Demonstration of terahertz ferroelectric metasurface ... - OSA Publishing

0 downloads 0 Views 5MB Size Report
Oct 9, 2018 - The ferroelectric-based all-dielectric metasurface ...... J. Yu, G. Zhao, and X. Yu, “Transmissive terahertz metalens with full phase ... for broadband linear polarization conversion and optical vortex ... “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,”.
Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27917

Demonstration of terahertz ferroelectric metasurface using a simple and scalable fabrication method JINGYI TIAN,1,2 FREDRIK LAURELL,1 VALDAS PASISKEVICIUS,1 MIN QIU,2,3 AND HOON JANG1,* 1Department

of Applied Physics, Royal Institute of Technology, KTH, 10691 Stockholm, Sweden Key Laboratory of Modern Optical Instrumentation, College of Optical Science and Engineering, Zhejiang University, 310027 Hangzhou, China 3Institute of Advanced Technology, Westlake Institute for Advanced Study, Westlake University, 310024 Hangzhou, China *[email protected] 2State

Abstract: We report on experimental implementation of a ferroelectric metasurface using an x-cut KTiOPO 4 (KTP) crystal for efficient manipulation of terahertz (THz) radiation. Based on the multipolar resonances that are accommodated in KTP micro-blocks in a square array, the metasurface is fabricated by precision diamond-blade dicing. Adjusting the size of the KTP micro-blocks to tailor the relative spectral positions of the anisotropic multipolar resonances, we demonstrate a subwavelength-thin THz polarizer that functions as a transparent film in the y-direction and a magnetic mirror in the z-direction with a transmission contrast of 13 dB near 0.37 THz (820 µm). The ferroelectric-based all-dielectric metasurface will provide a versatile platform to engineer the THz waves in the far field and could potentially be combined with THz generation in the same material. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction Terahertz (THz) radiation is of increasing technical importance with applications in communication, sensing, biomedical imaging, security and material science. Among various schemes to generate THz fields, photonics using ferroelectrics have been very successful in generating tunable and high-field THz radiation [1–11]. For instance, THz parametric oscillators (TPO) using ferroelectric crystals have facilitated THz sources with spectral tunability at room-temperature [1–4,10,11], while optical rectification with tilted pulse-front excitation in ferroelectrics yielded high-field THz waveforms [5,6]. Moreover, there is an increasing interest in exploiting the quasi-phase-matching capabilities in ferroelectrics [12] to generate high-field narrowband radiation in the spectral range below 1 THz and implement compact schemes for electron bunch acceleration [13–15]. Linear and nonlinear response functions are typically strongly dispersive in the THz region in polar solids, including ferroelectrics, due to strong coupling to transversal polar optical phonon resonances [16–21]. Strong dispersion of the linear susceptibility is crucial for phase-matching of tunable THz generation in TPO schemes [8,9]. However, the same phonon resonances are responsible for dipole-allowed transitions giving rise to strong absorption in adjacent spectral regions. For this reason, in most of the ferroelectric-based TPO devices, the strong THz absorption near the phonon resonances was alleviated by operating the device near the ferroelectric surfaces to minimize the THz propagation distance inside the crystal [2,3,10,11]. The absorption effects are much lower for frequencies around 0.5 THz, where there is substantial interest for high-field narrowband THz generation. Furthermore, the absorption can be further reduced by cooling the crystal to decrease damping of the phonon resonances. However, the issues of efficient out-coupling and in-coupling (as in proposed THz amplifiers [22]) of the generated THz waves still exist as a significant Fresnel reflection #341579 Journal © 2018

https://doi.org/10.1364/OE.26.027917 Received 6 Aug 2018; revised 30 Sep 2018; accepted 30 Sep 2018; published 9 Oct 2018

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27918

occurs at the crystal-air interface due to the large refractive indices of ferroelectrics in the THz region. For instance, in KTiOPO 4 (KTP), the z-polarized wave at 1 THz would experience 33% reflection loss for normal incidence and a total internal reflection at incidence angles exceeding 15.7°. In LiNbO 3 , these conditions are even more restrictive resulting in a reflection loss of 45% and total internal reflection at incidence angles above 11°. The THz transmission through the ferroelectric surface was often improved by placing silicon out-couplers or grating structures on the ferroelectric surface [2]. Nevertheless, the large impedance mismatch to the free space at THz frequencies remains a challenge for an efficient out- and in-coupling of the generated THz radiation. Besides, the transmitted THz waves in the far-field have to be processed by other optical elements such as lenses or waveplates for the practical application of the THz sources. On the other hand, a large index of refraction can, in fact, be beneficial for the enhanced out- and in-coupling schemes employing Mie-type resonances in microstructures [23–41]. In contrast to THz transmission based on the simple Fresnel equations at a planar interface, interference between electric and magnetic multipolar resonances in micro-structures allows us to take advantage of large refractive index to manipulate THz waves in the far-field [23– 29]. In this case, electric and magnetic resonances are often simultaneously supported by a high-index dielectric particle in a simple shape such as a disk [30] or a block [31]. This has led to the recent demonstrations of all-dielectric metasurfaces, where two-dimensional arrays of subwavelength dielectric particles are employed to implement various electromagnetic responses in the visible and the infrared regions [23–39]. Most of the demonstrated alldielectric metasurfaces have been made of semiconductor materials, such as Si [27–30] and Ge [41], owing to their high indices of refraction as well as low losses. In this case, one could easily pattern and create the artificial dielectric scatterer arrays using well-established nanofabrication technology [24–38]. If the surface of ferroelectrics could be structured in such a way that one would engineer the transmitted THz field via simultaneous excitation of electric and magnetic resonances, it would provide a versatile platform to monolithically combine a THz source with various functionalities for far-field manipulation. In our previous work [26], we have theoretically proposed ferroelectric metasurfaces for efficient manipulation of THz waves with functionalities such as polarization switching and beamsteering. In this paper, we report on experimental demonstration of a ferroelectric metasurface that consists of KTP micro-blocks in a square array. Taking advantage of the structural simplicity and relatively large characteristic dimensions between the blocks, we employ precision diamond-saw dicing [42] for fast fabrication of the structures. Based on the anisotropic multipolar resonances, this KTP metasurface functions as a transparent film in the y-direction while it becomes a magnetic mirror in the z-direction with a maximum transmission contrast of 13 dB near 0.37 THz, i.e. a wavelength of 820 µm in free space. 2. Design of KTP metasurfaces with numerical simulations KTP is a biaxial ferroelectric with high nonlinearities and strong phonon resonances in the THz region [43]. The refractive indices along the crystal x- and y-axes are very similar to each other and considerably lower than the one in the z-direction (see Appendix A for optical properties of KTP in the THz region). We used an x-cut KTP crystal, thereby aiming at exploiting the intrinsic anisotropy to obtain different responses for the orthogonal polarizations. In our design, a simple micro-block is adopted with a square shape in the x-face to form a dielectric antenna that accommodates anisotropic multipolar resonances. Varying the aspect ratio of the micro-block to spectrally position the resonances, we first set the height of our structure to 130 µm as it is easily achievable in practice with standard industrial polishing machines (e.g. Logitech PM5 Precision Lapping & Polishing Machine). As a first step in modelling the structure, we employed the finite-difference time-domain (FDTD) method (Lumerical FDTD Solutions, version 8.15.697) to calculate the resonant scattering behavior of a single KTP micro-block under the illumination of THz plane waves propagating

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27919

along the crystal x-axis. Figures 1(a) and (b) show an example in which the anisotropic scattering cross-section of a single KTP micro-block was calculated for the block-size of 150 µm under y- and z-polarized illuminations, respectively. In this case, the total scattering crosssection calculated in the FDTD simulation can be projected into each resonance through multipolar decomposition [26,44,45] to elucidate the origin of the spectral response. The insets in Figs. 1(a) and (b) show the electric field distribution of the electric and magnetic lowest dipole resonances, which further validates our multipolar decompositions. The spectral position of each resonance occurs at different frequencies for different polarization of the incoming radiation due to the birefringence of the material, therefore resulting in anisotropic scattering cross-section.

Fig. 1. Scattering cross-sections vs. frequency for a single KTP micro-block that has the block size of d = 150 µm and the height h = 130 µm in vacuum. At the normal incidence of (a) ypolarized or (b) z-polarized THz plane waves, we calculate the contributions from an electric dipole (ED, green line), a magnetic dipole (MD, blue line), an electric quadrupole (EQ, cyan line) and a magnetic quadrupole (MQ, magenta line) based on the equations in [26,44,45]. The total scattering cross-section calculated in FDTD (black solid line) is compared with the sum of the multipolar scattering cross-sections (red dashed line). All calculated cross-sections are normalized to the physical area of the block d 2. The insets describe the normalized electric field distribution at each dipole resonances in the x-y (x-z) plane under the y-polarized (zpolarized) illumination. (c) A schematic description of the metasurface with KTP micro-blocks in a square array on a polymethylpentene (TPx) substrate (n = 1.46), where h = 130 μm, g = 120 μm and the grating pitch, a = d + g. Transmission spectra are calculated under (d) ypolarization and (e) z-polarization, while the block size d is varied from 100 µm to 400 µm. The white dashed lines highlight the positions of excited magnetic and electric dipoles in the spectral domain as we vary the block size. (f) Spectral mapping of transmission contrast, defined by 10 log(T y /T z ), as a function of block size.

Next, by applying periodic boundary conditions along y- and z-axes, we addressed a twodimensional square array of the KTP micro-blocks that constitutes a uniform KTP metasurface. As shown in Fig. 1(c), the KTP metasurface is placed on a polymethylpentene (TPx) substrate, which offers nearly dispersionless low refractive index ( n = 1.46 ) and negligible absorption in the THz region. After fixing the gap-size to 120 µm that is determined by the diamond-blade dicing process, we varied the block-size from 100 µm to 400 µm to observe changes of the anisotropic spectral response in transmission through the metasurface to the substrate. The calculation results are shown in Figs. 1(d) and 1(e) under yand z-polarized illumination, respectively. In this case, the dipole resonances (white-dashed lines) are distributed across the range between 0.3 THz and 0.75 THz, where KTP provides a relatively high refractive-index and low absorption.

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27920

Compared with the transmission spectra along the y-axis shown in Fig. 1(d), the overall red-shift of the multipolar resonances can be observed in Fig. 1(e) with a significantly lower transmission near the resonances. This is attributed to the intrinsic anisotropy in KTP, which results in stronger reflection and absorption for z-polarized radiation. The corresponding reflection and absorption spectra are calculated for both polarizations and shown in Appendix B. Due to the shifted spectral responses under the orthogonal polarizations, the anisotropy can be enhanced near the resonances in the metasurface and used to implement a sharp polarization discrimination. Figure 1(f) describes the transmission contrast that is defined as the ratio between the two transmission spectra under the orthogonal polarizations. Among several notable positions with the contrast over 20 dB in the graph, our interest centers around the area with both high contrast and efficient transmission for one of the polarizations. Near the block-size of 340 µm, for example, a sharp contrast of 20 dB can be achieved while the efficient transmission Ty > 90 % for y-polarized radiation is maintained at the same time. In addition, the electric and magnetic dipoles are spectrally well-separated in this regime so that each resonance could be readily identified in the experiment. For these reasons, we have chosen to fabricate KTP metasurface with d = 340 µm, g = 120 µm and h = 130 µm for demonstrating an efficient THz polarizer based on anisotropic multipolar resonances. 3. Fabrication of the designed KTP metasurface Fabrication of the KTP metasurface on a TPx substrate can largely be divided into three steps; adhesive bonding, mechanical polishing and precision diamond-saw dicing. First, we start with preparing a TPx substrate for adhesive bonding with a bulk KTP crystal. In general, transparent polymers with low refractive indices in the THz range have very low surface tension (e.g. 24mN/m for TPx) that does not allow a strong adhesion to any dielectrics or even to epoxy materials. This intrinsically weak adhesion between the polymer substrate and the ferroelectric material must be overcome for the post-bonding processes including mechanical polishing and dicing on the KTP side. We used a 1 cm2-wide piece of 2 mm-thick TPx sheet (Grade: MX002) that was first treated with oxygen plasma on the surface. Meanwhile, a combination of an epoxy resin (Bisphenol A diglycidyl ether) and a hardener (1, 2 –Ethylenediamine, N-(2-aminoethyl)-, polymer with oxirane diethylenetriamine) was applied to a 500 µm-thick x-cut KTP crystal with the same lateral dimensions of 1 cm × 1 cm. After the TPx was attached to the adhesive on KTP, we applied a mechanical pressure and kept it over the curing process. The curing took > 12 h and was performed at room temperature in order to avoid stress due to significantly different thermal expansion coefficients between the two materials. The final thickness of the epoxy layer between the KTP and TPx was less than 10 μm (Fig. 2a), which is optically negligible at the operating wavelength near 800 µm. The bonding was strong enough so that the KTP could be mechanically polished down to a thickness of 130 μm, as shown in Fig. 2(b). This was followed by a mechanical dicing (Disco DAD 320 dicing saw) to create the KTP metasurface consisting of square blocks in a 2-dimensional square array. To our knowledge, this is the first demonstration of a metasurface fabricated by mechanical dicing without any need for patterning via lithography. Figure 2(c) shows a top view microscope image of the fabricated KTP metasurface, where the size of each block is measured to be 340 × 340 × 130 μm3 with the 120 μm gap to the neighboring blocks. The surface roughness that is observed at the corner of each block should not have a significant influence on the performance of the metasurface as the resonant field is very weak around the corner. A picture of the entire sample is presented in Fig. 2(d), where we emphasize the transparency of the overall structure in the visible spectral region. The transparency in the visible/near-infrared regions is important if one, for example, aims to combine the ferroelectric metasurface with a waveguide structure for THz generation via parametric processes, e.g. optical rectification, with the pump frequency near the visible spectrum [9].

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27921

Fig. 2. Fabrication process of the KTP metasurface. (a) Cross-section of the sample after the adhesive bonding between KTP and TPx. The thickness of the adhesive layer is less than 10 µm across the entire sample area. (b) A side-view microscope image of the KTP/TPx sample after mechanical polishing on the KTP side. The thickness of the KTP thin-film is measured to be 130 µm. (c) A top-view image of the KTP metasurface on TPx after precision diamond-saw dicing on the KTP thin-film. Following our design in FDTD, the size of each block is 340 × 340 × 130 μm3 with a 120 μm gap to the neighboring blocks. (d) A top view photo of the entire sample. The rainbow colors are clearly seen through the KTP and TPx layers.

4. Optical characterization of the fabricated KTP metasurface In order to characterize the fabricated KTP metasurface, we built a THz time-domain spectroscopy setup which is schematically described in Appendix C. A photoconductive antenna was used as a THz source that is optically triggered by a mode-locked Ti:Sapphire laser (800 nm wavelength, 100 fs pulse duration and 80 MHz repetition rate), while a 300 µm thick [110] ZnTe crystal was employed for detection by electrooptical sampling. The scanning range was over 200 ps for a high spectral resolution. After the reference signal was measured in air without any sample, we placed the fabricated KTP metasurface at the focus of the THz beam at normal incidence angle. The THz beam-size was approximately 5 mm in diameter. The transmittance through the sample was obtained by normalizing the extracted Fourier spectrum with respect to that of the reference signal. Portions of the measured time-domain THz signals traces, zoomed in around the signal peaks, are shown in Fig. 3(a). The black solid line represents the reference signal in the air while the red and the blue show the transmitted signals through the fabricated sample under ypolarized and z-polarized illuminations, respectively. The observed time-delay between the reference and the sample signal matches well to the thickness of our sample (the 130 µmthick KTP metasurface on the 2 mm-thick TPx substrate). These measured time-domain signals can readily be processed by Fast Fourier transform to obtain the spectral response under each polarization. Figure 3(b) shows the transmission spectrum for y-polarization, which is in good agreement with the FDTD simulation results. Transmission dips at the electric and magnetic dipole resonances are identified near 860 µm (0.35 THz) and 760 µm (0.39 THz) µm, respectively. In the range between the magnetic and electric dipole resonances, the metasurface functions as a transparent film with an efficient transmission around 80%. Subsequently, we rotated the sample by 90 ° around the x-axis and measured the transmission spectra under z-polarized THz illumination. The measurement data is presented in Fig. 3(c) together with the theoretical prediction from the FDTD calculation. Both, the experimental data and the calculation confirm the minimum transmission at the magnetic dipole resonance near 820 µm (0.37 THz) where the KTP metasurface acts as a magnetic mirror. In this case, the interference between the incident wave and the reflected wave forms a standing wave, of which the field intensity distribution is shown in the inset. Compared with the electric and magnetic resonances in Fig. 3(b), the corresponding resonances in Fig. 3(c) are red-shifted due to the intrinsic birefringence of KTP, while the

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27922

overall suppression in transmission is attributed to the stronger reflection and the absorption along the z-axis. Combining these results under the orthogonal polarizations, we show in Fig. 3(d) that the transmission contrast (purple solid line) reaches over 20 (13 dB) at 820 µm (0.37 THz) with a bandwidth of 50 µm (20 GHz, FWHM). As a comparison, the grey dashed line shows the measured intrinsic transmission contrast through a 130 µm-thick KTP film, which barely reaches 4 in this spectral region (See Appendix D for transmission spectra through the KTP film under each polarization). Based on the strongly enhanced anisotropy at the tailored spectral positions, our KTP metasurface can function as a subwavelength-thin THz polarizer with a transmission efficiency of over 80%.

Fig. 3. (a) The measured time-domain THz signals. The black line shows the reference THz pulse transmitted through air, while the red and blue lines represent the THz transmission through the sample under y-polarized and z-polarized illuminations, respectively. After Fast Fourier transform of each time-domain signal, transmission spectra are obtained when we normalize the sample signals with respect to the reference in the frequency domain. (b) The transmission spectrum under the y-polarized illumination. The measured data (red solid line) is compared to the FDTD simulation (black dashed line). (c) The transmission spectrum under zpolarized illumination. The measured data (blue solid line) is compared to the FDTD simulation (black dashed line). The inset shows the calculated field intensity distribution of the standing wave from the magnetic mirror. (d) The transmission contrast between the two orthogonal polarizations. The purple solid line shows the transmission contrast through the fabricated KTP metasurface, while the grey dashed line corresponds to the measured transmission contrast through a 130 µm-thick KTP film for a comparison.

5. Discussion and conclusion In conclusion, we have experimentally implemented a ferroelectric metasurface that consists of KTP micro-blocks in a square array. Based on the anisotropic multipolar resonances, a 130

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27923

µm-thin THz polarizer is demonstrated with the extinction ratio higher than 12 dB at the operation frequency near 0.37 THz. The fabrication method using the precision diamondblade dicing is rather general and applicable to all-dielectric metasurfaces based on various ferroelectric crystals. Obviously, the fabrication method is not limited to the uniform array geometry and can be used to implement a chirped metasurface for beam-steering or linefocusing as discussed in Appendix E. Although the refractive index of Si in the THz spectral region is very similar to that of KTP [46], Si lacks birefringence and electrooptic effect. Therefore, at least for frequencies below 1 THz, or at low temperatures where the absorption losses are low, the ferroelectric metasurfaces can offer wider scope of functionality, including active control over the phase properties of the metasurface as well as a possibility for direct integration with ferroelectric-based THz generators. Furthermore, our KTP metasurface on a TPx substrate is transparent in the visible and near-infrared regions. This can facilitate an efficient pumping scheme for optical rectification in a ferroelectric waveguide adjacent to the metasurface, and therefore paves the way for the future integration of THz generation and manipulation. Appendix A: Optical constants of KTiOPO 4 in the terahertz region The optical properties along the crystal axes of KTiOPO 4 (KTP) in the terahertz (THz) region at room temperature are shown in Fig. 4. As shown in Fig. 4(a), the KTP crystal exhibits high refractive indices and a strong birefringence = ( ∆n    nz – n y ≈ 0.65 ), which do not appreciably change in the frequency range of 0.3 THz – 0.75 THz (400 μm - 1000 μm) at room temperature. In this range, the absorption coefficients of α x ≈ α y < 5 cm −1 , α z < 25 cm −1 are also well-maintained, as depicted in Fig. 4(b).

Fig. 4. (a) Refractive indices and (b) absorption coefficient of KTiOPO 4 crystal in the terahertz region (0.3 THz –0.75 THz) at room temperature (296 K) [43].

Appendix B: Reflection and absorption in the uniform KTiOPO 4 metasurface Using the FDTD method, we calculated the anisotropic reflection and absorption spectra of the uniformly distributed KTP block array as a function of the block size and the frequency of incoming radiation. Figure 5(a) and 5(b) show the calculated reflection spectra for y-polarized and z-polarized illumination, respectively, while Fig. 5(c) and 5(d) show the corresponding absorption spectra. The white dashed lines in the figures follow the induced electric and magnetic dipole resonances to highlight their crossing in the spectral domain as we vary the block size. As shown in Figs. 5(a) and 5(b), reflection is approaching to 100% at the magnetic dipole resonances for both polarizations, at which the metasurface functions as a magnetic mirror. In Fig. 5(c) and 5(d), a significantly enhanced absorption is observed for both

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27924

polarizations near the crossing of magnetic and electric dipole resonances. The absorption for the z-polarized illumination can be as large as 70% near the intersection.

Fig. 5. 2D mapping of THz intensity reflected at the uniformly distributed KTP block array as a function of block-size d and the frequency of y-polarized (a) and z-polarized (b) illumination. The corresponding absorption spectra are also calculated for y-polarized (c) and z-polarized (d) illumination. The structural parameters are the same as those in the main text of the paper; h = 130 μm, g = 120 μm and a = d + g. The white dashed lines follow the induced magnetic (MD) and electric (ED) dipole resonances in the KTP micro-blocks.

Appendix C: Terahertz time-domain spectroscopy Our THz time-domain spectroscopy setup is schematically described in Fig. 6. We used a photoconductive antenna (Batop, iPCA 21-05-1000-800-h) as a THz source where DC voltage was applied across the antenna under 0.35 W optical power from Ti:sapphire laser (800 nm wavelength, 100 fs pulse duration and 80 MHz repetition rate). At the detection, a 300 µm thick [110] ZnTe crystal was used for electro-optical sampling with the 100 fs probe pulses from the same Ti:Sapphire laser. We covered the scanning range over 200 ps in timedomain, which gives a spectral resolution (5 GHz) that is sufficient for our experiment. The overall bandwidth from the photoconductive antenna was up to 3 THz.

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27925

Fig. 6. Terahertz time-domain spectroscopy using a photoconductive antenna as a THz source, which is optically triggered by 100 fs pulses at the wavelength of 800 nm.

In our experiment, the fabricated sample was located at the focus of the THz beam after the second parabolic mirror at normal incidence angle. The beam size was approximately 5 mm in diameter at the focus. The transmittance through the sample was obtained by normalizing the Fourier spectrum of the sample signal with respect to that of the reference signal. Appendix D: Transmission spectra of a KTiOPO 4 film on TPx substrate After the mechanical polishing of a bulk KTiOPO 4 (KTP) crystal, we first measured the transmission spectra of the resultant KTP thin-film and compared it with our theoretical prediction. Figures 7(a) and 7(b) show the calculated and measured transmission spectra of the 130 μm-thick KTP film on a 2 mm thick polymethylpentene (TPx) substrate for y- and zpolarized illumination, respectively. The large-period modulation in the spectra comes from the Fabry-Perot (FP) resonances inside the KTP thin-film, while the FP effect in the TPx substrate causes small-period ripples. The agreement between the measured data and the simulation result indicates a good surface quality after the mechanical polishing as well as a negligible influence of the adhesive layer that is less than 10 µm-thick.

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27926

Fig. 7. Calculated and measured transmission spectra of a 130 μm-thick KTiOPO 4 film on a 2 mm thick polymethylpentene substrate under (a) y-polarized and (b) z-polarized illuminations.

Appendix E: Non-uniform design for Terahertz wave manipulation Precision diamond-blade dicing lends itself for making more elaborate and non-uniform metasurfaces by employing a similar micro-block-array design strategy. A non-uniform design of the all-dielectric metasurface is of particular interest since one can obtain full phase (2 π) coverage in the transmitted THz fields and engineer the resulting interference pattern by varying the size of the rectangular block in one of the lateral directions. In our simulation, we varied the block size in the z-direction while the other parameters such as the block size in ydirection, height of the block and periodicity in the square array are fixed to 300 μm, 130 μm and 345 μm, respectively. Figure 8(a) shows the two-dimensional mapping of the transmitted THz intensity as a function of the block size d z and the frequency, while 8(b) shows the corresponding phase of the transmitted THz field. For example, changing the block size d z from zero (an empty spot) to 242 μm near the frequency of 0.43 THz, we can achieve the 2π phase coverage while maintaining the high THz transmission. Combining different sizes of the micro-blocks in one unit cell, we show that an anisotropic beam steering or a linefocusing can be implemented. First, we numerically demonstrated a non-uniform metasurface for anisotropic beam steering. Our chirped KTP metasurface features four rectangular blocks with different sizes in one unit cell that covers 2π phase shift. The sizes of the four rectangular blocks are denoted with stars in Fig. 8(a) and 8(b). The angular intensity distribution in the far-field was calculated using Fresnel–Kirchhoff integral at the operating frequency of 0.43 THz for each polarization. As shown in Fig. 8(c), nearly 80% of THz transmission is deflected under ypolarization at the angle of 30 ° off-normal, while more than 80% of the transmission under zpolarization passes without deflection. In this case, the designed metasurface resembles a Rochon prism for THz waves, where only the extraordinary ray is deflected.

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27927

Fig. 8. (a) 2D mapping of THz intensity transmitted through a uniform KTiOPO 4 (KTP) metasurface as a function of the block size d z and the frequency of the y-polarized incoming radiation. The height of the block, the dimension of the block in the y-direction and the periodicity are fixed to h = 130 µm, d y = 300 µm and a = 345 µm, respectively. (b) Calculated phase of the THz transmission shown in (a). The stars symbols in (a) and (b) mark the ranges of block size dimension d z for over which the transmitted y-polarized field experience phase change of 2π, while maintaining high transmission around 0.43 THz. (c) Comparison between the angular intensity distributions in the far-field when the y- and z-polarized THz waves are incident on a chirped KTP metasurface with the block sizes d 1 = 242 μm, d 2 = 225 μm, d 3 = 105 μm and d 4 = 10 μm along the z-direction. The corresponding electric field distributions near the KTP blocks are also given for each polarization at the frequency of 0.43 THz. The inset at the bottom right corner illustrates the chirped KTP metasurface under the THz illumination from the backside of the TPx substrate.

Secondly, combining two chirped KTP metasurfaces with opposite gradients, one can implement an anisotropic line-focusing. Figure 9(a) describes the focusing of y-polarized THz radiation at the frequency of 0.43 THz that is propagating along the x-axis. The periodicity, height and block size along y-axis are still 345 µm, 130 µm and 300 µm, respectively. The collection of data in Fig. 8(b) was used to find the block size along z-axis that leads to the phase change with a desired focal length via the geometrical phase function, 3 × 108 m 2π set λ = 690 µ m and f = 5λ (f is the focal = − ( z 2 + f 2 − f ) , where we ϕ ( z) = 0.43THz λ length). The block sizes along z-axis that we used in this example are given in Table 1. The FDTD simulation results in Figs. 9(b) and 9(c) show the changes of intensity distribution along the propagation direction for y- and z-polarization, respectively, when the KTP metasurface is illuminated from the backside by a Gaussian beam with a diverging angle of 4° at the operating frequency of 0.43 THz. The transmission intensity for the y-polarized illumination is over 75% with the focal length f = 5λ as designed, while the z-polarized THz wave is destructively interfered after the metasurface.

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27928

Fig. 9. (a) A schematic description of a chirped KTiOPO 4 metasurface working as a flat THz lens for an anisotropic line-focusing. The chirped KTP metasurface is illuminated from the backside of TPx substrate by a THz beam that has a gaussian profile with a diverging angle of 4° at the frequency of 0.43 THz. Using FDTD, far-field intensity distribution after the metasurface is calculated for y-polarized (b) and z-polarized (c) THz radiation. Table 1. List of block sizes along z-axis and their corresponding positions in the z-axis that are used to numerically simulate the anisotropic line-focusing shown in Fig. 5. Block Size ( µ m )

d0 225

d1 220

d2 190

d3 132

d4 50

d5 10

d6 225

d7 185

Position z ( µm )

0

345

690

1035

1380

1725

2070

2415

d8 45 2760

d9 245 3105

d 10 200 3450

d 11 28 3795

d 12 244 4140

d 13 140 4485

d 14 10 4830

Funding K. A. Wallenberg Foundation; Swedish Science Council (VR), Olle Engkvist Byggmästare Foundation; National Natural Science Foundation of China (NSFC) (61425023, 61575177, 61775194); China Scholarship Council (201600160020). References 1.

M. A. Piestrup, R. N. Fleming, and R. H. Pantell, “Continuously tunable submillimeter wave source,” Appl. Phys. Lett. 26(8), 418–421 (1975). 2. K. Kawase, M. Sato, T. Taniuchi, and H. Ito, “Coherent tunable THz-wave generation from LiNbO 3 with monolithic grating coupler,” Appl. Phys. Lett. 68(18), 2483–2485 (1996). 3. K. Kawase, J. I. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D Appl. Phys. 35(3), R1–R14 (2002). 4. K. Suizu and K. Kawase, “Monochromatic-tunable terahertz-wave sources based on nonlinear frequency conversion using lithium niobate crystal,” IEEE J. Sel. Top. Quantum Electron. 14(2), 295–306 (2008). 5. J. Hebling, K.-L. Yeh, M. C. Hoffmann, and K. A. Nelson, “High-power THz generation, THz nonlinear optics, and THz nonlinear spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 14(2), 345–353 (2008). 6. S. W. Huang, E. Granados, W. R. Huang, K. H. Hong, L. E. Zapata, and F. X. Kärtner, “High conversion efficiency, high energy terahertz pulses by optical rectification in cryogenically cooled lithium niobate,” Opt. Lett. 38(5), 796–798 (2013). 7. W. Wang, Z. Cong, X. Chen, X. Zhang, Z. Qin, G. Tang, N. Li, C. Wang, and Q. Lu, “Terahertz parametric oscillator based on KTiOPO 4 crystal,” Opt. Lett. 39(13), 3706–3709 (2014). 8. W. Wang, Z. Cong, Z. Liu, X. Zhang, Z. Qin, G. Tang, N. Li, Y. Zhang, and Q. Lu, “THz-wave generation via stimulated polariton scattering in KTiOAsO 4 crystal,” Opt. Express 22(14), 17092–17098 (2014). 9. M. H. Wu, Y. C. Chiu, T. D. Wang, G. Zhao, A. Zukauskas, F. Laurell, and Y. C. Huang, “Terahertz parametric generation and amplification from potassium titanyl phosphate in comparison with lithium niobate and lithium tantalate,” Opt. Express 24(23), 25964–25973 (2016). 10. T. A. Ortega, H. M. Pask, D. J. Spence, and A. J. Lee, “Stimulated polariton scattering in an intracavity RbTiOPO 4 crystal generating frequency-tunable THz output,” Opt. Express 24(10), 10254–10264 (2016). 11. T. A. Ortega, H. M. Pask, D. J. Spence, and A. J. Lee, “THz polariton laser using an intracavity Mg:LiNbO 3 crystal with protective Teflon coating,” Opt. Express 25(4), 3991–3999 (2017). 12. Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76(18), 2505–2507 (2000).

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27929

13. E. A. Nanni, W. R. Huang, K. H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6(1), 8486 (2015). 14. B. Green, S. Kovalev, V. Asgekar, G. Geloni, U. Lehnert, T. Golz, M. Kuntzsch, C. Bauer, J. Hauser, J. Voigtlaender, B. Wustmann, I. Koesterke, M. Schwarz, M. Freitag, A. Arnold, J. Teichert, M. Justus, W. Seidel, C. Ilgner, N. Awari, D. Nicoletti, S. Kaiser, Y. Laplace, S. Rajasekaran, L. Zhang, S. Winnerl, H. Schneider, G. Schay, I. Lorincz, A. A. Rauscher, I. Radu, S. Mährlein, T. H. Kim, J. S. Lee, T. Kampfrath, S. Wall, J. Heberle, A. Malnasi-Csizmadia, A. Steiger, A. S. Müller, M. Helm, U. Schramm, T. Cowan, P. Michel, A. Cavalleri, A. S. Fisher, N. Stojanovic, and M. Gensch, “High-field high-repetition-rate sources for the coherent THz control of matter,” Sci. Rep. 6(1), 22256 (2016). 15. K. Ravi, D. N. Schimpf, and F. X. Kärtner, “Pulse sequences for efficient multi-cycle terahertz generation in periodically poled lithium niobate,” Opt. Express 24(22), 25582–25607 (2016). 16. A. Mayer and F. Keilmann, “Far-infrared nonlinear optics. I. χ(2) near ionic resonance,” Phys. Rev. B Condens. Matter 33(10), 6954–6961 (1986). 17. W. L. Faust, C. H. Henry, and R. H. Eick, “Dispersion in the nonlinear susceptibility of GaP near the Reststrahl Band,” Phys. Rev. 173(3), 781–786 (1968). 18. A. S. Barker and R. Loudon, “Response functions in the theory of raman scattering by vibrational and polariton modes in dielectric crystals,” Rev. Mod. Phys. 44(1), 18–47 (1972). 19. M. Barmentlo, G. W. ’t Hooft, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and P. W. van Amersfoort, “Sum-frequency generation with a free-electron laser: A study of gallium phosphide,” Phys. Rev. A 50(1), R14–R17 (1994). 20. H. Jang, G. Strömqvist, V. Pasiskevicius, and C. Canalias, “Control of forward stimulated polariton scattering in periodically-poled KTP crystals,” Opt. Express 21(22), 27277–27283 (2013). 21. H. Jang, A. L. Viotti, G. Strömqvist, A. Zukauskas, C. Canalias, and V. Pasiskevicius, “Counter-propagating parametric interaction with phonon-polaritons in periodically poled KTiOPO 4 ,” Opt. Express 25(3), 2677–2686 (2017). 22. S. R. Tripathi, Y. Taira, S. Hayashi, K. Nawata, K. Murate, H. Minamide, and K. Kawase, “Terahertz wave parametric amplifier,” Opt. Lett. 39(6), 1649–1652 (2014). 23. K. Fan, J. Zhang, X. Liu, G. F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018). 24. D. Jia, Y. Tian, W. Ma, X. Gong, J. Yu, G. Zhao, and X. Yu, “Transmissive terahertz metalens with full phase control based on a dielectric metasurface,” Opt. Lett. 42(21), 4494–4497 (2017). 25. H. Zhang, X. Zhang, Q. Xu, C. Tian, Q. Wang, Y. Xu, Y. Li, J. Gu, Z. Tian, C. Ouyang, X. Zhang, C. Hu, J. Han, and W. Zhang, “High‐efficiency dielectric metasurfaces for polarization‐dependent terahertz wavefront manipulation,” Adv. Opt. Mater. 6(1), 1700773 (2018). 26. J. Tian, Y. Yang, M. Qiu, F. Laurell, V. Pasiskevicius, and H. Jang, “All-dielectric KTiOPO 4 metasurfaces based on multipolar resonances in the terahertz region,” Opt. Express 25(20), 24068–24080 (2017). 27. D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, “Dielectric resonator reflectarray as high-efficiency nonuniform terahertz metasurface,” ACS Photonics 3(6), 1019–1026 (2016). 28. Z. Ma, S. M. Hanham, P. Albella, B. Ng, H. T. Lu, Y. Gong, S. A. Maier, and M. Hong, “Terahertz all-dielectric magnetic mirror metasurfaces,” ACS Photonics 3(6), 1010–1018 (2016). 29. X. Liu, K. Fan, I. V. Shadrivov, and W. J. Padilla, “Experimental realization of a terahertz all-dielectric metasurface absorber,” Opt. Express 25(1), 191–201 (2017). 30. I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013). 31. J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012). 32. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). 33. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012). 34. S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1(4), 250 (2014). 35. Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko II, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014). 36. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). 37. B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).

Vol. 26, No. 21 | 15 Oct 2018 | OPTICS EXPRESS 27930

38. Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “Hightransmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photonics Rev. 9(4), 412–418 (2015). 39. M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High‐efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3(6), 813–820 (2015). 40. J. Li, N. Verellen, D. Vercruysse, T. Bearda, L. Lagae, and P. Van Dorpe, “All-dielectric antenna wavelength router with bidirectional scattering of visible light,” Nano Lett. 16(7), 4396–4403 (2016). 41. G. Grinblat, Y. Li, M. P. Nielsen, R. F. Oulton, and S. A. Maier, “Enhanced third harmonic generation in single germanium nanodisks excited at the anapole mode,” Nano Lett. 16(7), 4635–4640 (2016). 42. D. I. S. C. O. Corp, http://www.disco.co.jp. 43. V. D. Antsygin, A. B. Kaplun, A. A. Mamrashev, N. A. Nikolaev, and O. I. Potaturkin, “Terahertz optical properties of potassium titanyl phosphate crystals,” Opt. Express 22(21), 25436–25443 (2014). 44. J. Tian, Q. Li, Y. Yang, and M. Qiu, “Tailoring unidirectional angular radiation through multipolar interference in a single-element subwavelength all-dielectric stair-like nanoantenna,” Nanoscale 8(7), 4047–4053 (2016). 45. Y. Yang, A. E. Miroshnichenko, S. V. Kostinski, M. Odit, P. Kapitanova, M. Qiu, and Y. S. Kivshar, “Multimode directionality in all-dielectric metasurfaces,” Phys. Rev. B 95(16), 165426 (2017). 46. J. Li and J. Li, “Dielectric properties of silicon in terahertz wave region,” Microw. Opt. Technol. Lett. 50(5), 1143–1146 (2008).