Abstract

Efficient optical nonlinear effects in waveguides play an important role in integrated photonic functionalities. The dispersion characteristics need to be well designed to satisfy the phase-matching condition of the interacting waves in waveguides. Here we demonstrate a novel phase-matching process of second-harmonic generation (SHG) in a symmetrical metal-cladding optical waveguide (SMCOW) with a nonlinear guiding layer. Ultrahigh order modes in SMCOWs possess small propagation constants, and can be actively tuned to satisfy the phase-matching condition via free-space coupling. We establish a model of SHG in the SMCOW and experimentally verify it as well. This mechanism could also be applied to or referenced in other nonlinear frequency conversion processes.

© 2017 Optical Society of America

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References

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2016 (1)

2014 (2)

2013 (1)

2012 (2)

2011 (4)

2009 (2)

H. Ishikawa and T. Kondo, “Birefringent phase matching in thin rectangular high-index-contrast waveguides,” Appl. Phys. Express 2(4), 042202 (2009).
[Crossref]

Q. M. Ngo, S. Kim, S. H. Song, and R. Magnusson, “Optical bistable devices based on guided-mode resonance in slab waveguide gratings,” Opt. Express 17(26), 23459–23467 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (1)

2005 (1)

2004 (1)

H. Lu, Z. Cao, H. Li, and Q. Shen, “Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 85(20), 4579–4581 (2004).
[Crossref]

2003 (1)

H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83(14), 2757–2759 (2003).
[Crossref]

2000 (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

Alexeeva, N. V.

N. V. Alexeeva, I. V. Barashenkov, K. Rayanov, and S. Flach, “Actively coupled optical waveguides,” Phys. Rev. A 89(1), 57–62 (2014).
[Crossref]

Barashenkov, I. V.

N. V. Alexeeva, I. V. Barashenkov, K. Rayanov, and S. Flach, “Actively coupled optical waveguides,” Phys. Rev. A 89(1), 57–62 (2014).
[Crossref]

Bowers, J. E.

Cao, Z.

Y. Zheng, Z. Cao, and X. Chen, “Conical reflection of light during free-space coupling into a symmetrical metal-cladding waveguide,” J. Opt. Soc. Am. A 30(9), 1901–1904 (2013).
[Crossref] [PubMed]

Y. Zheng, W. Yuan, X. Chen, and Z. Cao, “Wideband slow-light modes for time delay of ultrashort pulses in symmetrical metal-cladding optical waveguide,” Opt. Express 20(9), 9409–9414 (2012).
[Crossref] [PubMed]

W. Yuan, C. Yin, H. Li, P. Xiao, and Z. Cao, “Wideband slow light assisted by ultrahigh-order modes,” J. Opt. Soc. Am. B 28(28), 968–971 (2011).
[Crossref]

Y. Wang, Z. Cao, T. Yu, H. Li, and Q. Shen, “Enhancement of the superprism effect based on the strong dispersion effect of ultrahigh-order modes,” Opt. Lett. 33(11), 1276–1278 (2008).
[Crossref] [PubMed]

L. Chen, Z. Cao, F. Ou, H. Li, Q. Shen, and H. Qiao, “Observation of large positive and negative lateral shifts of a reflected beam from symmetrical metal-cladding waveguides,” Opt. Lett. 32(11), 1432–1434 (2007).
[Crossref] [PubMed]

F. Chen, Z. Cao, Q. Shen, X. Deng, B. Duan, W. Yuan, M. Sang, and S. Wang, “Picometer displacement sensing using the ultrahigh-order modes in a submillimeter scale optical waveguide,” Opt. Express 13(25), 10061–10065 (2005).
[Crossref] [PubMed]

H. Lu, Z. Cao, H. Li, and Q. Shen, “Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 85(20), 4579–4581 (2004).
[Crossref]

H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83(14), 2757–2759 (2003).
[Crossref]

Chang, L.

Chen, F.

Chen, L.

Chen, R. T.

Chen, X.

Deng, X.

Denz, C.

Dou, X.

Duan, B.

Flach, S.

N. V. Alexeeva, I. V. Barashenkov, K. Rayanov, and S. Flach, “Actively coupled optical waveguides,” Phys. Rev. A 89(1), 57–62 (2014).
[Crossref]

Foster, A. C.

Foster, M. A.

Gaeta, A. L.

Ghosh, S.

J. Lugani, S. Ghosh, and K. Thyagarajan, “Generation of modal and path-entangled photons using a domain-engineered integrated optical waveguide device,” Phys. Rev. A 83(6), 922–925 (2011).
[Crossref]

Horn, W.

Imbrock, J.

Ishikawa, H.

H. Ishikawa and T. Kondo, “Birefringent phase matching in thin rectangular high-index-contrast waveguides,” Appl. Phys. Express 2(4), 042202 (2009).
[Crossref]

Kim, S.

Kondo, T.

H. Ishikawa and T. Kondo, “Birefringent phase matching in thin rectangular high-index-contrast waveguides,” Appl. Phys. Express 2(4), 042202 (2009).
[Crossref]

Kroesen, S.

Levy, J. S.

Li, H.

Li, Y.

Lin, X.

Lipson, M.

Lu, H.

H. Lu, Z. Cao, H. Li, and Q. Shen, “Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 85(20), 4579–4581 (2004).
[Crossref]

H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83(14), 2757–2759 (2003).
[Crossref]

Lugani, J.

J. Lugani, S. Ghosh, and K. Thyagarajan, “Generation of modal and path-entangled photons using a domain-engineered integrated optical waveguide device,” Phys. Rev. A 83(6), 922–925 (2011).
[Crossref]

Magnusson, R.

Ngo, Q. M.

Ou, F.

Peters, J.

Qiao, H.

Rayanov, K.

N. V. Alexeeva, I. V. Barashenkov, K. Rayanov, and S. Flach, “Actively coupled optical waveguides,” Phys. Rev. A 89(1), 57–62 (2014).
[Crossref]

Sang, M.

Shen, Q.

Song, S. H.

Thyagarajan, K.

J. Lugani, S. Ghosh, and K. Thyagarajan, “Generation of modal and path-entangled photons using a domain-engineered integrated optical waveguide device,” Phys. Rev. A 83(6), 922–925 (2011).
[Crossref]

Volet, N.

Wang, A. X.

Wang, K. Y.

Wang, L.

Wang, S.

Wang, Y.

Xiao, P.

Yariv, A.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

Yin, C.

Yu, T.

Yuan, W.

Zheng, Y.

Appl. Phys. Express (1)

H. Ishikawa and T. Kondo, “Birefringent phase matching in thin rectangular high-index-contrast waveguides,” Appl. Phys. Express 2(4), 042202 (2009).
[Crossref]

Appl. Phys. Lett. (2)

H. Lu, Z. Cao, H. Li, and Q. Shen, “Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 85(20), 4579–4581 (2004).
[Crossref]

H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83(14), 2757–2759 (2003).
[Crossref]

Electron. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

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

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

Opt. Express (6)

Opt. Lett. (3)

Optica (1)

Phys. Rev. A (2)

J. Lugani, S. Ghosh, and K. Thyagarajan, “Generation of modal and path-entangled photons using a domain-engineered integrated optical waveguide device,” Phys. Rev. A 83(6), 922–925 (2011).
[Crossref]

N. V. Alexeeva, I. V. Barashenkov, K. Rayanov, and S. Flach, “Actively coupled optical waveguides,” Phys. Rev. A 89(1), 57–62 (2014).
[Crossref]

Other (1)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, San Diego, 2008).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of SHG in an SMCOW. (b) Schematic of light rays and the formation of optical modes in waveguides. (c) SHG requires that the propagation constants of interacting modes are phase matched.

Fig. 2
Fig. 2

(a) Experimental setup for the observation of SHG in SMCOW. (b) The intensity dependence of generated SH coupled out versus incident angle.

Fig. 3
Fig. 3

(a) The experimental and simulation ATR spectra of the SMCOW sample at the wavelength of FW ( ε r =58.488+1.172i at 1064 nm). (b) The experimental ATR spectrum of the SMCOW at the wavelength of 532 nm.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

k 0 h n 2 - N 2 =mπ,
β SH =2 β FW ,
β i = k i sin( θ ),
P SH = C SH ( θ ) C P 2 ( θ ) ( ω p χ (2) L P P ) 2 8 n P 2 n SH c 3 ε 0 A P 2 A SH sin c 2 (ΔkL/2)f( A P , A SH ),
C i ( θ )= P WG P in =1- P out ( θ ) P in ( θ ) ,

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