3915) Metallic, opaque, and
absorbing coatings.
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1. Introduction
The parabolic trough is one of the most common concentrated solar thermal systems. In this
configuration sunlight is concentrated by an array of parabolic mirrors onto a heat collection
element (HCE) which runs along its focal point. The HCE consists of a steel tube which is
coated with a solar selective absorber coating. An evacuated glass envelope surrounds the
steel tube in order to reduce thermal losses and to extend the lifetime of the absorber coating.
Incoming solar radiation is absorbed by the HCE absorber coating and converted into heat.
The collected heat is extracted using a heat transfer fluid (HTF) and can be converted into
steam in order to drive a turbine and generate electricity. The Carnot efficiency, and thus the
maximum temperature of the working fluid, sets a thermodynamical limit to the overall
efficiency of the system. Parabolic troughs have concentration ratios of ~80, and operate at
temperatures up to 660K [1,2]. The working temperature is currently limited by the thermal
stability of the available absorber coatings and the cracking temperature of the synthetic oil
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Page 3
used as HTF. Cracking oil produces hydrogen which can permeate the steel tube and lead to
accelerated degradation of the absorber coating. Alternative working fluids such as molten
salts are being pursued to allow for operation at higher temperatures. To achieve these higher
temperatures, an increased spectral selectivity of the absorbing coating on the HCE is
required to prevent reemission of the absorbed energy as infrared (IR) radiation, while
ensuring that most photons are absorbed.
Numerous selective coatings have been deployed including intrinsic absorbers,
semiconductormetal tandems and cermets [3–6]. Recent advances in nanofabrication have
led to the exploration of spectral selectivity in onedimensional (1D) periodic multilayer
stacks [7–13], 1D gratings [14–18], twodimensional (2D) gratings [19–22], photonic cavities
[23] and threedimensional (3D) photonic crystals [24–26]. In all these approaches the
absorbing medium is nanostructured with feature sizes of the order of 100nm to 1µm in order
to tune the response of the medium in the visible and nearinfrared (NIR) spectral range.
Structuring the surface of refractory metals as 1D and 2D gratings has been suggested to
enhance the performance in solar thermal systems [14–16,20]. Here, we study the
performance of subwavelength Vgroove metal gratings coated with metaldielectric stacks.
We show that the combination of a nanostructured surface with an aperiodic metaldielectric
coating results in high performance solar thermal absorbers for operating at 720K.
2. Ideal absorber
Controlling this parasitic thermal emission from the absorber surface is crucial to increasing
the overall conversion efficiency of solar thermal systems. An ideal absorber coating behaves
as a perfect absorber (
solar
α
=1) for wavelengths shorter than a cutoff wavelength
optimize light absorption, and suppresses thermal emission (
cλ to minimize losses through infrared (IR) emission [27]. In accordance with
Kirchhoff’s law we assume here that the directional spectral absorptivity ( , )
ε θ λ for a system in thermal equilibrium. In order to
cλ and to evaluate the performance of solar selective coatings during optimization,
a merit function needs to be defined. The following merit function, F, was previously
suggested [27]:
cλ to
thermal
ε
=0) for wavelengths
longer than
α θ λ is equal to
the directional spectral emissivity ( , )
determine
[]
( )1 ( )
T
solar thermal
ε
F T
α
=×−
(1)
The first factor
at normal incidence. Solar absorptivity at normal incidence was chosen because for relatively
low concentration factors, the incidence angle of the solar radiation on the absorber coating
will be close to normal. This is in accordance to literature where absorptivity is typically
measured and cited for normal incidence [3]. In the second factor,
thermal emissivity at temperature T. This is given by the ratio of the emittance from the
surface of the selective coating over the emittance from a perfect blackbody (BB) radiator at
the same temperature T. This merit function F was chosen because it is independent of
geometry and operation [27]. The geometry of the design determines the concentration factor,
the uniformity and the angular distribution of the solar radiation on the absorber. The relative
importance of thermal emissivity and solar absorptivity is also determined by system
operation. For example, if the molten salts are pumped through the HCE at night time to
avoid solidification, achieving a low HCE emissivity is a priority. Therefore the product in
Eq. (1) results in a good performance evaluation when no assumptions are made about
geometry and operation.
Based on the merit function F, an ideal cutoff wavelength can be determined for a specific
operation temperature. Next generation parabolic solar troughs with molten salts are expected
to operate around 720K [1,2]. Therefore, the spectral performance will always be evaluated at
solar
α
is the fraction of the solar irradiance (AM1.5) absorbed by the stack
( )
thermalT
ε
is the integrated
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Page 4
720K in the following sections. According to Eq. (1) an ideal absorber for operation at 720K
has a cutoff wavelength
cλ =2.24µm.
3. Aperiodic metaldielectric stacks
Recently, we proposed aperiodic onedimensional metaldielectric multilayer stacks as
selective emitters in thermophotovoltaics [28] and selective absorbers for concentrated solar
thermal (CST) applications [27]. The metals inside the stacks act as emitters/absorbers and
the dielectrics as optical spacers, creating interference effects that enhance
emission/absorption in a desired spectral range. We first summarize briefly the results
obtained in [27] because in the next section, we will analyze whether the performance of the
aperiodic multilayer stacks proposed in [27] can be further improved by deposition onto
metallic Vgroove gratings. The planar aperiodic stacks described in [27] were modeled using
a standard transfer matrix method (TMM) [30] based on complex dielectric permittivity data
at room temperature obtained from the literature [31,32]. Dielectric dispersion data at room
temperature was used because of a lack of broadband data at elevated temperatures. It should
be noted that changes in dielectric properties upon heating modify the optical path lengths as
well as the amplitude and phase relationships at every interface. Generally the extinction
coefficient of conductors increases with increasing temperature [33]. In contrast the
emissivity of dielectrics can either increase or decrease upon heating depending on the
material used. It is known from theory that small variations in extinction coefficient have only
minor influence on spectral properties in spectral regions of high reflectance (IR) [34].
However we must point out that deviations in extinction coefficients might influence the
position of the cutoff between the spectral region of high absorption and the region of high
reflectance. In addition to dielectric properties, layer thicknesses will also vary under thermal
expansion. Since the coating is typically less than a micron thick, thermal expansion will be
largely dominated by the substrate. We have investigated the influence on the spectral
performance when individual layer thicknesses are varied up to 10% and found that spectral
performance or merit function F shows variations typically below 1%. It is however outside
the scope of this manuscript to study and quantify the effect of heating on the dielectric
properties and geometry of the structure and therefore these variations were not included in
the optical modeling.
Optimization was performed using the needle optimization method [35,36] with Eq. (1) as
performance merit. Because of their inherent spectral selectivity and stability at elevated
temperatures, Molybdenum (Mo) and Tungsten (W) were used for the metal substrate and the
thin metal layers in the stacks. For the dielectric spacer layers, Magnesium Fluoride (MgF2)
(n=1.37 at λ=1 µm) and Titanium Dioxide (TiO2  Rutile) (n=2.75 at λ=1 µm) were selected
in order to achieve high refractive index contrast ( n
absorptivity at normal incidence is shown for stacks composed of layers of Mo, MgF2 and
TiO2 (a) and layers of W, MgF2 and TiO2 (b). The stacks have respectively 5, 7, 9 or 11 layers
with layer thicknesses varying from 5 to 100 nm. When determining the number of layers in a
stack, the substrate also counts as one layer. The dotted black line in Fig. 1 represents the
spectral absorptivity of the ideal absorber at T=720K with a cutoff wavelength
Increasing the number of layers leads to improved spectral absorptivity, more closely
approximating the spectrum of the ideal absorber. The spectral behavior of the stacks
represented in Fig. 1 will now be studied when used as coatings on top of subwavelength V
groove gratings.
∆ =1.38 at λ=1 µm). In Fig. 1 the spectral
cλ =2.24µm.
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Page 5
0.30.50.712345 6 7 8
0
0.2
0.4
0.6
0.8
1
Wavelength (µ µ µ µm)
Spectral Normal Absorptivity
Ideal 720K
Mo
5
7
9
11
a.
0.3 0.5 0.712345 6 7 8
0
0.2
0.4
0.6
0.8
1
Wavelength (µ µ µ µm)
Spectral Normal Absorptivity
Ideal 720K
W
5
7
9
11
b.
Fig. 1. Spectral absorptivity at normal incidence for aperiodic metaldielectric stacks optimized
for operation at 720K using (a) Mo, TiO2 and MgF2 and (b) W, TiO2 and MgF2. The spectral
absorptivity of uncoated Mo (a) and W (b) are also shown. The stacks have respectively 5, 7, 9
or 11 layers [27]. The substrate is included when counting the number of layers. The spectral
absorptivity of an ideal absorber at 720K is also plotted for comparison. In contrast to [27]
where the spectral hemispherical absorptivity was show in Figure 5, in this figure the spectral
absorptivity is shown at normal incidence.
4. Subwavelength Vgroove gratings
4.1 Introduction
It was recently shown that tapered metallic subwavelength gratings (SWGs) can be
optimized to achieve excellent spectral selectivity [21,29]. The tapering increases absorption
because it provides an impedance matching between free space and the bulk metallic absorber
for wavelengths comparable to the period of the grating. For electromagnetic waves with a
wavelength much larger than the period of the grating, the impedance matching and thus the
absorption enhancement, is less pronounced. Therefore, by tuning the period of the grating
and the aspect ratio of the tapering the desired spectral selectivity can be obtained. Here, we
analyze whether the performance of aperiodic multilayer stacks, introduced above, can be
further improved by deposition onto Vgroove gratings. Such structures are expected to
combine the performance advantages of aperiodic metaldielectric stacks and tapered metal
gratings, and may be economical to fabricate using a vacuum deposition process on grooved
substrates. The resulting structure is illustrated in Fig. 2. The structure is characterized by its
period a, the angle
GR
θ
of the Vgroove, the material and the thickness of each layer of the
aperiodic stack. All layer thicknesses are measured normal to the faces of the grooves.
The melting temperatures of nanostructured materials are known to be lower than for bulk
materials [37]. 2D and 3D nanostructures have larger surface to volume ratios, making them
more prone to surface diffusion, especially at sharp edges, such as in Vgroove and pyramid
gratings. This could lead to a change in shape at temperatures well below the bulk melting
temperature, which in turn would lead to a degradation of the spectral properties. Schlemmer
et al. [38] have observed this effect. However they have shown that depositing a coating on
top of nanostructured metal gratings can enhance the thermal stability of the grating. This is
an additional motivation to study the effect of coatings on top of nanostructured refractive
metal surfaces.
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Page 6
Fig. 2. Two periods of the metallic subwavelength Vgroove grating coated with an aperiodic
multilayer stack. The grating period a and the Vgroove angle
GR
θ
are indicated.
4.2 Rigorous coupledwave analysis
The emissivity of aperiodic stacks deposited into these Vgrooves was evaluated using
rigorous coupledwave analysis (RCWA) based on the original algorithm [39] and
generalized for simulating arbitrary aperiodic layered 2D photonic crystals. The enhanced
transmittance matrix method [40] was used to enforce boundary conditions at the interface of
two grating layers. In order to model the structure, 3D space was discretized into boxes with a
defined dielectric permittivity, as shown schematically in Fig. 3. The complex dielectric
permittivity data for the materials simulated were obtained from the literature [31,32]. The
step size in the Y direction was set to 0.5 nm in all simulations. Because we are dealing with a
1D grating, no spatial dependence of the dielectric permittivity in the X direction was
incorporated. In the Z direction the structure was sliced into a number of grating layers L. In
order to obtain good convergence, the number of grating layers L was increased with the
height of the structure in the following way:
(
1
tot
Ltaµ
=⋅+
)
tan()
m GR
θ
⋅
(2)
where
m
aµis the Vgroove period in micron,
θ
is the angle of the Vgroove (see Fig. 3). In the case of an uncoated V
tot
t is the total thickness of the coating in
nanometers and
GR
groove tot
t was set to 200.
Fig. 3. Discretization of the coated Vgroove grating used in the RCWA simulations. We note
that actual simulations used a much finer grid.
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A convergence analysis was performed to check the number of diffraction orders or
modes that needed to be retained in the RCWA simulations. The result of the convergence
analysis for an uncoated Mo Vgroove with
absorptivity  α
∆
 when the number of retained diffraction orders m is increased stepwise with
m
∆
=7 is shown for various wavelengths. This convergence analysis was performed for a
period a=300nm and 260 grating layers. The change in absorptivity  α
wavelengths once >40 modes are retained. Similar results were obtained for the coated
structures and for different Vgroove angles and periods. Based on the convergence analysis
the number of diffraction orders in all simulations was set to 47.
GR
θ
=45° is shown in Fig. 4. The change in
∆
 is <102 for all
Fig. 4. Convergence analysis for an uncoated Mo Vgroove grating with
GR
θ
=45° and a
grating period a=300nm.
4.3 Uncoated subwavelength Vgroove gratings
We first investigate the spectral performance of uncoated Mo and W subwavelength V
groove gratings, which are similar to the tapered pyramid gratings reported by Rephaeli et al.
[29]. As illustrated in Fig. 2, the Vgrooves are 1Dgratings with discrete translational
symmetry along the Ydirection and continuous translational symmetry along the Xdirection.
In general, separation into distinct modes is only possible when there is a plane M for which
there is mirror symmetry for both the wavevector k and position vector r [14]. For the V
groove grating, we can only define one mirror plane which is independent of origin. This is
the plane perpendicular to the Xaxis, here called Mx. The TE and TM mode can thus be
defined with respect to this mirror plane Mx. The TE mode has field components Ey, Ez and Hx
and the TM mode has field components Hy, Hz and Ex. As a consequence, light polarized
along the Ydirection (Ey) can only couple into TE modes, and light polarized along the X
direction (Ex) can only couple into TM modes. This is also illustrated in the insets of Fig. 5(a)
and 5(b).
In Fig. 5(a), the spectral absorptivity of uncoated Mo Vgroove gratings with a period
a=300nm is shown for normally incident light polarized along the Ydirection (TE mode).
The spectral absorptivity is modeled for gratings with increasing depth of the groove (keeping
the period a=300nm constant), varying from planar geometry planar geometry (
0
GR
θ
= ° )
(dark blue) to deep Vgroove gratings with high aspect ratio (
light can couple into radiation modes of the subwavelength grating which conserve the
wavevector in the Ydirection (
y
k ) up to a reciprocal lattice vector, since there is discrete
translational symmetry in this direction. This means that the normally incident light in this
case (which has no wavevector component in the Ydirection) can couple into modes with
2
y
na
π
= ⋅
k
, where n is an integer. This means that diffraction peaks are expected at
λ =
. Therefore a sharp absorption peak is observed at
λ =a=300nm in Fig. 5(a).
For the TE mode, absorptivity is also enhanced for wavelengths larger than the grating
period, especially for deeper grooves (dark red). Since the incoming electric field is polarized
along the Ydirection, perpendicular to the groove, no continuous boundary matching is
80
GR
θ
=°) (dark red). Incident
wavelength
, / 2, /3, ... , /
a aaa n
(C) 2010 OSA15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5531
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required. As a consequence, the EM wave can propagate deep into the Vgroove, even for
wavelengths larger than the grating period. The result is that the absorption edge redshifts
when the depth of the groove increases (higher aspect ratio). The gradual impedance
matching strongly enhances the absorption of the TE mode up to wavelengths similar to the
depth of the groove.
0.3 0.50.712345 6 7 8
0
0.2
0.4
0.6
0.8
1
Wavelength (um)
Normal Spectral Absorptivity TE
a.
Ey
kz
Ey
Hx
Ez
MX
0.30.50.712345 6 7 8
0
0.2
0.4
0.6
0.8
1
Wavelength (um)
Normal Spectral Absorptivity TM
b.
Hy
Ex
Hz
Ex
kz
MX
TE
TM
Fig. 5. Normal spectral absorptivity for uncoated Mo Vgroove gratings with various Vgroove
angles for (a) TE mode (Ey, Ey, Hx) and (b) TM mode (Ex, Hy, Hz). The structure varies from
planar geometry (dark blue) to deep Vgroove gratings with high aspect ratio (dark red). The
period a=300nm is kept constant for all grooves. The captions illustrate the mirror symmetry
and define the (a) TE and (b) TM mode.
In Fig. 5(b), the spectral absorptivity is shown for normally incident EM waves polarized
along the Xdirection (TM mode). Again, the curves represent Vgroove gratings with
increasing depth of the groove, varying from planar geometry (
θ
now polarized along the groove, the field must be continuous across the metalair boundary.
As a consequence, EM waves with a wavelength much larger than the grating period will not
be able to penetrate deeply into the Vgroove. More incoming radiation is reflected and less
absorption enhancement is observed for the TM mode at longer wavelengths. No significant
redshift is observed for grooves with a higher aspect ratio (dark red).
In Fig. 6, the normal spectral absorptivity of uncoated Mo Vgroove gratings is shown as
a function of the angle
GR
θ
of the Vgroove. The angle is varied from planar geometry
(0
GR
θ
= ° ) to a very deep groove (80
GR
θ
=°), and for each structure the spectral absorptivity
is shown at normal incidence. For these calculations, the grating period a was kept constant at
300 nm (top), 500 nm (middle) and 700 nm (bottom), respectively. Here, the absorptivity is
averaged over the TE and TM polarization. The absorption for λ < 2.24µm is clearly enhanced
with increasing Vgroove angle, because a more gradual impedance matching is obtained, in
agreement with Rephaeli et al. [29]. This would result in a more optimal absorber for
operation at 720K. The periodicity of the grating influences the range over which enhanced
absorption is achieved. Larger periods lead to a broader range of enhanced absorption,
because EM waves with longer wavelengths can more easily penetrate into grooves with a
larger period. In order to achieve optimal coatings, the selectivity of the enhancement is
essential. Increased absorption for wavelengths above the cutoff wavelength
the ideal absorber at 720K will lead to thermal losses by IR emission. The obtained spectral
selectivity and the merit evaluations for these uncoated metal Vgroove gratings are discussed
in detail below.
0
GR
θ
= ° ) (dark blue) to deep
Vgroove gratings with high aspect ratio (80
GR
=°) (dark red). Since the electric field is
cλ = 2.24 µm of
(C) 2010 OSA15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5532
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Page 9
Fig. 6. Spectral normal absorptivity of uncoated Mo Vgroove subwavelength gratings as a
θ
. For the top, middle and bottom plot the grating period a is kept
function of the angle
GR
constant at 300 nm, 500 nm and 700 nm respectively.
For all uncoated Mo gratings in Fig. 6, distinct diffraction peaks can be observed, once the
groove becomes sufficiently deep. As mentioned above, diffraction peaks are expected at
wavelength
, / 2, /3, ... , /
a aa a n
λ =
. For the top, middle and bottom plot of Fig. 6 the first
diffraction peak is observed at 300nm, 500nm and 700nm respectively. For a = 700 nm
(bottom), the second order diffraction peak can also be observed at λ = 350 nm.
4.4 Coated subwavelength Vgroove gratings
We have simulated the spectral properties of coated Vgroove gratings for various depths and
periods using RCWA. The coatings that were applied to the Vgroove are those illustrated in
Fig. 1 and their design for planar substrates was previously described in [27]. First, we will
investigate the spectral selectivity for the 5layer stack composed of layers of Mo, MgF2 and
TiO2, illustrated in Fig. 1(a) (cyan). In Fig. 7, the normal spectral absorptivity is shown as a
function of the angle of the Vgroove for this 5 layer coating on top of a Mo Vgroove
grating. Again, the angle of the groove is varied from planar geometry (
θ
=°), and for each structure the spectral absorptivity is shown at normal
incidence. Similar to the case of uncoated Mo, the wavelength range of enhanced absorption
increases with the depth of the groove. However, the enhancement is more subtle, because the
5layer aperiodic metaldielectric coating was already optimized for planar geometry.
0
GR
θ
= ° ) to a very
deep groove (80
GR
(C) 2010 OSA15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5533
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Page 10
Fig. 7. Normal spectral absorptivity as a function of the angle
GR
θ
of the groove for Mo V
groove gratings coated with a 5layer stack composed of Mo, MgF2 and TiO2. For the top,
middle and bottom plot the grating period a is 300 nm, 500 nm and 700 nm respectively.
To compare the spectral performance of the uncoated and coated structures, the merit
function F, described in section 2, was evaluated. In Fig. 8, the merit evaluation is shown for
the uncoated Mo Vgroove gratings (blue) with a grating period a=300nm. The angle of the
groove is varied from planar geometry (0
GR
θ
= ° ) to a very deep groove (
each structure the merit F was evaluated at 720K, since we are optimizing the absorber for
solar thermal applications at this temperature. A significant increase in spectral performance
can be observed with increasing groove depth. This is due to the enhanced impedance
matching for deeper grooves causing a selective increase in absorption, in agreement with
Rephaeli et al. [29]. The merit F for the 5layer stack (cyan) is also shown in Fig. 8. The 5
layer metaldielectric coating was previously optimized for planar geometry (
thus the initial merit function is relatively high (F=0.85). However the spectral performance
further increases with
GR
θ
or groove depth. The increase in spectral performance can be
explained by the gradual increase in absorption for wavelengths shorter than the ideal cutoff
wavelength
cλ also gradually increases with increasing depth of the groove. This results in a
loss in spectral selectivity for very deep grooves, as observed in Fig. 8. These two effects lead
to a tradeoff and therefore an optimal angle
GR
θ
θ
and the corresponding merit evaluation for all coatings are given in Table 1 for
80
GR
θ
=°), and for
0
GR
θ
= ° ) and
cλ =2.24 µm, illustrated in Fig. 7. However, the absorptivity for wavelengths
larger than
,max
of the groove can be determined. Values
for
,max
GR
grating period a=300nm.
(C) 2010 OSA15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5534
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0 20 406080
0
0.2
0.4
0.6
0.8
1
Vgroove angle θ θ θ θGR ( ° ° ° ° )
Merit F at 720K
5
Mo
a = 300nm
Fig. 8. Merit function evaluation at 720K for a 5layer aperiodic coating (cyan) composed of
layers of Mo, TiO2 and MgF2 on top of Mo Vgroove gratings with grating period a=300nm
θ
. The merit evaluations for uncoated Mo Vgroove gratings are
and varying groove angle
GR
also shown (blue).
Fig. 9. Angular absorptivity
and (b,d) S polarization for a 5 layer aperiodic stack composed of Mo, TiO2 and MgF2 layers
( , )
α θ φ at (a,b) λ=0.8µm and (c,d) λ=3µm for (a,c) P polarization
on top of a Mo Vgroove with period a=300nm and
40
GR
θ
=° .
For
GR
θ
≤ 70°, significant higher spectral selectivity is obtained for Mo Vgroove gratings
coated with the 5layer stack composed of Mo, MgF2 and TiO2. The interference effects
created inside the aperiodic stack dictate the spectral properties and lead to an enhanced
spectral selectivity compared to the bare grating. Since the aperiodic stacks have wide angular
absorptivity [27], the interference effects dominate the spectral performance even for deep
grooves. However, for
GR
θ
> 70°, the angular spectral properties suffer in accordance to [27]
and the spectral performance of the coated gratings becomes worse than that of the uncoated
(C) 2010 OSA15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5535
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Page 12
gratings (see Fig. 8). Similar trends were observed for the Vgroove gratings with larger
grating period and the best results were obtained for the 300nm grating period. The highest
merit for the 5layer stack was obtained at
,max
GR
θ
The angular dependence of the absorptivity of the Vgroove gratings was also
investigated. For the optimal coated Mo grating with period a=300nm and
α θ φ is shown in Fig. 9(a) and 9(b) at λ=0.8µm for the P and S
polarization, respectively. Here the incident direction of radiation is defined by the polar
angle θ and the azimuthal angle φ . By convention, P (S) polarization is defined as the
electric field polarized parallel (perpendicular) to the plane of incidence. At λ=0.8µm, the
coated grooves behaves as a wideangular absorber, with little azimuthal dependence. Only
for very large polar angles the absorptivity decreases notably. The angular absorptivity at
λ=3µm is also shown in Fig. 9(c) and 9(d) for the P and S polarization, respectively. At this
wavelength, the coated groove behaves as a lowemissivity surface for all angles.
≈ 40° (merit F = 0.87).
40
GR
θ
=° the
angular absorptivity ( , )
Fig. 10. Spectral absorptivity at normal incidence
composed of Mo, TiO2 and MgF2 layers on top of a Mo Vgroove with period a=300nm and
θ
=° . Normal absorptivity when (a) electric field (Ey) is perpendicular to the groove
(0,0, )
αλ for a 5 layer aperiodic stack
40
GR
(couples into TE mode) and (b) electric field (Ex) is parallel to the groove (couples into TM
mode). Angular absorptivity
( , )
α θ φ at λ=1.4µm for (c) P polarization and (d) S polarization.
We also studied the angular dependence of the absorptivity close to the
spectral edge (1µm<λ<3µm) for the 5layer stack on the optimal Mo Vgroove with period
a=300nm and
40
GR
θ
=°. At λ=1.4µm, we see a significant angular dependence in the
absorptivity of the coated Vgroove grating for the P and S polarization [Fig. 10(c) and
10(d)]. To understand this angular dependence, we need to first consider the spectral
absorptivity at normal incidence. As explained above, light at normal incidence polarized
along the Ydirection (perpendicular to the groove) will couple into the TE mode. In contrast,
light polarized along the Xdirection (parallel to the groove) will couple into the TM mode.
The spectral edge for the TE mode is redshifted compared to the TM mode because the TE
waves penetrate more deeply into the groove. This is also illustrated in Fig. 10(a) and 10(b)
(C) 2010 OSA15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5536
#121444  $15.00 USDReceived 14 Dec 2009; revised 27 Feb 2010; accepted 28 Feb 2010; published 3 Mar 2010
Page 13
where the spectral absorptivity at normal incidence is plotted for the TE and TM mode
respectively. Let us now consider incoming light propagating in the ZY plane,
for
45
θ ≈° and
90
φ =°. In this direction, the absorptivity is significantly different for the P
and S polarization [Fig. 10(c) and 10(d)]. The P polarization will have an electric field
component in the Ydirection and can thus effectively couple into the TE mode, for which the
absorptivity is still >90%. As a consequence the absorptivity for the Ppolarization will also
by high. In contrast, the S polarization will have a field component along the Xdirection and
effectively couple into the TM mode. At λ=1.4µm, the TM mode has a lower absorptivity
(≈50%), and therefore the S polarization has a lower absorptivity at this angle of incidence.
When averaging over both S and P polarization for randomized incoming solar radiation, the
angular dependence is smoothened.
It is clear from the results above that the performance of uncoated metallic
Vgroove gratings can be improved by coating the gratings with an optimized
metaldielectric multilayer stack. An optimal Vgroove angle
determined for each selected coating. We modeled the spectral performance of all the
aperiodic stacks that were introduced in section 3, (see Fig. 1). In Fig. 11(a), the merit
evaluation at 720K is shown for the aperiodic stacks composed of Mo, TiO2 and MgF2 layers
on top of Mo Vgroove gratings with a period a=300nm. The stacks have 5, 7, 9 and 11 layers
and were previously optimized for the planar geometry [27]. At
the 11layer stack has the highest merit function (F=0.88). Trends similar to those observed
for the 5layer coating above are observed for coatings with more layers. However the
increase in merit is less pronounced, since the coatings had already excellent spectral
performance in the planar geometry.
GR
θ
can be
0
GR
θ
= ° (planar geometry),
020406080
0
0.2
0.4
0.6
0.8
1
Vgroove angle θ θ θ θGR ( ° ° ° ° )
Merit F at 720K
Mo579 11
a.
a = 300nm
0 20406080
0
0.2
0.4
0.6
0.8
1
Vgroove angle θ θ θ θGR ( ° ° ° ° )
Merit F at 720K
W579 11
b.
a = 300nm
Fig. 11. Merit evaluation at 720K as a function of angle
GR
θ
for aperiodic stacks composed of
(a) Mo, TiO2 and MgF2 layers on top of Mo Vgrooved substrates and (b) W, TiO2 and MgF2
layers on top of W Vgrooved substrates for period a=300nm. The stacks have respectively 5,
7, 9 and 11 layers and were previously optimized for planar geometry [27]. The merit is also
shown for the uncoated Vgrooves made of (a) Mo and (b) W.
For each coating, an optimal Vgroove angle
,max
GR
θ
and corresponding merit F can be
determined. The best result is obtained with the 9layer stack (orange) on top of a Mo V
groove with
,max
36
GR
θ
=° . This structure is predicted to have a solar absorptivity of >94%
while having a thermal emissivity as low as 6% of that of a blackbody at 720K (F=0.89). The
results are summarized in Table 1. In Fig. 11(b), the merit evaluation is shown for stacks
composed of W, TiO2 and MgF2 layers on top of W Vgroove gratings with a period
a=300nm. Again, similar trends are observed and an optimal Vgroove depth can be
(C) 2010 OSA15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5537
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Page 14
determined. Here, the results obtained for the 7, 9 and 11 layer coatings are similar, with an
optimal merit F around 0.89.
In Fig. 12, the spectral absorptivity at normal incidence is shown for the coated Vgroove
gratings with optimal aspect ratios (
,max
GRGR
θθ
=
the absorptivity is averaged over both polarizations. If we compare these spectral curves to
the planar geometry (Fig. 1), we observe an increased absorption for short wavelengths and a
slight redshift of the absorption edge. This redshift is related to the TE mode as discussed
above.
) for each stack under investigation. Here,
0.3 0.50.712345 6 7 8
0
0.2
0.4
0.6
0.8
1
Wavelength (µ µ µ µm)
Spectral Normal Absorptivity
Ideal 720K
Mo VGR
5 VGR
7 VGR
9 VGR
11 VGR
a.
0.30.50.712345 6 7 8
0
0.2
0.4
0.6
0.8
1
Wavelength (µ µ µ µm)
Spectral Normal Absorptivity
Ideal 720K
W VGR
5 VGR
7 VGR
9 VGR
11 VGR
b.
Fig. 12. Spectral absorptivity at normal incidence for aperiodic stacks composed of (a) Mo,
TiO2 and MgF2 layers on top of Mo Vgroove gratings with optimized aspect ratios and (b) W,
TiO2 and MgF2 layers on top of W Vgroove gratings with optimized aspect ratios. The grating
period a is 300nm. The stacks have respectively 5, 7, 9 and 11 layers and were previously
optimized for planar geometry [27]. The spectral absorptivity is also shown for the optimal
uncoated Vgroove gratings made of (a) Mo and (b) W. The optimal aspect ratio (
,max
GR
θ
) for
each of these coated gratings can be found in Table 1.
The merit evaluations of the coated Vgrooved structures with period a = 300nm are
summarized in Table 1. In general, stacks with more layers perform better. These coated sub
wavelength gratings are predicted to have performance in pair with commercially available
cermet coatings (PTR70) [2] and complex multilayer coatings previously suggested by
Kennedy et al. [4] (NREL 6A). For comparison, their spectral data and merit is also given in
Table 1.
(C) 2010 OSA15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5538
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Table 1. Merit F at 720K for coatings on planar geometry (
GR
θ
= 0) and optimal coated
Vgroove (
,max
GR GR
stack, the substrate layer also counts as a layer.
θθ
=
). When determining the number of layers Ls in an aperiodic
Ls
PLANAR
εthermal
VGROOVE GRATING a=300nm
Material Selection
αsolar
Merit
αsolar
εthermal
Merit
θGR,max
Uncoated Mo
Mo MgF2 TiO2
Mo MgF2 TiO2
Mo MgF2 TiO2
Mo MgF2 TiO2
Uncoated W
W MgF2 TiO2
W MgF2 TiO2
W MgF2 TiO2
W MgF2 TiO2
NREL 6A

5
7
9
11

5
7
9
11

0.36
0.88
0.90
0.91
0.94
0.45
0.91
0.92
0.92
0.95
0.96
0.02
0.03
0.04
0.05
0.06
0.03
0.05
0.05
0.05
0.06
0.07
0.36
0.85
0.86
0.87
0.88
0.43
0.87
0.87
0.87
0.89
0.89
0.83
0.92
0.94
0.94
0.96
0.89
0.95
0.95
0.95
0.95

0.08
0.05
0.06
0.06
0.08
0.11
0.06
0.07
0.07
0.06

0.77
0.88
0.89
0.89
0.88
0.79
0.89
0.89
0.89
0.89

78°
41°
36°
36°
24°
78°
36°
36°
30°
11°

PTR70

0.96
0.10
0.86




For the Wbased stacks, the increase in spectral selectivity obtained by depositing the
stacks onto Vgroove gratings might be insufficient to validate the more complex fabrication.
However, in this work we have limited our variable space. We believe that potential
improvements lie in optimizing multilayer coatings specific for each Vgroove. One potential
way of fabricating sub wavelength grooves is to use selective etching processes which results
in grooves where the angle of the groove is set by the preferential crystal planes. In this case
the Vgroove angle would be fixed, and the multilayer stack could be further optimized to
achieve optimal spectral performance. Other improvements lie in optimizing the periodicity
of the grating, as well as investigating 2D grating structures.
5. Conclusion
We previously reported on planar aperiodic metaldielectric stacks for use in solar thermal
systems. Here, the optical behavior of metallic Vgroove gratings coated with these aperiodic
stacks was modeled using RCWA. The spectral selectivity of these coated gratings was
investigated and compared to the planar geometry. We conclude that the performance of
uncoated metallic Vgroove gratings can be significantly improved by coating them with a
metaldielectric multilayer stack. The grating period a and groove angle
significant impact on the spectral absorptivity. For coated Vgrooves, the interference effects
of the coating still dominate the spectral behavior. However, optimized metaldielectric
coatings combined with the gradual impedance matching provided by the Vgroove, exhibit
improved performance. Even though the improvement in adding a Vgroove texture to the
multilayer stack is subtle, it is important to note that fewer layers in the coating are required
to achieve high performance. For a specific operational temperature, an optimal grating
period a and Vgroove angle
GR
θ
can always be determined depending on the selected
coating. It is important to note that alternative figures of merit that take geometry and
temperature into consideration will result in different optimal values for grating period and V
groove angle than the ones described in this manuscript. We must point out that the operation
lifetime of absorber coatings used in heat collection elements is critical and thus the thermal
stability of the proposed coated gratings will need to be verified. If they prove to be thermally
stable, these coated structures are good candidates for use in solar thermal applications
because of their potential to achieve excellent spectral performance.
GR
θ
have a
(C) 2010 OSA15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5539
#121444  $15.00 USDReceived 14 Dec 2009; revised 27 Feb 2010; accepted 28 Feb 2010; published 3 Mar 2010