Abstract

We theoretically propose an internal asymmetric plasmonic slot waveguide (IAPSW), containing two different materials in the slot region. The IAPSW is used for second harmonic generation (SHG) at a wavelength of 1.55 μm. The required phase matching condition is satisfied between the 0th-order mode at the fundamental frequency and the 1st-order mode at the second harmonic frequency. By choosing appropriate slot geometry and materials, the mode field distribution is engineered to enhance the nonlinear coupling coefficient for SHG. With an 11 μm long IAPSW, a conversion efficiency of 24% (1.8 × 105 W−1cm−2 normalized conversion efficiency) is predicted. Furthermore, the SHG efficiency is more pronounced in IAPSW with thinner slot.

© 2016 Optical Society of America

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References

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2015 (1)

2014 (5)

M. Mayy, G. Zhu, A. D. Webb, H. Ferguson, T. Norris, V. A. Podolskiy, and M. A. Noginov, “Toward parametric amplification in plasmonic systems: Second harmonic generation enhanced by surface plasmon polaritons,” Opt. Express 22(7), 7773–7782 (2014).
[Crossref] [PubMed]

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

Z. Zhang and J. Wang, “Long-range hybrid wedge plasmonic waveguide,” Sci. Rep. 4, 6870 (2014).
[Crossref] [PubMed]

A. Melikyan, M. Kohl, M. Sommer, C. Koos, W. Freude, and J. Leuthold, “Photonic-to-plasmonic mode converter,” Opt. Lett. 39(12), 3488–3491 (2014).
[Crossref] [PubMed]

I. Biaggio, V. Coda, and G. Montemezzani, “Coupling-length phase matching for nonlinear optical frequency conversion in parallel waveguides,” Phys. Rev. A 90(4), 043816 (2014).
[Crossref]

2013 (5)

2012 (2)

2011 (4)

2010 (2)

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics 4(8), 553–556 (2010).
[Crossref]

2009 (1)

2002 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Barz, S.

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics 4(8), 553–556 (2010).
[Crossref]

Biaggio, I.

I. Biaggio, V. Coda, and G. Montemezzani, “Coupling-length phase matching for nonlinear optical frequency conversion in parallel waveguides,” Phys. Rev. A 90(4), 043816 (2014).
[Crossref]

Bianco, F.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Borga, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Brambilla, G.

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

Cassan, E.

Cazzanelli, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Cheng, J.

Cheng, Q. Q.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Coda, V.

I. Biaggio, V. Coda, and G. Montemezzani, “Coupling-length phase matching for nonlinear optical frequency conversion in parallel waveguides,” Phys. Rev. A 90(4), 043816 (2014).
[Crossref]

Cronenberg, G.

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics 4(8), 553–556 (2010).
[Crossref]

Davoyan, A. R.

de Matos, C. J.

de Oliveira, R. E.

Degoli, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Fejer, M. M.

Ferguson, H.

Freude, W.

Fujimura, M.

Fürst, J.

G. Lin, J. Fürst, D. V. Strekalov, and N. Yu, “Wide-range cyclic phase matching and second harmonic generation in whispering gallery resonators,” Appl. Phys. Lett. 103(18), 181107 (2013).
[Crossref]

Gao, D.

Ghulinyan, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Hasan, S. B.

Hu, W.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Hu, X.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Hu, X. P.

Huang, T.

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Kauranen, M.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Khurgin, J. B.

Kivshar, Y. S.

Kohl, M.

Koos, C.

Kurz, J. R.

Lam, H. Q.

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

Lederer, F.

Lee, T.

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

Leuthold, J.

Li, L.

Li, T.

Lin, G.

G. Lin, J. Fürst, D. V. Strekalov, and N. Yu, “Wide-range cyclic phase matching and second harmonic generation in whispering gallery resonators,” Appl. Phys. Lett. 103(18), 181107 (2013).
[Crossref]

Lu, F. F.

Lu, Y.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Luppi, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Mayy, M.

Melikyan, A.

Modotto, D.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Montemezzani, G.

I. Biaggio, V. Coda, and G. Montemezzani, “Coupling-length phase matching for nonlinear optical frequency conversion in parallel waveguides,” Phys. Rev. A 90(4), 043816 (2014).
[Crossref]

Noginov, M. A.

Norris, T.

Ossicini, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Parameswaran, K. R.

Pavesi, L.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Pertsch, T.

Pierobon, R.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Podolskiy, V. A.

Pucker, G.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Qiao, G.

Rockstuhl, C.

Roussev, R. V.

Route, R. K.

Shadrivov, I. V.

Shao, X.

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

Shum, P. P.

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

Sommer, M.

Stockman, M. I.

Strekalov, D. V.

G. Lin, J. Fürst, D. V. Strekalov, and N. Yu, “Wide-range cyclic phase matching and second harmonic generation in whispering gallery resonators,” Appl. Phys. Lett. 103(18), 181107 (2013).
[Crossref]

Sun, G.

Sun, Y.

Y. Sun, Z. Zheng, J. Cheng, G. Sun, and G. Qiao, “Highly efficient second harmonic generation in hyperbolic metamaterial slot waveguides with large phase matching tolerance,” Opt. Express 23(5), 6370–6378 (2015).
[Crossref] [PubMed]

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

Véniard, V.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Wabnitz, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Walther, P.

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics 4(8), 553–556 (2010).
[Crossref]

Wang, J.

Z. Zhang and J. Wang, “Long-range hybrid wedge plasmonic waveguide,” Sci. Rep. 4, 6870 (2014).
[Crossref] [PubMed]

Webb, A. D.

Wu, T.

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

Wu, Z.

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Xie, Z. D.

Xu, F.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Xu, J.

Yu, N.

G. Lin, J. Fürst, D. V. Strekalov, and N. Yu, “Wide-range cyclic phase matching and second harmonic generation in whispering gallery resonators,” Appl. Phys. Lett. 103(18), 181107 (2013).
[Crossref]

Yu, Z.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Zeilinger, A.

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics 4(8), 553–556 (2010).
[Crossref]

Zhang, J.

Zhang, X.

Zhang, Z.

Z. Zhang and J. Wang, “Long-range hybrid wedge plasmonic waveguide,” Sci. Rep. 4, 6870 (2014).
[Crossref] [PubMed]

Zheng, Z.

Zhu, G.

Zhu, S. N.

Zhu, Y. Y.

Appl. Phys. Lett. (1)

G. Lin, J. Fürst, D. V. Strekalov, and N. Yu, “Wide-range cyclic phase matching and second harmonic generation in whispering gallery resonators,” Appl. Phys. Lett. 103(18), 181107 (2013).
[Crossref]

IEEE Photonics J. (1)

T. Huang, X. Shao, Z. Wu, T. Lee, T. Wu, Y. Sun, J. Zhang, H. Q. Lam, G. Brambilla, and P. P. Shum, “Efficient third-harmonic generation from 2 μm in asymmetric plasmonic slot waveguide,” IEEE Photonics J. 6(3), 4800607 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Mater. (1)

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Nat. Photonics (2)

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics 4(8), 553–556 (2010).
[Crossref]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Opt. Express (8)

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011).
[Crossref] [PubMed]

J. B. Khurgin and G. Sun, “Plasmonic enhancement of the third order nonlinear optical phenomena: figures of merit,” Opt. Express 21(22), 27460–27480 (2013).
[Crossref] [PubMed]

R. E. de Oliveira and C. J. de Matos, “Quasi-phase-matched second harmonic generation in silicon nitride ring resonators controlled by static electric field,” Opt. Express 21(26), 32690–32698 (2013).
[Crossref] [PubMed]

M. Mayy, G. Zhu, A. D. Webb, H. Ferguson, T. Norris, V. A. Podolskiy, and M. A. Noginov, “Toward parametric amplification in plasmonic systems: Second harmonic generation enhanced by surface plasmon polaritons,” Opt. Express 22(7), 7773–7782 (2014).
[Crossref] [PubMed]

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Quadratic phase matching in nonlinear plasmonic nanoscale waveguides,” Opt. Express 17(22), 20063–20068 (2009).
[Crossref] [PubMed]

J. Zhang, E. Cassan, D. Gao, and X. Zhang, “Highly efficient phase-matched second harmonic generation using an asymmetric plasmonic slot waveguide configuration in hybrid polymer-silicon photonics,” Opt. Express 21(12), 14876–14887 (2013).
[Crossref] [PubMed]

Y. Sun, Z. Zheng, J. Cheng, G. Sun, and G. Qiao, “Highly efficient second harmonic generation in hyperbolic metamaterial slot waveguides with large phase matching tolerance,” Opt. Express 23(5), 6370–6378 (2015).
[Crossref] [PubMed]

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Phys. Rev. A (1)

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 (a) 3D view and (b) cross-section view of the proposed IAPSW.
Fig. 2
Fig. 2 (a) Effective indices 0th-mode at FF and 1st-order mode at SHF with respected to the width of Si3N4, (b) Ey profile of 0th-mode at FF, and (c) 1st-mode at SHF.
Fig. 3
Fig. 3 (a) Ex distribution at x = 0 in an EAPSW [16], and Ey distribution at y = 0 in an IAPSW.
Fig. 4
Fig. 4 Si3N4 width to satisfy PMC with different total slot width and the corresponding NCC.
Fig. 5
Fig. 5 Optical power evolution of FF and SHF along propagation distance with 1 W pump power, and (b) peak efficiencies and their corresponding positions at different pump levels.
Fig. 6
Fig. 6 (a) Peak efficiencies and their corresponding peak positions, and (b) Normalized conversion efficiency at different PMC point with 1 W pump power.
Fig. 7
Fig. 7 Contour map of conversion efficiency with different phase mismatch.
Fig. 8
Fig. 8 PMC geometries, NCCs and losses versus slot thickness in (a, c) EAPSW and (b, d) IAPSW. Under 1 W pump, the achievable peak SHG efficiencies, required waveguide lengths, and normalized conversion efficiencies versus slot thickness in (e, g) EAPSW, and (f, h) IAPSW.
Fig. 9
Fig. 9 Effective indices of 0th-mode at FF and 1st-order mode at SHF versus Si3N4 width with (a) slot thickness fixed to be 30 nm and total slot width fixed to be 325 nm, and (b) slot thickness fixed to be 40 nm and total slot width fixed to be 375 nm.

Equations (5)

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κ= ε 0 A NL χ (2) : E 2 E 1 * E 1 * dxdy
d A FF dz = α FF 2 A FF +i ω FF 4 κ A FF * A SHF exp(iΔβz)
d A SHF dz = α SHF 2 A SHF +i ω FF 4 κ * A FF A FF exp(iΔβz)
η s = P 2 (L) P 1 (0)
η n = P 2 ( L P ) [ P 1 (0)] 2 [ L P (cm)] 2

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