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				In the last few decades, nanoscience and nanotechnology have been growing with breath taking speed, and how to break through the diffraction limit and tame the light on a nanoscale have become the major challenges in optics. In this field, several super-resolution optical nanoscopy techniques have been developed, leading to a series of breakthroughs in physics, chemistry, and life sciences. In the work, we give a retrospect of the newly developed techniques in diffraction theory of linear optical systems, including the solid immersion lens, structured light illumination microscopy, scanning near-field optical microscopy, metamaterial-based wide field near-field imaging technique and super-oscillatory lens. Brief discussion on their principles, advantages and applications is also provided.- 
										Keywords:
										
- diffraction limit /
- spatial frequency /
- super-resolution
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Methods 3 793 [14] Fang N, Lee H, Sun C, Zhang X 2005 Science 308 534 [15] Taubner T, Korobkin D, Urzhumov Y, et al. 2006 Science 313 1595 [16] Smolyaninov II, Hung Y J, Davis C C 2007 Science 315 1699 [17] Gustafsson M G L 2000 J. Microsc. 198 82 [18] Hell S W, Wichmann J 1994 Opt. Lett. 19 780 [19] Betzig E, et al. 2006 Science 313 1642 [20] Rogers E T F, et al. 2012 Nat. Materials 11 432 [21] Hell S W 2007 Science 316 1153 [22] Jones S A, Shim S H, He J, Zhuang X W 2011 Nat. Methods 8 499 [23] Pohl D W, Kawata S 2001 Near-Field Optics and Surface Plasmon Polaritons (Germany: Springer-Verlag) [24] Serrels K A, Ramsay E, Dalgarno P A, et al. 2008 J. Nanophoton. 2 021854 [25] Mansfield S M, Kino G S 1990 Appl. Phys. Lett. 57 2615 [26] Terris B D, Mamin H J, Rugar D 1994 Appl. Phys. Lett. 65 388 [27] Ghislain L P, Elings V B 1999 Appl. Phys. Lett. 74 501 [28] Wu Q, Feke C D, Crober R D 1999 Appl. Phys. Lett. 75 4064 [29] Ippolito S B, Goldberg B B, Unlu M S 2001 Appl. Phys. Lett. 78 4071 [30] Liu Z H, et al. 2005 Appl. Phys. Lett. 87 071905 [31] Serrels K A, et al. 2008 Nat. Photon. 2 311 [32] Lee J Y, et al. 2009 Nature 460 498 [33] Mason D R, Jouravlev M V, Kim K S 2010 Opt. Lett. 35 2007 [34] Wang Z, et al. 2011 Nat. Commun. 2 218 [35] Lukosz W, Marchand M 1963 J. Mod. Opt. 10 241 [36] Heintzmann R, Cremer C 1999 Proc. SPIE 3568 185 [37] Frohn J T, Knapp H F, Stemmer A 2000 Proc. Nat. Acad. Sci. USA 97 7232 [38] Gustafsson M G L, Agard D A, Sedat J W 2000 Proc. SPIE 3919 141 [39] Neil M A A, Juskaitis R, Wilson T 1997 Opt. Lett. 22 1905 [40] Gustafsson M G L., et al. 2008 Biophys. J. 94 4957 [41] Schermelleh L, et al. 2008 Science 320 1332 [42] Gustafsson M G L 2005 Proc. Nat. Acad. Sci. USA 102 13081 [43] Kner P, et al. 2009 Nat. Methods 6 339 [44] Planchon T A, et al. 2011 Nat. Methods 8 417 [45] Demmerle J, et al. 2017 Nat. Protoc. 12 988 [46] Weisenburger S, Sandoghdar V 2015 Contemp. Phys. 56 123 [47] De Wilde Y, et al. 2006 Nature 444 740 [48] Betzig E, Finn P, Weiner J 1992 Appl. Phys. Lett. 60 2484 [49] Betzig E, Chichester R J 1993 Science 262 1422 [50] Trautman J K, et al. 1994 Nature 369 40 [51] Xie X S, Dunn R C 1994 Science 265 361 [52] Matsuda K, et al. 2003 Phys. Rev. Lett. 91 177401 [53] Moerland R J, van Hulst N F 2005 Opt. Express 13 1604 [54] Taminiau T H, et al. 2007 Nano Lett. 7 28 [55] Rotenberg N, Kuipers L 2014 Nat. Photon. 8 919 [56] Reddick R, Warmack R, Ferrell T 1989 Phys. Rev. B 39 767 [57] Balistreri M, et al. 2001 Science 294 1080 [58] Balistreri M, et al. 2000 Phys. Rev. Lett. 85 294 [59] Veerman J A, et al. 1998 Appl. Phys. Lett. 72 3115 [60] Dunn R C 1999 Chem. Rev. 99 2891 [61] Knoll B, Keilmann F 1999 Nature 399 134 [62] Snchez E J, Novotny L, Xie X S 1999 Phys. Rev. Lett. 82 4014 [63] Gerton J M, et al. 2004 Phys. Rev. Lett. 93180801 [64] Anger P, Bharadwaj P, Novotny L 2006 Phys. Rev. Lett. 96 113002 [65] Hppener C, Novotny L 2008 Nano Lett. 8 642 [66] Eghlidi H, et al. 2009 Nano Lett. 9 4007 [67] Tam F, et al. 2007 Nano Lett. 7 496 [68] Wientjes E, et al. 2014 Nat. Commun. 5 4236 [69] Kneipp K, et al. 2002 J. Phys. 14 R597 [70] Anderson M S 2000 Appl. Phys. Lett. 76 3130 [71] Hayazawa N, et al. 2000 Opt. Commun. 183 333 [72] Stckle R M, et al. 2000 Chem. Phys. Lett. 318 131 [73] Hartschuh A., et al. 2003 Phys. Rev. Lett. 90 095503 [74] Ren B, Picardi G, Pettinger B 2004 Rev. Sci. Instru. 75 837 [75] Yeo B S, et al. 2007 Anal. Bioanal. Chem. 387 2655 [76] Zhang W, et al. 2007 J. Phys. Chem. C 111 1733 [77] Ichimura T, et al. 2007 J. Phys. Chem. C 111 9460 [78] Domke K F, Zhang D, Pettinger B 2006 J. Am. Chem. Soc. 128 147217 [79] Neacsu C C, et al. 2006 Phys. Rev. B 73 193406 [80] Pettinger B, et al. 2004 Phys. Rev. Lett. 92 096101 [81] Steidtner J, Pettinger B 2008 Phys. Rev. Lett. 100 236101 [82] Zhang R, et al. 2013 Nature 498 82 [83] Knoll B, Keilmann F 2000 Opt. Commun. 182 321 [84] Keilmann F, Hillenbrand R 2004 Philos. Trans. A 362 787 [85] Huth F, et al. 2011 Nat. Mater. 10 352 [86] Huth F, et al. 2012 Nano Lett. 12 3973 [87] Amenabar I, et al. 2013 Nat. Commun. 4 2890 [88] Huth F, et al. 2013 Nano Lett. 13 1065 [89] Hermann P, et al. 2014 Opt. Express 22 17948 [90] Chen J, et al. 2012 Nature 487 77 [91] Fei Z, et al. 2012 Nature 487 82 [92] Dai S, et al. 2014 Science 343 1125 [93] Li P, et al. 2015 Nat. Commun. 6 7507 [94] Jaque D, Vetrone F 2012 Nanoscale 4 430 [95] Michaelis J, et al. 2000 Nature 405 325 [96] Ebenstein Y, Mokari T, Banin U 2004 J. Phys. Chem. B 108 93 [97] Wagner C, et al. 2015 Phys. Rev. Lett. 115 026101 [98] Khn S, et al. 2001 J. Microsc. 202 2 [99] Pendry J B 2000 Phys. Rev. Lett. 85 3966 [100] Luo X G, Ishihara T 2004 Appl. Phys. Lett. 84 4780 [101] Liu Z W, et al. 2007 Science 315 1686 [102] Xiong Y, Liu Z, Zhang X 2009 Appl. Phys. Lett. 94 203108 [103] Ren G, et al. 2013 Plasmonics 8 1065 [104] Gao P, et al. 2015 Appl. Phys. Lett. 106 093110 [105] Ono A, Kato J, Kawata S 2005 Phys. Rev. Lett. 95 267407 [106] Ikonen P, et al. 2007 Appl. Phys. Lett. 91 104102 [107] Shvets G, et al. 2007 Phys. Rev. Lett. 99 053903 [108] Han S, et al. 2008 Nano Lett. 8 4243 [109] Kildishev A V, Shalaev V M 2008 Opt. Lett. 33 43 [110] Tsang M, Psaltis D 2008 Phys. Rev. B 77 035122 [111] Li J, et al. 2009 Opt. Lett. 34 3128 [112] Smolyaninov II, et al. 2005 Phys. Rev. Lett. 94 057401 [113] Hu H, Ma C, Liu Z 2010 Appl. Phys. Lett. 96 113107 [114] Wei F F, Liu Z W 2010 Nano Lett. 10 2531 [115] Yuan G, Wang Q, Yuan X 2012 Opt. Lett. 37 2715 [116] Berry M V, Popescu S 2006 J. Phys. A 39 6965 [117] Ferreira P J S G, Kempf A 2006 IEEE Trans. Sig. Proc. 54 3732 [118] Huang F M, et al. 2007 Appl. Phys. Lett. 90 091119 [119] Huang F M, Zheludev N I 2009 Nano Lett. 9 1249 [120] Rogers E T F, et al. 2013 Appl. Phys. Lett. 102 031108 [121] Baumgartl J, et al. 2011 Appl. Phys. Lett. 98 181109 [122] Kosmeier S, et al. 2011 J. Opt. 13 105707 [123] Tang D L, et al. 2015 Laser Photon. Rev. 9 713 [124] Zhang Y, et al. 2010 Phys. Rev. Lett. 104 183901 [125] Liu D, Zhang Y, Wen J, et al. 2014 Sci. Rep. 4 6134 [126] Huang B, Bates M, Zhuang X W 2009 Annu. Rev. Biochem. 78 993 [127] Chen B C, et al. 2014 Science 346 439 [128] Legant W R, et al. 2016 Nat. Methods 13 359 [129] Wang H, Han S, Kolobov M I 2012 Opt. Express 20 23235 [130] Nair R, Tsang M 2016 Phys. Rev. Lett. 117 190801 
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[1] Bradbury S 1967 The Evolution of the Microscope (London: Pregamon Press Ltd.) [2] Abbe E 1873 Archiv fr Mikroskopische Anatomie 9 413 [3] Borm M, Wolf E 1980 Principle of Optics (New York: Pergamon) [4] Synge E H 1928 Phil. Mag. 6 356 [5] Novotny L, Hecht B 2012 Principles of Nano-Optics (Cambridge: Cambridge University Press) [6] Betzig E, Trautman J K, Harris T D, et al. 1991 Science 251 1468 [7] Betzig E, Trautman J K 1992 Science 257 189 [8] Ash E A, Nicholls G 1972 Nature 237 510 [9] Lewis A, Isaacson M, Harootunian A, Muray A 1984 Ultramicroscopy 13 227 [10] Pohl D W, Denk W, Lanz M 1984 Appl. Phys. Lett. 44 651 [11] Binnig G R H 1981 IBM J. Res. Dev. 30 355 [12] Thomas A K, Hell S W 1999 Opt. Lett. 24 954 [13] Rust M J, Bates M, Zhuang X 2006 Nat. Methods 3 793 [14] Fang N, Lee H, Sun C, Zhang X 2005 Science 308 534 [15] Taubner T, Korobkin D, Urzhumov Y, et al. 2006 Science 313 1595 [16] Smolyaninov II, Hung Y J, Davis C C 2007 Science 315 1699 [17] Gustafsson M G L 2000 J. Microsc. 198 82 [18] Hell S W, Wichmann J 1994 Opt. Lett. 19 780 [19] Betzig E, et al. 2006 Science 313 1642 [20] Rogers E T F, et al. 2012 Nat. Materials 11 432 [21] Hell S W 2007 Science 316 1153 [22] Jones S A, Shim S H, He J, Zhuang X W 2011 Nat. Methods 8 499 [23] Pohl D W, Kawata S 2001 Near-Field Optics and Surface Plasmon Polaritons (Germany: Springer-Verlag) [24] Serrels K A, Ramsay E, Dalgarno P A, et al. 2008 J. Nanophoton. 2 021854 [25] Mansfield S M, Kino G S 1990 Appl. Phys. Lett. 57 2615 [26] Terris B D, Mamin H J, Rugar D 1994 Appl. Phys. Lett. 65 388 [27] Ghislain L P, Elings V B 1999 Appl. Phys. Lett. 74 501 [28] Wu Q, Feke C D, Crober R D 1999 Appl. Phys. Lett. 75 4064 [29] Ippolito S B, Goldberg B B, Unlu M S 2001 Appl. Phys. Lett. 78 4071 [30] Liu Z H, et al. 2005 Appl. Phys. Lett. 87 071905 [31] Serrels K A, et al. 2008 Nat. Photon. 2 311 [32] Lee J Y, et al. 2009 Nature 460 498 [33] Mason D R, Jouravlev M V, Kim K S 2010 Opt. Lett. 35 2007 [34] Wang Z, et al. 2011 Nat. Commun. 2 218 [35] Lukosz W, Marchand M 1963 J. Mod. Opt. 10 241 [36] Heintzmann R, Cremer C 1999 Proc. SPIE 3568 185 [37] Frohn J T, Knapp H F, Stemmer A 2000 Proc. Nat. Acad. Sci. USA 97 7232 [38] Gustafsson M G L, Agard D A, Sedat J W 2000 Proc. SPIE 3919 141 [39] Neil M A A, Juskaitis R, Wilson T 1997 Opt. Lett. 22 1905 [40] Gustafsson M G L., et al. 2008 Biophys. J. 94 4957 [41] Schermelleh L, et al. 2008 Science 320 1332 [42] Gustafsson M G L 2005 Proc. Nat. Acad. Sci. USA 102 13081 [43] Kner P, et al. 2009 Nat. Methods 6 339 [44] Planchon T A, et al. 2011 Nat. Methods 8 417 [45] Demmerle J, et al. 2017 Nat. Protoc. 12 988 [46] Weisenburger S, Sandoghdar V 2015 Contemp. Phys. 56 123 [47] De Wilde Y, et al. 2006 Nature 444 740 [48] Betzig E, Finn P, Weiner J 1992 Appl. Phys. Lett. 60 2484 [49] Betzig E, Chichester R J 1993 Science 262 1422 [50] Trautman J K, et al. 1994 Nature 369 40 [51] Xie X S, Dunn R C 1994 Science 265 361 [52] Matsuda K, et al. 2003 Phys. Rev. Lett. 91 177401 [53] Moerland R J, van Hulst N F 2005 Opt. Express 13 1604 [54] Taminiau T H, et al. 2007 Nano Lett. 7 28 [55] Rotenberg N, Kuipers L 2014 Nat. Photon. 8 919 [56] Reddick R, Warmack R, Ferrell T 1989 Phys. Rev. B 39 767 [57] Balistreri M, et al. 2001 Science 294 1080 [58] Balistreri M, et al. 2000 Phys. Rev. Lett. 85 294 [59] Veerman J A, et al. 1998 Appl. Phys. Lett. 72 3115 [60] Dunn R C 1999 Chem. Rev. 99 2891 [61] Knoll B, Keilmann F 1999 Nature 399 134 [62] Snchez E J, Novotny L, Xie X S 1999 Phys. Rev. Lett. 82 4014 [63] Gerton J M, et al. 2004 Phys. Rev. Lett. 93180801 [64] Anger P, Bharadwaj P, Novotny L 2006 Phys. Rev. Lett. 96 113002 [65] Hppener C, Novotny L 2008 Nano Lett. 8 642 [66] Eghlidi H, et al. 2009 Nano Lett. 9 4007 [67] Tam F, et al. 2007 Nano Lett. 7 496 [68] Wientjes E, et al. 2014 Nat. Commun. 5 4236 [69] Kneipp K, et al. 2002 J. Phys. 14 R597 [70] Anderson M S 2000 Appl. Phys. Lett. 76 3130 [71] Hayazawa N, et al. 2000 Opt. Commun. 183 333 [72] Stckle R M, et al. 2000 Chem. Phys. Lett. 318 131 [73] Hartschuh A., et al. 2003 Phys. Rev. Lett. 90 095503 [74] Ren B, Picardi G, Pettinger B 2004 Rev. Sci. Instru. 75 837 [75] Yeo B S, et al. 2007 Anal. Bioanal. Chem. 387 2655 [76] Zhang W, et al. 2007 J. Phys. Chem. C 111 1733 [77] Ichimura T, et al. 2007 J. Phys. Chem. C 111 9460 [78] Domke K F, Zhang D, Pettinger B 2006 J. Am. Chem. Soc. 128 147217 [79] Neacsu C C, et al. 2006 Phys. Rev. B 73 193406 [80] Pettinger B, et al. 2004 Phys. Rev. Lett. 92 096101 [81] Steidtner J, Pettinger B 2008 Phys. Rev. Lett. 100 236101 [82] Zhang R, et al. 2013 Nature 498 82 [83] Knoll B, Keilmann F 2000 Opt. Commun. 182 321 [84] Keilmann F, Hillenbrand R 2004 Philos. Trans. A 362 787 [85] Huth F, et al. 2011 Nat. Mater. 10 352 [86] Huth F, et al. 2012 Nano Lett. 12 3973 [87] Amenabar I, et al. 2013 Nat. Commun. 4 2890 [88] Huth F, et al. 2013 Nano Lett. 13 1065 [89] Hermann P, et al. 2014 Opt. Express 22 17948 [90] Chen J, et al. 2012 Nature 487 77 [91] Fei Z, et al. 2012 Nature 487 82 [92] Dai S, et al. 2014 Science 343 1125 [93] Li P, et al. 2015 Nat. Commun. 6 7507 [94] Jaque D, Vetrone F 2012 Nanoscale 4 430 [95] Michaelis J, et al. 2000 Nature 405 325 [96] Ebenstein Y, Mokari T, Banin U 2004 J. Phys. Chem. B 108 93 [97] Wagner C, et al. 2015 Phys. Rev. Lett. 115 026101 [98] Khn S, et al. 2001 J. Microsc. 202 2 [99] Pendry J B 2000 Phys. Rev. Lett. 85 3966 [100] Luo X G, Ishihara T 2004 Appl. Phys. Lett. 84 4780 [101] Liu Z W, et al. 2007 Science 315 1686 [102] Xiong Y, Liu Z, Zhang X 2009 Appl. Phys. Lett. 94 203108 [103] Ren G, et al. 2013 Plasmonics 8 1065 [104] Gao P, et al. 2015 Appl. Phys. Lett. 106 093110 [105] Ono A, Kato J, Kawata S 2005 Phys. Rev. Lett. 95 267407 [106] Ikonen P, et al. 2007 Appl. Phys. Lett. 91 104102 [107] Shvets G, et al. 2007 Phys. Rev. Lett. 99 053903 [108] Han S, et al. 2008 Nano Lett. 8 4243 [109] Kildishev A V, Shalaev V M 2008 Opt. Lett. 33 43 [110] Tsang M, Psaltis D 2008 Phys. Rev. B 77 035122 [111] Li J, et al. 2009 Opt. Lett. 34 3128 [112] Smolyaninov II, et al. 2005 Phys. Rev. Lett. 94 057401 [113] Hu H, Ma C, Liu Z 2010 Appl. Phys. Lett. 96 113107 [114] Wei F F, Liu Z W 2010 Nano Lett. 10 2531 [115] Yuan G, Wang Q, Yuan X 2012 Opt. Lett. 37 2715 [116] Berry M V, Popescu S 2006 J. Phys. A 39 6965 [117] Ferreira P J S G, Kempf A 2006 IEEE Trans. Sig. Proc. 54 3732 [118] Huang F M, et al. 2007 Appl. Phys. Lett. 90 091119 [119] Huang F M, Zheludev N I 2009 Nano Lett. 9 1249 [120] Rogers E T F, et al. 2013 Appl. Phys. Lett. 102 031108 [121] Baumgartl J, et al. 2011 Appl. Phys. Lett. 98 181109 [122] Kosmeier S, et al. 2011 J. Opt. 13 105707 [123] Tang D L, et al. 2015 Laser Photon. Rev. 9 713 [124] Zhang Y, et al. 2010 Phys. Rev. Lett. 104 183901 [125] Liu D, Zhang Y, Wen J, et al. 2014 Sci. Rep. 4 6134 [126] Huang B, Bates M, Zhuang X W 2009 Annu. Rev. Biochem. 78 993 [127] Chen B C, et al. 2014 Science 346 439 [128] Legant W R, et al. 2016 Nat. Methods 13 359 [129] Wang H, Han S, Kolobov M I 2012 Opt. Express 20 23235 [130] Nair R, Tsang M 2016 Phys. Rev. Lett. 117 190801 
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