Flat nonlinear optics: metasurfaces for efficient frequency mixing

Invited Paper Flat nonlinear optics: metasurfaces for efficient frequency mixing Nishant Nookala 1, Jongwon Lee 1,2, Yingnan Liu 1, Wells Bishop 1, Mykhailo Tymchenko 1, J. Sebastian Gomez-Diaz 1, Frederic Demmerle 3, Gerhard Boehm 3, Markus-Christian Amann 3, Omri Wolf 4, Igal Brener 4, Andrea Alu 1, and Mikhail A. Belkin 1* 1 Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712, USA 2 School of Electrical and Computer Engineering, Ulsan National Institute of Science and Technology, Ulsan, 44919, South Korea 3 Walter Schottky Institut, Technische Universität München, Am Coulombwall 4, Garching 85748, Germany 4 Sandia National Laboratories, Albuquerque, NM 87185 USA *E-mail: mbelkin@ece.utexas.edu ABSTRACT Gradient metasurfaces, or ultrathin optical components with engineered transverse impedance gradients along the surface, are able to locally control the phase and amplitude of the scattered fields over subwavelength scales, enabling a broad range of linear components in a flat, integrable platform 1 4. On the contrary, due to the weakness of their nonlinear optical responses, conventional nonlinear optical components are inherently bulky, with stringent requirements associated with phase matching and poor control over the phase and amplitude of the generated beam. Nonlinear metasurfaces have been recently proposed to enable frequency conversion in thin films without phase-matching constraints and subwavelength control of the local nonlinear phase 5 8. However, the associated optical nonlinearities are far too small to produce significant nonlinear conversion efficiency and compete with conventional nonlinear components for pump intensities below the materials damage threshold. Here, we report multi-quantum-well based gradient nonlinear metasurfaces with second-order nonlinear susceptibility over 10 6 pm/v for second harmonic generation at a fundamental pump wavelength of 10 μm, 5-6 orders of magnitude larger than traditional crystals. Further, we demonstrate the efficacy of this approach to designing metasurfaces optimized for frequency conversion over a large range of wavelengths, by reporting multi-quantum-well and metasurface structures optimized for a pump wavelength of 6.7 μm. Finally, we demonstrate how the phase of this nonlinearly generated light can be locally controlled well below the diffraction limit using the Pancharatnam-Berry phase approach 5,7,9, opening a new paradigm for ultrathin, flat nonlinear optical components. Keywords: Metamaterials, Plasmonics, Second harmonic generation, Intersubband transitions, Semiconductor nonlinear optics including MQW 1. INTRODUCTION The field of optical metamaterials has shown exciting advances in recent years, with many demonstrated applications based on their linear interaction with light, including super-resolution imaging 10, cloaking 11 13, and wavefront control 1,2. Recently, ultrathin (sub-wavelength thickness) nonlinear metasurfaces have been put forward to achieve super-resolution imaging, to produce frequency mixing with relaxed phase-matching conditions 14,15, to implement nonlinear photonic crystal structures 16, and to enable control of the output wavefront by continuously tailoring the phase of the local nonlinear response 5. For all practical purposes, however, the level of nonlinear responses enabled by traditional materials, such as metals and dielectric crystals, is too weak, and nonlinear metasurfaces with High Contrast Metastructures VI, edited by Connie J. Chang-Hasnain, Andrei Faraon, Fumio Koyama, Weimin Zhou, Proc. of SPIE Vol. 10113, 101130O 2017 SPIE CCC code: 0277-786X/17/$18 doi: 10.1117/12.2255915 Proc. of SPIE Vol. 10113 101130O-1

orders of magnitude larger nonlinear susceptibilities are necessary to realistically enable a new paradigm in nonlinear optics, based on efficient frequency mixing in sub-wavelength films with relaxed phase-matching conditions and local in-plane phase and amplitude control of the nonlinear response. We have recently reported a novel class of nonlinear metasurfaces based on coupling electromagnetic modes in plasmonic nanoresonators with quantum-engineered intersubband nonlinearities in multi-quantum-well (MQW) semiconductor heterostructures 14,15. This approach allows one to convert the giant resonant nonlinear susceptibility of MQW heterostructures (intrinsically polarized in the direction z normal to the surface 17,18 ) into any in-plane element MQW, zzz (i,j = x or y) of the overall nonlinear susceptibility tensor of the metasurface. We compute this effective ijk nonlinear susceptibility using the following overlap integral (2) (2) MQW, zzz 2 ω ω ω ijk = ξi (, x yz,) ξj (, xyz,) ξk (, xyzdv,), V (1) UC ω 2ω where ξ i ( ξ i ) is the local enhancement of the induced z-polarized E-field in the MQW structure normalized to the i- polarized incident wave ω (2ω), and the integration occurs over the entire unit-cell volume 14,15. In particular, if the resonator is suitably designed, the effective susceptibility of our metasurfaces can exceed the intrinsic value of the MQW alone. Here we report metasurfaces in which the giant nonlinear susceptibility MQW, zzz of quantum-engineered MQW heterostructures is not only converted to the transverse plane, but also further enhanced by plasmonic nanoresonators with electromagnetic resonances tailored for fundamental (FF) and second harmonic (SH) frequencies, reaching values that exceed 10 6 pm/v, and enabling efficient frequency conversion in sub-wavelength films for pump intensities well below 1 MW/cm 2. Our metasurfaces optimized for second harmonic generation (SHG) at λ ω =9.9 μm exhibit nonlinear susceptibilities of 1.2 10 6 pm/v in a MQW thickness of only 400 nm, and a nearly 0.1% power conversion efficiency using a pump intensity of only 15 kw/cm 2 15. Further illustrating the tailorability of our modality, we report on MQWs and nano-resonators optimized for SHG at λ ω =6.68 μm and demonstrate a resonator design that can operate free of a defined gold backplane. Given the record levels of nonlinearity in deeply subwavelength volumes that our metasurfaces afford, we apply the Pancharatnam-Berry (PB) phase approach to imprinting a transverse phase distribution on carefully patterned arrays of nano-resonators to demonstrate beam-steering of the nonlinearly generated signal 6,7. We believe our cumulative results thus unveil a flat nonlinear optics paradigm, based on which efficient frequency mixing, to levels that can be realistically brought above 2.5% 15,19, occurs in deeply sub-wavelength metasurfaces using low-intensity pumping, and allowing for the complete control of the output wavefront with subwavelength resolution. 2. NONLINEAR METASURFACE DESIGN The MQW optimized for SHG at λ ω =9.9 μm consists of 26 repetitions of the In 0.53 Ga 0.47 As/Al 0.52 In 0.48 As coupled quantum-well structure shown in Fig. 1(a). This MQW is purposefully designed to exhibit a 1-2 intersubband resonance approximately 25 mev detuned from the optimal pump photon energy of 124 mev, allowing us to reduce optical losses within the cavity at the pump wavelength and increase the intensity threshold at which the nonlinear response of the MQW starts to saturate. We measure the resulting epitaxially grown MQW to exhibit a 1-2 transition linewidth of 2hγ 21 25meV and 1-3 of 2hγ 31 29meV and calculate an intrinsic nonlinear susceptibility ( MQW, zzz ) of 2.8 10 5 pm/v at the pump wavelength of 9.9 μm, with the absolute value of the susceptibility plotted as a function of pump wavenumber in Fig. 1(b). Fabrication of the nano-resonator array starts by defining a gold ground plane underneath the MQW layer, as described in Ref. [15], which serves to verticalize the E-field within the cavity and thus increase the strength of the resonances and nonlinear response. We designed nano-resonators with a T-shaped geometry, where the FF resonance is controlled by the length of the long arm along the x-axis, and the SH resonance is dictated by the dipole created between the short and long arms along the y-axis. Etching the MQW material around this pattern further serves Proc. of SPIE Vol. 10113 101130O-2

to confine the E-field within the MQW and strengthens the nonlinear response, and the optimal dimensions of the fabricated and tested device are depicted in Fig. 1(c). The combination of all these factors allows a theoretical modal overlap integral above 4.25. b 300 c > 200 E 100 2 4 6 8 10 12 14 16 Thickness (nm) o 800 1000 1200 1400 Wavenumber (cm') a 800 Figure 1. (a) Conduction band diagram of one period of the In 0.53 Ga 0.47 As/Al 0.48 In 0.52 As MQW structure. The layer sequence (in nm) is 2.5/6.2/1.4/2.4/2.5 where AlInAs barriers are shown in bold, and the first 1.5 nm of the first 2.5 nm barrier and the last 1.5 nm of the last 2.5 nm barrier are n-doped to 6x10 18 cm -3. (b) Calculated intersubband nonlinear susceptibility of the structure in (a) as a function of wavenumber. (c) Schematic of one unit cell of the designed metasurface, units are in μm. (d) Simulated field distributions at the FF and SH resonances of the etched T structure. The FF resonance is controlled along the x-direction by the dipole along the long arm of the T, and the SH resonance is controlled by the dipole in the y-direction between the short and long arms. The SH wavelength of our metasurfaces is determined by the 1-3 transition in our MQWs, where the choice of MQW material composition determines the valence band offset and ultimately establishes a limit on our design space. Reliable optical sources in the 3μm range are of some interest, and to demonstrate that our modality can be successfully extended towards these shorter wavelengths (i.e. higher photon energy), we subsequently designed a MQW structure consisting of 31 repetitions of the In 0.59 Ga 0.41 As/Al 0.635 In 0.365 As coupled well design shown in Fig. 2(a), where the theoretical valence band offset is approximately 200 mev higher than that of our previously described design at 9.9 μm. Unfortunately, due to the lattice mismatch between the constituent materials of the heterostructure, the linewidths of the intersubband transitions are adversely affected, with the linewidth of the 1-2 transition ( 2h γ21 ) rising to 45 mev. This increase in linewidth largely contributes to a lower value of the intrinsic susceptibility evaluating to 4.9 10 4 pm/v at a pump wavelength of 6.68 μm, and the absolute value of susceptibility plotted as a function of pump wavenumber in Fig. 2(b). Fabrication of the metasurfaces follows largely the same method as the design for the λ ω =9.9 μm etched T, with the dimensions of the T altered for the new pump and second harmonic wavelengths of 6.68 μm and 3.34 μm, respectively. To explore the efficacy of a design and fabrication process that doesn t necessitate wafer bonding and substrate etching for creation of a full metal backplane, we additionally fabricated a metasurface with an artificial ground plane. In this design, we pattern and etch the MQWs into appropriately designed T shaped structures, and end by coating the entire sample with gold. While there is no metal directly underneath the etched resonators, the gold surrounding the structures serves a similar effect in confining and verticalizing the FF and SH light in the nano-resonators. The optimum dimensions of both resonators are outlined in Fig 2(c). 700 600 > 3 500 176 mev Z=0.6 nm 15 nm 400 1 2 EF=90meV 42 300 200 100 1111 In 2 4 6 8 10 12 14 Thickness (nm) > E rv,11 50 40 30 20 10 0 1000 200 1400 1600 1800 Wavenumber(cm 1) 2000 c Real backplane Artficial backplane Figure 2. (a) Conduction band diagram of one period of the In 0.59 Ga 0.41 As/Al 0.635 In 0.365 As MQW structure. The layer sequence (in nm) is 2.5/4.4/1.3/2.1/2.5 where AlInAs barriers are shown in bold, and the first 1.5 nm of the first 2.5 nm barrier and the last 1.5 nm of the last 2.5 nm barrier are n-doped to 7.8x10 18 cm -3. (b) Calculated intersubband nonlinear susceptibility of the structure in (a) as a function of wavenumber. (c) Schematics of one unit cell of the fabricated metasurfaces, left image depicts the unit cell of a structure with a defined backplane, and the right depicts that of an artificial backplane. All units are in μm. Proc. of SPIE Vol. 10113 101130O-3

3. NONLINEAR METASURFACE CHARACTERIZATION Experimentally, we fabricated three 400 μm by 400 μm metasurfaces using the unit cell designs shown in Figs. 1(c) and 2(c), with the fabrication steps for the metasurfaces with the defined backplane following the same procedure as in Ref. [15], where the backplane is first created via gold-gold thermos-compressive bonding to a dummy InP substrate. The MQW substrate is then removed by mechanical polishing and wet etching, and finally the T structures are patterned by electron-beam lithography (EBL) and etched by an inductively-coupled plasma reactive ion etching (ICP-RIE) system. For the etched T structure with the artificial backplane, the MQW wafer was instead first directly patterned and etched via EBL and ICP-RIE, before an approximately 50 nm thick gold film was evaporated onto the metasurface at normal incidence. The nonlinear response of all three metasurface designs was tested using the experimental setup shown in Fig. 3(a) and described in the figure caption. Figs. 3(b)-(c) shows the SHG conversion efficiency as a function of the fundamental power peak power and peak intensity for yxx polarization combination, where the first letter refers to the polarization of the generated SH beam and the other two refer to the polarization states of the pump beams. Other polarization combinations provide limited SHG response, since our nanoresonators only provide strong coupling of incident/outgoing waves to the MQW for x-polarized light at fundamental frequency and y-polarized light at SH frequency. We note that the conversion efficiency grows linearly with incident intensity before ultimately flattening due to optical saturation of the intersubband transition. a Collimating lens BS InSb detector SP ZnSe lens Polarizer LP Tunable CICL b FF intensity (kw cm') O 5 10 15 20 0.08 ú 0.06 N U m 0.04 ó 0.02 v yxx polarization = 9.94µm AtH= 4.97µm Ú 0.00 O 20 40 60 80 FF power (m W) C FF intensity (kw cm') 10 15 20 25 30 35 40 Artificial backplane Real backplane Trr=6.68pm sh=3.34pm r... > 5- ó C) 4 100 40 80 120 160 200 FF power (m W) Figure 3. (a) Schematic of the setup used to characterize the generated second harmonic light from the fabricated nonlinear metasurfaces. Light emitting from a tunable QCL (tuned to the optimum pump wavelength of the particular MQW employed, i.e. 9.94 μm and 6.68 μm) is focused onto the metasurface. The generated SH light reflects back towards the source, but is reflected by a beamsplitter and focused onto a LN 2 cooled InSb detector. SH light is discriminated from any reflected pump light via a linear polarizer. (b) Cartoon depicting the P-B approach to beam-steering, where RCP FF incident light converts to RCP and LCP outgoing SH light. (c)-(g) SEMs of fabricated gradient SRR arrays, with differing angular rotational steps Δ. Five samples with angular steps of 10, 15, 20, 24, and 30 deg were fabricated and tested. (h) RCP SH output given RCP FF input from gradient metasurface as a function of angle away from surface normal for each gradient array fabricated. estimate The value of yxx yxx for the λ ω =9.9 μm metasurface design can be obtained using the data in Fig. 3c, from which we 1.2 10 6 pm/v (0.66 10 6 pm/v) for low (high) pump intensity. These numbers represent the largest Proc. of SPIE Vol. 10113 101130O-4

values of second-order nonlinear susceptibility ever recorded to our knowledge in the infrared-visible range in a condensed matter system. Such giant values of optical nonlinearity achieve 0.075% conversion efficiency from a 400 nm-thick MQW layer using a pump intensity in the range 10-15 kw/cm 2. In comparison, the best traditional nonlinear materials 20 and nonlinear optical metasurfaces in infrared-visible range demonstrated to date 5,16,21 produce at least 8 orders of magnitude smaller conversion efficiency for the same thickness and pump intensity. Similarly, we can arrive at yxx 5.6 10 4 pm/v for the λ ω =6.68 μm structure with a real backplane, and yxx 3.5 10 4 pm/v for the structure with an artificial one, achieving conversion efficiencies of 9 10-4 % and 6 10-4 %, respectively. The reduction in measured nonlinear response when compared to the λ ω =9.9 μm design can be attributed to the overall intrinsic MQW susceptibility being lower in the short wavelength case due to the previously mentioned larger intersubband transition linewidths. Comparing the real and artificial backplane designs for the λ ω =6.68 μm MQW elucidates that significant SHG can indeed be observed in a structure with the artificial backplane, with a performance difference of only 50% favoring the design with the full bonded metal backplane. Importantly, this result potentially paves the way for nonlinear metasurfaces operating in transmission mode, where a full backplane would normally prevent any light from transmitting through the substrate, as well as opens the possibility of employing more exotic MQW materials grown on substrates that are not easily removed. 4. CONTINUOUS PHASE CONTROL To demonstrate local control of the nonlinear generation at the individual nanoresonator level with subwavelength resolution, we employ the Pancharatnam-Berry (PB) phase approach 5 7. We operate in a circular polarization basis, transforming the metasurface susceptibility tensor elements from (i,j = x or y) into, where α, β, and γ are R or L, corresponding to RCP or LCP polarizations, respectively. It can be shown that, irrespective of the unit cell design, the phase of the generated SH polarization currents in each unit cell is linearly proportional to the relative angle of rotation Δ ϕ of the corresponding unit cell (see Fig. 4(b)). More specifically, a linear gradient of rotation in the metasurface plane corresponds to a constant phase gradient Δ ϕ and 3 Δ ϕ for pumps with LCP (RCP) and RCP (LCP) polarization, respectively, applied to the distribution of RCP (LCP) SH currents. Importantly, the magnitude of the SH currents remains constant for all rotation angles. These features are ideal for locally controlling the phase of the emerging nonlinear wavefront with subwavelength resolution: different from conventional PB approaches based on linear phenomena 9, whose overall efficiency is largely dependent on the resonator design, here we can focus the design on maximizing the nonlinear conversion efficiency, based on the previous discussion. Then, we can simply rotate the optimized design pixel-by-pixel to imprint the desired transverse phase pattern on the metasurface plane. The unit-cell of the proposed metasurface is shown in Fig 4(a), where the MQW used is the previously described λ ω =9.9 μm semiresonant design. This configuration is similar to the design discussed above, but the T-shaped resonator has been changed to a split-ring resonator (SRR), which offers a smaller spatial footprint in all dimensions and a square unit-cell that allows arbitrary rotation. The resonator dimensions and unit cell are depicted in Fig. 4(a) and have been optimized to provide strong absorption for x-polarized beams at the fundamental frequency and for y-polarized beams at the SH frequency. When the resonators are spatially arranged as shown in Figs. 4(c)-(g), with an angular rotation step of Δ ϕ between resonators of adjacent unit cells along one direction, the metasurface provides a nonlinear response with a linear phase gradient along the same direction. Then, from basic reflectarray theory, it follows that a normally incident RCP θ = arcsin 3 Δ ϕ / 360 λ / d and beam generates two SH beams, one RCP polarized towards the direction [( ) ] R( R) 2ω another LCP polarized towards = arcsin [( Δ / 360 ) / d] 1,2,7,22. θ ϕ λ L( R) 2 ω ijk αβγ Proc. of SPIE Vol. 10113 101130O-5

d Ay- 15 h1 o.- 1 4m =10 0 1 4vp 15 4q -20,A p40ccgonc: Ay 24.,..,....,..., x o 1n 1 CL 4=24 ó 49 =30 Jl -50-40 -30-20 -10 0 10 20 30 40 50 Angle (deg) Figure 4. (a) Schematic of one unit cell of the designed metasurface for SH beam steering. (b) Cartoon depicting the P-B approach to beam-steering, where RCP FF incident light converts to RCP and LCP outgoing SH light. (c)-(g) SEMs of fabricated gradient SRR arrays, with differing angular rotational steps Δϕ. Five samples with angular steps of 10, 15, 20, 24, and 30 deg were fabricated and tested. (h) RCP SH output given RCP FF input from gradient metasurface as a function of angle away from surface normal for each gradient array fabricated. To demonstrate SH beam steering, we fabricated metasurfaces with Δ ϕ of 10, 15, 20, 24, and 30 degrees, with scanning electron microscope images given in Figs. 4(c)-(g), and pumped the structures with RCP light. Following the previous formulation, we expect to observe RCP (LCP) SH output at 13.3, 20.2, 27.4, 33.5, and 43.7 (4.4, 6.6, 8.8, 10.6, and 13.3) degrees for Δ ϕ of 10, 15, 20, 24, and 30 degrees, respectively. Experimental measurements of the far-field SH emission from the metasurface was obtained by pumping our metasurface arrays with a CW CO 2 laser tuned to the optimal FF, and moving the detector in a hemisphere around the metasurface, with full details described in Ref [6]. The measured results, shown in Fig. 4(h) for RRR polarization combination, are in very good agreement with our predictions, fully confirming the large control of the generated SH beam with subwavelength resolution. We do note small peaks in the RCP SHG signal corresponding to the angle provided by LRR and RLL polarization combinations, which we attribute to imperfect retardation offered by the available quarter wave plates in our laboratory. 5. SUMMARY In conclusion, we ve reported metasurfaces whose second-order nonlinear susceptibility exceeds 10 6 pm/v, which is, to the best of our knowledge, the highest second-order optical nonlinearity reported from any condensed matter system in infrared/visible spectral range. Giant nonlinear response was enabled by combining quantum-mechanicallyengineered intersubband transitions in MQW systems with electromagnetically-engineered plasmonic nanoresonators with tailored optical resonances for input and output frequencies. Further, by incorporating a slightly different material composition in our MQWs, we successfully demonstrated SHG at a pump wavelength of 6.8 μm, opening a new avenue to creating short-wave-infrared sources. Our work demonstrates the feasibility of achieving efficient frequency mixing in optical films of sub-wavelength thickness using pumping intensity well below materials damage threshold even for continuous-wave excitation, and opens a new paradigm in nonlinear optics, based on which efficient frequency conversion may be achieved in deeply subwavelength films with sub-diffractive control of the outgoing nonlinear wavefront and relaxed phase-matching conditions. ACKNOWLEDGEMENTS This work was supported by the AFOSR award No. FA9550-14-1-0105, ONR MURI grant No. N00014-10-1-0942, and Nano Initiative Munich. Sample fabrication was carried out in the Microelectronics Research Center at the University of Texas at Austin. M.A.B. acknowledges support from the Alexander von Humboldt Foundation Friedrich Wilhelm Bessel Research Award. Proc. of SPIE Vol. 10113 101130O-6

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