S. A. Kuznetsov - Research Scientist, Analytical & Technological Innovation Center - High technologies and novel materials?, Novo-sibirsk State University; Leading Engineer, Budker Institute of Nuclear Physics SB RAS and Novosibirsk Branch of Institute of Semi-conductor Physics SB RAS "KTIPM" (Novosibirsk) E-mail: SAKuznetsov@nsm.nsu.ru M. A. Astaf-ev - Post-graduate Student, Novosibirsk State University; Laboratory Assistant, Analytical & Technological Innovation Center - High technologies and novel materials?, Novosibirsk State University E. A. Lonshakov - Engineer, Analytical & Technological Innovation Center - High technologies and novel materials?, Novosibirsk State University A. V. Arzhannikov - Dr.Sc. (Phys.-Math.), Professor, Head of Analytical & Technological Innovation Center - High technologies and novel materials?, Novosibirsk State University; Chief Research Scientist, Budker Institute of Nuclear Physics SB RAS E-mail: A.V.Arzhannikov@inp.nsk.su

A progress of research in the range of submillimeter/terahertz waves of the electromagnetic spectrum requires a variety of quasi-optical devices used for manipulating electromagnetic properties of radiation beams propagating in free space. In many cases, the amplitude, polarization and phase control of submm-wave/THz radiation is realized most effectively by using planar metallized microstructures of subwavelength topology, which are known in literature as "frequency selective surfaces" or "metasurfaces". Manufactured with well-tailored and relatively inexpensive industrial technologies of photolithography and laser micromachining, such structures can be optimized for the desired wavelength λ0 and have the thickness typically smaller or much smaller than λ0.This advantageously enables to reduce the thickness and weight of the quasi-optical element compared to traditional solutions known from optics and, in particular, to realize pure flat focusing devices serving as the alternative to bulkier and usually more expensive lenses and curved mirrors. Moreover, by applying a computer holography technique to synthesize a proper transmission/reflection phase distribution over the element-s surface it is feasible to achieve focusing into a focal area of an arbitrarily complicated shape. In this paper we present the results of the experimental development of flat diffractive elements based on metasurfaces with spatially non-uniform pattern of unit cells optimized for simple and complex focusing of Gaussian beams at the frequency of 0,35 THz (λ0 = 857 μm). The considered diffractive elements (hereafter DEHMs) exploits the reflectarray configuration with a single-layer me-tasurface lying upon a thin low-absorbing grounded dielectric slab and were realized in the 900-reflection scheme by the examples of the structures of two kinds - the focusators into 1 and 4 spaced spots. DEHMs were optimized for the focal distance of 60 mm and had the overall dimensions of 70×70 mm. In both cases the required reflection phase distribution over the DEHM surface were synthesized with a holographic algorithm of Gerchberg-Saxton. As a dielectric slab material, polypropylene (PP) with the thickness of 190 μm was utilized. The metasurface pattern was produced by removing the 0.35-μm-thick aluminum layer deposited onto the PP slab via its laser ablation with ultrashort optical pulses without destructing the polymer. To attain the continuous variation of the reflection phase within the 360° interval, we proposed using the topological morphing of the metasurface pattern from square metallic patches to U-shaped resonator elements («USRs») and then to split-ring resonators («SRRs»), which are excited by the wave polarized transversely to USR and SRR gaps. To figure out the correspondence between the local geometry of the metasurface unit cells and the DEHMs reflection phase, the full-wave electromagnetic simulator ANSYS HFSS - v.12 was utilized. As the full-wave modeling of the oversized DEHMs composed of non-uniform unit cells requires enormous amount of computational resources, the problem was reduced to the following approximation: separate modeling of uniform grounded-PP-backed metasurfaces differed in unit cell geometry. Each of such structures was considered as an infinite regular 2D array simulated in the Floquet ports regime. It should be pointed out that - Patch-to-USR-to-SRR - morphing was found to be optimal in the view of maximizing the subwalengthness factor λ0/g (g is the lateral periodicity of the metasurface unit cells) under the restriction of 56 μm imposed on the minimal feature size technologically allowable for the metasurface. According to the simulations, the TE-polarized excitation was chosen to be more preferable for practice versus the TM one due to minimized cross-polarization conversion. In this case, the optimal (minimal) value of g was determined to be 286 μm (λ0/g  3). The experimental testing of the developed DEHMs was carried out using a backward-wave oscillator as a source of TE-polarized radi-ation and a compact pyroelectric detector combined with a 2D scanner to measure the intensity distribution in the DEHM-s focal plane. The experiment revealed a relatively good agreement between the simulations and measurements. The discrepancy is manifested as some reduction and broadening, as well as a slight deformation of the experimental intensity peaks compared to the simulated ones. The variance is explained by mismatch between the actual and calculated reflection phase distributions over the DEHM-s surface caused by two factors: 1) the limited accuracy of the aforementioned approximation of the uniform metasurfaces; 2) appearance of local defects in the metasurface pattern when it is produced with laser micromachining. The actually measured values of the diffraction efficiency were found to be 76% when focusing into 1 spot and 73% for the case of 4 spots. Such quantities are estimated to be high and, in principle, can be further increased by using the metasurface with more subwavelength unit cells and/or improving accuracy of the micropatterning technology.

 

1. Munk B. Frequency selective surfaces: Theory and design. NY: Wiley. 2000.
2. Kasjanov A.O., Obukhovec V.A. CHastotno-izbiratelnye poverkhnosti. Osnovnyeoblastiprimenenija // Antenny.2005. № 9. C. 4-12.
3. Holloway C.L. et al. An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials // IEEE Antennas Propag. Mag. 2012. V. 54. № 2. P. 10-35.
4. Balanis C.A. Modern antenna handbook. Hoboken, NJ: John Wiley & Sons. 2008.
5. Huang J., Encinar J.A. Reflectarray antennas. Hoboken, NJ: John Wiley & Sons. 2008.
6. Shaker J., Reza Ch.M., Ethier J. Reflectarray antennas: Analysis, design, fabrication, and measurement. Boston: Artech House. 2013.
7. Gerchberg R.W., Saxton W.O. A practical algorithm for the determination of the phase from image and diffraction plane pictures // Optik. 1972. V. 35. P. 237-242.
8. Soifer V., Kotlyar V., Doskolovich L. Iterative methods for diffractive optical elements computation. London: Taylor & Francis. 1997.
9. Sojjfer V.A. Metody kompjuternojj optiki. M.: FIZMATLIT. 2003.
10. Vedernikov V.M., Dutov P.M., Kokarev A.I. i dr. Difrakcionnye ehlementy dlja lazera na svobodnykh ehlektronakh // Avtometrija. 2010. T. 46. № 4. S. 365-375.
11. Agafonov A.N., Volodkin B.O., Kaveev A.K. i dr. Kremnievye difrakcionnye opticheskie ehlementy dlja moshhnogo monokhromaticheskogo teragercovogo izluchenija // Avtometrija. 2013. T. 49. № 2. S. 98-105.
12. High frequency structure simulator. ANSYS Corporation. URL: http://www.ansys.com/
13. Kurushin A.A. Ispolzovanie kanalov Floke dlja modelirovanija periodicheskojj nanostruktury // ZHurnal radioehlektroniki. 2010.№ 11. S. 1-22.
14. Navarro-Cía M., Kuznetsov S.A., Aznabet M. et. al. Route for bulk millimeter wave and terahertz metamaterial design // IEEE J. Quant. Electron.2011. V. 47. № 3. P. 375-385.
15. Kuznecov S.A., Astafev M.A., Lazorskijj P.A. i dr. Spektralnye izmerenija diehlektricheskikh svojjstv polipropilenovykh pljonok v subteragercovom diapazone chastot // Vestnik NGU. SerijaFizika. 2014. T. 9. Vyp. 4. (vpechati)
16. Beruete M., Sorolla M., Marque´s R. et al. Resonance and cross-polarization effects in conventional and complementary split ring resonator periodic screens // Electromagnetics. 2006. V. 26. P. 247-260.