Abstract

While single-mode waveguides are commonly used in integrated photonic circuits, emerging applications in nonlinear and quantum optics rely fundamentally on interactions between modes of different order. Here we propose several methods to evaluate the modal composition of both externally and device-internally excited guided waves and discuss a technique for efficient excitation of arbitrary modes. The applicability of these methods is verified in photonic circuits based on aluminum nitride. We control modal excitation through suitably engineered grating couplers and are able to perform a detailed study of waveguide-internal second harmonic generation. Efficient and broadband power conversion between orthogonal polarizations is realized within an asymmetric directional coupler to demonstrate selective excitation of arbitrary higher-order modes. Our approach holds promise for applications in nonlinear optics and frequency up/down-mixing in a chipscale framework.

© 2013 Optical Society of America

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  1. G. P. Agrawal, “Nonlinear fiber optics: its history and recent progress [Invited],” J. Opt. Soc. Am. B28(12), A1–A10 (2011).
    [CrossRef]
  2. A. Politi, J. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
    [CrossRef]
  3. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320(5876), 646–649 (2008).
    [CrossRef] [PubMed]
  4. M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O'Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
    [CrossRef]
  5. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express19(11), 10462–10470 (2011).
    [CrossRef] [PubMed]
  6. S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A-Pure. Appl. Opt.6, 569 (2004).
  7. Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ² microring resonators,” Opt. Express20(7), 7526–7543 (2012).
    [CrossRef] [PubMed]
  8. J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express19(12), 11415–11421 (2011).
    [CrossRef] [PubMed]
  9. M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A66(2), 023815 (2002).
    [CrossRef]
  10. K. Banaszek, A. B. U’ren, and I. A. Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett.26(17), 1367–1369 (2001).
    [CrossRef] [PubMed]
  11. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75(24), 4337–4341 (1995).
    [CrossRef] [PubMed]
  12. J. L. O’Brien, “Optical quantum computing,” Science318(5856), 1567–1570 (2007).
    [CrossRef] [PubMed]
  13. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462(7269), 78–82 (2009).
    [CrossRef] [PubMed]
  14. T. P. M. Alegre, A. Safavi-Naeini, M. Winger, and O. Painter, “Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap,” Opt. Express19(6), 5658–5669 (2011).
    [CrossRef] [PubMed]
  15. C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012).
    [CrossRef]
  16. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett.100(9), 091105 (2012).
    [CrossRef]
  17. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett.100(22), 223501 (2012).
    [CrossRef]
  18. P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol4, 300–305 (2013).
    [CrossRef] [PubMed]
  19. S. Ghosh, C. R. Doerr, and G. Piazza, “Aluminum nitride grating couplers,” Appl. Opt.51(17), 3763–3767 (2012).
    [CrossRef] [PubMed]
  20. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
    [CrossRef]
  21. C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) films produced by thermal curing,” J. Mater. Chem.12(4), 1138–1141 (2002).
    [CrossRef]
  22. Handbook of Optics (McGraw-Hill, 1994).
  23. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).
  24. X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
    [CrossRef]
  25. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express15(20), 12949–12958 (2007).
    [CrossRef] [PubMed]
  26. J.-M. Liu, Photonic Devices (Cambridge University, 2009).
  27. Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett.31(12), 815–816 (1977).
    [CrossRef]
  28. M. Stegmaier and W. H. P. Pernice, “Broadband directional coupling in aluminum nitride nanophotonic circuits,” Opt. Express21(6), 7304–7315 (2013).
    [CrossRef] [PubMed]
  29. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S.-i. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express16(7), 4872–4880 (2008).
    [CrossRef] [PubMed]
  30. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express19(13), 12646–12651 (2011).
    [CrossRef] [PubMed]
  31. M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett.30(2), 138–140 (2005).
    [CrossRef] [PubMed]
  32. J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron.16(1), 53–60 (2010).
    [CrossRef]

2013 (2)

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol4, 300–305 (2013).
[CrossRef] [PubMed]

M. Stegmaier and W. H. P. Pernice, “Broadband directional coupling in aluminum nitride nanophotonic circuits,” Opt. Express21(6), 7304–7315 (2013).
[CrossRef] [PubMed]

2012 (5)

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ² microring resonators,” Opt. Express20(7), 7526–7543 (2012).
[CrossRef] [PubMed]

S. Ghosh, C. R. Doerr, and G. Piazza, “Aluminum nitride grating couplers,” Appl. Opt.51(17), 3763–3767 (2012).
[CrossRef] [PubMed]

C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012).
[CrossRef]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett.100(9), 091105 (2012).
[CrossRef]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett.100(22), 223501 (2012).
[CrossRef]

2011 (6)

2010 (2)

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron.16(1), 53–60 (2010).
[CrossRef]

2009 (2)

A. Politi, J. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462(7269), 78–82 (2009).
[CrossRef] [PubMed]

2008 (2)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320(5876), 646–649 (2008).
[CrossRef] [PubMed]

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S.-i. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express16(7), 4872–4880 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (1)

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

2005 (1)

2004 (1)

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A-Pure. Appl. Opt.6, 569 (2004).

2002 (2)

C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) films produced by thermal curing,” J. Mater. Chem.12(4), 1138–1141 (2002).
[CrossRef]

M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A66(2), 023815 (2002).
[CrossRef]

2001 (1)

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

1977 (1)

Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett.31(12), 815–816 (1977).
[CrossRef]

Agrawal, G. P.

Alegre, T. P. M.

Atatüre, M.

M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A66(2), 023815 (2002).
[CrossRef]

Ayre, M.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Baets, R.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Banaszek, K.

Bi, Z.-F.

Bienstman, P.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Bogaerts, W.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Booth, M. C.

M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A66(2), 023815 (2002).
[CrossRef]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Chan, J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Chen, W.-C.

C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) films produced by thermal curing,” J. Mater. Chem.12(4), 1138–1141 (2002).
[CrossRef]

Chen, X.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Di Giuseppe, G.

M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A66(2), 023815 (2002).
[CrossRef]

Ding, Y.

Doerr, C. R.

Duchesne, D.

Ebrahimzadeh, M.

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A-Pure. Appl. Opt.6, 569 (2004).

Eichenfield, M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Fong, K. Y.

C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012).
[CrossRef]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express19(11), 10462–10470 (2011).
[CrossRef] [PubMed]

Foster, M. A.

Fujii, Y.

Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett.31(12), 815–816 (1977).
[CrossRef]

Fukuda, H.

Fung, C. K. Y.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

Gaeta, A. L.

Ghosh, S.

Hashemi, H.

Haus, H. A.

Hvam, J. M.

Itabashi, S.-i.

Johnson, S. G.

Khasminskaya, S.

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol4, 300–305 (2013).
[CrossRef] [PubMed]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Kwong, D.-L.

J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron.16(1), 53–60 (2010).
[CrossRef]

Laere, F. V.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Levy, J. S.

Li, C.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

Lipson, M.

Liu, L.

Lo, G.-Q.

J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron.16(1), 53–60 (2010).
[CrossRef]

Lo, S. M. G.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

Loncar, M.

Maekawa, S.

Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett.31(12), 815–816 (1977).
[CrossRef]

Matthews, J.

A. Politi, J. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

Matthews, J. C. F.

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O'Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Misawa, S.

Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett.31(12), 815–816 (1977).
[CrossRef]

Moutzouris, K.

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A-Pure. Appl. Opt.6, 569 (2004).

Nebel, C.

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol4, 300–305 (2013).
[CrossRef] [PubMed]

O’Brien, J. L.

A. Politi, J. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320(5876), 646–649 (2008).
[CrossRef] [PubMed]

J. L. O’Brien, “Optical quantum computing,” Science318(5856), 1567–1570 (2007).
[CrossRef] [PubMed]

O'Brien, J. L.

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O'Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

Painter, O.

Palacios, T.

Pernice, W.

Pernice, W. H. P.

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol4, 300–305 (2013).
[CrossRef] [PubMed]

M. Stegmaier and W. H. P. Pernice, “Broadband directional coupling in aluminum nitride nanophotonic circuits,” Opt. Express21(6), 7304–7315 (2013).
[CrossRef] [PubMed]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett.100(22), 223501 (2012).
[CrossRef]

C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012).
[CrossRef]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett.100(9), 091105 (2012).
[CrossRef]

Piazza, G.

Politi, A.

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O'Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

A. Politi, J. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Rao, S. V.

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A-Pure. Appl. Opt.6, 569 (2004).

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Rath, P.

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol4, 300–305 (2013).
[CrossRef] [PubMed]

Rodriguez, A. W.

Ryu, K. K.

Safavi-Naeini, A.

Sakudo, T.

Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett.31(12), 815–816 (1977).
[CrossRef]

Saleh, B. E. A.

M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A66(2), 023815 (2002).
[CrossRef]

Salem, R.

Schuck, C.

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett.100(22), 223501 (2012).
[CrossRef]

C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012).
[CrossRef]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett.100(9), 091105 (2012).
[CrossRef]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express19(11), 10462–10470 (2011).
[CrossRef] [PubMed]

Sergienko, A. V.

M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A66(2), 023815 (2002).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Shinojima, H.

Stegmaier, M.

Sun, X.

C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012).
[CrossRef]

Taillaert, D.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Tang, H. X.

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett.100(9), 091105 (2012).
[CrossRef]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett.100(22), 223501 (2012).
[CrossRef]

C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012).
[CrossRef]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express19(11), 10462–10470 (2011).
[CrossRef] [PubMed]

Teich, M. C.

M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A66(2), 023815 (2002).
[CrossRef]

Thompson, M. G.

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O'Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

A. Politi, J. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

Thourhout, D. V.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Tsang, H. K.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

Tsuchizawa, T.

Turner, A. C.

U’ren, A. B.

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Walmsley, I. A.

Wang, K.-M.

Watanabe, T.

Watts, M. R.

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Wild, C.

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol4, 300–305 (2013).
[CrossRef] [PubMed]

Winger, M.

Xiong, C.

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett.100(22), 223501 (2012).
[CrossRef]

C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012).
[CrossRef]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett.100(9), 091105 (2012).
[CrossRef]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express19(11), 10462–10470 (2011).
[CrossRef] [PubMed]

Yamada, K.

Yang, C.-C.

C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) films produced by thermal curing,” J. Mater. Chem.12(4), 1138–1141 (2002).
[CrossRef]

Yoshida, S.

Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett.31(12), 815–816 (1977).
[CrossRef]

Yu, M.

J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron.16(1), 53–60 (2010).
[CrossRef]

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Yvind, K.

Zeilinger, A.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron.16(1), 53–60 (2010).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett.31(12), 815–816 (1977).
[CrossRef]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett.100(9), 091105 (2012).
[CrossRef]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett.100(22), 223501 (2012).
[CrossRef]

Beilstein J Nanotechnol (1)

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol4, 300–305 (2013).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (2)

A. Politi, J. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron.16(1), 53–60 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

IET Circuits Devices Syst. (1)

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O'Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

J. Mater. Chem. (1)

C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) films produced by thermal curing,” J. Mater. Chem.12(4), 1138–1141 (2002).
[CrossRef]

J. Opt. A-Pure. Appl. Opt. (1)

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A-Pure. Appl. Opt.6, 569 (2004).

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

Jpn. J. Appl. Phys. (1)

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Nature (1)

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462(7269), 78–82 (2009).
[CrossRef] [PubMed]

New J. Phys. (1)

C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012).
[CrossRef]

Opt. Express (8)

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ² microring resonators,” Opt. Express20(7), 7526–7543 (2012).
[CrossRef] [PubMed]

M. Stegmaier and W. H. P. Pernice, “Broadband directional coupling in aluminum nitride nanophotonic circuits,” Opt. Express21(6), 7304–7315 (2013).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express15(20), 12949–12958 (2007).
[CrossRef] [PubMed]

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S.-i. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express16(7), 4872–4880 (2008).
[CrossRef] [PubMed]

T. P. M. Alegre, A. Safavi-Naeini, M. Winger, and O. Painter, “Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap,” Opt. Express19(6), 5658–5669 (2011).
[CrossRef] [PubMed]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express19(11), 10462–10470 (2011).
[CrossRef] [PubMed]

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express19(12), 11415–11421 (2011).
[CrossRef] [PubMed]

L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express19(13), 12646–12651 (2011).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (1)

M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A66(2), 023815 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75(24), 4337–4341 (1995).
[CrossRef] [PubMed]

Science (2)

J. L. O’Brien, “Optical quantum computing,” Science318(5856), 1567–1570 (2007).
[CrossRef] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320(5876), 646–649 (2008).
[CrossRef] [PubMed]

Other (3)

J.-M. Liu, Photonic Devices (Cambridge University, 2009).

Handbook of Optics (McGraw-Hill, 1994).

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).

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Figures (10)

Fig. 1
Fig. 1

(a) Basic structure of the studied AOI based ridge-type waveguides. The AlN film of height hAlN = 500 nm is fully etched down to the underlying silica layer while the remaining e-beam resist HSQ of approximately hHSQ = 140 nm is left on top. Resulting from the fabrication, sloped sidewalls with θ = 12° are observed. (b) Optical micrograph of a fabricated device with evanescently coupled ring resonator for evaluation of the group index from measured free spectral ranges (FSRs). Light is coupled into the structure by the grating coupler on the lower left and out by the one on the lower right. The ring resonator is separated from the waveguide of width ww = 650 nm by a small gap g = 550 nm.

Fig. 2
Fig. 2

Adjustment of the extraordinary refractive index nAlN,e of the used polycrystalline AlN at λ = 1550 nm. Due to its polarization, the TM-like mode of the ridge-type waveguide is almost exclusively affected by nAlN,e and can therefore be used for the respective adjustment. (a) Simulated dependence of ngTM on nAlN,e for a waveguide with ww = 650 nm. For nAlN,e = 2.106 the simulated value matches the measured one. (b) Comparison of measured and simulated group indices for a different waveguide geometry with ww = 450 nm after the adjustment of the refractive indices.

Fig. 3
Fig. 3

(a) FEM-simulation of the geometric dispersion at λ = 1550 nm and field profiles (|(E)|) of the respective guided modes. For widths ww between 0.4 µm and 1.2 µm, the waveguide supports the fundamental TE- and TM-like mode only. (b) Measured transmission of an apodized grating coupler for different polarizations of the incident light. Two clearly separated coupling curves corresponding to the TE- and TM- like mode are observed while the resonance peaks result from a coupled ring resonator. The excitation of different modes is confirmed by the observation of different types of resonances (different resonance wavelengths and FSRs) in dependence on the incident polarization.

Fig. 4
Fig. 4

(a) Comparison of measured and simulated group refractive indices at λ = 1520 nm. Due to good agreement of the observed trends, the measured modes can be related to the simulated ones. The observed small deviations are expected to result from of sub-optimal input parameters for the simulation (b) Transmission of apodized couplers for different waveguide widths. While in case of ww = 800 nm and ww = 600 nm two Gaussian shape coupling curves can be observed (TE + TM), the right one vanishes in the structure with just ww = 400 nm. Inset: Simulation of the geometric dispersion like in Fig. 3(a). As marked, the TE-like mode is expected to be cut-off below the critical waveguide width of wwc = 400 nm.

Fig. 5
Fig. 5

(a) Calculated geometric dispersion of both the fundamental modes at λ = 1550 nm and the 2nd-harmonic modes at λ = 775 nm. The higher-order modes are numbered according to their critical waveguide widths, i.e. their first guidance while gradually increasing ww. Nine phase matching points are observed within the presented waveguide width regime. (b) Measured geometric dispersion of the phase matching wavelength λPM around ww = 1000 nm. A linear decrease is observed which represents the discussed anomalous behaviour. Inset: The respective extracted proportionalities CFIT(λ) for various devices with different waveguide widths. (c) Exemplary higher-order mode profiles (|(E)|).

Fig. 6
Fig. 6

(a) Optical micrograph of a photonic circuit designed for measuring the coupling length of visible light generated by SHG. While the waveguide width ww is designed to achieve phase matching and generate visible light, the width ww’ = ww + 30 nm is chosen sufficiently off- resonance in order to prevent further SHG within and behind the directional coupler. (b) Pictures of visible scattered light for devices with different interaction lengths L. The pictures were taken with a CCD-camera by using a sufficiently long integration time. (c) Measured conversion efficiencies in the directional coupler in case of the phase matching point at ww = 800 nm.

Fig. 7
Fig. 7

(a) Cross-sectional sketch of an asymmetric co-directional waveguide structure. Two parallel waveguides with different widths ww and ww’ are separated by a gap g. (b) Calculated geometric dispersion of an asymmetric directional coupler with a gap of 200 nm. Here, the right waveguide width was kept constant at ww = 1060 nm while the left one was varied. Due to the evanescent coupling, the degeneracy of neff at the phase matching point is lifted. The presented field profiles (|(E)|2) of the supermodes at phase matching show the characteristic superposition of the coupled single-waveguide modes. (c) Calculated coupling efficiency of the studied system for various waveguide widths around the phase matching point at ww’ = 830 nm. η was derived from the simulated geometric dispersion by using Eq. (6).

Fig. 8
Fig. 8

(a) Optical micrograph of a photonic circuit for efficient TE-TM mode conversion. The power transfer takes place in the central asymmetric directional coupler of interaction length L if the two different waveguide widths ww and ww’ are chosen properly. In order to be able to measure the mode conversion, the grating couplers 2 and 3 were designed to excite exclusively the TM-like and the grating couplers 1 and 4 the TE-like mode around λ = 1520 nm. Hence, measured signals between the ports 1/3 or 2/4 can only result from converted powers between TE and TM. (b) Measured transmission curves of two reference grating couplers identical to the ones used for the mode converter and fabricated on the same chip. Clearly, two distinct coupling curves corresponding to the TM- (left) and TE-like (right) mode (cf. section 3.1) are observed. As intended, the TE-coupling curve of the 1/4 port lies at the same position as the TM-coupling curve of the 2/3 port.

Fig. 9
Fig. 9

Experimental results for mode converter devices with phase-matched waveguide width ww’ = 780 nm. The measurements were carried out with the white light source. (a) The TM-like light in T3→2 decreases gradually with increasing interaction length L until almost no power is transmitted anymore at L = 360 µm (b) With increasing L, more and more TE-like light is measured at port 1 which indicates that more and more power is converted.

Fig. 10
Fig. 10

TE-TM conversion efficiencies derived from the measured data, Eq. (9) and Eq. (10). Over a bandwidth of 30 nm and 120 nm, conversion efficiencies of over 70% and 50% are achieved, respectively. For clarity, error bars (average variance of 5.1% within the shown wavelength interval) are suppressed.

Tables (1)

Tables Icon

Table 1 Calculated nonlinear coupling coefficients of SHG in AlN ridge-waveguide structures between the TM-mode at λ = 1550 nm and various higher-order modes at λ = 775 nm according to Eq. (4).

Equations (10)

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

n AlN,o ( λ=1550nm )=2.076 n AlN,e ( λ=1550nm )=2.106.
P wg = ω 2 | C | 2 ( P ω,0 wg ) 2 L 2 sin c 2 ( ΔβL /2 )= C ¯ ( P ω,0 wg ) 2 .
C FIT =2 η η ω 2 C ¯ .
C=4 ε 0 2 2ω * d( 2ω=ω+ω ): ω ω dxdy d 31 C 31 + d 33 C 33 .
Δ λ PM = n eff 1 ww ( λ )  n eff 2 ww ( λ/2 ) n eff 1 λ ( λ )  1 2 n eff 2 ( λ/2 ) ( λ/2 ) Δww.
η max ( Δ n eff )= ( L c ( Δ n eff ) L c,max ) 2 .
T 41 = η 41 ( 1 η TE-TM ) η 41            T 32 = η 3-2 (1- η TM-TE ) η 3-2 .
η TE η TM = η 4-1 η 3-2 = ( T 41 T 32 ) 1/2 .
η TMTE = P converted wg P transmitted wg + P converted wg = ( 1+ P transmitted wg P converted wg ) 1 = ( 1+ P transmitted out P converted out η converted η transmitted ) 1 .
η TMTE = ( 1+ ( 1 η TMTE measured )( 1 η TETM measured ) η TMTE measured η TMTE measured ) 1 .

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