Second harmonic generation based on strong field enhancement in nanostructured THz materials

doi:10.1364/OE.19.007262

Second harmonic generation based on strong field enhancement in nanostructured THz materials

Hannes Merbold, Andreas Bitzer, and Thomas Feurer »View Author Affiliations

Optics Express, Vol. 19, Issue 8, pp. 7262-7273 (2011)
http://dx.doi.org/10.1364/OE.19.007262

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Abstract

The THz response of slit structures and split-ring resonators (SRRs) featuring extremely small gaps on the micro- or nanoscale is investigated numerically. Both structures exhibit strong field enhancement in the gap region due to light-induced current flows and capacitive charging across the gap. Whereas nanoslits allow for broadband enhancement the resonant behavior of the SRRs leads to narrowband amplification and results in significantly higher field enhancement factors reaching several 10,000. This property is particularly beneficial for the realization of nonlinear THz experiments which is exemplarily demonstrated by a second harmonic generation process in a nonlinear substrate material. Positioning nanostructures on top of the substrate is found to result in a significant increase of the generation efficiency for the frequency doubled component.

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(190.4360) Nonlinear optics : Nonlinear optics, devices
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Nonlinear Optics

History
Original Manuscript: February 17, 2011
Revised Manuscript: March 12, 2011
Manuscript Accepted: March 13, 2011
Published: March 31, 2011

Citation
Hannes Merbold, Andreas Bitzer, and Thomas Feurer, "Second harmonic generation based on strong field enhancement in nanostructured THz materials," Opt. Express 19, 7262-7273 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7262

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References

G. P. Williams, “Filling the THz gap-high power sources and applications,” Rep. Prog. Phys. 69, 301 (2006). [CrossRef]
E. Budiarto, J. Margolies, S. Jeong, and J. Song, “High-intensity terahertz pulses at 1-kHz repetition rate,” IEEE J. Quantum Electron. 32, 1839 (1996).
T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805–2807 (2005). [CrossRef] [PubMed]
K. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007). [CrossRef]
M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156 (2009). [CrossRef]
H. R. Park, Y. M. Park, H. S. Kim, J. S. Kyoung, M. A. Seo, D. J. Park, Y. H. Ahn, K. J. Ahn, and D. S. Kim, “Terahertz nanoresonators: Giant field enhancement and ultrabroadband performance,” Appl. Phys. Lett. 96, 121106 (2010). [CrossRef]
J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999). [CrossRef]
S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004). [CrossRef] [PubMed]
J. Jin, The Finite Element Method in Electromagnetics , 2nd ed. (Wiley-IEEE Press, 2002).
COMSOL Multiphysics 3.5.
M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24, 4493–4499 (1985). [CrossRef] [PubMed]
N. Laman and D. Grischkowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93, 051105 (2008). [CrossRef]
M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A, Pure Appl. Opt. 7, S12–S22 (2005). [CrossRef]
A. Bitzer, J. Wallauer, H. Helm, H. Merbold, T. Feurer, and M. Walther, “Lattice modes mediate radiative coupling in metamaterial arrays,” Opt. Express 17, 22108–22113 (2009). [CrossRef] [PubMed]
P. Gay-Balmaz and O. J. F. Martin, “Electromagnetic resonances in individual and coupled split-ring resonators,” J. Appl. Phys. 92, 2929–2936 (2002). [CrossRef]
N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004). [CrossRef]
S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010). [CrossRef] [PubMed]
J. García-García, F. Martín, J. D. Baena, R. Marqués, and L. Jelinek, “On the resonances and polarizabilities of split ring resonators,” J. Appl. Phys. 98, 033103 (2005). [CrossRef]
M. Shalaby, H. Merbold, M. Peccianti, L. Razzari, G. Sharma, R. Morandotti, T. Ozaki, T. Feurer, A. Weber, L. Heyderman, H. Sigg, and B. Patterson, “Concurrent field enhancement and high transmission of THz radiation in nanoslit arrays,” in preparation (2011).
D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006). [CrossRef] [PubMed]
J. Kyoung, M. Seo, H. Park, S. Koo, H. sun Kim, Y. Park, B.-J. Kim, K. Ahn, N. Park, H.-T. Kim, and D.-S. Kim, “Giant nonlinear response of terahertz nanoresonators on VO2 thin film,” Opt. Express 18, 16452–16459 (2010). [CrossRef] [PubMed]
S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008). [CrossRef] [PubMed]
T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Satz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37, 317–350 (2007). [CrossRef]
M. C. Hoffmann, N. C. Brandt, H. Y. Hwang, K. Yeh, and K. A. Nelson, “Terahertz Kerr effect,” Appl. Phys. Lett. 95, 231105 (2009). [CrossRef]
H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007). [CrossRef]
I. Inbar and R. E. Cohen, “Comparison of the electronic structures and energetics of ferroelectric LiNbO3 and LiTaO3,” Phys. Rev. B 53, 1193 (1996). [CrossRef]
V. Romero-Rochin, R. M. Koehl, C. J. Brennan, and K. A. Nelson, “Anharmonic phonon-polariton excitation through impulsive stimulated Raman scattering and detection through wave vector overtone spectroscopy: theory and comparison to experiments on lithium tantalate,” J. Chem. Phys. 11, 3559 (1999). [CrossRef]
R. W. Boyd, Nonlinear Optics , 1st ed. (Academic Press, 1992).
D. W. Ward, “Polaritonics: An Intermediate Regime Between Electronics and Photonics,” Ph.D. thesis, Department of Chemistry – Massachusetts Institute of Technology (2005).
H. Boysen and F. Altorfer, “A neutron powder investigation of the high-temperature structure and phase transition in LiNbO3,” Acta Crystallogr., Sect. B 50, 405 (1994). [CrossRef]
R. Hsu, E. N. Maslen, D. du Boulay, and N. Ishizawa, “Synchrotron X-ray Studies of LiNbO3 and LiTaO3,” Acta Crystallogr., Sect. B 53, 420 (1997). [CrossRef]

Acta Crystallogr., Sect. B

H. Boysen and F. Altorfer, “A neutron powder investigation of the high-temperature structure and phase transition in LiNbO3,” Acta Crystallogr., Sect. B 50, 405 (1994). [CrossRef]
R. Hsu, E. N. Maslen, D. du Boulay, and N. Ishizawa, “Synchrotron X-ray Studies of LiNbO3 and LiTaO3,” Acta Crystallogr., Sect. B 53, 420 (1997). [CrossRef]

Annu. Rev. Mater. Res.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Satz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37, 317–350 (2007). [CrossRef]

Appl. Opt.

M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24, 4493–4499 (1985). [CrossRef] [PubMed]

Appl. Phys. Lett.

N. Laman and D. Grischkowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93, 051105 (2008). [CrossRef]
N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004). [CrossRef]
K. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007). [CrossRef]
H. R. Park, Y. M. Park, H. S. Kim, J. S. Kyoung, M. A. Seo, D. J. Park, Y. H. Ahn, K. J. Ahn, and D. S. Kim, “Terahertz nanoresonators: Giant field enhancement and ultrabroadband performance,” Appl. Phys. Lett. 96, 121106 (2010). [CrossRef]
M. C. Hoffmann, N. C. Brandt, H. Y. Hwang, K. Yeh, and K. A. Nelson, “Terahertz Kerr effect,” Appl. Phys. Lett. 95, 231105 (2009). [CrossRef]

IEEE J. Quantum Electron.

E. Budiarto, J. Margolies, S. Jeong, and J. Song, “High-intensity terahertz pulses at 1-kHz repetition rate,” IEEE J. Quantum Electron. 32, 1839 (1996).

IEEE Trans. Microwave Theory Tech.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999). [CrossRef]

J. Appl. Phys.

P. Gay-Balmaz and O. J. F. Martin, “Electromagnetic resonances in individual and coupled split-ring resonators,” J. Appl. Phys. 92, 2929–2936 (2002). [CrossRef]
J. García-García, F. Martín, J. D. Baena, R. Marqués, and L. Jelinek, “On the resonances and polarizabilities of split ring resonators,” J. Appl. Phys. 98, 033103 (2005). [CrossRef]

J. Chem. Phys.

V. Romero-Rochin, R. M. Koehl, C. J. Brennan, and K. A. Nelson, “Anharmonic phonon-polariton excitation through impulsive stimulated Raman scattering and detection through wave vector overtone spectroscopy: theory and comparison to experiments on lithium tantalate,” J. Chem. Phys. 11, 3559 (1999). [CrossRef]

J. Opt. A, Pure Appl. Opt.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A, Pure Appl. Opt. 7, S12–S22 (2005). [CrossRef]

Nanotechnology

S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010). [CrossRef] [PubMed]

Nat. Photonics

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156 (2009). [CrossRef]

Nature

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008). [CrossRef] [PubMed]

Opt. Express

Opt. Lett.

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805–2807 (2005). [CrossRef] [PubMed]

Phys. Rev. B

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007). [CrossRef]
I. Inbar and R. E. Cohen, “Comparison of the electronic structures and energetics of ferroelectric LiNbO3 and LiTaO3,” Phys. Rev. B 53, 1193 (1996). [CrossRef]

Rep. Prog. Phys.

G. P. Williams, “Filling the THz gap-high power sources and applications,” Rep. Prog. Phys. 69, 301 (2006). [CrossRef]

Science

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004). [CrossRef] [PubMed]
D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006). [CrossRef] [PubMed]

Other

M. Shalaby, H. Merbold, M. Peccianti, L. Razzari, G. Sharma, R. Morandotti, T. Ozaki, T. Feurer, A. Weber, L. Heyderman, H. Sigg, and B. Patterson, “Concurrent field enhancement and high transmission of THz radiation in nanoslit arrays,” in preparation (2011).
R. W. Boyd, Nonlinear Optics , 1st ed. (Academic Press, 1992).
D. W. Ward, “Polaritonics: An Intermediate Regime Between Electronics and Photonics,” Ph.D. thesis, Department of Chemistry – Massachusetts Institute of Technology (2005).
J. Jin, The Finite Element Method in Electromagnetics , 2nd ed. (Wiley-IEEE Press, 2002).
COMSOL Multiphysics 3.5.

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[1] G. P. Williams, “Filling the THz gap-high power sources and applications,” Rep. Prog. Phys. 69, 301 (2006). [CrossRef]

[2] E. Budiarto, J. Margolies, S. Jeong, and J. Song, “High-intensity terahertz pulses at 1-kHz repetition rate,” IEEE J. Quantum Electron. 32, 1839 (1996).

[3] T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805–2807 (2005). [CrossRef] [PubMed]

[4] K. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90, 171121 (2007). [CrossRef]

[5] M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156 (2009). [CrossRef]

[6] H. R. Park, Y. M. Park, H. S. Kim, J. S. Kyoung, M. A. Seo, D. J. Park, Y. H. Ahn, K. J. Ahn, and D. S. Kim, “Terahertz nanoresonators: Giant field enhancement and ultrabroadband performance,” Appl. Phys. Lett. 96, 121106 (2010). [CrossRef]

[7] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999). [CrossRef]

[8] S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004). [CrossRef] [PubMed]

[9] J. Jin, The Finite Element Method in Electromagnetics , 2nd ed. (Wiley-IEEE Press, 2002).

[10] COMSOL Multiphysics 3.5.

[11] M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24, 4493–4499 (1985). [CrossRef] [PubMed]

[12] N. Laman and D. Grischkowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93, 051105 (2008). [CrossRef]

[13] M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A, Pure Appl. Opt. 7, S12–S22 (2005). [CrossRef]

[14] A. Bitzer, J. Wallauer, H. Helm, H. Merbold, T. Feurer, and M. Walther, “Lattice modes mediate radiative coupling in metamaterial arrays,” Opt. Express 17, 22108–22113 (2009). [CrossRef] [PubMed]

[15] P. Gay-Balmaz and O. J. F. Martin, “Electromagnetic resonances in individual and coupled split-ring resonators,” J. Appl. Phys. 92, 2929–2936 (2002). [CrossRef]

[16] N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004). [CrossRef]

[17] S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010). [CrossRef] [PubMed]

[18] J. García-García, F. Martín, J. D. Baena, R. Marqués, and L. Jelinek, “On the resonances and polarizabilities of split ring resonators,” J. Appl. Phys. 98, 033103 (2005). [CrossRef]

[19] M. Shalaby, H. Merbold, M. Peccianti, L. Razzari, G. Sharma, R. Morandotti, T. Ozaki, T. Feurer, A. Weber, L. Heyderman, H. Sigg, and B. Patterson, “Concurrent field enhancement and high transmission of THz radiation in nanoslit arrays,” in preparation (2011).

[20] D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006). [CrossRef] [PubMed]

[21] J. Kyoung, M. Seo, H. Park, S. Koo, H. sun Kim, Y. Park, B.-J. Kim, K. Ahn, N. Park, H.-T. Kim, and D.-S. Kim, “Giant nonlinear response of terahertz nanoresonators on VO2 thin film,” Opt. Express 18, 16452–16459 (2010). [CrossRef] [PubMed]

[22] S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008). [CrossRef] [PubMed]

[23] T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Satz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37, 317–350 (2007). [CrossRef]

[24] M. C. Hoffmann, N. C. Brandt, H. Y. Hwang, K. Yeh, and K. A. Nelson, “Terahertz Kerr effect,” Appl. Phys. Lett. 95, 231105 (2009). [CrossRef]

[25] H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007). [CrossRef]

[26] I. Inbar and R. E. Cohen, “Comparison of the electronic structures and energetics of ferroelectric LiNbO3 and LiTaO3,” Phys. Rev. B 53, 1193 (1996). [CrossRef]

[27] V. Romero-Rochin, R. M. Koehl, C. J. Brennan, and K. A. Nelson, “Anharmonic phonon-polariton excitation through impulsive stimulated Raman scattering and detection through wave vector overtone spectroscopy: theory and comparison to experiments on lithium tantalate,” J. Chem. Phys. 11, 3559 (1999). [CrossRef]

[28] R. W. Boyd, Nonlinear Optics , 1st ed. (Academic Press, 1992).

[29] D. W. Ward, “Polaritonics: An Intermediate Regime Between Electronics and Photonics,” Ph.D. thesis, Department of Chemistry – Massachusetts Institute of Technology (2005).

[30] H. Boysen and F. Altorfer, “A neutron powder investigation of the high-temperature structure and phase transition in LiNbO3,” Acta Crystallogr., Sect. B 50, 405 (1994). [CrossRef]

[31] R. Hsu, E. N. Maslen, D. du Boulay, and N. Ishizawa, “Synchrotron X-ray Studies of LiNbO3 and LiTaO3,” Acta Crystallogr., Sect. B 53, 420 (1997). [CrossRef]

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Second harmonic generation based on strong field enhancement in nanostructured THz materials

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Abstract

References

Acta Crystallogr., Sect. B

Annu. Rev. Mater. Res.

Appl. Opt.

Appl. Phys. Lett.

IEEE J. Quantum Electron.

IEEE Trans. Microwave Theory Tech.

J. Appl. Phys.

J. Chem. Phys.

J. Opt. A, Pure Appl. Opt.

Nanotechnology

Nat. Photonics

Nature

Opt. Express

Opt. Lett.

Phys. Rev. B

Rep. Prog. Phys.

Science

Other

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