Progress and Perspectives of Nonlinear Plasmonics

Yang Li; Junjun Shi; Di Zheng; Meng Kang; Tong Fu; Shunping Zhang; Hongxing Xu

doi:10.3788/LOP56.202401

[1] Shen Y R. The principles of nonlinear optics[M]. New York: Wiley-Interscience, 575(1984).

[2] Boyd R W[M]. Nonlinear optics(2008).

[3] Kauranen M, Zayats A V. Nonlinear plasmonics[J]. Nature Photonics, 6, 737-748(2012).

[4] Maier S A. Plasmonics: fundamentals and applications[M]. Berlin: Springer Science & Business Media(2007).

[5] Gramotnev D K, Bozhevolnyi S I. Plasmonics beyond the diffraction limit[J]. Nature Photonics, 4, 83-91(2010). http://www.nature.com/nphoton/journal/v4/n2/abs/nphoton.2009.282.html

[6] Atwater H A, Polman A. Plasmonics for improved photovoltaic devices[J]. Nature Materials, 9, 205-213(2010). http://www.nature.com/nmat/journal/v9/n3/abs/nmat2629.html

[7] Barnes W L, Dereux A, Ebbesen T W. Surface plasmon subwavelength optics[J]. Nature, 424, 824-830(2003).

[8] Schuller J A, Barnard E S, Cai W S et al. Plasmonics for extreme light concentration and manipulation[J]. Nature Materials, 9, 193-204(2010). http://www.nature.com/uidfinder/10.1038/nmat2736

[9] Butet J, Brevet P F. Martin O J F. Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications[J]. ACS Nano, 9, 10545-10562(2015). http://pubs.acs.org/doi/abs/10.1021/acsnano.5b04373

[10] Ren M X, Xu J J. Surface plasmon polariton enhanced nonlinearity and applications[J]. Laser & Optoelectronics Progress, 50, 080002(2013).

[11] Xu H X, Bjerneld E J, Käll M et al. Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering[J]. Physical Review Letters, 83, 4357-4360(1999).

[12] Xu H X, Aizpurua J, Käll M et al. Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering[J]. Physical Review E, 62, 4318-4324(2000). http://www.ncbi.nlm.nih.gov/pubmed/11088961

[13] Anker J N, Hall W P, Lyandres O et al. Biosensing with plasmonic nanosensors[J]. Nature Materials, 7, 442-453(2008).

[14] Laing S, Jamieson L E, Faulds K et al. Surface-enhanced Raman spectroscopy for in vivo biosensing[J]. Nature Reviews Chemistry, 1, 0060(2017). http://www.nature.com/articles/s41570-017-0060

[15] Chen W, Hu H T, Jiang W et al. Ultrasensitive nanosensors based on localized surface plasmon resonances: from theory to applications[J]. Chinese Physics B, 27, 107403(2018). http://www.cnki.com.cn/Article/CJFDTotal-ZGWL201810005.htm

[16] Pillai S, Catchpole K R, Trupke T et al. Surface plasmon enhanced silicon solar cells[J]. Journal of Applied Physics, 101, 093105(2007). http://scitation.aip.org/content/aip/journal/jap/101/9/10.1063/1.2734885

[17] Baffou G, Quidant R. Nanoplasmonics for chemistry[J]. Chemical Society Reviews, 43, 3898-3907(2014).

[18] Hou W B, Cronin S B. A review of surface plasmon resonance-enhanced photocatalysis[J]. Advanced Functional Materials, 23, 1612-1619(2013). http://onlinelibrary.wiley.com/doi/10.1002/adfm.201202148/full

[19] Liu Z W, Hou W B, Pavaskar P et al. Plasmon resonant enhancement of photocatalytic water splitting under visible illumination[J]. Nano Letters, 11, 1111-1116(2011). http://pubs.acs.org/doi/abs/10.1021/nl104005n

[20] Sun M T, Xu H X. A novel application of plasmonics: plasmon-driven surface-catalyzed reactions[J]. Small, 8, 2777-2786(2012). http://www.ncbi.nlm.nih.gov/pubmed/22777813

[21] Ding S Y, Yi J, Li J F et al. Nanostructure-based plasmon-enhanced Raman spectroscopy for surface analysis of materials[J]. Nature Reviews Materials, 1, 16021(2016). http://www.nature.com/articles/natrevmats201636

[22] Hartmann N, Piatkowski D, Ciesielski R et al. Radiation channels close to a plasmonic nanowire visualized by back focal plane imaging[J]. ACS Nano, 7, 10257-10262(2013). http://europepmc.org/abstract/med/24131299

[23] Akselrod G M, Argyropoulos C, Hoang T B et al. Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas[J]. Nature Photonics, 8, 835-840(2014). http://www.nature.com/nphoton/journal/v8/n11/nphoton.2014.228/metrics

[24] Akselrod G M, Ming T, Argyropoulos C et al. Leveraging nanocavity harmonics for control of optical processes in 2D semiconductors[J]. Nano Letters, 15, 3578-3584(2015). http://europepmc.org/abstract/MED/25914964

[25] Wei H, Pan D, Zhang S P et al. Plasmon waveguiding in nanowires[J]. Chemical Reviews, 118, 2882-2926(2018). http://www.ncbi.nlm.nih.gov/pubmed/29446301

[26] Fang Y R, Sun M T. Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits[J]. Light: Science & Applications, 4, e294(2015). http://www.nature.com/articles/lsa201567

[27] Pyayt A L, Wiley B, Xia Y N et al. Integration of photonic and silver nanowire plasmonic waveguides[J]. Nature Nanotechnology, 3, 660-665(2008). http://www.nature.com/nnano/journal/v3/n11/abs/nnano.2008.281.html

[28] Liu Y M, Palomba S, Park Y et al. Compact magnetic antennas for directional excitation of surface plasmons[J]. Nano Letters, 12, 4853-4858(2012).

[29] Wei H, Wang Z X, Tian X R et al. Cascaded logic gates in nanophotonic plasmon networks[J]. Nature Communications, 2, 387(2011). http://pubmedcentralcanada.ca/pmcc/articles/PMC3144585/

[30] Mühlschlegel P, Eisler H J. Martin O J F, et al. Resonant optical antennas[J]. Science, 308, 1607-1609(2005).

[31] Celebrano M, Wu X F, Baselli M et al. Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation[J]. Nature Nanotechnology, 10, 412-417(2015). http://europepmc.org/abstract/MED/25895003

[32] Cai W, Vasudev A P, Brongersma M L. Electrically controlled nonlinear generation of light with plasmonics[J]. Science, 333, 1720-1723(2011). http://europepmc.org/abstract/med/21940887

[33] Zayats A V, Smolyaninov I I, Maradudin A A. Nano-optics of surface plasmon polaritons[J]. Physics Reports, 408, 131-314(2005). http://www.sciencedirect.com/science/article/pii/S0370157304004600

[34] Maiman T H. Stimulated optical radiation in ruby[J]. Nature, 187, 493-494(1960). http://www.nature.com/nature/journal/v187/n4736/abs/187493a0.html

[35] Franken P A, Hill A E, Peters C W et al. Generation of optical harmonics[J]. Physical Review Letters, 7, 118-119(1961).

[36] Shen Y R. 50 years of nonlinear optics[J]. Physics, 41, 71-81(2012).

[37] Wurtz G A, Pollard R, Zayats A V. Optical bistability in nonlinear surface-plasmon polaritonic crystals[J]. Physical Review Letters, 97, 057402(2006). http://www.ncbi.nlm.nih.gov/pubmed/17026140

[38] Wurtz G A, Zayats A V. Nonlinear surface plasmon polaritonic crystals[J]. Laser & Photonics Reviews, 2, 125-135(2008). http://onlinelibrary.wiley.com/doi/10.1002/lpor.200810006/full

[39] Pu Y, Grange R, Hsieh C L et al. Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation[J]. Physical Review Letters, 104, 207402(2010). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=VIRT01000021000022000037000001&idtype=cvips&gifs=Yes

[40] Park I Y, Kim S, Choi J et al. Plasmonic generation of ultrashort extreme-ultraviolet light pulses[J]. Nature Photonics, 5, 677-681(2011). http://www.nature.com/nphoton/journal/v5/n11/abs/nphoton.2011.258.html

[41] Mesch M, Metzger B, Hentschel M et al. Nonlinear plasmonic sensing[J]. Nano Letters, 16, 3155-3159(2016).

[42] Yu R W. Cox J D, de Abajo F J G. Nonlinear plasmonic sensing with nanographene[J]. Physical Review Letters, 117, 123904(2016).

[43] Butet J, Russier-Antoine I, Jonin C et al. Sensing with multipolar second harmonic generation from spherical metallic nanoparticles[J]. Nano Letters, 12, 1697-1701(2012). http://pubs.acs.org/doi/abs/10.1021/nl300203u

[44] Butet J, Thyagarajan K. Martin O J F. Ultrasensitive optical shape characterization of gold nanoantennas using second harmonic generation[J]. Nano Letters, 13, 1787-1792(2013). http://pubs.acs.org/doi/abs/10.1021/nl400393e

[45] Thyagarajan K, Rivier S, Lovera A et al. Enhanced second-harmonic generation from double resonant plasmonic antennae[J]. Optics Express, 20, 12860-12865(2012). http://www.sciencedirect.com/science/article/pii/S1751722212000492

[46] Wang B L, Wang R, Liu R J et al. Origin of shape resonance in second-harmonic generation from metallic nanohole arrays[J]. Scientific Reports, 3, 2358(2013). http://www.ncbi.nlm.nih.gov/pubmed/23912881

[47] Aouani H, Navarro-Cia M, Rahmani M et al. Multiresonant broadband optical antennas as efficient tunable nanosources of second harmonic light[J]. Nano Letters, 12, 4997-5002(2012). http://www.ncbi.nlm.nih.gov/pubmed/22916834

[48] Zhang S, Li G C, Chen Y Q et al. Pronounced Fano resonance in single gold split nanodisks with 15 nm split gaps for intensive second harmonic generation[J]. ACS Nano, 10, 11105-11114(2016). http://www.ncbi.nlm.nih.gov/pubmed/28024358

[49] Liu S D. Leong E S P, Li G C, et al. Polarization-independent multiple Fano resonances in plasmonic nonamers for multimode-matching enhanced multiband second-harmonic generation[J]. ACS Nano, 10, 1442-1453(2016).

[50] Bachelier G, Butet J, Russier-Antoine I et al. Origin of optical second-harmonic generation in spherical gold nanoparticles: local surface and nonlocal bulk contributions[J]. Physical Review B, 82, 235403(2010). http://arxiv.org/abs/1107.3708v1

[51] Butet J, Duboisset J, Bachelier G et al. Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium[J]. Nano Letters, 10, 1717-1721(2010). http://www.ncbi.nlm.nih.gov/pubmed/20420409

[52] Czaplicki R, Zdanowicz M, Koskinen K et al. Dipole limit in second-harmonic generation from arrays of gold nanoparticles[J]. Optics Express, 19, 26866-26871(2011). http://europepmc.org/abstract/MED/22274269

[53] Valev V K, Smisdom N, Silhanek A V et al. Plasmonic ratchet wheels: switching circular dichroism by arranging chiral nanostructures[J]. Nano Letters, 9, 3945-3948(2009). http://europepmc.org/abstract/MED/19863052

[54] Linden S. Niesler F B P, Förstner J, et al. Collective effects in second-harmonic generation from split-ring-resonator arrays[J]. Physical Review Letters, 109, 015502(2012).

[55] Zhang Y, Grady N K, Ayala-Orozco C et al. Three-dimensional nanostructures as highly efficient generators of second harmonic light[J]. Nano Letters, 11, 5519-5523(2011). http://pubs.acs.org/doi/abs/10.1021/nl2033602

[56] Min C J, Wang P, Chen C C et al. All-optical switching in subwavelength metallic grating structure containing nonlinear optical materials[J]. Optics Letters, 33, 869-871(2008). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=VIRT05000007000006000152000001&idtype=cvips&gifs=Yes

[57] Min C J, Wang P, Jiao X J et al. Beam manipulating by metallic nano-optic lens containing nonlinear media[J]. Optics Express, 15, 9541-9546(2007). http://www.tandfonline.com/servlet/linkout?suffix=CIT0013&dbid=16&doi=10.1080%2F09500340.2015.1111453&key=10.1364%2FOE.15.009541

[58] Shi J W, Liang W Y, Raja S S et al. Plasmonic enhancement and manipulation of optical nonlinearity in monolayer tungsten disulfide[J]. Laser & Photonics Reviews, 12, 1800188(2018).

[59] Shen Q X, Hoang T B, Yang G C et al. Probing the origin of highly-efficient third-harmonic generation in plasmonic nanogaps[J]. Optics Express, 26, 20718-20725(2018). http://meetings.aps.org/Meeting/MAR18/Session/K07.3

[60] Chen J W, Wang K, Long H et al. Tungsten disulfide-gold nanohole hybrid metasurfaces for nonlinear metalenses in the visible region[J]. Nano Letters, 18, 1344-1350(2018). http://pubs.acs.org/doi/10.1021/acs.nanolett.7b05033

[61] Shi J J, Li Y, Kang M et al. Efficient second harmonic generation in a hybrid plasmonic waveguide by mode interactions[J]. Nano Letters, 19, 3838-3845(2019).

[62] Guo T J, Jin B Y, Argyropoulos C. Hybrid graphene-plasmonic gratings to achieve enhanced nonlinear effects at terahertz frequencies[J]. Physical Review Applied, 11, 024050(2019). http://www.onacademic.com/detail/journal_1000041623515799_3805.html

[63] Wen X L, Xu W G, Zhao W J et al. Plasmonic hot carriers-controlled second harmonic generation in WSe2 bilayers[J]. Nano Letters, 18, 1686-1692(2018). http://www.ncbi.nlm.nih.gov/pubmed/29376381

[64] Ding S J, Luo Z J, Xie Y M et al. Strong magnetic resonances and largely enhanced second-harmonic generation of colloidal MoS2 and ReS2@Au nanoantennas with assembled 2D nanosheets[J]. Nanoscale, 10, 124-131(2018). http://www.ncbi.nlm.nih.gov/pubmed/29231226

[65] Liu X F, Zhang Q, Chong W K et al. Cooperative enhancement of second-harmonic generation from a single CdS nanobelt-hybrid plasmonic structure[J]. ACS Nano, 9, 5018-5026(2015). http://europepmc.org/abstract/MED/25905978

[66] Ren M L, Liu W J, Aspetti C O et al. Enhanced second-harmonic generation from metal-integrated semiconductor nanowires via highly confined whispering gallery modes[J]. Nature Communications, 5, 5432(2014). http://europepmc.org/abstract/MED/25388766

[67] Li Y L, Rao Y, Mak K F et al. Probing symmetry properties of few-layer MoS2 and h-BN by optical second-harmonic generation[J]. Nano Letters, 13, 3329-3333(2013). http://pubs.acs.org/doi/abs/10.1021/nl401561r

[68] Malard L M, Alencar T V. Barboza A P M, et al. Observation of intense second harmonic generation from MoS2 atomic crystals[J]. Physical Review B, 87, 201401(2013). http://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.201401

[69] Kumar N, Najmaei S, Cui Q N et al. Second harmonic microscopy of monolayer MoS2[J]. Physical Review B, 87, 161403(2013).

[70] Mukherjee S, Libisch F, Large N et al. Hot electrons do the impossible: plasmon-induced dissociation of H2 on Au[J]. Nano Letters, 13, 240-247(2013). http://europepmc.org/abstract/MED/23194158

[71] Zhang C, Zhao H Q, Zhou L N et al. Al-Pd nanodisk heterodimers as antenna-reactor photocatalysts[J]. Nano Letters, 16, 6677-6682(2016). http://www.ncbi.nlm.nih.gov/pubmed/27676189

[72] Baumberg J J, Lagoudakis P G. Parametric amplification and polariton liquids in semiconductor microcavities[J]. Physica Status Solidi (b), 242, 2210-2223(2005). http://onlinelibrary.wiley.com/doi/10.1002/pssb.200560960/full

[73] Savvidis P G, Ciuti C, Baumberg J J et al. Off-branch polaritons and multiple scattering in semiconductor microcavities[J]. Physical Review B, 64, 075311(2001). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRBMDO000064000007075311000001&idtype=cvips&gifs=Yes

[74] Wouters M, Carusotto I. Parametric oscillation threshold of semiconductor microcavities in the strong coupling regime[J]. Physical Review B, 75, 075332(2007). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRBMDO000075000007075332000001&idtype=cvips&gifs=Yes

[75] Saba M, Ciuti C, Bloch J et al. High-temperature ultrafast polariton parametric amplification in semiconductor microcavities[J]. Nature, 414, 731-735(2001). http://palgrave.nature.com/nature/journal/v414/n6865/abs/414731a.html

[76] Sich M, Krizhanovskii D N, Skolnick M S et al. Observation of bright polariton solitons in a semiconductor microcavity[J]. Nature Photonics, 6, 50-55(2012). http://www.nature.com/nphoton/journal/v6/n1/nphoton.2011.267/metrics/

[77] Sanvitto D, Marchetti F M, Szymańska M H et al. Persistent currents and quantized vortices in a polariton superfluid[J]. Nature Physics, 6, 527-533(2010). http://www.nature.com/nphys/journal/v6/n7/abs/nphys1668.html

[78] Baas A, Karr J P, Eleuch H et al. Optical bistability in semiconductor microcavities[J]. Physical Review A, 69, 023809(2004). http://prola.aps.org/abstract/PRA/v69/i2/e023809

[79] Baas A, Karr J P, Romanelli M et al. Optical bistability in semiconductor microcavities in the nondegenerate parametric oscillation regime: analogy with the optical parametric oscillator[J]. Physical Review B, 70, 161307(2004). http://arxiv.org/abs/cond-mat/0407553

[80] Karr J P, Baas A, Houdré R et al. Publisher's note: squeezing in semiconductor microcavities in the strong-coupling regime [Phys. Rev. A69, 031802 (2004)][J]. Physical Review A, 69, 069901(2004). http://adsabs.harvard.edu/abs/2004PhRvA..69f9901K

[81] Chervy T, Xu J L, Duan Y L et al. High-efficiency second-harmonic generation from hybrid light-matter states[J]. Nano Letters, 16, 7352-7356(2016). http://pubs.acs.org/doi/abs/10.1021/acs.nanolett.6b02567

[82] Pimenta A C S, Faria L C, González J C et al. . Nonlinear optical effects with polariton lasers in a GaAs microcavity[J]. The Journal of Physical Chemistry C, 122, 17501-17506(2018). http://pubs.acs.org/doi/10.1021/acs.jpcc.8b02803

[83] Barachati F, Simon J, Getmanenko Y A et al. Tunable third-harmonic generation from polaritons in the ultrastrong coupling regime[J]. ACS Photonics, 5, 119-125(2018). http://pubs.acs.org/doi/10.1021/acsphotonics.7b00305

[84] Lassiter J B, Chen X S, Liu X J et al. Third-harmonic generation enhancement by film-coupled plasmonic stripe resonators[J]. ACS Photonics, 1, 1212-1217(2014). http://pubs.acs.org/doi/abs/10.1021/ph500276v

[85] Metzger B, Hentschel M, Schumacher T et al. Doubling the efficiency of third harmonic generation by positioning ITO nanocrystals into the hot-spot of plasmonic gap-antennas[J]. Nano Letters, 14, 2867-2872(2014). http://europepmc.org/abstract/med/24730433

[86] Halas N J, Lal S, Chang W S et al. Plasmons in strongly coupled metallic nanostructures[J]. Chemical Reviews, 111, 3913-3961(2011). http://europepmc.org/abstract/med/21542636

[87] Baumberg J J, Aizpurua J, Mikkelsen M H et al. Extreme nanophotonics from ultrathin metallic gaps[J]. Nature Materials, 18, 668-678(2019).

[88] Chikkaraddy R, de Nijs B, Benz F et al. . Single-molecule strong coupling at room temperature in plasmonic nanocavities[J]. Nature, 535, 127-130(2016). http://www.nature.com/nature/journal/v535/n7610/nature17974/metrics

[89] Tserkezis C, Esteban R, Sigle D O et al. Hybridization of plasmonic antenna and cavity modes: extreme optics of nanoparticle-on-mirror nanogaps[J]. Physical Review A, 92, 053811(2015). http://adsabs.harvard.edu/abs/2015PhRvA..92e3811T

[90] Chen W, Zhang S P, Kang M et al. Probing the limits of plasmonic enhancement using a two-dimensional atomic crystal probe[J]. Light: Science & Applications, 7, 56(2018).

[91] Chen W, Zhang S P, Deng Q et al. Probing of sub-picometer vertical differential resolutions using cavity plasmons[J]. Nature Communications, 9, 801(2018). http://www.nature.com/articles/s41467-018-03227-7

[92] Ciracì C, Hill R T, Mock J J et al. Probing the ultimate limits of plasmonic enhancement[J]. Science, 337, 1072-1074(2012). http://www.jstor.org/stable/23268963

[93] Lassiter J B. McGuire F, Mock J J, et al. Plasmonic waveguide modes of film-coupled metallic nanocubes[J]. Nano Letters, 13, 5866-5872(2013).

[94] Shen S X, Meng L Y, Zhang Y J et al. Plasmon-enhanced second-harmonic generation nanorulers with ultrahigh sensitivities[J]. Nano Letters, 15, 6716-6721(2015). http://www.ncbi.nlm.nih.gov/pubmed/26372425

[95] Hajisalem G, Nezami M S, Gordon R. Probing the quantum tunneling limit of plasmonic enhancement by third harmonic generation[J]. Nano Letters, 14, 6651-6654(2014). http://www.ncbi.nlm.nih.gov/pubmed/25322471

[96] Marinica D C, Kazansky A K, Nordlander P et al. Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer[J]. Nano Letters, 12, 1333-1339(2012). http://europepmc.org/abstract/MED/22320125

[97] Wang Z, Dong Z G, Zhu H et al. Selectively plasmon-enhanced second-harmonic generation from monolayer tungsten diselenide on flexible substrates[J]. ACS Nano, 12, 1859-1867(2018). http://pubs.acs.org/doi/10.1021/acsnano.7b08682

[98] Aouani H, Rahmani M, Navarro-Cía M et al. Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna[J]. Nature Nanotechnology, 9, 290-294(2014). http://europepmc.org/abstract/med/24608232

[99] Yan R X, Gargas D, Yang P D. Nanowire photonics[J]. Nature Photonics, 3, 569-576(2009).

[100] Wang J F, Gudiksen M S, Duan X F et al. Highly polarized photoluminescence and photodetection from single indium phosphide nanowires[J]. Science, 293, 1455-1457(2001). http://www.ncbi.nlm.nih.gov/pubmed/11520977

[101] Hayden O, Agarwal R, Lieber C M. Nanoscale avalanche photodiodes for highly sensitive and spatially resolved photon detection[J]. Nature Materials, 5, 352-356(2006). http://europepmc.org/abstract/MED/16617344

[102] Law M, Sirbuly D J, Johnson J C et al. Nanoribbon waveguides for subwavelength photonics integration[J]. Science, 305, 1269-1273(2004). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=VIRT01000010000010000060000001&idtype=cvips&gifs=Yes

[103] Duan X F, Huang Y, Agarwal R et al. Single-nanowire electrically driven lasers[J]. Nature, 421, 241-245(2003). http://www.ncbi.nlm.nih.gov/pubmed/12529637

[104] Johnson J C, Choi H J, Knutsen K P et al. Single gallium nitride nanowire lasers[J]. Nature Materials, 1, 106-110(2002). http://www.ncbi.nlm.nih.gov/pubmed/12618824

[105] Moss D J, Morandotti R, Gaeta A L et al. New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics[J]. Nature Photonics, 7, 597-607(2013). http://www.nature.com/nphoton/journal/v7/n8/abs/nphoton.2013.183.html

[106] Oulton R F, Sorger V J, Genov D A et al. A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation[J]. Nature Photonics, 2, 496-500(2008). http://www.nature.com/nphoton/journal/v2/n8/abs/nphoton.2008.131.html

[107] Suchowski H. O'Brien K, Wong Z J, et al. Phase mismatch-free nonlinear propagation in optical zero-index materials[J]. Science, 342, 1223-1226(2013).

[108] Lan S F, Kang L, Schoen D T et al. Backward phase-matching for nonlinear optical generation in negative-index materials[J]. Nature Materials, 14, 807-811(2015). http://www.nature.com/nmat/journal/v14/n8/abs/nmat4324.html

[109] Yin H Z. Surface plasmonic for nonlinear optical conversion[D]. Beijing: Beijing University of Posts and Telecommunications(2014).

[110] Viarbitskaya S, Demichel O, Cluzel B et al. Delocalization of nonlinear optical responses in plasmonic nanoantennas[J]. Physical Review Letters, 115, 197401(2015). http://www.ncbi.nlm.nih.gov/pubmed/26588413

[111] Grosse N B, Heckmann J, Woggon U. Nonlinear plasmon-photon interaction resolved by k-space spectroscopy[J]. Physical Review Letters, 108, 136802(2012).

[112] de Hoogh A, Opheij A, Wulf M et al. . Harmonics generation by surface plasmon polaritons on single nanowires[J]. ACS Photonics, 3, 1446-1452(2016). http://pubs.acs.org/doi/abs/10.1021/acsphotonics.5b00686

[113] Chen C K, Shen Y R. Coherent second-harmonic generation by counterpropagating surface plasmons[J]. Optics Letters, 4, 393-394(1979). http://europepmc.org/abstract/MED/19687915

[114] Li Y, Kang M, Shi J J et al. Transversely divergent second harmonic generation by surface plasmon polaritons on single metallic nanowires[J]. Nano Letters, 17, 7803-7808(2017). http://www.ncbi.nlm.nih.gov/pubmed/29140716

[115] Sederberg S, Elezzabi A Y. Coherent visible-light-generation enhancement in silicon-based nanoplasmonic waveguides via third-harmonic conversion[J]. Physical Review Letters, 114, 227401(2015). http://www.ncbi.nlm.nih.gov/pubmed/26196643

[116] Nielsen M P, Shi X Y, Dichtl P et al. Giant nonlinear response at a plasmonic nanofocus drives efficient four-wave mixing[J]. Science, 358, 1179-1181(2017). http://europepmc.org/abstract/MED/29191907

[117] Bonaccorso F, Sun Z, Hasan T et al. Graphene photonics and optoelectronics[J]. Nature Photonics, 4, 611-622(2010).

[118] Mikhailov S A. Non-linear electromagnetic response of graphene[J]. Europhysics Letters (EPL), 79, 27002(2007).

[119] Ishikawa K L. Nonlinear optical response of graphene in time domain[J]. Physical Review B, 82, 201402(2010). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=VIRT01000022000020000051000001&idtype=cvips&gifs=Yes

[120] Grigorenko A N, Polini M, Novoselov K S. Graphene plasmonics[J]. Nature Photonics, 6, 749-758(2012).

[122] Low T, Avouris P. Graphene plasmonics for terahertz to mid-infrared applications[J]. ACS Nano, 8, 1086-1101(2014). http://pubs.acs.org/doi/abs/10.1021/nn406627u

[123] Hendry E, Hale P J, Moger J et al. Coherent nonlinear optical response of graphene[J]. Physical Review Letters, 105, 097401(2010). http://www.ncbi.nlm.nih.gov/pubmed/20868195/

[124] Gullans M, Chang D E. Koppens F H L, et al. Single-photon nonlinear optics with graphene plasmons[J]. Physical Review Letters, 111, 247401(2013).

[125] Mikhailov S A. Theory of the giant plasmon-enhanced second-harmonic generation in graphene and semiconductor two-dimensional electron systems[J]. Physical Review B, 84, 045432(2011). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=VIRT01000024000005000060000001&idtype=cvips&gifs=Yes

[126] Smirnova D A, Shadrivov I V, Miroshnichenko A E et al. Second-harmonic generation by a graphene nanoparticle[J]. Physical Review B, 90, 035412(2014). http://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.035412

[127] Manzoni M T. Silveiro I, de Abajo F J G, et al. Second-order quantum nonlinear optical processes in single graphene nanostructures and arrays[J]. New Journal of Physics, 17, 083031(2015).

[128] Weismann M, Panoiu N C. Theoretical and computational analysis of second- and third-harmonic generation in periodically patterned graphene and transition-metal dichalcogenide monolayers[J]. Physical Review B, 94, 035435(2016). http://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.035435

[129] Hong S Y, Dadap J I, Petrone N et al. Optical third-harmonic generation in graphene[J]. Physical Review X, 3, 021014(2013).

[130] You J W, You J, Weismann M et al. Double-resonant enhancement of third-harmonic generation in graphene nanostructures[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 375, 20160313(2017). http://europepmc.org/abstract/MED/28220005

[131] Cox J D. Electrically tunable nonlinear plasmonics in graphene nanoislands[J]. Nature Communications, 5, 5725(2014). http://www.nature.com/ncomms/2014/141211/ncomms6725/abs/ncomms6725.html

[132] Cox J D. Plasmon-enhanced nonlinear wave mixing in nanostructured graphene[J]. ACS Photonics, 2, 306-312(2015). http://pubs.acs.org/doi/abs/10.1021/ph500424a

[133] Cox J D. Marini A, de Abajo F J G. Plasmon-assisted high-harmonic generation in graphene[J]. Nature Communications, 8, 14380(2017).