Abstract

We report the observation of type-0 phase-matching in bulk z-grown AlxGa1−xAs Bragg reflection waveguides where TM-polarized second-harmonic is generated using TM-polarized pump. For a pulsed pump with 1.8 ps temporal width and an average power of 3.3 mW, second-harmonic power of 16 µW was detected at 1567.8 nm. The normalized nonlinear conversion efficiency was obtained to be 2.84 × 103 %W−1cm−2 in a 2.2 mm long waveguide. The highly versatile modal birefringence in Bragg reflection waveguides enabled the phase-matching of the three modalities; namely type-0 TMω→TM2ω, type-I TEω→TM2ω and type-II TEω+TMω→TE2ω interactions to simultaneously take place within a spectral bandwidth as small as 17 nm.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Shih, “Entangled biphoton source-property and preparation,” Rep. Prog. Phys. 66, 1009 (2003).
    [CrossRef]
  2. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between 2 photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
    [CrossRef] [PubMed]
  3. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear optical coefficients,” J. Opt. Soc. Am. B 14, 2268–2294 (1997).
    [CrossRef]
  4. E. D. Palik, Handbook of Optical Constants of Solids (Academic Prsee, Orlando, Florida, 1985).
  5. M. Ravaro, M. Le Dû, J. P. Likforman, S. Ducci, V. Berger, G. Leo, and X. Marcadet, “Estimation of parametric grain in GaAs/AlOx waveguides by fluorescence and second harmonic generation measurements,” Appl. Phys. Lett. 91, 191119 (2007).
    [CrossRef]
  6. X. Yu, L. Scaccabarozzi, J. S. Harris, P. S. Kuo, and M. M. Fejer, “Efficient continuous wave second harmonic generation pumped at 1.55 µm in quasi-phase-matched AlGaAs waveguides,” Opt. Express 13, 10742–10748 (2005).
    [CrossRef] [PubMed]
  7. B. R. West, and A. S. Helmy, “Analysis and design equations for phase matching using Bragg reflection waveguides,” IEEE J. Quantum Electron. 12, 431–442 (2006).
    [CrossRef]
  8. P. Abolghasem, J. Han, A. Arjmand, B. J. Bijlani, and A. S. Helmy, “Highly efficient second-harmonic generation in monolithic matching-layer enhanced AlxGa1−xAs Bragg reflection waveguides,” IEEE Photon. Technol. Lett. 21, 1462–1464 (2009).
    [CrossRef]
  9. J. S. Aitchison, M. W. Street, N. D. Whitbread, D. C. Hutchings, J. H. Marsh, G. T. Kennedy, and W. Sibbet, “Modulation of the second-order nonlinear tensor components in multiple-quantum-well structures,” IEEE J. Sel. Top. Quantum Electron. 4, 695–700 (1998).
    [CrossRef]
  10. J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
    [CrossRef]
  11. P. N. Butcher, and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, Cambridge, UK. 1990).
  12. Lumerical Solutions, www.lumerical.com.
  13. S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, “The refractive index of AlxGa1xAs below the band gap: Accurate determination and empirical modeling,” Appl. Phys. (Berl.) 87, 7825–7837 (2000).
    [CrossRef]
  14. B. R. West, and A. S. Helmy, “Analysis and design equations for phase matching using Bragg reflection waveguides,” IEEE J. Quantum Electron. 12, 431–442 (2006).
    [CrossRef]
  15. K. Moutzouris, S. V. Rao, M. Ebrahimzadeh, A. De Rossi, V. Berger, M. Calligaro, and V. Ortiz, “Efficient second harmonic generation in birefringently phase-matched GaAs/Al2O3 waveguides,” Opt. Lett. 26, 1785–1787 (2001).
    [CrossRef]

2009

P. Abolghasem, J. Han, A. Arjmand, B. J. Bijlani, and A. S. Helmy, “Highly efficient second-harmonic generation in monolithic matching-layer enhanced AlxGa1−xAs Bragg reflection waveguides,” IEEE Photon. Technol. Lett. 21, 1462–1464 (2009).
[CrossRef]

2007

M. Ravaro, M. Le Dû, J. P. Likforman, S. Ducci, V. Berger, G. Leo, and X. Marcadet, “Estimation of parametric grain in GaAs/AlOx waveguides by fluorescence and second harmonic generation measurements,” Appl. Phys. Lett. 91, 191119 (2007).
[CrossRef]

2006

B. R. West, and A. S. Helmy, “Analysis and design equations for phase matching using Bragg reflection waveguides,” IEEE J. Quantum Electron. 12, 431–442 (2006).
[CrossRef]

B. R. West, and A. S. Helmy, “Analysis and design equations for phase matching using Bragg reflection waveguides,” IEEE J. Quantum Electron. 12, 431–442 (2006).
[CrossRef]

2005

2003

Y. Shih, “Entangled biphoton source-property and preparation,” Rep. Prog. Phys. 66, 1009 (2003).
[CrossRef]

2001

2000

J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
[CrossRef]

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, “The refractive index of AlxGa1xAs below the band gap: Accurate determination and empirical modeling,” Appl. Phys. (Berl.) 87, 7825–7837 (2000).
[CrossRef]

1998

J. S. Aitchison, M. W. Street, N. D. Whitbread, D. C. Hutchings, J. H. Marsh, G. T. Kennedy, and W. Sibbet, “Modulation of the second-order nonlinear tensor components in multiple-quantum-well structures,” IEEE J. Sel. Top. Quantum Electron. 4, 695–700 (1998).
[CrossRef]

1997

1987

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between 2 photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Abolghasem, P.

P. Abolghasem, J. Han, A. Arjmand, B. J. Bijlani, and A. S. Helmy, “Highly efficient second-harmonic generation in monolithic matching-layer enhanced AlxGa1−xAs Bragg reflection waveguides,” IEEE Photon. Technol. Lett. 21, 1462–1464 (2009).
[CrossRef]

Aitchison, J. S.

J. S. Aitchison, M. W. Street, N. D. Whitbread, D. C. Hutchings, J. H. Marsh, G. T. Kennedy, and W. Sibbet, “Modulation of the second-order nonlinear tensor components in multiple-quantum-well structures,” IEEE J. Sel. Top. Quantum Electron. 4, 695–700 (1998).
[CrossRef]

Akano, U. G.

J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
[CrossRef]

Arjmand, A.

P. Abolghasem, J. Han, A. Arjmand, B. J. Bijlani, and A. S. Helmy, “Highly efficient second-harmonic generation in monolithic matching-layer enhanced AlxGa1−xAs Bragg reflection waveguides,” IEEE Photon. Technol. Lett. 21, 1462–1464 (2009).
[CrossRef]

Berger, V.

M. Ravaro, M. Le Dû, J. P. Likforman, S. Ducci, V. Berger, G. Leo, and X. Marcadet, “Estimation of parametric grain in GaAs/AlOx waveguides by fluorescence and second harmonic generation measurements,” Appl. Phys. Lett. 91, 191119 (2007).
[CrossRef]

K. Moutzouris, S. V. Rao, M. Ebrahimzadeh, A. De Rossi, V. Berger, M. Calligaro, and V. Ortiz, “Efficient second harmonic generation in birefringently phase-matched GaAs/Al2O3 waveguides,” Opt. Lett. 26, 1785–1787 (2001).
[CrossRef]

Bijlani, B. J.

P. Abolghasem, J. Han, A. Arjmand, B. J. Bijlani, and A. S. Helmy, “Highly efficient second-harmonic generation in monolithic matching-layer enhanced AlxGa1−xAs Bragg reflection waveguides,” IEEE Photon. Technol. Lett. 21, 1462–1464 (2009).
[CrossRef]

Bouchard, J. P.

J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
[CrossRef]

Calligaro, M.

De Rossi, A.

Ducci, S.

M. Ravaro, M. Le Dû, J. P. Likforman, S. Ducci, V. Berger, G. Leo, and X. Marcadet, “Estimation of parametric grain in GaAs/AlOx waveguides by fluorescence and second harmonic generation measurements,” Appl. Phys. Lett. 91, 191119 (2007).
[CrossRef]

Ebrahimzadeh, M.

Fejer, M. M.

Gehrsitz, S.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, “The refractive index of AlxGa1xAs below the band gap: Accurate determination and empirical modeling,” Appl. Phys. (Berl.) 87, 7825–7837 (2000).
[CrossRef]

Gourgon, C.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, “The refractive index of AlxGa1xAs below the band gap: Accurate determination and empirical modeling,” Appl. Phys. (Berl.) 87, 7825–7837 (2000).
[CrossRef]

Han, J.

P. Abolghasem, J. Han, A. Arjmand, B. J. Bijlani, and A. S. Helmy, “Highly efficient second-harmonic generation in monolithic matching-layer enhanced AlxGa1−xAs Bragg reflection waveguides,” IEEE Photon. Technol. Lett. 21, 1462–1464 (2009).
[CrossRef]

Harris, J. S.

Helmy, A. S.

P. Abolghasem, J. Han, A. Arjmand, B. J. Bijlani, and A. S. Helmy, “Highly efficient second-harmonic generation in monolithic matching-layer enhanced AlxGa1−xAs Bragg reflection waveguides,” IEEE Photon. Technol. Lett. 21, 1462–1464 (2009).
[CrossRef]

B. R. West, and A. S. Helmy, “Analysis and design equations for phase matching using Bragg reflection waveguides,” IEEE J. Quantum Electron. 12, 431–442 (2006).
[CrossRef]

B. R. West, and A. S. Helmy, “Analysis and design equations for phase matching using Bragg reflection waveguides,” IEEE J. Quantum Electron. 12, 431–442 (2006).
[CrossRef]

Herres, N.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, “The refractive index of AlxGa1xAs below the band gap: Accurate determination and empirical modeling,” Appl. Phys. (Berl.) 87, 7825–7837 (2000).
[CrossRef]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between 2 photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Hutchings, D. C.

J. S. Aitchison, M. W. Street, N. D. Whitbread, D. C. Hutchings, J. H. Marsh, G. T. Kennedy, and W. Sibbet, “Modulation of the second-order nonlinear tensor components in multiple-quantum-well structures,” IEEE J. Sel. Top. Quantum Electron. 4, 695–700 (1998).
[CrossRef]

Ito, R.

Janz, S.

J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
[CrossRef]

Kennedy, G. T.

J. S. Aitchison, M. W. Street, N. D. Whitbread, D. C. Hutchings, J. H. Marsh, G. T. Kennedy, and W. Sibbet, “Modulation of the second-order nonlinear tensor components in multiple-quantum-well structures,” IEEE J. Sel. Top. Quantum Electron. 4, 695–700 (1998).
[CrossRef]

Kitamoto, A.

Kondo, T.

Kuo, P. S.

Le Dû, M.

M. Ravaro, M. Le Dû, J. P. Likforman, S. Ducci, V. Berger, G. Leo, and X. Marcadet, “Estimation of parametric grain in GaAs/AlOx waveguides by fluorescence and second harmonic generation measurements,” Appl. Phys. Lett. 91, 191119 (2007).
[CrossRef]

Leo, G.

M. Ravaro, M. Le Dû, J. P. Likforman, S. Ducci, V. Berger, G. Leo, and X. Marcadet, “Estimation of parametric grain in GaAs/AlOx waveguides by fluorescence and second harmonic generation measurements,” Appl. Phys. Lett. 91, 191119 (2007).
[CrossRef]

Likforman, J. P.

M. Ravaro, M. Le Dû, J. P. Likforman, S. Ducci, V. Berger, G. Leo, and X. Marcadet, “Estimation of parametric grain in GaAs/AlOx waveguides by fluorescence and second harmonic generation measurements,” Appl. Phys. Lett. 91, 191119 (2007).
[CrossRef]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between 2 photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Marcadet, X.

M. Ravaro, M. Le Dû, J. P. Likforman, S. Ducci, V. Berger, G. Leo, and X. Marcadet, “Estimation of parametric grain in GaAs/AlOx waveguides by fluorescence and second harmonic generation measurements,” Appl. Phys. Lett. 91, 191119 (2007).
[CrossRef]

Marsh, J. H.

J. S. Aitchison, M. W. Street, N. D. Whitbread, D. C. Hutchings, J. H. Marsh, G. T. Kennedy, and W. Sibbet, “Modulation of the second-order nonlinear tensor components in multiple-quantum-well structures,” IEEE J. Sel. Top. Quantum Electron. 4, 695–700 (1998).
[CrossRef]

Mitchell, I. V.

J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
[CrossRef]

Moutzouris, K.

Ortiz, V.

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between 2 photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Piva, P.

J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
[CrossRef]

Rao, S. V.

Ravaro, M.

M. Ravaro, M. Le Dû, J. P. Likforman, S. Ducci, V. Berger, G. Leo, and X. Marcadet, “Estimation of parametric grain in GaAs/AlOx waveguides by fluorescence and second harmonic generation measurements,” Appl. Phys. Lett. 91, 191119 (2007).
[CrossRef]

Reinhart, F. K.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, “The refractive index of AlxGa1xAs below the band gap: Accurate determination and empirical modeling,” Appl. Phys. (Berl.) 87, 7825–7837 (2000).
[CrossRef]

Scaccabarozzi, L.

Shih, Y.

Y. Shih, “Entangled biphoton source-property and preparation,” Rep. Prog. Phys. 66, 1009 (2003).
[CrossRef]

Shirane, M.

Shoji, I.

Sibbet, W.

J. S. Aitchison, M. W. Street, N. D. Whitbread, D. C. Hutchings, J. H. Marsh, G. T. Kennedy, and W. Sibbet, “Modulation of the second-order nonlinear tensor components in multiple-quantum-well structures,” IEEE J. Sel. Top. Quantum Electron. 4, 695–700 (1998).
[CrossRef]

Sigg, H.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, “The refractive index of AlxGa1xAs below the band gap: Accurate determination and empirical modeling,” Appl. Phys. (Berl.) 87, 7825–7837 (2000).
[CrossRef]

Street, M. W.

J. S. Aitchison, M. W. Street, N. D. Whitbread, D. C. Hutchings, J. H. Marsh, G. T. Kennedy, and W. Sibbet, “Modulation of the second-order nonlinear tensor components in multiple-quantum-well structures,” IEEE J. Sel. Top. Quantum Electron. 4, 695–700 (1998).
[CrossRef]

Tetu, M.

J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
[CrossRef]

Vonlanthen, A.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, “The refractive index of AlxGa1xAs below the band gap: Accurate determination and empirical modeling,” Appl. Phys. (Berl.) 87, 7825–7837 (2000).
[CrossRef]

Wasilewski, Z. R.

J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
[CrossRef]

West, B. R.

B. R. West, and A. S. Helmy, “Analysis and design equations for phase matching using Bragg reflection waveguides,” IEEE J. Quantum Electron. 12, 431–442 (2006).
[CrossRef]

B. R. West, and A. S. Helmy, “Analysis and design equations for phase matching using Bragg reflection waveguides,” IEEE J. Quantum Electron. 12, 431–442 (2006).
[CrossRef]

Whitbread, N. D.

J. S. Aitchison, M. W. Street, N. D. Whitbread, D. C. Hutchings, J. H. Marsh, G. T. Kennedy, and W. Sibbet, “Modulation of the second-order nonlinear tensor components in multiple-quantum-well structures,” IEEE J. Sel. Top. Quantum Electron. 4, 695–700 (1998).
[CrossRef]

Xu, D. X.

J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
[CrossRef]

Yu, X.

Appl. Phys. (Berl.)

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, “The refractive index of AlxGa1xAs below the band gap: Accurate determination and empirical modeling,” Appl. Phys. (Berl.) 87, 7825–7837 (2000).
[CrossRef]

Appl. Phys. Lett.

J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski, P. Piva, U. G. Akano, and I. V. Mitchell, “Quasiphase matched second-harmonic generation in an AlxGa1-xAs asymmetric quantum-well waveguide using ion implantation-enhanced intermixing,” Appl. Phys. Lett. 77, 4247–4249 (2000).
[CrossRef]

M. Ravaro, M. Le Dû, J. P. Likforman, S. Ducci, V. Berger, G. Leo, and X. Marcadet, “Estimation of parametric grain in GaAs/AlOx waveguides by fluorescence and second harmonic generation measurements,” Appl. Phys. Lett. 91, 191119 (2007).
[CrossRef]

IEEE J. Quantum Electron.

B. R. West, and A. S. Helmy, “Analysis and design equations for phase matching using Bragg reflection waveguides,” IEEE J. Quantum Electron. 12, 431–442 (2006).
[CrossRef]

B. R. West, and A. S. Helmy, “Analysis and design equations for phase matching using Bragg reflection waveguides,” IEEE J. Quantum Electron. 12, 431–442 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. S. Aitchison, M. W. Street, N. D. Whitbread, D. C. Hutchings, J. H. Marsh, G. T. Kennedy, and W. Sibbet, “Modulation of the second-order nonlinear tensor components in multiple-quantum-well structures,” IEEE J. Sel. Top. Quantum Electron. 4, 695–700 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

P. Abolghasem, J. Han, A. Arjmand, B. J. Bijlani, and A. S. Helmy, “Highly efficient second-harmonic generation in monolithic matching-layer enhanced AlxGa1−xAs Bragg reflection waveguides,” IEEE Photon. Technol. Lett. 21, 1462–1464 (2009).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between 2 photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Rep. Prog. Phys.

Y. Shih, “Entangled biphoton source-property and preparation,” Rep. Prog. Phys. 66, 1009 (2003).
[CrossRef]

Other

E. D. Palik, Handbook of Optical Constants of Solids (Academic Prsee, Orlando, Florida, 1985).

P. N. Butcher, and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, Cambridge, UK. 1990).

Lumerical Solutions, www.lumerical.com.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of waveguide where xyz′ and xyz indicating the laboratory and crystal frames, respectively. (b) Orientation of the reference frames with an orientation angle of ϕ = π/4. (c) Schematic of the cross section of the characterized matching-layer enhanced BRW[8] with the ridge width of W = 4.4 µm and the ridge depth of D=3.6 µm. For type-0 TMω→TM2ω, type-I TEω→TM2ω and type-II TEω+TMω→TE2ω interactions the angle between the electric field of the incident pump beam with [001] crystal axis is θ = 0,π/4 and π/2, respectively.

Fig. 2.
Fig. 2.

Simulated magnitudes of electric field components [V/m] for TMω propagating pump at ω frequency (Exω, Eyω, Ezω) and those for TM2ω propagating second-harmonic at 2ω frequency (Ex2ω, Ey2ω, Ez2ω). The fields profiles were simulated using Lumerical mode solver [12].

Fig. 3.
Fig. 3.

(a) Second-harmonic power as a function of pump wavelength measured for three phase-matching scheme. The solid lines are the Lorentzian fit to the measured date. (Inset) Variation of TE2ω and TM2ω components of SH power as a function of pump angle θ at phase-matching wavelength of 1567.8 nm. (b) Simulated modal dispersion of fundamental modes of pump and SH. The crossing points P1, P2 and P3 denote the phase-matching point for TEω→TM2ω, TEω+TMω→TE2ω and TMω→TM2ω processes, respectively.

Fig. 4.
Fig. 4.

Modal birefringence of pump (solid-line) and second-harmonic (dashed-line) as functions of the waveguide ridge width. The crossing point between the modal birefringence of SH with the zero birefringence (dotted-line) indicates a design for which the SH mode is polarization degenerate.

Fig. 5.
Fig. 5.

Second-harmonic power as a function of pump plotted on a log-log scale. (Inset) Normalized spectra of pump (dashed-line) and SH (solid-line) obtained for the pump power of 3.3 mW.

Tables (1)

Tables Icon

Table 1. Summary of the three phase-matched second-harmonic generation

Equations (8)

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

E ω σ μ ( x , y , z ) = A ω σ ( y ) E ω σ μ ( x , z ) exp ( i k ω σ y )
[ P 2 ω ( 2 ) ] μ = ε 0 K χ μ α β ( 2 ) E ω α E ω β
χ μ α β ( 2 ) = R μ μ ( ϕ ) R α α ( ϕ ) R β β ( ϕ ) χ μ α β ( 2 )
χ x x z ( 2 ) = χ x z x ( 2 ) = χ z x z ( 2 ) = + χ xyz ( 2 )
χ y y z ( 2 ) = χ y z y ( 2 ) = χ z y y ( 2 ) = χ xyz ( 2 )
[ P 2 ω ( 2 ) ] x = 0
[ P 2 ω ( 2 ) ] y = ε 0 χ xyz ( 2 ) E ω z E ω y
[ P 2 ω ( 2 ) ] z = ε 0 2 χ xyz ( 2 ) E ω y E ω y

Metrics