Abstract

A novel design to achieve phase matching between modes of a vertical distributed Bragg reflector waveguide and those of a conventional total internal reflection waveguide is reported for the first time. The device design and structure lend themselves to monolithic integration with active devices using well developed photonic fabrication technologies. Due to the lack of any modulation of the optical properties in the direction of propagation, the device promises very low insertion loss. This property together with the large overlap integral between the interacting fields dramatically enhances the conversion efficiency. The phase matching bandwidth, tunability and dimensions of these structures make them excellent contenders to harness optical nonlinearities in compact, low insertion loss monolithically integrable devices.

© 2006 Optical Society of America

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  1. C. B. Ebert, L. A. Eyres, M. M. Fejer, J. H. Harris, "GaAs/Ge/GaAs sublattice reversal epitaxy and its application to nonlinear optical devices," J. Cryst. Growth 227, 183-192 (1999).
  2. J. B. Khurgin, E. Rosencher, Y. J. Ding, "Analysis of all-semiconductor intracavity optical parametric oscillators," J. Opt. Soc. Am. B 15, 1726-1734 (1998).
    [CrossRef]
  3. A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998).
    [CrossRef]
  4. A. S. Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, and J. S. Aitchison, C. T. A. Brown, K. Moutzouris and M. Ebrahimzadeh, "Quasi phase matching in GaAs-AlAs superlattice waveguides via bandgap tuning using quantum well intermixing," Opt. Lett. 25, 1370-1373 (2000).
    [CrossRef]
  5. R. Haidar, N. Forget, E. Rosencher, "Optical parametric oscillation in micro-cavities based on isotropic semiconductors: a theoretical study," IEEE J. Quantum Electron. 39, 569-576 (2003).
    [CrossRef]
  6. D. Faccio, F. Bragheri, M. Cherchi, "Optical Bloch-mode-induced quasi phase matching of quadratic interactions in one-dimensional photonic crystals," J. Opt. Soc. Am. B 21, 296-301 (2004).
    [CrossRef]
  7. K. L. Vodopyanov, O. Levi, P.S. Kuo, T.J. Pinguet, J.S. Harris, M.M. Fejer, B. Gerard, L. Becouarn, E. Lallier "Optical parametric oscillation in quasi-phase-matched GaAs," Opt. Lett. 29, 1912-1914, (2004).
    [CrossRef] [PubMed]
  8. A. S. Helmy, BrianR.  West "Phase Matching using Bragg Reflector Waveguides," IEEE LEOS Annual Meeting, Sydney, (2005).
    [CrossRef]
  9. P. Yeh, A. Yariv, " Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
    [CrossRef]
  10. P. Yeh, A. Yariv, C Hong "Electromagnetic propagation in periodic stratified media: I. General Theory," J. Appl. Phys.,  67, 423-438 (1977).
  11. S. R. A. Dods, "Bragg reflection waveguides," J. Opt. Soc. Am. A,  6, 1465-1475 (1989).
    [CrossRef]
  12. E. Simova, I. Golub, "Polarization splitter/combiner in high index contrast reflector waveguides," Opt. Express 11, 3425-3430 (2003).
    [CrossRef] [PubMed]
  13. A. Mizrahi, L. Schächter, "Bragg reflection waveguides with a matching layer," Opt. Express 12, 3156-3170 (2004).
    [CrossRef] [PubMed]
  14. C. Wätcher, F. Lederer, L. Leine, U. Trutschel, M. Mann, " Nonlinear Bragg reflection waveguide," J. Appl. Phys. 71, 3688-3692 (1992).
    [CrossRef]
  15. P. M. Lambkin, K. A. Shore, "Nonlinear semiconductor Bragg reflection waveguide structures," IEEE J. Quantum Eletron. 27, 824-828 (1991).
    [CrossRef]
  16. T. C. Kleckner, A. S. Helmy, K. Zeaiter, D. C. Hutchings, J. S. Aitchison, "Dispersion and Modulation of the Linear Optical Properties of GaAs/AlAs Superlattices Waveguides using Quantum Well Intermixing," IEEE J. Quantum Eletron. (Accepted).
  17. P. Yeh, Optical Waves in layered media, (Wiley, 1988).
  18. J. Chilwell, I. Hodgkinson, "Thin-film field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides," J. Opt. Soc. Am. A 1, 742-753 (1984)
    [CrossRef]
  19. J. Khurgin, "Improvement of frequency-conversion efficiency in waveguides with rotationally twinned layers," Opt. Lett,  13, 603-605 (1988).
    [CrossRef] [PubMed]
  20. S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, M. Calligaro, "Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84,2974-2976 (2004).
    [CrossRef]
  21. P. Dong, A. G. Kirk, "Nonlinear frequency conversion in waveguide directional couplers," Phys. Rev. Lett. 93,133901 (2004).
    [CrossRef] [PubMed]
  22. N. Yokouchi, A. J. Danner, K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron.,  9, 1439-1447 (2003).
    [CrossRef]

2004

2003

N. Yokouchi, A. J. Danner, K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron.,  9, 1439-1447 (2003).
[CrossRef]

R. Haidar, N. Forget, E. Rosencher, "Optical parametric oscillation in micro-cavities based on isotropic semiconductors: a theoretical study," IEEE J. Quantum Electron. 39, 569-576 (2003).
[CrossRef]

E. Simova, I. Golub, "Polarization splitter/combiner in high index contrast reflector waveguides," Opt. Express 11, 3425-3430 (2003).
[CrossRef] [PubMed]

2000

1999

C. B. Ebert, L. A. Eyres, M. M. Fejer, J. H. Harris, "GaAs/Ge/GaAs sublattice reversal epitaxy and its application to nonlinear optical devices," J. Cryst. Growth 227, 183-192 (1999).

1998

A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998).
[CrossRef]

J. B. Khurgin, E. Rosencher, Y. J. Ding, "Analysis of all-semiconductor intracavity optical parametric oscillators," J. Opt. Soc. Am. B 15, 1726-1734 (1998).
[CrossRef]

1992

C. Wätcher, F. Lederer, L. Leine, U. Trutschel, M. Mann, " Nonlinear Bragg reflection waveguide," J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

1991

P. M. Lambkin, K. A. Shore, "Nonlinear semiconductor Bragg reflection waveguide structures," IEEE J. Quantum Eletron. 27, 824-828 (1991).
[CrossRef]

1989

1988

J. Khurgin, "Improvement of frequency-conversion efficiency in waveguides with rotationally twinned layers," Opt. Lett,  13, 603-605 (1988).
[CrossRef] [PubMed]

1984

1977

P. Yeh, A. Yariv, C Hong "Electromagnetic propagation in periodic stratified media: I. General Theory," J. Appl. Phys.,  67, 423-438 (1977).

1976

P. Yeh, A. Yariv, " Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Aitchison, J. S.

A. S. Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, and J. S. Aitchison, C. T. A. Brown, K. Moutzouris and M. Ebrahimzadeh, "Quasi phase matching in GaAs-AlAs superlattice waveguides via bandgap tuning using quantum well intermixing," Opt. Lett. 25, 1370-1373 (2000).
[CrossRef]

T. C. Kleckner, A. S. Helmy, K. Zeaiter, D. C. Hutchings, J. S. Aitchison, "Dispersion and Modulation of the Linear Optical Properties of GaAs/AlAs Superlattices Waveguides using Quantum Well Intermixing," IEEE J. Quantum Eletron. (Accepted).

Arnold, J. M.

Becouarn, L.

Berger, V.

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, M. Calligaro, "Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84,2974-2976 (2004).
[CrossRef]

A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998).
[CrossRef]

Bragheri, F.

Bravetti, P.

A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998).
[CrossRef]

Brown, C. T. A.

Bryce, A. C.

Calligaro, M.

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, M. Calligaro, "Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84,2974-2976 (2004).
[CrossRef]

Cherchi, M.

Chilwell, J.

Choquette, K. D.

N. Yokouchi, A. J. Danner, K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron.,  9, 1439-1447 (2003).
[CrossRef]

Danner, A. J.

N. Yokouchi, A. J. Danner, K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron.,  9, 1439-1447 (2003).
[CrossRef]

De Rossi, A.

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, M. Calligaro, "Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84,2974-2976 (2004).
[CrossRef]

Delobel, L.

A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998).
[CrossRef]

Ding, Y. J.

Dods, S. R. A.

Dong, P.

P. Dong, A. G. Kirk, "Nonlinear frequency conversion in waveguide directional couplers," Phys. Rev. Lett. 93,133901 (2004).
[CrossRef] [PubMed]

Ducci, S.

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, M. Calligaro, "Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84,2974-2976 (2004).
[CrossRef]

Ebert, C. B.

C. B. Ebert, L. A. Eyres, M. M. Fejer, J. H. Harris, "GaAs/Ge/GaAs sublattice reversal epitaxy and its application to nonlinear optical devices," J. Cryst. Growth 227, 183-192 (1999).

Ebrahimzadeh, M.

Eyres, L. A.

C. B. Ebert, L. A. Eyres, M. M. Fejer, J. H. Harris, "GaAs/Ge/GaAs sublattice reversal epitaxy and its application to nonlinear optical devices," J. Cryst. Growth 227, 183-192 (1999).

Faccio, D.

Fejer, M. M.

C. B. Ebert, L. A. Eyres, M. M. Fejer, J. H. Harris, "GaAs/Ge/GaAs sublattice reversal epitaxy and its application to nonlinear optical devices," J. Cryst. Growth 227, 183-192 (1999).

Fejer, M.M.

Fiore, A.

A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998).
[CrossRef]

Forget, N.

R. Haidar, N. Forget, E. Rosencher, "Optical parametric oscillation in micro-cavities based on isotropic semiconductors: a theoretical study," IEEE J. Quantum Electron. 39, 569-576 (2003).
[CrossRef]

Gerard, B.

Golub, I.

Haidar, R.

R. Haidar, N. Forget, E. Rosencher, "Optical parametric oscillation in micro-cavities based on isotropic semiconductors: a theoretical study," IEEE J. Quantum Electron. 39, 569-576 (2003).
[CrossRef]

Harris, J. H.

C. B. Ebert, L. A. Eyres, M. M. Fejer, J. H. Harris, "GaAs/Ge/GaAs sublattice reversal epitaxy and its application to nonlinear optical devices," J. Cryst. Growth 227, 183-192 (1999).

Harris, J.S.

Helmy, A. S.

A. S. Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, and J. S. Aitchison, C. T. A. Brown, K. Moutzouris and M. Ebrahimzadeh, "Quasi phase matching in GaAs-AlAs superlattice waveguides via bandgap tuning using quantum well intermixing," Opt. Lett. 25, 1370-1373 (2000).
[CrossRef]

T. C. Kleckner, A. S. Helmy, K. Zeaiter, D. C. Hutchings, J. S. Aitchison, "Dispersion and Modulation of the Linear Optical Properties of GaAs/AlAs Superlattices Waveguides using Quantum Well Intermixing," IEEE J. Quantum Eletron. (Accepted).

Hodgkinson, I.

Hong, C

P. Yeh, A. Yariv, C Hong "Electromagnetic propagation in periodic stratified media: I. General Theory," J. Appl. Phys.,  67, 423-438 (1977).

Hutchings, D. C.

A. S. Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, and J. S. Aitchison, C. T. A. Brown, K. Moutzouris and M. Ebrahimzadeh, "Quasi phase matching in GaAs-AlAs superlattice waveguides via bandgap tuning using quantum well intermixing," Opt. Lett. 25, 1370-1373 (2000).
[CrossRef]

T. C. Kleckner, A. S. Helmy, K. Zeaiter, D. C. Hutchings, J. S. Aitchison, "Dispersion and Modulation of the Linear Optical Properties of GaAs/AlAs Superlattices Waveguides using Quantum Well Intermixing," IEEE J. Quantum Eletron. (Accepted).

Janz, S.

A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998).
[CrossRef]

Khurgin, J.

J. Khurgin, "Improvement of frequency-conversion efficiency in waveguides with rotationally twinned layers," Opt. Lett,  13, 603-605 (1988).
[CrossRef] [PubMed]

Khurgin, J. B.

Kirk, A. G.

P. Dong, A. G. Kirk, "Nonlinear frequency conversion in waveguide directional couplers," Phys. Rev. Lett. 93,133901 (2004).
[CrossRef] [PubMed]

Kleckner, T. C.

A. S. Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, and J. S. Aitchison, C. T. A. Brown, K. Moutzouris and M. Ebrahimzadeh, "Quasi phase matching in GaAs-AlAs superlattice waveguides via bandgap tuning using quantum well intermixing," Opt. Lett. 25, 1370-1373 (2000).
[CrossRef]

T. C. Kleckner, A. S. Helmy, K. Zeaiter, D. C. Hutchings, J. S. Aitchison, "Dispersion and Modulation of the Linear Optical Properties of GaAs/AlAs Superlattices Waveguides using Quantum Well Intermixing," IEEE J. Quantum Eletron. (Accepted).

Kuo, P.S.

Lallier, E.

Lambkin, P. M.

P. M. Lambkin, K. A. Shore, "Nonlinear semiconductor Bragg reflection waveguide structures," IEEE J. Quantum Eletron. 27, 824-828 (1991).
[CrossRef]

Lanco, L.

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, M. Calligaro, "Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84,2974-2976 (2004).
[CrossRef]

Lederer, F.

C. Wätcher, F. Lederer, L. Leine, U. Trutschel, M. Mann, " Nonlinear Bragg reflection waveguide," J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

Leine, L.

C. Wätcher, F. Lederer, L. Leine, U. Trutschel, M. Mann, " Nonlinear Bragg reflection waveguide," J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

Levi, O.

Mann, M.

C. Wätcher, F. Lederer, L. Leine, U. Trutschel, M. Mann, " Nonlinear Bragg reflection waveguide," J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

Marsh, J. H.

Mizrahi, A.

Moutzouris, K.

Ortiz, V.

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, M. Calligaro, "Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84,2974-2976 (2004).
[CrossRef]

Pinguet, T.J.

Rosencher, E.

R. Haidar, N. Forget, E. Rosencher, "Optical parametric oscillation in micro-cavities based on isotropic semiconductors: a theoretical study," IEEE J. Quantum Electron. 39, 569-576 (2003).
[CrossRef]

A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998).
[CrossRef]

J. B. Khurgin, E. Rosencher, Y. J. Ding, "Analysis of all-semiconductor intracavity optical parametric oscillators," J. Opt. Soc. Am. B 15, 1726-1734 (1998).
[CrossRef]

Schächter, L.

Shore, K. A.

P. M. Lambkin, K. A. Shore, "Nonlinear semiconductor Bragg reflection waveguide structures," IEEE J. Quantum Eletron. 27, 824-828 (1991).
[CrossRef]

Simova, E.

Stanley, C. R.

Trutschel, U.

C. Wätcher, F. Lederer, L. Leine, U. Trutschel, M. Mann, " Nonlinear Bragg reflection waveguide," J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

van der Meer, P.

A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998).
[CrossRef]

Vodopyanov, K. L.

Wätcher, C.

C. Wätcher, F. Lederer, L. Leine, U. Trutschel, M. Mann, " Nonlinear Bragg reflection waveguide," J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

Yariv, A.

P. Yeh, A. Yariv, C Hong "Electromagnetic propagation in periodic stratified media: I. General Theory," J. Appl. Phys.,  67, 423-438 (1977).

P. Yeh, A. Yariv, " Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Yeh, P.

P. Yeh, A. Yariv, C Hong "Electromagnetic propagation in periodic stratified media: I. General Theory," J. Appl. Phys.,  67, 423-438 (1977).

P. Yeh, A. Yariv, " Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Yokouchi, N.

N. Yokouchi, A. J. Danner, K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron.,  9, 1439-1447 (2003).
[CrossRef]

Zeaiter, K.

T. C. Kleckner, A. S. Helmy, K. Zeaiter, D. C. Hutchings, J. S. Aitchison, "Dispersion and Modulation of the Linear Optical Properties of GaAs/AlAs Superlattices Waveguides using Quantum Well Intermixing," IEEE J. Quantum Eletron. (Accepted).

Appl. Phys. Lett.

A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998).
[CrossRef]

S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, M. Calligaro, "Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84,2974-2976 (2004).
[CrossRef]

IEEE J. Quantum Electron.

R. Haidar, N. Forget, E. Rosencher, "Optical parametric oscillation in micro-cavities based on isotropic semiconductors: a theoretical study," IEEE J. Quantum Electron. 39, 569-576 (2003).
[CrossRef]

IEEE J. Quantum Eletron.

P. M. Lambkin, K. A. Shore, "Nonlinear semiconductor Bragg reflection waveguide structures," IEEE J. Quantum Eletron. 27, 824-828 (1991).
[CrossRef]

T. C. Kleckner, A. S. Helmy, K. Zeaiter, D. C. Hutchings, J. S. Aitchison, "Dispersion and Modulation of the Linear Optical Properties of GaAs/AlAs Superlattices Waveguides using Quantum Well Intermixing," IEEE J. Quantum Eletron. (Accepted).

IEEE J. Sel. Top. Quantum Electron.

N. Yokouchi, A. J. Danner, K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron.,  9, 1439-1447 (2003).
[CrossRef]

J. Appl. Phys.

P. Yeh, A. Yariv, C Hong "Electromagnetic propagation in periodic stratified media: I. General Theory," J. Appl. Phys.,  67, 423-438 (1977).

C. Wätcher, F. Lederer, L. Leine, U. Trutschel, M. Mann, " Nonlinear Bragg reflection waveguide," J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

J. Cryst. Growth

C. B. Ebert, L. A. Eyres, M. M. Fejer, J. H. Harris, "GaAs/Ge/GaAs sublattice reversal epitaxy and its application to nonlinear optical devices," J. Cryst. Growth 227, 183-192 (1999).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

P. Yeh, A. Yariv, " Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Opt. Express

Opt. Lett

J. Khurgin, "Improvement of frequency-conversion efficiency in waveguides with rotationally twinned layers," Opt. Lett,  13, 603-605 (1988).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

P. Dong, A. G. Kirk, "Nonlinear frequency conversion in waveguide directional couplers," Phys. Rev. Lett. 93,133901 (2004).
[CrossRef] [PubMed]

Other

A. S. Helmy, BrianR.  West "Phase Matching using Bragg Reflector Waveguides," IEEE LEOS Annual Meeting, Sydney, (2005).
[CrossRef]

P. Yeh, Optical Waves in layered media, (Wiley, 1988).

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Figures (5)

Fig. 1.
Fig. 1.

A schematic diagram of a BRW with the propagation direction orthogonal to the Bragg stack.

Fig. 2.
Fig. 2.

Plot of the refractive index dispersion of a BRW similar to that shown in Fig. 1. The waveguide structure that resulted in this dispersion curve is a 200 nm core (nc) of Al0.24G0.76aAs, sandwiched in a Bragg stack made of alternating layers of Al0.3G0.7aAs and Al0.5G0.5aAs (n1 and n2).

Fig. 3.
Fig. 3.

A graphical example of the solution of both the TIR and BR modes. The waveguide structure that resulted in this dispersion curve is a 310 nm core of 30% AlGaAs, sandwiched in a Bragg stack made of alternating quarter wave layers of 20% and 40% AlGaAs.

Fig. 4.
Fig. 4.

Field profiles of both the TE-polarized TIR mode @ 1550 nm and the TM-polarized BRW mode at 775nm.

Fig. 5.
Fig. 5.

Modal index of both the TIR and BR modes due to the change of the core bandgap, and hence refractive index.

Equations (14)

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E ( x , z , t ) = { E K ( x d c 2 ) e iK ( x d c 2 ) e i ( ωt βz ) x > d c 2 [ C 1 cos ( k c x ) + C 2 sin ( k c x ) ] e i ( ωt βz ) d c 2 < x d c 2 E K ( x d c 2 ) e iK ( x + d c 2 ) e i ( ωt βz ) x d c 2
k c 2 = ( ω . n c c ) 2 = β 2 + k x 2
k ix d i = π 2 , i = 1,2
k ix 2 = ( ω . n i c ) 2 β 2 , i = 1,2
i k 1 x e iK Λ + k 1 x k 2 x e iK Λ + k 2 x k 1 x = { k c tan ( k c d c ) for even TE modes k c cot ( k c d c ) for odd TE modes
i k 1 x n c 2 e iK Λ + n 2 2 k 1 x n 1 2 k 2 x e iK Λ + n 1 2 k 2 x n 2 2 k 1 x = { k c n 1 2 tan ( k c d c ) for even TE modes k c n 1 2 cot ( k c d c ) for odd TE modes
K = Λ ± i κ i , m = 1,2 . .
Λ κ i { ln ( k 2 x k 1 x ) for TE modes ln ( n 1 2 k 2 x n 2 2 k 1 x ) for TE mode
M structure = ( m 11 m 12 m 21 m 22 ) = j = 1 l M j , total number of layers = l
M j = ( cos Φ j i γ j sin Φ j i γ j sin Φ j cos Φ j )
Φ j = k jx d j
γ j = { n j 2 n eff 2 c μ o for TE modes n j 2 n eff 2 c ε o for TM modes
χ M ( n eff ) = γ c m 11 + γ c γ s m 12 + m 21 + γ s m 22 ,
Δ ω gap ω o 2 π ( k 2 x k 1 x k 2 x ) ,

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