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Nonlinear holographic all-dielectric metasurfaces Yisheng Gao, Yubin Fan, Yujie Wang, Wenhong Yang, Qinghai Song, and Shumin Xiao Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b04311 • Publication Date (Web): 27 Nov 2018 Downloaded from http://pubs.acs.org on November 28, 2018

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Nonlinear holographic all-dielectric metasurfaces Yisheng Gao1, Yubin Fan1, Yujie Wang1, Wenhong Yang1, Qinghai Song1,2,*, Shumin Xiao1,2,# 1State

Key Laboratory on Tunable laser Technology, Ministry of Industry and Information

Technology Key Lab of Micro-Nano Optoelectronic Information System, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China. 2Collaborative

Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006

China. Table of Contents Graphic

ABSTRACT

Nonlinear holographic metasurfaces have been intensively studied due to their potentials in practical applications. So far, nonlinear holographic metasurfaces have only been realized with plasmonic nanoantennas, suffering from high absorption loss and low damage

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threshold. Herein we propose and experimentally demonstrate a novel mechanism for nonlinear holographic metasurfaces. In contrast to conventional studies, the all-dielectric metasurface is composed of C-shaped Si nanoantennas. The incident laser is enhanced by their fundamental resonance, whereas the generated third-harmonic generation (THG) signals are re-distributed to the air gap region via the higher-order resonance, significantly reducing the absorption loss at short wavelength and resulting in an enhancement factor as high as 230. After introducing abrupt phase changes from 0 to 2π to the C-elements, highefficiency cyan and blue THG holograms have been experimentally generated with the Si metasurface for the very first time. This research shall shed light on the advances of nonlinear all-dielectric metasurfaces.

KEYWORDS: nonlinear hologram, all-dielectric metasurface, higher-order resonance, metasurface Metasurface, a kind of ultrathin and quasi-two-dimensional metamaterial, have recently attracted tremendous research attention in optics community.1-6 By spatially varying the structural geometries or rotating the nanoantennas, metasurfaces are able to offer the required phase discontinuities for a full wavefront control.7-12 As a result, the amplitude, phase, and polarization of the transmitted and reflected light can be precisely tailored and several novel optical elements have been realized with nanostructures, e.g. reflection mirror,13 vortex generators,14 diffractive gratings,15 and flat lens3,

4, 16-19

et al. Metasurface

based hologram is one prominent example.8, 17, 20-22 With the digital processing of the target


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image and the recording of numerically calculated phase shifts into nanoantennas, the holographic image can simply be reconstructed by shining a reading laser beam on it. In past decade, high-efficiency and broadband holographic images have been realized with plasmonic metasurfaces8,

20, 21, 23, 24

and all-dielectric metasurfaces11,

17, 22, 25

in the near

infrared and visible spectral regions, respectively. Meanwhile, a large number of practical applications such as three-dimensional displays,20 volumetric data storage, optical tweezers, and anti-counterfeiting have been proposed and experimentally demonstrated.23, 26 So far, most of these metasurfaces are designed and operated in a linear regime, i.e. the frequency of reading laser won’t be altered. Very recently, the demands for high-density optical storage, biomedical manipulation, and optical information security have driven the intensive research attention into the nonlinear holographic metasurfaces. In past few years, nonlinear phase control has been widely demonstrated for second harmonic optical vortex in arrays of metallic split-ring resonators, THG in metallic nano-crosses, four-wave mixing in metallic film, and holographic images in V-shaped metallic antenna array.24, 27-31 However, all of the nonlinear holographic metasurfaces are realized with plasmonic nanostructures. While the nonlinear optical effects can be significantly boosted by the “hot spots”, the conversion efficiency is limited by the weak penetration of exciting fields into the metal, the strong material loss, and the small damage threshold.32 The recent experiments show that the all-dielectric nanoparticles and nanoantennas can solve the above intrinsic limitations.33-37 The Mie resonances in Si and Ge nanostructures have shown their ability of enhancing the THG by a factor of 100.33, 36 With the assistance of Fano-resonance, the enhancement factor


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can be as large as 105.34 Despite of these progresses, the applications of all-dielectric nonlinear metasurfaces are still restricted by the material loss at shorter wavelengths34, 36-39 and the full phase control of THG signals. As a result, up to now, all-dielectric metasurface based nonlinear holograms are still absent yet. Herein, we propose and experimentally demonstrate the high-efficiency cyan and blue color THG holograms from Si metasurfaces for the first time. The enhanced THG in C-shaped Si nanoantennas. In principle, the nanoantenna can be approximated as a point dipole with effective third-harmonic (TH) nonlinear susceptibility

 eff3 . Then the corresponding third order polarization generated by the antenna can be expressed as  3 P  3  3    eff  3 ,    E1ei   

3

(1)

Following Equation 1 it is easy to know that the THG signals are proportional to the local field intensity cubed. As a result, much efforts have been paid to the field enhancement of fundamental waves, e.g. the magnetic dipole resonance in Si nanodisk or electromagnetically induced transparency (EIT) in coupled systems

25, 35, 38, 39.

In order to enhance the light-

matter interaction, the electromagnetic fields of resonances are mostly confined within Si. In this sense, the generated THG signals shall experience strong material loss and suppressed, especially for the shorter wavelengths.


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Figure 1. The optical characteristics of the C-shaped Si nanoantenna based metasurface. A) The schematic picture of the metasurface and the detail parameters. B) The calculated transmission spectrum of the Si metasurface in the visible (blue line) and infrared regions (black line). Here the structural parameters are fixed at p=660 nm, t = 230 nm, Ro = 260 nm,

Ri = 35 nm, and θ = 37o. C)-F) are the field patterns of electric resonance (up panel) and magnetic resonance (down panel) at ω and 3ω, respectively. The white cones show the displacement current distribution. Here the incident light is y-polarized.


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In contrast to previous reports,25, 35, 38, 39 we adapt a C-shaped silicon nanoantenna as the building block of the nonlinear metasurface.25 As schematically shown in Figure 1A, the Cshaped nanoantenna is made of single-crystalline silicon and is positioned onto a sapphire substrate. The period is p. The inner and outer radiuses of C-element are Ri and Ro, respectively. The thickness is t and the opening angle is θ. The numerical calculations (see methods) show that Si based C-element also has magnetic and electric responses. Once example is shown as black line in Figure 1B, where two resonances appear at 1400 nm and

1220 nm. According to their field patterns in Figure 1C and 1D, these two transmission dips correspond to the magnetic resonance and electric resonance, respectively. While hot sports appear in the opening air gap, their main electromagnetic fields are still confined within silicon, enabling the adequate interaction between pump laser and nonlinear medium. Compared with the circular nanodisk, the C-elements have intrinsic advantages for the THG process. Not only the outer radius, the inner radius and the opening angle can also affect the resonant wavelength. In this sense, the positions of fundamental resonances and higher-order resonances in Si nanoantenna can be precisely controlled. The fundamental resonance is applied to enhance the THG process following equation 1. Once the higherorder resonance is tuned to overlap the wavelength of THG signals. The generated THG shall be re-distributed by the higher order resonance. As illustrated in Figure 1E and Figure 1F, the THG signals can be partially trapped at the air gap and efficiently emit to far field.25 Thus the material loss of THG signals can be effectively relieved. This effect will be more dramatic at shorter wavelength, i.e. blue, violet, and even ultraviolet (UV) ranges. Considering the


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possible experiment, here we design the higher-order resonance to match the magnetic dipole resonance at 1400 nm only and leave the electric dipole resonance as a reference for a direct comparison.

Figure 2. The experimentally recorded THG signals from the C-shaped Si nanoantenna based metasurface. A) Top-view SEM image of the metasurface. The insets in upper right and left corner show the high-resolution top-view and side-view SEM images, respectively. B) The experimentally recorded transmission visual (blue line) and infrared (black dots) spectrum of


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the metasurface. C) The enhancement of THG signals as a function of wavelength. The insets show the microscope (upper corner) and naked eyes (lower corner) image of THG, respectively. D) The dependence of output intensity on the input power. The inset shows the calculated conversion efficiency. Here the wavelength of incident laser is 1400 nm. Based on the above analysis and numerical calculations, we have experimentally fabricated the single-crystalline Si based metasurface on a sapphire substrate with the electron-beam lithography and the inductively coupled plasma etching (see methods). Figure 2A shows the top-view scanning electron microscope (SEM) image of the metasurface. The overall size of the metasurface is 100 μm × 100 μm, which is large enough for optical characterization. The high-resolution SEM image of the metasurfaces (insets in Figure 2A) shows that the in-plane structural parameters are the same as the design in Figure 1. The sidewall is straight in vertical direction and the thickness is 230 nm. Then the Si metasurfaces was placed into a home-built optical microscope to measure its linear optical properties (see methods and section 1 of supplemental information). The transmission spectra of Si metasurface were obtained by using one spectrometer with two different detectors. For the fundamental waves, two resonances are seen at 1400 nm and 1240 nm in Figure 2B (black dotted), matching the numerical results in Figure 1B very well. Similar to the numerical calculations, the transmission spectrum at the visible spectral range has also been recorded and plotted as blue line in Figure 2B, where two resonances can also be observed at 460 nm and 510 nm, respectively.


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The THG measurements were performed in a home-built laser scanning microscope (see methods and section 1 of supplemental information). When a femtosecond pulsed laser at

1400 nm is focused to a 335 μm in diameter spot onto the metasurface, a blue spot at 467 nm can be clearly seen with naked eyes (see the lower inset in Figure 2C) and a strong bright sign can be observed on the sample surface by microscope camera (see the upper inset in Figure 2C). Note that, the sapphire substrate has much smaller nonlinear susceptibility than silicon and the pumping laser rapidly divergent out of the silicon sample. The THG from the substrate was negligibly small and thus the signals were mainly generated by the metasurface (see section 2 of supplemental information). To confirm the enhancement of the resonances in Si metasurfaces, the central wavelength of pumping laser was scanned from 1200 nm to

1596 nm and the corresponding THG signals were recorded with a spectrometer (see section 1 of supplemental information) by fixing the pumping power of laser pulse at 0.7 μJ. After normalizing with a single crystal silicon film with the same area, the enhancement factor of THG is calculated and plotted in Figure 2C as a function of wavelength. We can see that the intensity of THG signals is much higher than the other wavelengths when the central wavelength of pumping laser matches the wavelength of magnetic dipole resonance. Such kind of enhanced THG signals are consistent with the previous reports on all-dielectric nonlinear metasurfaces,35, 38, 39 clearly demonstrating the impacts of magnetic resonance on the THG signals. Interestingly, the maximal enhancement factor of THG signals appears at

460 nm and is as high as 230 times, which is much higher than the previous studies.33, 36 This additional improvement can be attributed to the reduction of absorption loss. For a direct


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comparison, we have also measured the THG signals of the electric dipole resonance at 1240

nm. Due to the absence of 3ω resonance, the enhancement factor around 413 nm is negligibly small in Figure 2C even though the electric dipole resonance is also quite strong. This is also consistent with our above analysis and clearly demonstrate the advantages of Celements in nonlinear metasurfaces. The above experiments show that the Si metasurfaces can remarkably enhance the TH process. To estimate the nonlinear efficiency, we have calibrated the spectrum intensity measured by CCD camera with a photo-diode power meter (see section 1 of supplemental information) and measured the output power as a function of incident power (see section 3 of supplemental information). All the results are summarized in Figure 2D. In the log-log plot, the output intensity increases linearly with the incident power. The fitted power slope is 3.07, clearly confirming the THG process. The infrared to visible conversion efficiency

η=P3ω/ Pω has also been calculated and plotted as the inset of Figure 2D. The conversion efficiency also increases with the pumping power. Owing to the properties of singlecrystalline Si, no saturation has been observed even though the incident power density has been increased to ~ 33 GW/cm2. The maximal output power of THG signals at 467 nm is around 1×10-3 nJ and the conversion efficiency is around η = 1.1 × 10-6. This value is about two orders of magnitude higher than the efficiency of its metallic counterparts (~ 10-8)24 and can be further improved by either introducing Fano resonance34 or hybridizing with better nonlinear materials such as lead halide perovsites40, 41.


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The THG hologram of Si metasurfaces. Based on the above nonlinear process, it is interesting to explore the potential applications of Si metasurfaces in nonlinear hologram, especially for short wavelength. To generate a hologram, the computed phase information must be encoded into the nanoantennas. For the THG holography, the phase information shall be calculated for the third harmonic frequency at 3ω. In principle, the resonance of a nanoantenna can endow an additional phase shift to the incident light (see section 4 of supplemental information). This property has been applied to generate linear metahologram. Interestingly, according to the equation 1, the phase shifts between fundamental waves and THG signals are closely correlated. A phase shift σ(ω) in fundamental waves corresponds to a change of 3σ(ω) at the THG signals. As a result, by controlling the fundamental of the Si nanoantennas, the phase shift of THG can be simply designed and tailored. Meanwhile, the strong enhancement on THG signals can also be primarily preserved, making the THG holography highly possible. In case of C-shaped nanoantenna, the three parameters (outer radius Ro, inner radius Ri, and opening angle θ) are changed to control the resonant properties. The other parameters (period p=700 nm and thickness t =230

nm) are kept as constants. With the change of Ri and θ, the transmittance (T) and phase change (σω) for the incident light at 1500 nm have been calculated. These simulations were performed with an individual antenna and periodic boundary condition (see methods and see section 4 of supplemental information). The lattice size and outer radius were set as 700 nm and 282 nm to minimize the coupling between neighboring antennas. The calculated results are summarized and plotted as two-dimensional color maps in Figure 3A and Figure 3B. A


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region with extremely low transmittance can be seen in Figure 3A, clearly demonstrating the possible enhancement of THG signals. Within the region in Figure 3A, the corresponding phases can also change from 0 to 2π/3 for the fundamental waves. In case of experiment, the tolerance of fabrication deviation must be considered. As a result, we have to scarified the enhancement factor a little bit and selected the following ten nano-antennas (see Figure 3C and Figure 3D) to realize the required abrupt phase shift from 0 to 2π/3 for the fundamental waves. Interestingly, the influences of higher order resonance at third-harmonic wavelength on the phase changes are negligible. This is because the phase change is usually dramatic around peak position (see section 4 of supplemental information). In our design, the higher order resonance doesn’t exactly the 1/3 of fundamental wavelength. Its main influences happen on levitating the absorption and the efforts on phase changes is negligibly small (see section 4 of supplemental information). In this sense, the design at the fundamental resonance is

good enough and much simpler.


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Figure 3. Design of phase-controlled nonlinear nanoantennas. A) and B) are the calculated transmittance and the phase maps of the fundamental waves with varying θ and Ri. The P and Ro are fixed at 700 nm and 282 nm, respectively. C). The corresponding transmittance and phases of the selected C-shaped nanoantennas. D). The phase and the transmittance information of the selected C-shaped nanoantennas.


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Figure 4. The design of nonlinear holography. A). The illustration of the THG hologram. B). The 10-level phase distribution. C). The simulated graph of the designed holographic image. Based on the selected gradient phase shift, we have designed a hologram for normal incident light with 3ω frequency following the Gerchberg-Saxton algorithm. Figure 4A shows the schematic picture of the nonlinear hologram. The incident light is coupled to the magnetic resonance of the Si nanoantennas. Due to the size distributions, each Si nanoantenna can endow an additional phase to THG signal for the THG hologram in the far field. Simultaneously, the field enhancement of the fundamental waves can significantly improve the intensity of THG hologram. Talking the abbreviation of our university Harbin


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Institute of Technology (HIT) as a target image, we have computed and optimized the phase distributions by considering the key parameters such as conversion efficiency, signal-to-noise ratio, and uniformity (see section 4 of supplemental information). Given the influences of inhomogeneous distribution of amplitude caused by individual antenna does not affect the fidelity of hologram24, the phase with higher enhancement for the THG response was chosen. The phase distributions of the designed hologram is illustrated in Figure 4B. Figure 4C shows the simulated holographic image, which matches the designed image well. To simplify the experimental process, the holographic image is designed to be off-center to avoid the overlapping with the zero-order spot. Note that the phase changes of fundamental wavelength can also form a similar holographic image. However, as its phase changes only cover 2π/3, the intensity of hologram is orders of magnitude smaller than the zero-order spot and thus can be neglected (see section 4 of supplemental information). The nonlinear Si metasurface for THG hologram has been fabricated with the same process as the metasurface in Figure 2. Here the total size of the sample is 180 μm×180 μm. Figure 5A is the top-view SEM image of the nonlinear metasurface and its inset is the enlarged topview SEM image. Clearly, the designed Si nano-antennas have been successfully produced. The black circle dotted line in Figure 5B shows the transmission spectrum in the near infrared region. While the geometry of each C-nanoantenna has been modified to endow a designed phase, two resonant peaks can still be observed at 1475 nm and 1256 nm, indicating that the nonlinear process can still be significantly enhanced. Then a near infrared femtosecond laser at 1450 nm was irradiated onto the Si metasurface (The detailed


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experimental setup is shown in the section 1 of supplemental information). As shown in the top-panel of Figure 5C, a cyan image of “HIT” can be clearly seen, which exactly happens at the third harmonic frequency of the incident laser. The corresponding spectrum and the input-output dependence confirm the onset of THG, consistent well with the THG experiment in Figure 2 (see section 5 of supplemental information). Therefore, we can confirm that the third harmonic hologram has been generated by the Si metasurface. Such kind of infrared to visible up-conversion image usually has extremely low noise background and shall be very important for particular applications such as anti-counterfeiting, banknote security, and high-density storage.


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Figure 5. Nonlinear metasurface hologram. A). The top-view SEM image of the C-shaped Si metasurface. The inset shows the enlarged top-view SEM image. B). The transmission spectra of the metasurface at the near infrared (black dots) and visible frequency regions (blue line). C). The experimentally obtained holographic images at 483 nm (top) and 417 nm (bottom). D). The THG efficiency of the C-shaped Si metasurface as a function of incident wavelength. To confirm the enhancement of the THG signals, we have also measured the intensity of THG hologram by scanning the incident wavelength from 1200 nm to 1596 nm. Figure 5D


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summarizes the wavelength dependent conversion efficiency of the THG hologram. Similar to the THG experiment in Figure 2, the intensity of THG hologram is also dependent on the resonance of fundamental waves. A peak of THG signals can be clearly seen at 486 nm. Compared with the near-infrared and visible transmission spectra in Figure 5B, it is easy to know that the THG signals are enhanced by the magnetic resonance at the fundamental wavelength and the higher order resonance at the THG wavelength. The corresponding peak value is 5.59 × 10-7. This value is relatively smaller than the value in Figure 2 because the Celements are slightly detuned from their maximal positions to realize the designed phase shifts and the best fabrication tolerance. Similar to the results of metasurface with uniform structures, these values are still large enough to make the THG hologram visible to naked eye. The THG hologram is not limited to the magnetic resonance and relatively long wavelength (~ or > 500 nm). Our designs with C-elements also have the capabilities of generating THG hologram at much shorter wavelength. As mentioned above, the designed Si metasurface can also support an electric dipole resonance at 1256 nm (see Figure 5B). Interestingly, the ten C-elements of Si metasurface make the higher order resonance much broader (see Figure 5B) and thus can partially overlap the electric dipole resonance. Then the THG around 430 nm can be enhanced (see Figure 5D) and their absorption loss can be partially suppressed. In this sense, when the Si metasurface is irradiated with a laser beam at

1250 nm, a violet “HIT” can also be observed (bottom panel in Figure 5C). Compared with Figure 2, we note that the reduction of absorption loss plays a more dramatic role in shorter


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wavelength THG hologram. While the intensity of THG signals at 430 nm is much smaller than the one at 486 nm. Its corresponding enhancement factor is about twice larger (see section 6 of supplemental information), confirming the importance of double resonances in C-elements based Si metasurface once again. In summary, we have studied the THG hologram from all-dielectric metasurfaces. We show that the magnetic resonance and electric resonance of C-shaped Si nanoantennas at fundamental wavelength can significantly enhance the THG process, whereas the higher order resonances at the THG wavelengths can suppress the absorption loss of THG signals. Meanwhile, abrupt phase changes from 0 to 2π have been endowed the THG signals by varying the structural parameters of the C-elements. As a result, by defining the phase for each nanoantenna following the Gerchberg-Saxton algorithm, cyan and violet THG holograms have been simply realized for the very first time. Our Si metasurface can convert the near infrared beam into visible image with extremely low noise background. It shall expand the applications of all-dielectric metasurface to anti-counterfeiting, banknote security, biomedical manipulation, and volumetric data storage et al. In addition, our proposed double resonance mechanism is not restricted to visible spectrum. As the absorption is an intrinsic limitation of nonlinear materials and devices, the design of proper nanostructures in this research can be an alternative approach to develop and optimize the nonlinear metasurfaces for UV and deep-UV regions. ASSOCIATED CONTENT


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Supporting Information. The following files are available free of charge. The optical setup for THG experiments; The THG signal comparison between silicon and sapphire; The characterization of nonlinear efficiency; The simulation and principle of phase choice; The THG output power of hologram; The double resonances in Si holographic metasurface AUTHOR INFORMATION Corresponding Author *[email protected]

#[email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT Shenzhen Fundamental research projects (JCYJ20160427183259083), Public platform for fabrication and detection of micro- & nano-sized aerospace devices, and Shenzhen engineering laboratory on organic-inorganic perovskite devices


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ABBREVIATIONS EIT, electromagnetically induced transparency; TH, third-harmonic; THG, third-harmonic generation; SEM, scanning electron microscope; HIT, Harbin Institute of Technology; UV, ultraviolet. REFERENCES (1)

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Nonlinear holographic all-dielectric metasurfaces - ACS Publications

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