Progress in far-field focusing and imaging with super-oscillation

Jiang Zhong-Jun; Liu Jian-Jun

doi:10.7498/aps.65.234203

Abstract

Superoscillation is known as a counter-intuitive property of a band-limited function that oscillates faster than its highest Fourier component in a prescribed interval. Based on superoscillation, micro/nano optical devices, breaking through the diffraction limit in the far-field independent of evanescent waves, have potential applications, including super-resolution, nano-photolithography, high-density optical storage, etc. In this paper, superoscillation is introduced simply, and several optical superoscillatory designs with focusing and imaging abilities are summarized primarily, and some defects and future research emphases in these designs are pointed out.

Keywords:

Authors and contacts

1.
Laboratory for Micro-/Nano-Optoelectronic Devices of the Ministry of Education, School of Physics and Electronics, Hunan University, Changsha 410082, China;
2.
Institute for Lasers, Photonics and Biophotonics, State University of New York at Buffalo, Buffalo, New York 14260, USA

Corresponding author: Liu Jian-Jun, jianjun.liu@hnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61405058).

References

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[2]	Rayleigh L 1903 Journal of the Royal Microscopical Society 23 447
[3]	Pohl D W, Denk W, Lanz M 1984 Appl. Phys. Lett. 44 651
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[6]	Smolyaninov I I, Hung Y J, Davis C C 2007 Science 315 1699
[7]	Grbic A, Eleftheriades G V 2004 Phys. Rev. Lett. 92 117403
[8]	Liu Z, Lee H, Xiong Y, Sun C, Zhang X 2007 Science 315 1686
[9]	Rust M J, Bates M, Zhuang X 2006 Nat. Methods 3 793
[10]	Hell S W, Wichmann J 1994 Opt. Lett. 19 780
[11]	Betzig E, Patterson G H, Sougrat R, Lindwasser O W, Olenych S, Bonifacino J S, Davidson M W, Lippincott S J, Hess H F 2006 Science 313 1642
[12]	Denk W, Strickler J H, Webb W W 1990 Science 248 73
[13]	Stöckle R M, Suh Y D, Deckert V, Zenobi R 2000 Chem. Phys. Lett. 318 131
[14]	Nie S, Emory S R 1997 Science 275 1102
[15]	Berry M V, Popescu S 2006 J. Phys. A-Math. Gen. 39 6965
[16]	Aharonov Y, Albert D Z, Vaidman L 1988 Phys. Rev. Lett. 60 1351
[17]	Aharonov Y, Anandan J, Popescu S, Vaidman L 1990 Phys. Rev. Lett. 64 2965
[18]	Kempf A 2000 J. Math. Phys. 41 2360
[19]	Kempf A, Ferreira P J S G 2004 J. Phys. A-Math. Gen. 37 12067
[20]	Calder M S, Kempf A 2005 J. Math. Phys. 46 012101
[21]	Ferreira P J S G, Kempf A 2006 IEEE Trans. Signal Process. 54 3732
[22]	Ferreira P J S G, Kempf A 2002 11th European Signal Processing Conference Toulouse, September 3-6, 2002 p1
[23]	Landau H J, Pollak H O 1961 Bell System Technical Journal 40 65
[24]	Zheludev N I 2008 Nat. Mater. 7 420
[25]	Huang F M, Zheludev N I 2009 Nano Lett. 9 1249
[26]	Schelkunoff S A 1943 Bell System Technical Journal 22 80
[27]	Di Francia G T 1952 Il Nuovo Cimento 9 426
[28]	Di Francia G T 1956 IEEE Trans. Antennas Propag. 4 473
[29]	Rogers E T F, Lindberg J, Roy T, Savo S, Chad J E, Dennis M R, Zheludev N I 2012 Nat. Mater. 11 432
[30]	Bucklew J A, Saleh B E A 1985 J. Opt. Soc. Am. A 2 1233
[31]	Berry M V 1994 Quantum Coherence and Reality in Celebration of the 60th Birthday of Yakir Aharonov (Singapore:World Scientific) pp55-65
[32]	Berry M V 1994 J. Phys. A-Math. Gen. 27 L391
[33]	Lindberg J 2012 J. Opt. 14 083001
[34]	Aharonov Y, Colombo F, Sabadini I, Struppa D C, Tollaksen J 2011 J. Phys. A-Math. Theor. 44 365304
[35]	Dennis M R, Hamilton A C, Courtial J 2008 Opt. Lett. 33 2976
[36]	Berry M V, Dennis M R 2009 J. Phys. A-Math. Theor. 42 022003
[37]	Qiao W 1996 J. Phys. A-Math. Gen. 29 2257
[38]	Ferreira P J S G 2014 New Perspectives on Approximation and Sampling Theory (Berlin:Springer-Verlag) pp247-268
[39]	Rogers E T F, Zheludev N I 2013 J. Opt. 15 094008
[40]	Shechtman D, Blech I, Gratias D, Cahn J W 1984 Phys. Rev. Lett. 53 1951
[41]	Feng Z, Zhang X, Wang Y, Li Z Y, Cheng B, Zhang D Z 2005 Phys. Rev. Lett. 94 247402
[42]	Zhang X, Li Z Y, Cheng B, Zhang D Z 2007 Opt. Express 15 1292
[43]	Gennaro E D, Morello D, Miletto C, Savo S, Andreone A, Castaldi G, Galdi V, Pierro V 2008 Photonic. Nanostruct. Fund. Appl. 6 60
[44]	Ren K, Ren X B 2009 Acta Opt. Sin. (in Chinese) 29 2317 (in Chinese)[任坤, 任晓斌2009光学学报29 2317]
[45]	Ren K, Ren X B 2011 Eur. Phys. J. Appl. Phys. 54 10501
[46]	Liu J J, Fan Z G 2014 Opt. Eng. 53 077101
[47]	Ren K, Ren X B, Li Z Y, Zhang D Z 2008 Eur. Phys. J. Appl. Phys. 42 281
[48]	Liu J J, Liu E X, Zhang T H, Fang Z G 2015 Solid State Commun. 201 68
[49]	Gennaro E D, Miletto C, Savo S, Andreone A, Morello D, Galdi V, Castaldi G, Pierro V 2008 Phys. Rev. B 77 193104
[50]	Liu J J, Liu E X, Fan Z G 2015 J. Mod. Opt. 63 692
[51]	Liu J J, Fan Z G, Hu H L, Yang M H, Guan C Y, Yuan L B, Guo H, Zhang X 2012 Opt. Lett. 37 1730
[52]	Liu J J, Zuo B J, Chen S Q, Hu H L, Xiao H S, Zhang W, Fang Z G, Guo H, Zhang X 2012 Opt. Eng. 51 074005
[53]	Liu J J, Hu H L, Zhang W, Fang Z G 2014 Photonic. Nanostruct. Fun. Appl. 12 138
[54]	Liu J J, Liu E X, Fan Z G, Zhang X 2015 Appl. Phys. Express 8 112003
[55]	Liu J J, Tan W, Liu E X, Hu H L, Fan Z G, Zhang T H, Zhang X 2016 J. Opt. Soc. Am. A 33 978
[56]	Huang F M, Zheludev N I, Chen Y, de Abajo F J G 2007 Appl. Phys. Lett. 90 091119
[57]	Huang F M, Chen Y, de Abajo F J G, Zheludev N I 2007 J. Opt. A-Pure Appl. Opt. 9 S285
[58]	Patorski K 1989 Prog. Opt. 27 1
[59]	Huang F M, Kao T S, Fedotov V A, Chen Y, Zheludev N I 2008 Nano Lett. 8 2469
[60]	Schmid H, Biebuyck H, Michel B, Martin O J F 1998 Appl. Phys. Lett. 72 2379
[61]	Cox I J 1984 Appl. Opt. 23 3260
[62]	Ebbesen T W, Lezec H J, Ghaemi H F, Thio T, Wolff P A 1998 Nature 391 667
[63]	Przybilla F, Genet C, Ebbesen T W 2006 Appl. Phys. Lett. 89 121115
[64]	Wang X, Fu J, Liu X, Tong L M 2009 J. Opt. Soc. Am. A 26 1827
[65]	Wang T T, Wang X, Kuang C F, Hao X, Liu X 2010 Appl. Phys. Lett. 97 231105
[66]	Liu Z, Steele J M, Srituravanich W, Pikus Y, Sun C, Zhang X 2005 Nano Lett. 5 1726
[67]	Rogers E T F, Savo S, Lindberg J, Roy T, Dennis M R, Zheludev N I 2013 Appl. Phys. Lett. 102 031108
[68]	Roy T, Rogers E T F, Yuan G, Zheludev N I 2014 Appl. Phys. Lett. 104 231109
[69]	Yuan G, Rogers E T F, Roy T, Shen Z, Zheludev N I 2014 Opt. Express 22 6428
[70]	Huang K, Ye H, Teng J, Yeo S P, Luk'Yanchuk B 2014 Laser Photon. Rev. 8 152
[71]	Ye H, Qiu C W, Huang K, Teng J, Luk'Yanchuk B 2013 Laser Phys. Lett. 10 065004
[72]	Liu T, Tan J, Liu J, Wang H T 2013 Opt. Express 21 15090
[73]	Liu T, Shen T, Yang S M, Jiang Z D 2015 J. Opt. 17 035610
[74]	Chen Z, Zhang Y, Xiao M 2015 J. Opt. Soc. Am. B 32 1731
[75]	Yuan G, Rogers E T F, Roy T, Adamo G, Shen Z, Zheludev N I 2014 Sci. Rep. 4 6333
[76]	Qin F, Huang K, Wu J, Jiao J, Luo X, Qiu C, Hong M 2015 Sci. Rep. 5 9977
[77]	Wong A M H, Eleftheriades G V 2010 IEEE Antennas Wirel. Propag. Lett. 9 315
[78]	Wong A M H, Eleftheriades G V 2011 IEEE Trans. Antennas Propag. 59 4766
[79]	Wong A M H, Eleftheriades G V 2014 The 8th European Conference on Antennas and Propagation (EuCAP 2014) The Hague, April 6-11, 2014 p1340
[80]	Wong A M H, Eleftheriades G V 2015 Sci. Rep. 5 8449
[81]	Wong A M H, Eleftheriades G V 2013 Sci. Rep. 3 1715
[82]	Amineh R K, Eleftheriades G V 2013 Opt. Express 21 8142
[83]	Mazilu M, Baumgartl J, Kosmeier S, Dholakia K 2011 Opt. Express 19 933
[84]	Baumgartl J, Kosmeier S, Mazilu M, Rogers E T F, Zheludev N I, Dholakia K 2011 Appl. Phys. Lett. 98 181109
[85]	Kosmeier S, Mazilu M, Baumgartl J, Dholakia K 2011 J. Opt. 13 105707
[86]	Piché K, Leach J, Johnson A S, Salvail J Z, Kolobov M I, Boyd R W 2012 Opt. Express 20 26424
[87]	Roy T, Rogers E T F, Zheludev N I 2013 Opt. Express 21 7577
[88]	He Y, Wen Z, Chen L, Li Y, Ning Y, Chen G 2014 IEEE Photonics Technol. Lett. 26 1801
[89]	Chen G, Li Y, Wang X, Wen Z, Lin F, Dai L, Chen L, He Y, Liu S 2016 IEEE Photonics Technol. Lett. 28 335
[90]	Chen G, Zhang K, Yu A, Wang X, Zhang Z, Li Y, Wen Z, Li C, Dai L, Jiang S, Lin F 2016 Opt. Express 24 11002
[91]	Makris K G, Psaltis D 2011 Opt. Lett. 36 4335
[92]	Greenfield E, Schley R, Hurwitz I, Nemirovsky J, Makris K G, Segev M 2013 Opt. Express 21 13425

Cited By

[1]	Abbe E 1873 Archiv Fr Mikroskopische Anatomie 9 413
[2]	Rayleigh L 1903 Journal of the Royal Microscopical Society 23 447
[3]	Pohl D W, Denk W, Lanz M 1984 Appl. Phys. Lett. 44 651
[4]	Betzig E, Lewis A, Harootunian A, Isaacson M, Kratschmer, E 1986 Biophys. J. 49 269
[5]	Pendry J B 2000 Phys. Rev. Lett. 85 3966
[6]	Smolyaninov I I, Hung Y J, Davis C C 2007 Science 315 1699
[7]	Grbic A, Eleftheriades G V 2004 Phys. Rev. Lett. 92 117403
[8]	Liu Z, Lee H, Xiong Y, Sun C, Zhang X 2007 Science 315 1686
[9]	Rust M J, Bates M, Zhuang X 2006 Nat. Methods 3 793
[10]	Hell S W, Wichmann J 1994 Opt. Lett. 19 780
[11]	Betzig E, Patterson G H, Sougrat R, Lindwasser O W, Olenych S, Bonifacino J S, Davidson M W, Lippincott S J, Hess H F 2006 Science 313 1642
[12]	Denk W, Strickler J H, Webb W W 1990 Science 248 73
[13]	Stöckle R M, Suh Y D, Deckert V, Zenobi R 2000 Chem. Phys. Lett. 318 131
[14]	Nie S, Emory S R 1997 Science 275 1102
[15]	Berry M V, Popescu S 2006 J. Phys. A-Math. Gen. 39 6965
[16]	Aharonov Y, Albert D Z, Vaidman L 1988 Phys. Rev. Lett. 60 1351
[17]	Aharonov Y, Anandan J, Popescu S, Vaidman L 1990 Phys. Rev. Lett. 64 2965
[18]	Kempf A 2000 J. Math. Phys. 41 2360
[19]	Kempf A, Ferreira P J S G 2004 J. Phys. A-Math. Gen. 37 12067
[20]	Calder M S, Kempf A 2005 J. Math. Phys. 46 012101
[21]	Ferreira P J S G, Kempf A 2006 IEEE Trans. Signal Process. 54 3732
[22]	Ferreira P J S G, Kempf A 2002 11th European Signal Processing Conference Toulouse, September 3-6, 2002 p1
[23]	Landau H J, Pollak H O 1961 Bell System Technical Journal 40 65
[24]	Zheludev N I 2008 Nat. Mater. 7 420
[25]	Huang F M, Zheludev N I 2009 Nano Lett. 9 1249
[26]	Schelkunoff S A 1943 Bell System Technical Journal 22 80
[27]	Di Francia G T 1952 Il Nuovo Cimento 9 426
[28]	Di Francia G T 1956 IEEE Trans. Antennas Propag. 4 473
[29]	Rogers E T F, Lindberg J, Roy T, Savo S, Chad J E, Dennis M R, Zheludev N I 2012 Nat. Mater. 11 432
[30]	Bucklew J A, Saleh B E A 1985 J. Opt. Soc. Am. A 2 1233
[31]	Berry M V 1994 Quantum Coherence and Reality in Celebration of the 60th Birthday of Yakir Aharonov (Singapore:World Scientific) pp55-65
[32]	Berry M V 1994 J. Phys. A-Math. Gen. 27 L391
[33]	Lindberg J 2012 J. Opt. 14 083001
[34]	Aharonov Y, Colombo F, Sabadini I, Struppa D C, Tollaksen J 2011 J. Phys. A-Math. Theor. 44 365304
[35]	Dennis M R, Hamilton A C, Courtial J 2008 Opt. Lett. 33 2976
[36]	Berry M V, Dennis M R 2009 J. Phys. A-Math. Theor. 42 022003
[37]	Qiao W 1996 J. Phys. A-Math. Gen. 29 2257
[38]	Ferreira P J S G 2014 New Perspectives on Approximation and Sampling Theory (Berlin:Springer-Verlag) pp247-268
[39]	Rogers E T F, Zheludev N I 2013 J. Opt. 15 094008
[40]	Shechtman D, Blech I, Gratias D, Cahn J W 1984 Phys. Rev. Lett. 53 1951
[41]	Feng Z, Zhang X, Wang Y, Li Z Y, Cheng B, Zhang D Z 2005 Phys. Rev. Lett. 94 247402
[42]	Zhang X, Li Z Y, Cheng B, Zhang D Z 2007 Opt. Express 15 1292
[43]	Gennaro E D, Morello D, Miletto C, Savo S, Andreone A, Castaldi G, Galdi V, Pierro V 2008 Photonic. Nanostruct. Fund. Appl. 6 60
[44]	Ren K, Ren X B 2009 Acta Opt. Sin. (in Chinese) 29 2317 (in Chinese)[任坤, 任晓斌2009光学学报29 2317]
[45]	Ren K, Ren X B 2011 Eur. Phys. J. Appl. Phys. 54 10501
[46]	Liu J J, Fan Z G 2014 Opt. Eng. 53 077101
[47]	Ren K, Ren X B, Li Z Y, Zhang D Z 2008 Eur. Phys. J. Appl. Phys. 42 281
[48]	Liu J J, Liu E X, Zhang T H, Fang Z G 2015 Solid State Commun. 201 68
[49]	Gennaro E D, Miletto C, Savo S, Andreone A, Morello D, Galdi V, Castaldi G, Pierro V 2008 Phys. Rev. B 77 193104
[50]	Liu J J, Liu E X, Fan Z G 2015 J. Mod. Opt. 63 692
[51]	Liu J J, Fan Z G, Hu H L, Yang M H, Guan C Y, Yuan L B, Guo H, Zhang X 2012 Opt. Lett. 37 1730
[52]	Liu J J, Zuo B J, Chen S Q, Hu H L, Xiao H S, Zhang W, Fang Z G, Guo H, Zhang X 2012 Opt. Eng. 51 074005
[53]	Liu J J, Hu H L, Zhang W, Fang Z G 2014 Photonic. Nanostruct. Fun. Appl. 12 138
[54]	Liu J J, Liu E X, Fan Z G, Zhang X 2015 Appl. Phys. Express 8 112003
[55]	Liu J J, Tan W, Liu E X, Hu H L, Fan Z G, Zhang T H, Zhang X 2016 J. Opt. Soc. Am. A 33 978
[56]	Huang F M, Zheludev N I, Chen Y, de Abajo F J G 2007 Appl. Phys. Lett. 90 091119
[57]	Huang F M, Chen Y, de Abajo F J G, Zheludev N I 2007 J. Opt. A-Pure Appl. Opt. 9 S285
[58]	Patorski K 1989 Prog. Opt. 27 1
[59]	Huang F M, Kao T S, Fedotov V A, Chen Y, Zheludev N I 2008 Nano Lett. 8 2469
[60]	Schmid H, Biebuyck H, Michel B, Martin O J F 1998 Appl. Phys. Lett. 72 2379
[61]	Cox I J 1984 Appl. Opt. 23 3260
[62]	Ebbesen T W, Lezec H J, Ghaemi H F, Thio T, Wolff P A 1998 Nature 391 667
[63]	Przybilla F, Genet C, Ebbesen T W 2006 Appl. Phys. Lett. 89 121115
[64]	Wang X, Fu J, Liu X, Tong L M 2009 J. Opt. Soc. Am. A 26 1827
[65]	Wang T T, Wang X, Kuang C F, Hao X, Liu X 2010 Appl. Phys. Lett. 97 231105
[66]	Liu Z, Steele J M, Srituravanich W, Pikus Y, Sun C, Zhang X 2005 Nano Lett. 5 1726
[67]	Rogers E T F, Savo S, Lindberg J, Roy T, Dennis M R, Zheludev N I 2013 Appl. Phys. Lett. 102 031108
[68]	Roy T, Rogers E T F, Yuan G, Zheludev N I 2014 Appl. Phys. Lett. 104 231109
[69]	Yuan G, Rogers E T F, Roy T, Shen Z, Zheludev N I 2014 Opt. Express 22 6428
[70]	Huang K, Ye H, Teng J, Yeo S P, Luk'Yanchuk B 2014 Laser Photon. Rev. 8 152
[71]	Ye H, Qiu C W, Huang K, Teng J, Luk'Yanchuk B 2013 Laser Phys. Lett. 10 065004
[72]	Liu T, Tan J, Liu J, Wang H T 2013 Opt. Express 21 15090
[73]	Liu T, Shen T, Yang S M, Jiang Z D 2015 J. Opt. 17 035610
[74]	Chen Z, Zhang Y, Xiao M 2015 J. Opt. Soc. Am. B 32 1731
[75]	Yuan G, Rogers E T F, Roy T, Adamo G, Shen Z, Zheludev N I 2014 Sci. Rep. 4 6333
[76]	Qin F, Huang K, Wu J, Jiao J, Luo X, Qiu C, Hong M 2015 Sci. Rep. 5 9977
[77]	Wong A M H, Eleftheriades G V 2010 IEEE Antennas Wirel. Propag. Lett. 9 315
[78]	Wong A M H, Eleftheriades G V 2011 IEEE Trans. Antennas Propag. 59 4766
[79]	Wong A M H, Eleftheriades G V 2014 The 8th European Conference on Antennas and Propagation (EuCAP 2014) The Hague, April 6-11, 2014 p1340
[80]	Wong A M H, Eleftheriades G V 2015 Sci. Rep. 5 8449
[81]	Wong A M H, Eleftheriades G V 2013 Sci. Rep. 3 1715
[82]	Amineh R K, Eleftheriades G V 2013 Opt. Express 21 8142
[83]	Mazilu M, Baumgartl J, Kosmeier S, Dholakia K 2011 Opt. Express 19 933
[84]	Baumgartl J, Kosmeier S, Mazilu M, Rogers E T F, Zheludev N I, Dholakia K 2011 Appl. Phys. Lett. 98 181109
[85]	Kosmeier S, Mazilu M, Baumgartl J, Dholakia K 2011 J. Opt. 13 105707
[86]	Piché K, Leach J, Johnson A S, Salvail J Z, Kolobov M I, Boyd R W 2012 Opt. Express 20 26424
[87]	Roy T, Rogers E T F, Zheludev N I 2013 Opt. Express 21 7577
[88]	He Y, Wen Z, Chen L, Li Y, Ning Y, Chen G 2014 IEEE Photonics Technol. Lett. 26 1801
[89]	Chen G, Li Y, Wang X, Wen Z, Lin F, Dai L, Chen L, He Y, Liu S 2016 IEEE Photonics Technol. Lett. 28 335
[90]	Chen G, Zhang K, Yu A, Wang X, Zhang Z, Li Y, Wen Z, Li C, Dai L, Jiang S, Lin F 2016 Opt. Express 24 11002
[91]	Makris K G, Psaltis D 2011 Opt. Lett. 36 4335
[92]	Greenfield E, Schley R, Hurwitz I, Nemirovsky J, Makris K G, Segev M 2013 Opt. Express 21 13425

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