Metasurface holograms reaching 80% efficiency

TLDR: The design of the hologram integrates a ground metal plane with a geometric metasurface that enhances the conversion efficiency between the two circular polarization states, leading to high diffraction efficiency without complicating the fabrication process.

Abstract: Using a metasurface comprising an array of nanorods with different orientations and a backreflector, a hologram image can be obtained in the visible and near-infrared with limited loss of light intensity.

Figures

Figure 1 | Illustration of the unit-cell structure and its polarization conversion efficiency by numerical simulations. a, One pixel cell structure of the nanorod based hologram. The nanorod can rotate in the x-y plane with an orientation angle ϕ to create different phase delay. The pixels are arranged with periods Px=300 nm and Py=300 nm. The nanorods have a length of L=200 nm, a width of W=80 nm and a height of H=30 nm. The MgF2 and gold film have thicknesses of h1=90 nm and h2=130 nm, respectively. b, Cross section of the pixel cell. The MgF2 film acts as a Fabry-Pérot cavity, which can let the returned beam keep exciting the nanorod and generate the output beam with phase-delay. The gold film acts as the mirror to reflect the incident light. c, Phase delay for the different phase levels. On each knot, the orientation of nanorod has been annotated. d and e, Simulated amplitude |rl|, |rs|, phase φl, φs and phase difference Δφls of the reflection coefficients rl and rs, where l and s denote the long and short axis directions of the nanorods, respectively. f, Simulated cross-polarization and co-polarization reflectivity upon normal light incidence.

Figure 3 | Experimental results for the holographic image generation. a, Scanning electron microscopy image of the fabricated nanorod array (partial view). b, Experimentally obtained optical efficiency for both image and 0th-order beam. The measurements show very high optical efficiency above 50% for the image beam over a range of 630-1050 nm. c, d and e, Simulated holographic image of Einstein’s portrait with enlarged zoom of his face and the character ‘M’. f, g and h, Experimentally obtained images that are captured by a visible camera in a far field. The operation wavelength is 632.8 nm. i, j and k, Experimentally obtained images that are captured by an infrared camera in the far field,

Figure 2 | Working principle and phase distribution of the periodic hologram. a, Illustration of the reflective nanorod-based CGH under a circularly polarized incident beam. The circularly polarized incident beam, which is converted from a linear polarized one by passing through a quarter waveplate (QWP), falls on the metasurface. The reflected beam forms the holographic image in the far-field (at any plane vertical to the optical axis of incident beam). b, Target image with 256 greyscale levels and a size of 550×300 pixels used for the generation of the hologram. c, To generate the target holographic image in the far field, the designed 16-level phase distribution with 2×2 periods and a scale bar of 200 µm is illustrated. d, An enlarged phase distribution with 100×100 pixels and a scale bar of 10 µm at up-left corner of c is shown separately.

Full text

University of Birmingham
Metasurface holograms reaching 80% efficiency
Zheng, Guoxing; Zhang, Shuang; Li, Guixin; Kenney, Mitchell; Mühlenbernd, Holger;
Zentgraf, Thomas
DOI:
10.1038/nnano.2015.2
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None: All rights reserved
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Peer reviewed version
Citation for published version (Harvard):
Zheng, G, Zhang, S, Li, G, Kenney, M, Mühlenbernd, H & Zentgraf, T 2015, 'Metasurface holograms reaching
80% efficiency', Nature Nanotechnology, vol. 10, pp. 308-312. https://doi.org/10.1038/nnano.2015.2
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2. School of Electronic Information, Wuhan University, Wuhan, 430072, China
3. Department of Physics, University of Paderborn, Warburger Straße 100, D-33098 Paderborn,
Germany
4. Department of Physics, Hong Kong Baptist University, Hong Kong, China
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!
!
In! traditional! phase-only!computer!generated!hologram!designs,! the!phase!profile!is! controlled!
by!etching! different!depths!into!a !transparent!substrate.!Due! to! the! ease! of! fabrication,! two!level!
binary!CGHs! have! been!widely!employed.!Such!CGHs!have!a!theoretical!diffraction!efficiency!of!
only!40.5%! and!th e! issue! of!tw in-image! generation! cannot! be! avoided.! Multi-level! phase! CGHs!
can!alleviate!the!problem!of!low!efficiency!and!twin-im age!generation;!however,! fabricating!such!
CGHs! requires! expensive! and! complicated! grayscale! lithography,! variable-dose,! or! multi-step!
lithography
20
.!Furthermore,!the!unavoidable!etching!error,!resolution! error! and!alignment!error!
can! dramatically! degrade! the! performance! of! CGHs,! such! as! low! signal-to-noise! ratio,! poor!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*
! These!authors!contributed!equally!to!this!work.!
†
! gxli@hkbu.edu.hk!
‡
! thom as.ze ntgra f@ u ni-paderborn.de!
§
! s.zhang@b ham .ac.uk!

!
uniformity!and!strong!zero-order!intensity.!To! obtain !a!higher!efficiency! and! less!manufacturing!
complexity,! an! effective! medium! approach ! has! been! proposed
20
,! where! two-level! depth!
subwavelength!structures!with!variable!cell!dimension!can!functio n!as!an!effective!mediu m !with!
geometry! controlled! effective! refractive! index,! and! consequently! act! as! a! multi-level! CGH.!
However,!such!a!design!involves!extreme!small!feature!sizes!with!high!aspect!ratios,!limit in g !the!
observed!efficiency! of!a! three!level!CGH! to!less!than! 30%,!which! is! significantly!lower!than!the!
theoretical!value!of!48 % .!
!
GEMS! provide!an! alternative!approach!towards!high! efficiency!holograms!without!complicated!
fabrication! procedures.! The! operation!of! GEMS!relies!on! the!inversion!of! the!absolute!rotation!
direction!of!the!electric!field!of!the!radiation!(in!transmission!or!reflection)!compared!to!that!of!
the!incident!circularly!pola rized!one
21,!22
.!This!is!e q u ivalent!to!flipping!the !c ircular!polarization!in!
transmission! or! maintaining! the! s am e ! circular! polarization! in! reflection.! A! geometric! phase,! or!
Pancharatnam- Berry!phase,!is! acquired! through!the!inversion!of!electric! field! rotation,! leading!to!
an!antenna-orientation!controlled!phase!which!does!not!depend!on!the!specific!antenna!design!
or! wavelength,! thus! making! its! performance! broadband,! and! highly! robust! against! fabrication!
latitude! and! variation! of! material! p ropertie s.! However,! GEMS! operating! at! visible! and! near!
infrared! wavelengths!have! been!limited!so! far! by!th e! low! efficiency!in ! conversion! between!the!
two!circular!polarization!states.! !
!
In!o rder! to!increase ! the! efficien c y! of! GEMS,! a!multilayer!design! is!employed!for! achieving! high!
polarization! conversion
23-26
.! The! reflective! metasurface! hologram! consists! of! three! layers:! a!
ground! metal! plane,! a! dielectric! spacer! layer! and! a ! top! layer! of! a ntennas! (Figure! 1).! It! is! well!
known! that! a! half! wave! plate! can! fully! convert! a! circular! polarized! beam ! to! the! oppositely!
polarized!one!in!transmission!due!to!a!phase!delay!of!π!between!the!fast!and!slow!axis.!H e n ce ,!
for!achieving!high!conversion!between!the!two!circular!polarization!states,!it!is!desired!that!the!
phase!difference!between!the!reflection!with!polarization!along!the!long!axis!(r
l
)!and! sh ort!axis!(r
s
)!
of! the! nanorod! antenna! equals! π.! The! simulated! results! in! Figure! 1d-e! show! that,! with! an!
optimized! configuration,! the! phase! difference! between! th e! reflection! coefficients! r
l#
and! r
s#
approaches! π! within! a! wide! wavelength! range! of! 600- 1000! nm.! At! the! s ame! time,! the!
configuration! maintains! very! large! reflection! am plitudes! over! 0.8! for! both! linear! polarizations.!
Therefore,!regardless!the!orientation!of!the!antennas,!it!is!expected!that!the!circularly!p ola rized!
incident! light! almost! completely! flips! the! absolute! rotation! direction! o f! the! electric! field! up on !
reflection,! thus! preserving! its! circular! polarization! state! considering! that! the! wave! vector! is!
reversed! as! well.! This! forms!the! basis! of! the! high! efficiency!geom etric! metasurface.!A! detailed!
discussion! and!a!simplified!model!for!explaining!the!high!efficiency!and!broadband!responses!of!
the!nanorod!metasurface!can!be!found!in!the!SI!(Supplementary!Fig.!1-7).!
!
The!high!efficiency!of!maintaining!the! same!circular!polarization! state!upon!reflection!is !verified!
by!numerical! simulations!for! a!uniform!metasurface!with!all!nanorod!antennas!aligned!along!the!
same! direction,! as! sh o w n ! in! Figure! 1f. ! The! reflected! wave! in! general! consists! of! both! circular!
polarization!states:!on e !is !th e !same!handedness! as!the!incident!circularly!polarized!light!but!with!
an!additional!phase!delay!2ϕ,!where!ϕ is!the!orientation!angle!of!th e!nanorod!antenna,!and !the!
other! one! is! the! opposite! handedness! without! the! additional! phase! delay.! For! the! specific!

!
geometry! configuration! shown! in! Figure! 1a! upon! normal! lig ht! incidence,! the! nu m erical!
simulation!shows!that!the ! reflectivity!of!light!w ith! th e! sa m e! circular!polarization!state!is!over!80% !
in! a !broad!wavelength!range!between!550!nm!and!1000!nm ,! covering!nearly!a!full!optical!octave.!
This! efficiency! is! surprising ly! h ig h ! cons id er ing ! th e ! o h m ic ! lo ss! o f ! m etal! at! the! visible! and! near!
infrared!frequencies .!Interestingly,!the !the!ohmic!loss!in!our!configuration!is!very!clo se!to!that!of!
light! transmitting! through! a! single! metasurface! layer! (with o ut ! the ! ground! m etal! plane )! around!
the!resonance!wavelength!(800!-!850! nm)!of!the!antenna!(Supplementary! Fig.!8).!On!the!other!
hand,!the!efficiency!of!the!unwanted!opposite!polarization! is!extremely!low,! less!than!3%,! over!a!
broad!wavelength!range.!
!
To!confirm!the!high! efficiency!of!our!numerical!simulations!we!designed!a!geometric!metasurface!
based!CGH!as!shown! in!Figure!2.! The!CGH!was! designed!for!circularly!polarized!light!at!normal!
incidence.! We! used! a! design! so! th at! the! holographic! image! appears! off-axis! to! avoid! the!
overlapping! betwee n! the! holographic! image! and! the! zero-order! spot.! The! CGH! is! designed! to!
create! a! wide! image! angle! of! 60°×30°.! In! our! structure! we! used! a! 2×2! periodic! array! of! the!
hologram! pattern!(Figure!2d),! more!details! of!the! advantages!of! the!2x2! periodic!arrangement!
over! single! hologram! is! given! in! the! SI! (Supplementary! Fig.! 9).! To! create! a n! holograp hic! image!
with!a!pixel!array!of! m×n#within!the!angular!range!of! α
x
×α
y
!in!the!far!field,!the!period!of!th e!CGH!
at!x!and!y!direction!can!be!calculated!by!d
x
=m
λ
/[2tan(α
x
/2)]!and!d
y
=nλ/[2tan(α
y
/2)],!respectively.!
The!number! of!pixels!of! the!CGH!is!determined!by!M=#d
x
/Δp!and!N=d
y
/Δp, where! Δp!is!the!pixel!
size!of!the!CGH!in!both!x!and!y!directions.!
!
With! th e!ab ove! structural!parameters,!a !phase-only!CGH!with!pixel!s ize! of!300!nm!×!300!nm!and!
periods! of! 333.3! μm! × 333.3! μm! was! de signe d! by ! the! classical! Gerchberg−Saxton! algorithm
27
.!
Note!that!the!size!of!the!pixel!along!each!direction!is!les s!than!half!of!the!wavelength,!ensuring!
that!the!hologram!p attern!is!sampled!at!least!at!twice !the!maximum!spatial!frequency!in!either!
direction,! which! satisfies! the! Shannon-Nyquist! sampling! theorem.! The! obtained! phase!
distribution!for! the! hologram!is! shown!in! Figure!2c.!In! the!CGH ! design,! we!take! the!conversion!
efficiency,! signal- to-noise! ratio! and! uniformity! as! merit! functions! for! optimization.! Sin c e! the!
phase! delay! is! determined! solely! by! the! orientation! of! the! nanorod! antennas,! 16! phase! levels!
(Figure! 1c)! are! used! to! obtain! a! high! performance! of! the! CGH.! Simulation! shows! that! in! ou r!
optimized!design!with!an!ideal!hologram!neglecting!optical!losses,!the!window!efficiency,!which!
is!defined! as!the!ratio!between!the!o ptical!power!projected!into!the!image!region!and!the!inp u t!
power,!reaches!94%.!
!
The!metasurface! CGH! is! fabricated! on!top! of!a! Silicon!substrate! following! the! design! described!
above! (Figure! 3a).! Th e! simulated! and! measured! holographic! images,! includin g ! b o th ! the!
zoomed-in! views! of! t he ! face! and! th e! letter! ‘M’,! show! goo d ! ag reem e nt! w ith ! e a ch ! o th e r.! This!
demonstrates! the! extremely! high! fidelity! of! the! metasurface! hologram.! To ! determine! the!
conversion! efficiency,! the!lin e a r! polarization! state!o f ! light! from! a!su p er ! continuum ! light! source!
(Fianium!supercontinuum)!is!converted!to!circular!polarization! by!using!a! linear!polarizer!and! a!
quarter! waveplate.! The! reflected! holographic! im a ge! is ! collected! by! two! condenser! lenses! w it h !
high! numerical! aperture! and! the! hologram! image!wa s! measured!in ! th e ! range! from! 600! nm! to!
1100! nm! in! steps! of! 25! nm.! The! optical! efficiency! (holog raphic! window! efficiency)! is! finally!

!
determined! by! subtracting! th e ! 0
th
-order!beam! signal! from! the! image! intensity! (Figure! 3b).! We!
find!a!relatively!broad!spectral!range!from! 630! n m! to!1050!nm!with!high!window!efficiency!larger!
than! 50%! that!reaches! its! maximum! of! 80%! at! a!wavelength!of! 825!nm. ! At! the! same! time! the!
unwanted!0
th
-order!efficiency!is!only!around!2.4%.!More!importantly,! we !do!n o t!observe!the!tw in!
image!effect!th at!traditional!binary!holograms!usually!suffer!from.! !
!
Theoretically!the!m etasurface!hologram!has!an!even!broader!spectral!response!(Figure!1f)!when!
compared! to! the! measured!efficiency.!The! lower!ban dwidth! likely!arises!from!the!fact!that!the!
calculated!conversion!efficiency!is!obtained!on!a!metasurface!under!normal!incidence.!Whereas!
in! the! experiment! the! holographic! image! from! the! m etasurface! hologram! is! projected! into! a!
broad! angular! range.! We! expected! that! this! broad! an gle! scattering! induces! the! narrower!
bandwidth!and!lower! peak!reflection!tha n! the!calculated! results! shown! in! Figure!1f.! A!detailed!
discussion! of! the! diffraction! efficiency! of! th e! metasurface! consisting! of! nanoantennas! with!
nonuniform! orientations! is! given! in! the! SI! (Supplementary! Fig.! 10,! 11).! In! addition,! a! weak!
near-field! coupling! effect! amon g! neighbo rin g! nanorod! antennas! introduces! a! small! phase!
deviation!compared!to!the!design!(Supp lem e ntary!Fig.!12).! !
!
In! su mmary,! we! h ave! presented! a! reflective! p h as e-only! hologram! based! on! geometric!
metasurfaces! that! shows! a! diffraction! efficiency! as! high! as! 80%,! an! extrem ely! low! 0
th
-order!
efficiency! and!a! broadband ! spectral!response! in!the!visible/near-IR!range.!Our!metasurface!has!
an!ultrathin! and!uniform!thickness!of!30!nm!and!is!compatible!with!the!scalar! diffraction!th eo r y!
even!for!subwavelength!p i xel!sizes
28
,!thus ! simplifyin g ! the!desig n ! of!holo g rams.! Given!its!simple!
and!robust!ph ase!control,!its!good!tolerance!to!wavelength!variations!and!fabrication!errors,!our!
geometric! phase! based! CGH! design! could! overcome! the! current! limitations! of! traditional!
depth-controlled!CGH!and!find! application!in! fields!such!as!laser!holographic!keyboard,!random!
spots!generator!for!body !motion,!optical!anti-counterfeiting,!and!laser!beam!shaping.!Moreover,!
our!approach!can!be!readily!extended!from !phase-only!to!amplitude-controlled!holograms!simply!
by!c ha n g ing ! the! size! of!th e! nanorods.! Since!we! exploit!a!phase! effect! due!to!polarization!state!
change,! the!on ly! restriction! of! our! technique!is! the! fact!that! the! polarization! state!of! the! light!
cannot! be! controlled,!that! is,! the!incident! light!has! to! be! circularly!polarized.! Finally,!we! would!
like!to!note!that! su c h !na n orod!metasurfaces!could!be !fabricated!o n!a!large!scale!and!mu ch !lower!
costs! by! nano-imprinting,! thus! m a king ! th em! promising! candidates! for! large-scale! holo graphic!
technology.!
!
!
!"#+,@%[*
9P*H0/ &-$#0,1*,(*#+"*),1J"'%0,1*"((0)0"1)5.!The!nanorod! cell!was!designed!and!simulated!by!CST!
microwave!studio!software.!In!the!simulation,!a!line a rly !polarized!plan e !wave!is!norm a lly!incide nt!
onto!a!single!nanorod!with!periodic!boundary!conditions.! Th e!spectra!of!reflection!coefficients!r
xx
,!
r
xy
,!r
yy
,!r
yx
!are!obtained!from!the!simulation.!From!the!reflection!of!linear!polarized!light!we!can!
retrieve! the! reflection! coefficients! for! circularly! polarized! light! as! r
rr
=! [r
xx
+r
yy
-! (r
xy
-r
yx
)·i]/2! and!
r
lr
=[r
xx
-r
yy
-(r
yx
+r
xy
)·i]/2.!T h e!performance!of!the!nanorods!is!optim ized!by!sweeping!the!geometric!
parameters!of!the!nanorod!includin g !th e !ce ll!size,!spacer!and!gold!thickness.!
;P*\"%0.1*,(*/ "#$%&'($)"*+,-,.'$/P!In!th e !design ,!a!complex!digital!image!containing!Einstein’s!

Frequently asked questions

Q1. What are the contributions in this paper?

The concept of fair dealing under the Copyright, Designs and Patents Act 1988 ( CCDPA ) was introduced in this paper. 

Q2. What are the main reasons for the poor performance of CGHs?

the unavoidable etching error, resolution error and alignment error can dramatically degrade the performance of CGHs, such as low signal-to-noise ratio, poor * 

Q3. What is the polarization state of the incident light?

Since the authors exploit a phase effect due to polarization state change, the only restriction of their technique is the fact that the polarization state of the light cannot be controlled, that is, the incident light has to be circularly polarized. 

Q4. What is the way to achieve a higher efficiency and less complexity?

To obtain a higher efficiency and less manufacturing complexity, an effective medium approach has been proposed20, where two-level depth subwavelength structures with variable cell dimension can function as an effective medium with geometry controlled effective refractive index, and consequently act as a multi-level CGH. 

Q5. What is the diffraction efficiency of the geometric phase based CGH?

Given its simple and robust phase control, its good tolerance to wavelength variations and fabrication errors, their geometric phase based CGH design could overcome the current limitations of traditional depth-controlled CGH and find application in fields such as laser holographic keyboard, random spots generator for body motion, optical anti-counterfeiting, and laser beam shaping. 

Q6. How many pixel arrays are used to create a holographic image?

The reflected holographic image is collected by two condenser lenses with high numerical aperture and the hologram image was measured in the range from 600 nm to 1100 nm in steps of 25 nm. 

Q7. What is the concept of Dammann gratings30?

To avoid the formation of laser speckles in the holographic image, the concept of Dammann gratings30 is utilized for the hologram design. 

Q8. How many phase levels are used to obtain a high performance of the CGH?

Since the phase delay is determined solely by the orientation of the nanorod antennas, 16 phase levels (Figure 1c) are used to obtain a high performance of the CGH. 

Q9. How can The authorcalculate the period of the CGH at x and y?

To create an holographic image with a pixel array of m×n within the angular range of αx×αy in the far field, the period of the CGH at x and y direction can be calculated by dx=mλ/[2tan(αx/2)] and dy=nλ/[2tan(αy/2)], respectively. 

Q10. How is the performance of the nanorods optimized?

The performance of the nanorods is optimized by sweeping the geometric parameters of the nanorod including the cell size, spacer and gold thickness. 

Q11. What is the phase profile of a computer generated hologram?

In traditional phase-only computer generated hologram designs, the phase profile is controlled by etching different depths into a transparent substrate. 

Q12. What is the effect of the polarization of the incident light on the wave vector?

regardless the orientation of the antennas, it is expected that the circularly polarized incident light almost completely flips the absolute rotation direction of the electric field upon reflection, thus preserving its circular polarization state considering that the wave vector is reversed as well. 

Q13. What is the ohmic loss of the nanorod antenna?

the the ohmic loss in their configuration is very close to that of light transmitting through a single metasurface layer (without the ground metal plane) around the resonance wavelength (800 - 850 nm) of the antenna (Supplementary Fig. 8). 

Q14. What is the effect of the near-field coupling effect on the metasurface?

In addition, a weak near-field coupling effect among neighboring nanorod antennas introduces a small phase deviation compared to the design (Supplementary Fig. 12). 

Q15. What is the effect of the broad angle scattering on the metasurface?

The authors expected that this broad angle scattering induces the narrower bandwidth and lower peak reflection than the calculated results shown in Figure 1f. 

Q16. How much is the efficiency of a three level CGH?

such a design involves extreme small feature sizes with high aspect ratios, limiting the observed efficiency of a three level CGH to less than 30%, which is significantly lower than the theoretical value of 48%. 

Q17. What is the composition of the reflective metasurface hologram?

The reflective metasurface hologram consists of three layers: a ground metal plane, a dielectric spacer layer and a top layer of antennas (Figure 1). 

Q18. What is the reflection coefficient of a linear polarized light?

From the reflection of linear polarized light the authors can retrieve the reflection coefficients for circularly polarized light as rrr= [rxx+ryy- (rxy-ryx)·i]/2 and rlr=[rxx-ryy-(ryx+rxy)·i]/2.