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Physical principles of filtration and the design of terahertz radiation filters

  a,  b
a Ioffe Institute, ul. Polytekhnicheskaya 26, St. Petersburg, 194021, Russian Federation
b Tydex LLC, Domostroitelnaya str. 16, St. Peterburg, 194292, Russian Federation

Present review examines the basic physical principles of operation of terahertz radiation filters. The main types of filters are presented, namely, based on absorbing/scattering materials, metamaterials (frequency-selective surfaces), interference, polarization, and some exotic types. The basic principles of calculating the filters transmission based on matrix methods are described, as well as based on solving Maxwell's equations. The areas of application of THz filters are listed.

Typically, an English full text is available in about 1 month from the date of publication of the original article.

Keywords: THz, cutoff filters, high-pass filters, band-pass filters, notch filters, absorption, metamaterials, frequency-selective surface
PACS: 07.57.−c, 42.25.Ja, 42.81.Gs (all)
DOI: 10.3367/UFNe.2025.11.040059
URL: https://ufn.ru/en/articles/2026/2/e/
Citation: Kaveev A K, Kropotov G I "Physical principles of filtration and the design of terahertz radiation filters" Phys. Usp. 69 (2) (2026)

Received: 16th, March 2025, revised: 9th, November 2025, 11th, November 2025

Оригинал: Кавеев А К, Кропотов Г И «Физические принципы фильтрации и устройство фильтров терагерцового излучения» УФН 196 182–204 (2026); DOI: 10.3367/UFNr.2025.11.040059

References (238) ↓ Similar articles (20)

  1. Federici J F et al Semicond. Sci. Technol. 20 S266 (2005)
  2. Friederich F et al IEEE Trans. Terahertz Sci. Technol. 1 183 (2011)
  3. Ajito K, Ueno Y IEEE Trans. Terahertz Sci. Technol. 1 293 (2011)
  4. Humphreys K et al Proc. Of The 26th Annual Intern. Conf. Of The IEEE Engineering In Medicine And Biology Society, San Francisco, CA, USA, 1-5 September 2004 (Piscataway, NJ: IEEE, 2005)
  5. Zhang X-C, Xu J Introduction To THz Wave Photonics (New York: Springer, 2010) p. 49
  6. Jepsen P U, Cooke D G, Koch M Laser Photon. Rev. 5 124 (2011)
  7. Averitt R D, Taylor A J J. Phys. Condens. Matter 14 R1357 (2002)
  8. Taylor Z D et al IEEE Trans. Terahertz Sci. Technol. 1 201 (2011)
  9. Nuss M C, Orenstein J Millimeter And Submillimeter Wave Spectroscopy Of Solids (Topics In Applied Physics, Vol. 74, Eds G Grüner) (Berlin: Springer, 2007) p. 7
  10. Ashkroft N, Mermin N Fizika Tverdogo Tela (M.: Mir, 1979); Per. s angl. yaz., Ashcroft N W, Mermin N D Solid State Physics (New York: Holt, Rinehart and Winston, 1976)
  11. van Exter M, Grischkowsky D Phys. Rev. B 41 12140 (1990)
  12. Piccioli N et al Appl. Opt. 16 1236 (1977)
  13. Ghosh G Handbook Of Refractive Index And Dispersion Of Water For Scientists And Engineers (Brisbane: S. Ghosh, 2005); Available online, https://refractiveindex.info/?shelf=3d&book=liquids&page=water
  14. Banda E J K B et al J. Phys. C 20 2323 (1987)
  15. Benford D J, Gaidis M C, Kooi J W Appl. Opt. 42 5118 (2003)
  16. THz Low Pass Filters. TYDEX. Available online, https://www.tydexoptics.com/products/thz_assemblies/thz_low_pass_filter/
  17. Shen Y C, Taday P F, Pepper M Appl. Phys. Lett. 92 051103 (2008)
  18. Franz M, Fischer B M, Walther M Appl. Phys. Lett. 92 021107 (2008)
  19. Kock W E Bell Syst. Tech. J. 27 (1) 58 (1948)
  20. Jones S S D, Brown J Nature 163 324 (1949)
  21. Brown J Proc. IEEE 97 45 (1950)
  22. Rotman W IRE Trans. Antennas Propag. 10 82 (1962)
  23. Pendry J B et al Phys. Rev. Lett. 76 4773 (1996)
  24. Pendry J B et al J. Phys. Condens. Matter 10 4785 (1998)
  25. Pendry J B et al IEEE Trans. Microwave Theory Tech. 47 2075 (1999)
  26. Smith D R et al Phys. Rev. Lett. 84 4184 (2000)
  27. Shelby R A, Smith D R, Schultz S Science 292 77 (2001)
  28. Veselago V G Usp. Fiz. Nauk 92 517 (1967); Veselago V G Sov. Phys. Usp. 10 509 (1968)
  29. Schurig D et al Science 314 977 (2006)
  30. Schurig D, Pendry J B, Smith D R Opt. Express 14 9794 (2006)
  31. Alù A, Engheta N Phys. Rev. E 72 016623 (2005)
  32. Milton G W, Nicorovici N-A P Proc. R. Soc. London A 462 3027 (2006)
  33. Nachman A I Ann. Math. 128 531 (1988)
  34. Gbur G Prog. Opt. 45 273 (2003)
  35. Greenleaf A, Lassas M, Uhlmann G Physiol. Meas. 24 413 (2003)
  36. Greenleaf A, Lassas M, Uhlmann G Math. Res. Lett. 10 685 (2003)
  37. Cummer S A et al Phys. Rev. E 74 036621 (2006)
  38. Greegor R B et al Appl. Phys. Lett. 87 091114 (2005)
  39. Driscoll T et al Appl. Phys. Lett. 88 081101 (2006)
  40. Justice B J et al Opt. Express 14 8694 (2006)
  41. Rybin M V et al Sci. Rep. 5 8774 (2015)
  42. Gaillot D P, Croënne C, Lippens D Opt. Express 16 3986 (2008)
  43. Leonhardt U Science 312 1777 (2006)
  44. Shalaev V M Science 322 384 (2008)
  45. Leonhardt U New J. Phys. 8 118 (2006)
  46. Ramakrishna S A, Pendry J B Phys. Rev. B 67 201101 (2003)
  47. Schurig D et al Science 314 977 (2006)
  48. Schurig D et al Opt. Express 15 14772 (2007)
  49. Rahm M et al Phys. Rev. Lett. 100 063903 (2008)
  50. Zhang P, Jin Y, He S Opt. Express 16 3161 (2008)
  51. Kildishev A V, Shalaev V M Opt. Lett. 33 43 (2008)
  52. Narimanov E E, Shalaev V M Nature 447 266 (2007)
  53. Kil’dishev A V, Shalaev V M Usp. Fiz. Nauk 181 59 (2011); Kildishev A V, Shalaev V M Phys. Usp. 54 53 (2011)
  54. Lu X et al Front. Phys. 10 1 (2022)
  55. Cao L et al Adv. Mater. Technol. 10 2401358 (2024)
  56. Cong L, Singh R "Sensing with THz metamaterial absorbers" arXiv:1408.3711
  57. Prasad T et al Opt. Lett. 32 683 (2007)
  58. Pendry J B Phys. Rev. Lett. 85 3966 (2000)
  59. Podolskiy V A, Narimanov E E Phys. Rev. B 71 201101 (2005)
  60. Podolskiy V A, Alekseyev L V, Narimanov E E J. Mod. Opt. 52 2343 (2005)
  61. Wangberg R et al J. Opt. Soc. Am. B 23 498 (2006)
  62. Podolskiy V A, Narimanov E E Opt. Lett. 30 75 (2005)
  63. Durant S et al J. Opt. Soc. Am. B 23 2383 (2006)
  64. Liu Z et al Nano Lett. 7 403 (2007)
  65. Liu Z et al Opt. Express 15 6947 (2007)
  66. Lee H et al Opt. Express 15 15886 (2007)
  67. Pendry J B, Ramakrishna S A J. Phys. Condens. Matter 14 8463 (2002)
  68. Shalaev V M Nature Photon. 1 41 (2007)
  69. Wood B Laser Photon. Rev. 1 249 (2007)
  70. Goussetis G, Feresidis A P, Harvey A R J. Mod. Opt. 57 1 (2010)
  71. Cai W, Shalaev V Optical Metamaterials: Fundamentals And Applications 1st ed. (New York: Springer-Verlag, 2010)
  72. Smith D R et al Phys. Rev. Lett. 84 4184 (2000)
  73. Shelby R A, Smith D R, Schultz S Science 292 77 (2001)
  74. Yen T J et al Science 303 1494 (2004)
  75. Moser H O et al Phys. Rev. Lett. 94 063901 (2005)
  76. Katsarakis N et al Opt. Lett. 30 1348 (2005)
  77. Azad A K, Dai J, Zhang W Opt. Lett. 31 634 (2006)
  78. Schurig D, Mock J J, Smith D R Appl. Phys. Lett. 88 041109 (2006)
  79. Chen H-T et al Opt. Express 15 1084 (2007)
  80. Padilla W J et al Phys. Rev. B 75 041102 (2007)
  81. Azad A K et al Appl. Phys. Lett. 92 011119 (2008)
  82. Shalaev V M et al Opt. Lett. 30 3356 (2005)
  83. Zhang S et al Phys. Rev. Lett. 95 137404 (2005)
  84. Dolling G et al Science 312 892 (2006)
  85. Dolling G et al Opt. Lett. 30 3198 (2005)
  86. Gundogdu T F et al Opt. Express 16 9173 (2008)
  87. Awad M, Nagel M, Kurz H Opt. Lett. 33 2683 (2008)
  88. Paul O et al Opt. Express 16 6736 (2008)
  89. Beruete M, Sorolla M, Campillo I Opt. Express 14 5445 (2006)
  90. Croënne C et al Appl. Phys. Lett. 94 133112 (2009)
  91. Wang S et al Appl. Phys. Lett. 97 181902 (2010)
  92. Wang S et al J. Appl. Phys. 107 074510 (2010)
  93. Ishikawa A et al Phys. Rev. Lett. 102 043904 (2009)
  94. Tavallaee A A et al IEEE J. Quantum Electron. 46 1091 (2010)
  95. Linden S et al Science 306 1351 (2004)
  96. Zhou J et al Phys. Rev. Lett. 95 223902 (2005)
  97. Chen H-T et al Laser Photon. Rev. 5 513 (2011)
  98. Sternberg O "Resonances of periodic metal-dielectric structures at the infrared wavelength region" PhD Dissertation (Newark, NJ: New Jersey Institute of Technology, 2002); Available online, https://digitalcommons.njit.edu/dissertations/548
  99. Russer P "The transmission line matrix method" New Trends And Concepts In Microwave Theory And Technics (Trivandrum, India: Research Signpost, 2004)
  100. Munk B A Frequency Selective Surfaces: Theory And Design (New York: John Wiley and Sons, 2000)
  101. Ade P et al Proc. SPIE 6275 62750U1 (2006)
  102. Leipoldt K J et al Int. J. Infrared Millimeter Waves 12 263 (1991)
  103. Mittra R, Chan C H, Cwik T Proc. IEEE 76 1593 (1988)
  104. THz Materials. TYDEX. Available online, https://www.tydexoptics.com/products/thz_optics/thz_materials/
  105. Rogalin V E, Kaplunov I A, Kropotov G I Optika Spektroskopiya 125 851 (2018); Rogalin V E, Kaplunov I A, Kropotov G I Opt. Spectrosc. 125 1053 (2018)
  106. Ulrich R Infrared Phys. 7 37 (1967)
  107. Porterfield D W et al Appl. Opt. 33 6046 (1994)
  108. Irwin P G J et al Infrared Phys. 34 549 (1993)
  109. Melo A M et al Appl. Opt. 47 6064 (2008)
  110. Kuznetsov S A et al Key Eng. Mater. 437 276 (2010)
  111. Baumann F et al Opt. Lett. 28 938 (2003)
  112. Winnewisser C et al Appl. Opt. 38 3961 (1999)
  113. Bortolucci E et al Proc. of the II Workshop on Semiconductors and Micro and Nano Technology, Seminatec, Sao Bernardo do Campo, Brazil, 2012
  114. Kharvei A F Tekhnika Sverkhvysokikh Chastot (M.: Sov. radio, 1965); Per. s angl. yaz., Harvey A F Microwave Engineering (London: Academic Press, 1963); Marcuvitz N Waveguide Handbook (New York: McGraw-Hill, 1951)
  115. TGts polosovye rezonansnye fil’try. TYDEX. Available online, https://www.tydexoptics.com/ru/products/tgc-ustrojstva/thz_band_pass_filter/
  116. Gentselev A N i dr Avtometriya 55 (2) 14 (2019); Gentselev A N et al Optoelectron. Instrum. Data Proces. 55 115 (2019)
  117. Melo A M et al Adv. Opt. Technol. 2012 530512 (2012)
  118. Ma Y et al Opt. Lett. 35 469 (2010)
  119. Bark H S et al Sci. Rep. 11 1307 (2021)
  120. Liu D et al Opt. Express 29 24779 (2021)
  121. Liu D et al Opt. Lett. 46 4370 (2021)
  122. Shahounvand H, Fard A, Tavakoli M B Opt. Quantum Electron. 54 120 (2022)
  123. Landy N I et al Phys. Rev. Lett. 100 207402 (2008)
  124. Tao H et al Opt. Express 16 7181 (2008)
  125. Tao H et al Phys. Rev. B 78 241103 (2008)
  126. Diem M, Koschny T, Soukoulis C M Phys. Rev. B 79 033101 (2009)
  127. Landy N I et al Phys. Rev. B 79 125104 (2009)
  128. Shchegolkov D Yu et al Phys. Rev. B 82 205117 (2010)
  129. Li Y et al J. Phys. D 42 095408 (2009)
  130. Chen H-T et al Phys. Rev. Lett. 105 073901 (2010)
  131. Wen Q-Y et al Opt. Express 17 20256 (2009)
  132. O’Hara J, Azad A K, Taylor A J Eur. Phys. J. D 58 243 (2010)
  133. Richards P L J. Appl. Phys. 76 1 (1994)
  134. Kuznetsov S A et al Appl. Phys. Lett. 99 023501 (2011)
  135. Ye Y Q, Jin Y, He S J. Opt. Soc. Am. B 27 498 (2010)
  136. Wen Q-Y et al Appl. Phys. Lett. 95 241111 (2009)
  137. Tao H et al J. Phys. D 43 225102 (2010)
  138. Engheta N, Ziolkowski R W (Eds) Metamaterials: Physics And Engineering Explorations (New York: Wiley, IEEE Press, 2006)
  139. Balanis C A Modern Antenna Handbook (New York: John Wiley and Sons, 2008)
  140. Capolino F Theory And Phenomena Of Metamaterials (Boca Raton, FL: CRC Press, 2009)
  141. Kul’chitskii N A i dr Uspekhi Prikladnoi Fiziki 10 (2) 203 (2022)
  142. Chen H-T et al Nature 444 597 (2006)
  143. Prasankumar R P et al Appl. Phys. Lett. 86 201107 (2005)
  144. Chen H-T et al Opt. Lett. 32 1620 (2007)
  145. Azad A K et al Appl. Phys. Lett. 95 011105 (2009)
  146. Chen H-T et al Nature Photon. 2 295 (2008)
  147. Shen N-H et al Phys. Rev. B 79 161102 (2009)
  148. Syzranov V S i dr Pribory Tekhnika Eksperimenta (6) 70 (2012); Syzranov V S et al Instrum. Exp. Tech. 55 673 (2012)
  149. Chen Y C et al Appl. Phys. Express 5 012201 (2012)
  150. TGts fil’try vysokikh chastot. TYDEX. Available online, https://www.tydexoptics.com/pdf/ru/High-Pass-Filters_ru.pdf
  151. Edelman V S, Tarasov M A, Chekushkin A M ""Capillary quasioptical highpass filter" Proc. of the 25th Intern. Symp. on Space Terahertz Technology, 27-30 April 2014, Moscow, Russia Vol. 1 p. 46-48
  152. Standard filters. Multi-mesh filters. THz optical components. QMC Instruments Ltd. Availble online, https://www.terahertz.co.uk/qmci/thz-optical-components/multi-mesh-filters/standard
  153. Chen C-C IEEE Trans. Microwave Theory Tech. 21 1 (1973)
  154. Walther M et al Appl. Phys. Lett. 95 251107 (2009)
  155. Takano K et al Appl. Phys. Express 3 016701 (2010)
  156. Hor Y L et al Appl. Opt. 49 1179 (2010)
  157. Kaur A et al Proc. Of The IEEE 65th Electronic Components And Technology Conf., ECTC, 26-29 May 2015, San Diego, CA, USA (Piscataway, NJ: IEEE, 2015) p. 2071-2076
  158. Aznabet M et al Opt. Express 16 18312 (2008)
  159. Tao H et al J. Phys. D 41 232004 (2008)
  160. Miyamaru F, Takeda M W, Taima K Appl. Phys. Express 2 042001 (2009)
  161. Liu X et al Appl. Phys. Lett. 96 011906 (2010)
  162. Tao H et al Adv. Mater. 22 3527 (2010)
  163. Bruning J Proc. SPIE 652 6520 (2007)
  164. Spiro P Electroforming: A Comprehensive Survey Of Theory, Practice And Commercial Applications (Teddington: Draper, 1971)
  165. Holloway S L et al Metamaterials 3 100 (2009)
  166. Gokkavas M et al Phys. Rev. B 73 193103 (2006)
  167. Casse B D F et al Appl. Phys. Lett. 90 254106 (2007)
  168. Azad A et al THz Sci. Technol. 2 15 (2009)
  169. Peralta X G et al Appl. Phys. Lett. 94 161113 (2009)
  170. Miyamaru F et al Appl. Phys. Lett. 96 081105 (2010)
  171. Tao H et al Phys. Rev. Lett. 103 147401 (2009)
  172. Randhawa J S et al Appl. Phys. Lett. 96 191108 (2010)
  173. Burckel D B et al Adv. Mater. 22 3171 (2010)
  174. Wendt J R et al J. Vac. Sci. Technol. B 28 C6O30 (2010)
  175. Han M et al Micromachines 13 1170 (2022)
  176. Kaveev A K, Kropotov G I Usp. Fiz. Nauk 195 311 (2025); Kaveev A K, Kropotov G I Phys. Usp. 68 294 (2025)
  177. Bloom A L J. Opt. Soc. Am. 64 447 (1974)
  178. Kobtsev S M Optika Spektroskopiya 63 1139 (1987); Kobtsev S M Opt. Spectrosc. 63 672 (1987)
  179. Lee Y L et al Opt. Lett. 32 2813 (2007)
  180. Evans J W J. Opt. Soc. Am. 48 142 (1958)
  181. Zhou Y et al J. Opt. Soc. Am. A 20 733 (2003)
  182. Shabtay G et al Opt. Express 10 1534 (2002)
  183. Yang X et al J. Opt. Soc. Am. A 22 752 (2005)
  184. Wang X, Yao J Appl. Opt. 31 4505 (1992)
  185. Preuss D R, Gole J L Appl. Opt. 19 702 (1980)
  186. Mentel J, Schmidt E, Mavrudis T Appl. Opt. 31 5022 (1992)
  187. Title A M Appl. Opt. 15 2871 (1976)
  188. von Willisen F K Appl. Opt. 5 97 (1966)
  189. Title A M Appl. Opt. 14 445 (1975)
  190. Yang D et al Opt. Fiber Technol. 80 103426 (2023)
  191. Melich R, Melich Z, Šolc I The Physics Of Chromospheric Plasmas. Proc. Of The Conf., 9-13 October, 2006, Coimbra, Portugal (ASP Conf. Ser.) Vol. 368 (Eds P Heinzel, I Dorotovič, R J Rutten) (San Francisco, CA: Astronomical Society of the Pacific, 2007) p. 621
  192. Yu X J et al Displays 3 145 (2002)
  193. Yeh P Opt. Commun. 29 1 (1979)
  194. Yariv A, Yeh P Optical Waves In Crystal: Propagation And Control Of Laser Radiation (New York: John Wiley and Sons, 1984) p. 32-158
  195. Chen C-Y et al Appl. Phys. Lett. 88 101107 (2006)
  196. Šolc I J. Opt. Soc. Am. 55 621 (1965)
  197. Pinnow D A et al Appl. Phys. Lett. 34 391 (1979)
  198. Tarry H A Electron. Lett. 11 471 (1975)
  199. Ho I-C et al Opt. Lett. 33 1401 (2008)
  200. Jones R C J. Opt. Soc. Am. 31 488 (1941)
  201. Vasil’ev N, Zelevinskii A "Mnogochleny Chebysheva i rekurrentnye sootnosheniya" Kvant (1) 12 (1982)
  202. Zhou Y et al J. Opt. Soc. Am. A 20 733 (2003)
  203. Melich R, Melich Z, Šolc I Proc. SPIE 7018 701854 (2008)
  204. Yeh P Opt. Commun. 29 1 (1979)
  205. Ghosh A, Chakraborty A K Opt. Acta Int. J. Opt. 29 1407 (1982)
  206. Kuan W-H et al arXiv:2103.13779
  207. Jung H Int. J. Opt. 2010 626583 (2010)
  208. Hong H-G et al Opt. Express 17 15455 (2009)
  209. Kaveev A K et al Appl. Opt. 53 5410 (2014)
  210. TGts perestraivaemyi preobrazovatel’ polyarizatsii. TYDEX. Available online, https://www.tydexoptics.com/ru/products/thz_polarizers/tunable_thz_polarization_converter/
  211. Gay-Balmaz P, Maccio C, Martin O J F Appl. Phys. Lett. 81 2896 (2002)
  212. Muravev V M et al Phys. Rev. Applied 21 034041 (2024)
  213. Gallant A J et al J. Appl. Phys. 102 023102 (2007)
  214. Yee K IEEE Trans. Antennas Propag. 14 302 (1966)
  215. Gomon D A i dr Nauchno-tekhnicheskii Vestnik Informatsionnykh Tekhnologii, Mekhaniki Optiki 19 775 (2019)
  216. Odit M et al "Tunable THz band-pass filter" Metamaterials 2012. The 6th Intern. Congress on Advanced Electromagnetic Materials in in Microwaves and Optics, 17-22 September 2012, St. Petersburg, Russia, 2012 p. 541-543
  217. Li C et al J. Electromagn. Waves Appl. 32 2481 (2018)
  218. Azimbeik M et al Optik 198 163246 (2019)
  219. Mohammadi G, Orouji A, Danaie M Results Opt. 13 100575 (2023)
  220. Tian Z et al Opt. Express 32 24251 (2024)
  221. Stecher M et al "Fiber Drawn 2D polymeric photonic crystal THz filters" Conf. on Lasers and Electro-Optics 2012, San Jose, CA, USA, 6-11 May 2012 (OSA Technical Digest) (Washington, DC: Optica Publ. Group, 2012), paper CM4J.2
  222. Yuan J et al Results Phys. 13 102198 (2019)
  223. Lee E-S, Jeon T-I J. Opt. Soc. Korea 13 423 (2009)
  224. Wang J, Guo K, Guo Z AIP Adv. 9 045106 (2019)
  225. Withayachumnankul W, Fischer B M, Abbott D Opt. Commun. 281 2374 (2008)
  226. Beheshti Asl A, Rostami A, Amiri I S Opt. Quantum Electron. 52 155 (2020)
  227. Hussain S, Min Woo J, Jang J-H Appl. Phys. Lett. 101 091103 (2012)
  228. Chen Y, Cheng J, Liang C Adv. Condens. Matter Phys. 2020 3902835 (2020)
  229. Drysdale T D, Blaikie R J, Cumming D R S Proc. SPIE 5070 89 (2003)
  230. Drysdale T D, Blaikie R J, Cumming D R S Appl. Phys. Lett. 83 5362 (2003)
  231. Gregory I S et al Appl. Phys. Lett. 87 034106 (2005)
  232. Drysdale T D et al Microelectron. Eng. 73-74 441 (2004)
  233. Němec H et al Opt. Lett. 30 549 (2005)
  234. Li J Opt. Commun. 283 2647 (2010)
  235. Villa F, Gaspar-Armenta J A Opt. Express 12 2338 (2004)
  236. Jacob D K, Dunn S C, Moharam M G Appl. Opt. 41 1241 (2002)
  237. Mendis R et al Appl. Phys. Lett. 97 131106 (2010)
  238. Zhao Y, Grischkowsky D Opt. Lett. 31 1534 (2006)

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