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Full-color hologram using spatial multiplexing of dielectric metasurface WENYU ZHAO, 1 BINGYI LIU, 1 HUAN JIANG, 1 JIE SONG, 1,2 YANBO PEI, 1,2 AND YONGYUAN JIANG 1,2, * 1 Department of Physics, Harbin Institute of Technology, Harbin 150001, China 2 Key Lab of Micro-Optics and Photonic Technology of Heilongjiang Province, Harbin 150001, China *Corresponding author: [email protected] Received 19 October 2015; revised 18 November 2015; accepted 24 November 2015; posted 24 November 2015 (Doc. ID 252171); published 22 December 2015 In this Letter, we demonstrate theoretically a full-color hologram using spatial multiplexing of dielectric metasur- face for three primary colors, capable of reconstructing arbitrary RGB images. The discrete phase maps for the red, green, and blue components of the target image are ex- tracted through a classical GerchbergSaxton algorithm and reside in the corresponding subcells of each pixel. Silicon nanobars supporting narrow spectral response at the wave- lengths of the three primary colors are employed as the basic meta-atoms to imprint the PancharatnamBerry phase while maintaining minimum crosstalk between dif- ferent colors. The reconstructed holographic images agree well with the target images making it promising for colorful display. © 2015 Optical Society of America OCIS codes: (090.1705) Color holography; (310.6628) Subwavelength structures, nanostructures; (160.3918) Metamaterials; (240.0310) Thin films. http://dx.doi.org/10.1364/OL.41.000147 Phase-only computer-generated holography (CGH) possessing the merits of flexibility, simplicity, and low cost is a preferred technique that can reconstruct both real and virtual objects in display applications [1,2]. Taking advantage of recently devel- oped metasurfaces to imprint abrupt interfacial phase changes at subwavelength scale [36], great achievements such as wide- angle projection, elimination of high-order diffraction, and broadband spectral response have been made toward promising applications for optical trapping [7], quantum optics [8], and integrated photonics [9]. However, most existing metasurface holograms can only reconstruct monochromatic images [1016], which strongly limits their practical applications. To date, only a few research efforts have been conducted to construct meta- surfaces having multicolor responses [17,18], and some issues such as the nontrivial spatial alignment, color crosstalk, low fidelity, and color mismatch between the hologram and com- puter display colorimetric systems have not been stressed yet. A colorful hologram is especially challenging for existing metasur- faces relying on metal antennas for phase modulation due to the operating wavelength is usually limited in near-infrared range, which is beyond the percept of human naked eyes, and the scal- ing down to visible range is hindered by the strong intrinsic loss and saturation effects in metal toward a short wavelength [19,20]. Therefore, a colorful metasurface hologram remains a major challenge, and more research efforts are highly desirable. In this Letter, we demonstrate theoretically a full-color phase-only hologram using spatial multiplexing of dielectric metasurface subcells that can respond to three primary colors to reconstruct arbitrary RGB images. The target image with color quantity in computer display colorimetric system is con- verted to a hologram colorimetric system determined by the three primary colors according to color matching and transfer theory. The phase maps for the red, green, and blue compo- nents of the target image are then extracted through a classical GerchbergSaxton algorithm based on 16-level discreteness. Silicon nanobars are chosen as the basic meta-atoms to imprint the PancharatnamBerry phase due to its relatively low loss in visible range and narrow spectral response for low color cross- talk. The reconstructed images agree well with the target im- ages, making such a scheme promising for colorful display. The proposed scheme aims at illuminating the metasurface hologram with RGB lights simultaneously to get the recon- structions of the three RGB components of the target image at the same locations with the same sizes. Figure 1 shows the working principle of the metasurface hologram; incident red, green, and blue lights impinge on the metasurface and imprint the phases for each color component separately through corre- sponding subcells. The reflected lights of the three primary colors then propagate onto the image plane where three com- ponents of the reconstructed images compose to reproduce the colorful holographic image. Usually, the target colorful image for the CGH is obtained from the computer system where it is digitalized and stored under the RGB colorimetric system. The digitalized data uses R;G;B to denote the quantities of the three color components, and each number ranges from 0 to 255 to represent different color levels [21]. The exact quantities of R;G;B needed to mix a certain color vary dramatically ac- cording to the choice of the three primary colors. Therefore, the color conversion between the RGB colorimetric system and the hologram colorimetric system Rh;Gh;Bh is the starting point Letter Vol. 41, No. 1 / January 1 2016 / Optics Letters 147 0146-9592/16/010147-04$15/0$15.00 © 2016 Optical Society of America

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Page 1: Full-color hologram using spatial multiplexing of …...Full-color hologram using spatial multiplexing of dielectric metasurface WENYU ZHAO,1 BINGYI LIU,1 HUAN JIANG,1 JIE SONG,1,2

Full-color hologram using spatial multiplexingof dielectric metasurfaceWENYU ZHAO,1 BINGYI LIU,1 HUAN JIANG,1 JIE SONG,1,2 YANBO PEI,1,2 AND YONGYUAN JIANG1,2,*1Department of Physics, Harbin Institute of Technology, Harbin 150001, China2Key Lab of Micro-Optics and Photonic Technology of Heilongjiang Province, Harbin 150001, China*Corresponding author: [email protected]

Received 19 October 2015; revised 18 November 2015; accepted 24 November 2015; posted 24 November 2015 (Doc. ID 252171);published 22 December 2015

In this Letter, we demonstrate theoretically a full-colorhologram using spatial multiplexing of dielectric metasur-face for three primary colors, capable of reconstructingarbitrary RGB images. The discrete phase maps for thered, green, and blue components of the target image are ex-tracted through a classical Gerchberg–Saxton algorithm andreside in the corresponding subcells of each pixel. Siliconnanobars supporting narrow spectral response at the wave-lengths of the three primary colors are employed as thebasic meta-atoms to imprint the Pancharatnam–Berryphase while maintaining minimum crosstalk between dif-ferent colors. The reconstructed holographic images agreewell with the target images making it promising forcolorful display. © 2015 Optical Society of America

OCIS codes: (090.1705) Color holography; (310.6628)

Subwavelength structures, nanostructures; (160.3918)

Metamaterials; (240.0310) Thin films.

http://dx.doi.org/10.1364/OL.41.000147

Phase-only computer-generated holography (CGH) possessingthe merits of flexibility, simplicity, and low cost is a preferredtechnique that can reconstruct both real and virtual objects indisplay applications [1,2]. Taking advantage of recently devel-oped metasurfaces to imprint abrupt interfacial phase changesat subwavelength scale [3–6], great achievements such as wide-angle projection, elimination of high-order diffraction, andbroadband spectral response have been made toward promisingapplications for optical trapping [7], quantum optics [8], andintegrated photonics [9]. However, most existing metasurfaceholograms can only reconstruct monochromatic images [10–16],which strongly limits their practical applications. To date, onlya few research efforts have been conducted to construct meta-surfaces having multicolor responses [17,18], and some issuessuch as the nontrivial spatial alignment, color crosstalk, lowfidelity, and color mismatch between the hologram and com-puter display colorimetric systems have not been stressed yet. Acolorful hologram is especially challenging for existing metasur-faces relying on metal antennas for phase modulation due to theoperating wavelength is usually limited in near-infrared range,

which is beyond the percept of human naked eyes, and the scal-ing down to visible range is hindered by the strong intrinsic lossand saturation effects in metal toward a short wavelength[19,20]. Therefore, a colorful metasurface hologram remainsa major challenge, and more research efforts are highlydesirable.

In this Letter, we demonstrate theoretically a full-colorphase-only hologram using spatial multiplexing of dielectricmetasurface subcells that can respond to three primary colorsto reconstruct arbitrary RGB images. The target image withcolor quantity in computer display colorimetric system is con-verted to a hologram colorimetric system determined by thethree primary colors according to color matching and transfertheory. The phase maps for the red, green, and blue compo-nents of the target image are then extracted through a classicalGerchberg–Saxton algorithm based on 16-level discreteness.Silicon nanobars are chosen as the basic meta-atoms to imprintthe Pancharatnam–Berry phase due to its relatively low loss invisible range and narrow spectral response for low color cross-talk. The reconstructed images agree well with the target im-ages, making such a scheme promising for colorful display.

The proposed scheme aims at illuminating the metasurfacehologram with RGB lights simultaneously to get the recon-structions of the three RGB components of the target imageat the same locations with the same sizes. Figure 1 shows theworking principle of the metasurface hologram; incident red,green, and blue lights impinge on the metasurface and imprintthe phases for each color component separately through corre-sponding subcells. The reflected lights of the three primarycolors then propagate onto the image plane where three com-ponents of the reconstructed images compose to reproduce thecolorful holographic image. Usually, the target colorful imagefor the CGH is obtained from the computer system where it isdigitalized and stored under the RGB colorimetric system. Thedigitalized data uses �R; G; B� to denote the quantities of thethree color components, and each number ranges from 0 to255 to represent different color levels [21]. The exact quantitiesof �R; G; B� needed to mix a certain color vary dramatically ac-cording to the choice of the three primary colors. Therefore, thecolor conversion between the RGB colorimetric system and thehologram colorimetric system �Rh; Gh; Bh� is the starting point

Letter Vol. 41, No. 1 / January 1 2016 / Optics Letters 147

0146-9592/16/010147-04$15/0$15.00 © 2016 Optical Society of America

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of our hologram design. During the color match process, all thecolors can be mixed by adjusting the color quantities of�Rh; Gh; Bh�; it is also necessary to ensure the gamut of thehologram colorimetric system determined by the three primarycolors wider than that of the RGB. Therefore, the wavelengthsof the three primary colors in our hologram are chosen as633 nm for red (λRh), 532 nm for green (λGh), and 465 nmfor blue (λBh), which also takes future experimental realizationinto consideration. The transfer matrix between the RGB col-orimetric system �R;G; B� and the hologram colorimetric sys-tem �Rh; Gh; Bh� can be calculated with the help of the CIE1931-XYZ standard colorimetric system [22]:"Rh

GhBh

#�

"0.771 0.221 0.0080.139 0.813 0.0490.026 0.103 0.872

#•

"RGB

#: (1)

The holographic image is treated as the superposition of thethree reconstructed components at the same locations with thesame sizes. As the diffraction angle of the hologram is stronglydependent on the operating wavelength, the three componentsshould be adjusted to counteract the size mismatch. The dif-fraction angle of the hologram, α, can be calculated accordingto ΔP � λ∕�2 tan�α∕2��, where λ is the operating wavelength,and ΔP is the pixel size of the hologram [10]. Thus, the sizes ofthe three color components should be pre-scaled according to1∕λRh:1∕λGh:1∕λBh to make sure the first-order diffraction ofthe three images is spatially overlapped and aligned on the im-age plane.

The discrete phase map for each color component of thetarget image, �Rh; Gh; Bh�, can then be extracted separately us-ing a classical Gerchberg–Saxton algorithm [23]. The algorithminvolves iterative loops of propagations between the hologramplane and image plane. (1) The iteration starts on the imageplane with a random initial phase and an amplitude of the tar-get color component. (2) The wavefront is then propagatedback to the hologram plane using inverse Fresnel diffraction.In the hologram plane, the phase map is extracted and discre-tized according to the phase discreteness level. Here, to ensurethe fidelity of the holographic image, we adopt a high discrete-ness level of 16 with phase modulations from 0 to 2π by anincrement of π∕8, which is also feasible for state-of-the-artnanofabrication. (3) The new wavefront in the hologram planecalculated with the discrete phases and unit amplitude is thenpropagated to the image plane through Fresnel diffraction.(4) The phase of the new wavefront on the image plane is kept

unchanged, while the amplitude is forced to be the amplitudeof the corresponding target color component. One iterationcontains the successive processes from (2)–(4), and 20 itera-tions are enough to get a convergent phase map.

To imprint the calculated phase maps of the �Rh; Gh; Bh�components onto the metasurface, silicon nanobar is chosenas the basic element to realize phase modulation due to its rel-atively low loss in a short wavelength compared with metal an-tennas and narrow spectral response for low crosstalk betweendifferent colors. The phase modulation mechanism relies on thePancharatnam–Berry phase acquiring from the inversion of theabsolute rotation direction of the electric field of radiation (intransmission or reflection) with respect to that of the incidentone [24,25]. By tiling the silicon nanobars with angle denotedas θ�x; y�, part of the incident circularly polarized light beamwill be transformed to a beam of opposite helicity and im-printed with a geometric phase equal to φ�x; y� � 2θ�x; y�.This is equivalent to flipping the circular polarization in trans-mission or maintaining the same circular polarization in reflec-tion. The orientation-controlled phase covers 0 to 2π rangewhile maintaining nearly equal reflection for all rotation angles,thus providing the full control over the wavefront.

To interpret the phase modulation of the silicon nanobarmore clearly, a gradient metasurface supporting anomalous re-flection light is demonstrated. Figure 2(a) shows the unit cell ofthe metasurface; silicon nanobars with rotation angles respectto Z axis from 0 to π with an increment of Δθ � π∕8 arepositioned on a glass substrate. The simulations are conductedusing commercial finite-difference-time-domain method software,FDTD Solutions from Lumerical, Inc. In the simulations, theincident left-handed circularly polarized light is normal to the ar-ray plane, and periodic condition is used in each boundary of the

Fig. 1. Artistic impression of the full-color metasurface hologram.

Fig. 2. (a) Unit cell of silicon nanobars for wavefront shaping.(b) Phase distribution of the reflected left-handed circularly polarizedlight (W � 60 nm, L � 105 nm, P � 150 nm). (c) Reflections ofthe left-handed circularly polarized light of the nanobars with differentgeometric parameters for red, green, and blue colors. The geometricparameters are chosen as W � 110 nm, L � 340 nm, and P �420 nm for red; W � 80 nm, L � 200 nm, and P � 350 nm forgreen; and W � 60 nm, L � 105 nm, and P � 150 nm for blue.The heights of the nanobars are fixed at 120 nm, and the periodsare identical in both X and Y directions.

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unit cell to reduce the amount of computation. The permittivityof glass and silicon are extracted from the experimental data [26].

Figure 2(b) shows the phase distribution of the reflected left-handed circularly polarized light at 465 nm, which indicatesthat the normally incident plane wave is tilted as it is reflectedfrom the nanobar array. The anomalous angle extracted fromsimulation is 23.4° and agrees well with that calculated from thetheoretical expression arcsin�2Δθ∕Pk0� � 22.8°, where k0 is thewave number in free space [4]. Even though the Pancharatnam–Berry phase does not rely on the wavelength for making its per-formance non-dispersive and highly robust against fabricationvariations, the exact spectral response strongly depends on theantenna design. For a metasurface composed of metal antennas,the spectral response is usually wide because of the low Q-factorof the resonances, which is favorable for monochromatic holo-grams allowing broadband operation. However, this is no longertrue for the colorful hologram because the broadband responseleads to dramatic crosstalk between different primary colors.An ideal metasurface for high color fidelity is single frequencyor at least narrowband, and this is satisfied by using silicon nano-bar as a basic meta-atom. Figure 2(c) shows the reflections of theleft-handed circularly polarized light of the silicon nanobars withdifferent geometric parameters under the incident left-handed cir-cularly polarized light. The reflection for circularly polarized lightis calculated by RLL � j�rxx � ryy − �rxy − ryx� · i�∕2j2, whererxx , ryy, rxy, and ryx are the reflection coefficients for the linearpolarized light [10]. The nanobar can be tuned to support a re-sponse from the three primary colors while still maintaining rel-atively narrow spectral response which is essential to alleviate thecolor crosstalk. One can notice that the reflection of the nanobarfor blue light is relatively lower than that for green and red; this isdue to the increasing loss of silicon toward the short wavelength.

Figure 3(a) shows one pixel of the proposed hologram com-posed of four metasurface subcells, one for red consisting of10 × 10 units of silicon nanobars capable of responding to633 nm incident light, one for green (12 × 12 units for532 nm light), and two for blue (30 × 30 units for 465 nmlight) to compensate for the low reflection. The minimum in-terval between the subcells is 750 nm, which is much largerthan λRh∕2 to ensure that the coupling between the subcellscan be safely ignored and different subcells can operate inde-pendently. Figure 3(b) shows the calculated reflection of thehologram array. The subcells for corresponding primary colorsoperate independently; the color crosstalk mainly comes fromthe non-zero reflection at other primary colors. The efficiencyof our hologram is mainly affected by the co-polarized conver-sion efficiency of the silicon nanobars. As demonstrated in theprevious text, the co-polarized light is capable of manipulatingthe phase in reflection mode only. The maximum co-polarizedconversion efficiency of nanobars can reach 100% when no lossis introduced but, for the real case, the conversion efficiency isdegraded by the intrinsic loss in silicon which gradually in-creases toward a short wavelength. The total efficiencies whichalso take the spatial multiplexing into consideration are 13.2%for red, 11.1% for green, and 8.9% for blue. A further boost ofefficiency can be realized by seeking low loss dielectric or intro-ducing gain materials in the nanostructures.

To verify our design, the red, green, and blue components ofthe target image are reconstructed using Fresnel diffraction andcomposed to reproduce the holographic image [27]. The phasemaps are multiplied with the amplitudes calculated from

corresponding reflection coefficients, and then numericallypropagated to the image plane 1 m away from the hologram.The wavefront amplitude of the blue component on the imageplane consists of the responses from the Bh-subcells (ABh→Bh),Gh-subcells (AGh→Bh), and Rh-subcells (ARh→Bh). The rule alsoholds for the other components:

ARh � ARh→Rh � AGh→Rh � ABh→Rh

AGh � ARh→Gh � AGh→Gh � ABh→Gh

ABh � ARh→Bh � AGh→Bh � ABh→Bh: (2)

The three color components are then scaled and reconverted toa RGB colorimetric system to display on the computer system.The obtained intensity images are colored red, green, blue, andcombined using photo editor software. The numerical opera-tion is equivalent to observing a screen placed at a distance of1 m away if the hologram is illuminated with correspondinglights. Except for experimental realization, the final color com-pound on the image plane depends not only on the intensitiesof the reconstructed components, but also on the power dis-tribution of the illumination and the visual function of theprimary colors on human eyes. To maintain the color ofthe holographic image and the target image are equivalent,the intensities of the three incident lights should conform toP�λRh�:P�λGh�:P�λBh� � 8.2:6.9:8.6 [22]. The results areshown in Fig. 4; the central patches in the images belong tothe direct reflection light (zero-order diffraction) of the holo-

Fig. 3. (a) One pixel of the metasurface hologram(10 μm × 10 μm); the phase maps for red, green, and blue compo-nents of the target image reside in corresponding subcells. The bluecomponents reside in two subcells due to the low reflection of the meta-surface at a short wavelength. (b) Calculated reflections of the subcellsand the hologram pixel.

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gram. Speckle noise is observed in the reconstruction imagesdue to the color crosstalk and phase discreteness, which canbe further improved by increasing the phase level. Figures 5(a)and 5(b) show an arbitrary RGB image and its holographic im-age; the target image can be well reconstructed using our meta-surface hologram. The colors reproduced from the hologramare less saturated due to the degraded contrast ratio in thereconstruction caused by color crosstalk.

In summary, we demonstrate theoretically a full-color meta-surface hologram capable of reconstructing arbitrary RGB im-ages by spatial multiplexing of subcells for three primary colors.A silicon nanobar having a narrow spectral response, and a rel-atively low loss in short wavelength is chosen as the basic meta-atom to imprint the phase maps which are extracted througha classical Gerchberg–Saxton algorithm for the red, green, andblue components of the target image. The crosstalk betweendifferent colors, spatial overlap and alignment of the three im-age components, incident intensities for primary colors, andcolor match between computer display and hologram colori-metric system are demonstrated. The reconstructed image agreeswell with the target image making such a metasurface hologramsuitable for future colorful display.

Funding. National Natural Science Foundation of China(NSFC) (50836002, 51176041).

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Fig. 4. (a) Red, (b) green, and (c) blue components of the recon-structed holographic image. (d) Composition of the target image.

Fig. 5. (a) Target image and (b) its holographic image.

150 Vol. 41, No. 1 / January 1 2016 / Optics Letters Letter