Abstract

We propose a scheme for on-chip isolation in chalcogenide (As2S3) rib waveguides, in which Stimulated Brillouin Scattering is used to induce non-reciprocal mode conversion within a multi-moded waveguide. The design exploits the idea that a chalcogenide rib buried in a silica matrix acts as waveguide for both light and sound, and can also be designed to be multi-moded for both optical and acoustic waves. The enhanced opto-acoustic coupling allows significant isolation (> 20 dB) within a chip-scale (cm-long) device (< 10 cm). We also show that the bandwidth of this device can be dramatically increased by tuning the dispersion of the waveguide to match the group velocity between optical modes: we find that 20 dB isolation can be extended over a bandwidth of 25 nm.

© 2012 OSA

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  1. M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals.” Nat. Mater.3, 211–219 (2004).
    [CrossRef]
  2. X. Huang and S. Fan, “Complete all-optical silica fiber isolator via Stimulated Brillouin Scattering,” J. Lightwave Technol.29, 2267–2275 (2011).
    [CrossRef]
  3. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3, 91–94 (2009).
    [CrossRef]
  4. Z. Yu and S. Fan, “Integrated nonmagnetic optical isolators based on photonic transitions,” IEEE J. Sel. Top. Quantum Electron.16, 459–466 (2010).
    [CrossRef]
  5. L. J. Aplet and J. W. Carson, “A Faraday effect optical isolator,” Appl. Optics3, 544–545 (1964).
    [CrossRef]
  6. M. Levy, “The on-chip integration of magnetooptic waveguide isolators,” IEEE J. Sel. Top. Quantum Electron.8, 1300–1306 (2002).
    [CrossRef]
  7. Y. Shoji, T. Mizumoto, H. Yokoi, I. Hsieh, and R. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett.92, 071117 (2008).
    [CrossRef]
  8. M.-C. Tien, T. Mizumoto, P. Pintus, H. Kroemer, and J. Bowers, “Silicon ring isolators with bonded nonreciprocal magneto-optic garnets,” Opt. Express19, 11740–11745 (2011).
    [CrossRef] [PubMed]
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  13. R. W. Boyd, Nonlinear optics, 3rd ed. (Academic Press, 2003).
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    [CrossRef]
  15. B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics5, 141–148 (2011).
  16. R. Pant, C. G. Poulton, D.-Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering.” Opt. Express19, 8285–8290 (2011).
    [CrossRef] [PubMed]
  17. R. Pant, E. Li, D.-Y. Choi, C. G. Poulton, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Cavity enhanced stimulated Brillouin scattering in an optical chip for multiorder Stokes generation,” Opt. Lett.36, 3687–3689 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  22. K. Finsterbusch, N. J. Baker, V. G. Ta’eed, B. J. Eggleton, D.-Y. Choi, S. Madden, and B. Luther-Davies, “Higher-order mode grating devices in As2S3 chalcogenide glass rib waveguides,” J. Opt. Soc. Am. B24, 1283–1290 (2007).
    [CrossRef]
  23. R. Pant, A. Byrnes, C. G. Poulton, E. Li, D.-y. Choi, S. Madden, B. Luther-davies, and B. J. Eggleton, “Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering,” Opt. Lett.37, 969–971 (2012).
    [CrossRef] [PubMed]
  24. J. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J.48, 2133–2160 (1969).
  25. N. Uchida and N. Niizeki, “Acoustooptic Deflection Materials and Techniques,” Proc. IEEE61, 1073–1092 (1973).
    [CrossRef]
  26. S. Ramachandran, Z. Wang, and M. Yan, “Bandwidth control of long-period grating-based mode converters in few-mode fibers,” Opt. Lett.27, 698–700 (2002).
    [CrossRef]
  27. M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D.-Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett.34, 3671–3673 (2009).
    [CrossRef] [PubMed]
  28. M. Shokooh-Saremi, V. G. Ta, N. J. Baker, I. C. M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer,” J. Opt. Soc. Am. B23, 1323–1331 (2006).
    [CrossRef]

2012 (5)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode.” Science335, 447–450 (2012).
[CrossRef]

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett.109, 033901 (2012).
[CrossRef] [PubMed]

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength Limit,” Phys. Rev. X2, 1–15 (2012).
[CrossRef]

J. D. Love and N. Riesen, “Single-, Few-, and Multimode Y-Junctions,” J. Lightwave Technol.30, 304–309 (2012).
[CrossRef]

R. Pant, A. Byrnes, C. G. Poulton, E. Li, D.-y. Choi, S. Madden, B. Luther-davies, and B. J. Eggleton, “Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering,” Opt. Lett.37, 969–971 (2012).
[CrossRef] [PubMed]

2011 (6)

2010 (1)

Z. Yu and S. Fan, “Integrated nonmagnetic optical isolators based on photonic transitions,” IEEE J. Sel. Top. Quantum Electron.16, 459–466 (2010).
[CrossRef]

2009 (2)

2008 (1)

Y. Shoji, T. Mizumoto, H. Yokoi, I. Hsieh, and R. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett.92, 071117 (2008).
[CrossRef]

2007 (1)

2006 (2)

2004 (1)

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals.” Nat. Mater.3, 211–219 (2004).
[CrossRef]

2002 (2)

M. Levy, “The on-chip integration of magnetooptic waveguide isolators,” IEEE J. Sel. Top. Quantum Electron.8, 1300–1306 (2002).
[CrossRef]

S. Ramachandran, Z. Wang, and M. Yan, “Bandwidth control of long-period grating-based mode converters in few-mode fibers,” Opt. Lett.27, 698–700 (2002).
[CrossRef]

1999 (1)

1995 (1)

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.13, 615–627 (1995).
[CrossRef]

1973 (1)

N. Uchida and N. Niizeki, “Acoustooptic Deflection Materials and Techniques,” Proc. IEEE61, 1073–1092 (1973).
[CrossRef]

1969 (1)

J. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J.48, 2133–2160 (1969).

1964 (1)

L. J. Aplet and J. W. Carson, “A Faraday effect optical isolator,” Appl. Optics3, 544–545 (1964).
[CrossRef]

Aplet, L. J.

L. J. Aplet and J. W. Carson, “A Faraday effect optical isolator,” Appl. Optics3, 544–545 (1964).
[CrossRef]

Assanto, G.

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids, Volume II, 1st ed. (John Wiley & Sons, 1973).

Baker, N. J.

Bowers, J.

Boyd, R. W.

R. W. Boyd, Nonlinear optics, 3rd ed. (Academic Press, 2003).

Bulla, D. A. P.

Butsch, A.

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5, 549–553 (2011).
[CrossRef]

Byrnes, A.

Camacho, R.

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength Limit,” Phys. Rev. X2, 1–15 (2012).
[CrossRef]

Carson, J. W.

L. J. Aplet and J. W. Carson, “A Faraday effect optical isolator,” Appl. Optics3, 544–545 (1964).
[CrossRef]

Choi, D.-y.

Davids, P.

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength Limit,” Phys. Rev. X2, 1–15 (2012).
[CrossRef]

Eggleton, B. J.

R. Pant, A. Byrnes, C. G. Poulton, E. Li, D.-y. Choi, S. Madden, B. Luther-davies, and B. J. Eggleton, “Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering,” Opt. Lett.37, 969–971 (2012).
[CrossRef] [PubMed]

R. Pant, E. Li, D.-Y. Choi, C. G. Poulton, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Cavity enhanced stimulated Brillouin scattering in an optical chip for multiorder Stokes generation,” Opt. Lett.36, 3687–3689 (2011).
[CrossRef] [PubMed]

R. Pant, C. G. Poulton, D.-Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering.” Opt. Express19, 8285–8290 (2011).
[CrossRef] [PubMed]

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics5, 141–148 (2011).

M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D.-Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett.34, 3671–3673 (2009).
[CrossRef] [PubMed]

K. Finsterbusch, N. J. Baker, V. G. Ta’eed, B. J. Eggleton, D.-Y. Choi, S. Madden, and B. Luther-Davies, “Higher-order mode grating devices in As2S3 chalcogenide glass rib waveguides,” J. Opt. Soc. Am. B24, 1283–1290 (2007).
[CrossRef]

M. Shokooh-Saremi, V. G. Ta, N. J. Baker, I. C. M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer,” J. Opt. Soc. Am. B23, 1323–1331 (2006).
[CrossRef]

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode.” Science335, 447–450 (2012).
[CrossRef]

Fan, S.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett.109, 033901 (2012).
[CrossRef] [PubMed]

X. Huang and S. Fan, “Complete all-optical silica fiber isolator via Stimulated Brillouin Scattering,” J. Lightwave Technol.29, 2267–2275 (2011).
[CrossRef]

Z. Yu and S. Fan, “Integrated nonmagnetic optical isolators based on photonic transitions,” IEEE J. Sel. Top. Quantum Electron.16, 459–466 (2010).
[CrossRef]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3, 91–94 (2009).
[CrossRef]

Finsterbusch, K.

Freude, W.

Fujii, M.

Gai, X.

Gallo, K.

Goell, J.

J. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J.48, 2133–2160 (1969).

Grillet, C.

Hile, S.

Hsieh, I.

Y. Shoji, T. Mizumoto, H. Yokoi, I. Hsieh, and R. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett.92, 071117 (2008).
[CrossRef]

Huang, X.

Joannopoulos, J. D.

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals.” Nat. Mater.3, 211–219 (2004).
[CrossRef]

Kang, M. S.

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5, 549–553 (2011).
[CrossRef]

Kroemer, H.

Lee, M. W.

Leuthold, J.

Levy, M.

M. Levy, “The on-chip integration of magnetooptic waveguide isolators,” IEEE J. Sel. Top. Quantum Electron.8, 1300–1306 (2002).
[CrossRef]

Li, E.

Lipson, M.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett.109, 033901 (2012).
[CrossRef] [PubMed]

Lira, H.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett.109, 033901 (2012).
[CrossRef] [PubMed]

Littler, I. C. M.

Love, J. D.

Luther-davies, B.

R. Pant, A. Byrnes, C. G. Poulton, E. Li, D.-y. Choi, S. Madden, B. Luther-davies, and B. J. Eggleton, “Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering,” Opt. Lett.37, 969–971 (2012).
[CrossRef] [PubMed]

R. Pant, E. Li, D.-Y. Choi, C. G. Poulton, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Cavity enhanced stimulated Brillouin scattering in an optical chip for multiorder Stokes generation,” Opt. Lett.36, 3687–3689 (2011).
[CrossRef] [PubMed]

R. Pant, C. G. Poulton, D.-Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering.” Opt. Express19, 8285–8290 (2011).
[CrossRef] [PubMed]

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics5, 141–148 (2011).

M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D.-Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett.34, 3671–3673 (2009).
[CrossRef] [PubMed]

K. Finsterbusch, N. J. Baker, V. G. Ta’eed, B. J. Eggleton, D.-Y. Choi, S. Madden, and B. Luther-Davies, “Higher-order mode grating devices in As2S3 chalcogenide glass rib waveguides,” J. Opt. Soc. Am. B24, 1283–1290 (2007).
[CrossRef]

M. Shokooh-Saremi, V. G. Ta, N. J. Baker, I. C. M. Littler, D. J. Moss, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer,” J. Opt. Soc. Am. B23, 1323–1331 (2006).
[CrossRef]

Madden, S.

Madden, S. J.

Mägi, E. C.

Maitra, A.

Mcfarlane, H.

Mizumoto, T.

M.-C. Tien, T. Mizumoto, P. Pintus, H. Kroemer, and J. Bowers, “Silicon ring isolators with bonded nonreciprocal magneto-optic garnets,” Opt. Express19, 11740–11745 (2011).
[CrossRef] [PubMed]

Y. Shoji, T. Mizumoto, H. Yokoi, I. Hsieh, and R. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett.92, 071117 (2008).
[CrossRef]

Moss, D. J.

Niizeki, N.

N. Uchida and N. Niizeki, “Acoustooptic Deflection Materials and Techniques,” Proc. IEEE61, 1073–1092 (1973).
[CrossRef]

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode.” Science335, 447–450 (2012).
[CrossRef]

Osgood, R.

Y. Shoji, T. Mizumoto, H. Yokoi, I. Hsieh, and R. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett.92, 071117 (2008).
[CrossRef]

Pant, R.

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.13, 615–627 (1995).
[CrossRef]

Pintus, P.

Poulton, C.

Poulton, C. G.

Qi, M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode.” Science335, 447–450 (2012).
[CrossRef]

Rakich, P.

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength Limit,” Phys. Rev. X2, 1–15 (2012).
[CrossRef]

Ramachandran, S.

Reinke, C.

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength Limit,” Phys. Rev. X2, 1–15 (2012).
[CrossRef]

Richardson, K.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics5, 141–148 (2011).

Riesen, N.

Ruan, Y.

Russell, P. S. J.

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5, 549–553 (2011).
[CrossRef]

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode.” Science335, 447–450 (2012).
[CrossRef]

Shoji, Y.

Y. Shoji, T. Mizumoto, H. Yokoi, I. Hsieh, and R. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett.92, 071117 (2008).
[CrossRef]

Shokooh-Saremi, M.

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol.13, 615–627 (1995).
[CrossRef]

Soljacic, M.

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals.” Nat. Mater.3, 211–219 (2004).
[CrossRef]

Ta, V. G.

Ta’eed, V. G.

Thevenaz, L.

Tien, M.-C.

Tomljenovic-Hanic, S.

Uchida, N.

N. Uchida and N. Niizeki, “Acoustooptic Deflection Materials and Techniques,” Proc. IEEE61, 1073–1092 (1973).
[CrossRef]

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode.” Science335, 447–450 (2012).
[CrossRef]

Wang, J.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode.” Science335, 447–450 (2012).
[CrossRef]

Wang, Z.

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength Limit,” Phys. Rev. X2, 1–15 (2012).
[CrossRef]

S. Ramachandran, Z. Wang, and M. Yan, “Bandwidth control of long-period grating-based mode converters in few-mode fibers,” Opt. Lett.27, 698–700 (2002).
[CrossRef]

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode.” Science335, 447–450 (2012).
[CrossRef]

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode.” Science335, 447–450 (2012).
[CrossRef]

Yan, M.

Yokoi, H.

Y. Shoji, T. Mizumoto, H. Yokoi, I. Hsieh, and R. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett.92, 071117 (2008).
[CrossRef]

Yu, Z.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett.109, 033901 (2012).
[CrossRef] [PubMed]

Z. Yu and S. Fan, “Integrated nonmagnetic optical isolators based on photonic transitions,” IEEE J. Sel. Top. Quantum Electron.16, 459–466 (2010).
[CrossRef]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3, 91–94 (2009).
[CrossRef]

Appl. Optics (1)

L. J. Aplet and J. W. Carson, “A Faraday effect optical isolator,” Appl. Optics3, 544–545 (1964).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Shoji, T. Mizumoto, H. Yokoi, I. Hsieh, and R. Osgood, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett.92, 071117 (2008).
[CrossRef]

Bell Syst. Tech. J. (1)

J. Goell, “A circular-harmonic computer analysis of rectangular dielectric waveguides,” Bell Syst. Tech. J.48, 2133–2160 (1969).

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

M. Levy, “The on-chip integration of magnetooptic waveguide isolators,” IEEE J. Sel. Top. Quantum Electron.8, 1300–1306 (2002).
[CrossRef]

Z. Yu and S. Fan, “Integrated nonmagnetic optical isolators based on photonic transitions,” IEEE J. Sel. Top. Quantum Electron.16, 459–466 (2010).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (3)

Nat. Mater. (1)

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals.” Nat. Mater.3, 211–219 (2004).
[CrossRef]

Nat. Photonics (3)

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3, 91–94 (2009).
[CrossRef]

M. S. Kang, A. Butsch, and P. S. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics5, 549–553 (2011).
[CrossRef]

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics5, 141–148 (2011).

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett.109, 033901 (2012).
[CrossRef] [PubMed]

Phys. Rev. X (1)

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength Limit,” Phys. Rev. X2, 1–15 (2012).
[CrossRef]

Proc. IEEE (1)

N. Uchida and N. Niizeki, “Acoustooptic Deflection Materials and Techniques,” Proc. IEEE61, 1073–1092 (1973).
[CrossRef]

Science (1)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode.” Science335, 447–450 (2012).
[CrossRef]

Other (2)

R. W. Boyd, Nonlinear optics, 3rd ed. (Academic Press, 2003).

B. A. Auld, Acoustic Fields and Waves in Solids, Volume II, 1st ed. (John Wiley & Sons, 1973).

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Figures (9)

Fig. 1
Fig. 1

Schematic of isolator operation. Two pump modes are mixed into the fundamental and first higher-order mode of a multi-mode chalcogenide rib waveguide. These pumps excite a guided acoustic mode in the long central section, which drives a transition from the signal in the fundamental mode at ω3 to a higher-order mode at frequency ω4. The higher-order mode is then filtered out using symmetry. A signal propagating in the reverse direction does not undergo mode conversion, and so can propagate from the right to the left of the device unimpeded except for losses at the waveguide transitions.

Fig. 2
Fig. 2

(a) Dispersion diagram showing the optical and acoustic modes: energy and momentum conservation must be satisfied to drive the transition from one optical mode to another; (b) Rib waveguide design used in our simulations.

Fig. 3
Fig. 3

Electromagnetic modes for the rib waveguide depicted in Fig. 2(b): the z-component of the time-averaged Poynting vector is depicted.

Fig. 4
Fig. 4

Fundamental and first higher-order acoustic modes for the rib waveguide depicted in Fig. 2(b). The normalized acoustic energy density is depicted.

Fig. 5
Fig. 5

Computed isolation as a function of initial power in pump 1, as given by Eq. (9). Computed by solving Eq. (5)(8) with power in pump 2 of P2(0) = 400 mW.

Fig. 6
Fig. 6

Power in optical and acoustic modes mode as a function of waveguide length, as computed by solving Eq. (5)(8) with initial power in pump 2 P2(0) = 400 mW; (a) The maximum-isolation point predicted by Fig. 5, with P1(0) = 200 μW; (b) Lower isolation point, with P1(0) = 100 mW.

Fig. 7
Fig. 7

Maximum isolation, given by Eq. (9), as a function of total power and wavelength, for waveguide lengths of (a) 5 cm and (b) 10 cm. Obtained by numerical solution of (5)–(8).

Fig. 8
Fig. 8

(a) Cross-section of photo-induced perturbation across the chalcogenide rib; (b) Group index of the optical modes as a function of perturbation height; (c) Mode fields for the first two modes with Δn = 0.04.

Fig. 9
Fig. 9

Maximum isolation IdB for waveguide with vg-matched modes with lengths of (a) 5 cm and (b) 10 cm, showing broadband operation. Note that the wavelength scale is ∼ 60 times larger than for the non-dispersion-tuned waveguide (Fig. 7).

Equations (10)

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E k ( x , y , z , t ) = a k ( z , t ) e k ( x , y ) e i ( β k z ω k t ) + c.c .
ρ ( x , y , z , t ) = b ( z , t ) ρ ac ( x , y ) e i ( q z Ω t ) + c.c .
2 ρ ac + ( Ω ac 2 V ac 2 q 2 ) ρ ac = 0 ,
b ( z ) = ε 0 Q 12 a 1 * ( z ) a 2 ( z ) ,
d a 1 d z = i ω 1 Q 12 2 n 1 c ( 1 K 1 ) a 2 b * , d a 2 d z = i ω 2 Q 21 2 n 2 c ( 1 K 2 ) a 1 b .
Q i j = A γ e ρ 0 e i e j * ρ ac * d x d y , Q i j " = A γ e Γ B 2 ( e i e j * ) ρ ac * d x d y ,
K j = A | [ e j ] z | 2 + 1 2 i β j ( [ e j ] z * [ e j ] + [ e j ] * [ e j ] z ) d x d y .
d a 3 d z = i ω 3 Q 34 2 n 3 c ( 1 K 3 ) e i Δ β z a 4 b * , d a 4 d z = i ω 4 Q 43 2 n 4 c ( 1 K 4 ) e i Δ β z a 3 b .
I dB = 10 log 10 ( P 3 ( z = z max ) P 3 ( z = 0 ) ) ,
P k = 2 ε 0 n k c | a k | 2 A e k × h k * d x d y .

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