Abstract

We propose to use the unidirectionality of the optical Bloch oscillation phenomenon achievable in a magneto-optic asymmetric waveguide array to achieve optical isolation. At the 1.55 μm telecommunication wavelength, our isolator design exhibits an isolation ratio of 36 dB between forward- and backward-propagating waves. The proposed design consists of a waveguide array made in a silicon-on-insulator substrate with a magnetic garnet cover layer. A key role is played by the transverse-magnetic mode nonreciprocal phase shift effect.

© 2012 Optical Society of America

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  1. D. Dai, J. Bauters, and J. E. Bowers, Light: Sci. Applic. 1, 1 (2012).
    [CrossRef]
  2. Y. Vlasov, W. M. J. Green, and F. Xia, Nature Photon. 2, 242 (2008).
    [CrossRef]
  3. S. Wang, M. Shah, and J. D. Crow, J. Appl. Phys. 43, 1861 (1972).
    [CrossRef]
  4. M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photon. Technol. Lett. 8, 903 (1996).
    [CrossRef]
  5. J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
    [CrossRef]
  6. S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, Electron. Lett. 40, 1293 (2004).
    [CrossRef]
  7. M.-C. Tien, T. Mizumoto, P. Pintus, H. Kromer, and J. E. Bowers, Opt. Express 19, 11740 (2011).
    [CrossRef]
  8. L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nature Photon. 5, 758 (2011).
    [CrossRef]
  9. V. Zayets, H. Saito, K. Ando, and S. Yuasa, Materials 5, 857 (2012).
    [CrossRef]
  10. K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
    [CrossRef]
  11. Y. Shoji, I.-W. Hsieh, R. M. Osgood, and T. Mizumoto, J. Lightwave Technol. 25, 3108 (2007).
    [CrossRef]
  12. Z. Yu and S. Fan, Nature Photon. 3, 91 (2009).
    [CrossRef]
  13. Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Appl. Phys. Lett. 92, 071117 (2008).
    [CrossRef]
  14. H. L. Lira, Z. Yu, M. Lipson, and S. Fan, in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CW1K.5.
  15. P. Kumar and M. Levy, Opt. Lett. 36, 4359 (2011), and references therein.
    [CrossRef]
  16. M. Levy and P. Kumar, Opt. Lett. 35, 3147 (2010).
    [CrossRef]
  17. R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
    [CrossRef]
  18. C. Zener, Proc. R. Soc. A 145, 523 (1934).
    [CrossRef]
  19. U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
    [CrossRef]
  20. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
    [CrossRef]
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  23. R. Chen, G. Jiang, Y. Hao, J. Yang, M. Wang, and X. Jiang, Opt. Lett. 35, 1335 (2010).
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2012 (3)

D. Dai, J. Bauters, and J. E. Bowers, Light: Sci. Applic. 1, 1 (2012).
[CrossRef]

V. Zayets, H. Saito, K. Ando, and S. Yuasa, Materials 5, 857 (2012).
[CrossRef]

K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
[CrossRef]

2011 (5)

2010 (2)

2009 (1)

Z. Yu and S. Fan, Nature Photon. 3, 91 (2009).
[CrossRef]

2008 (2)

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

Y. Vlasov, W. M. J. Green, and F. Xia, Nature Photon. 2, 242 (2008).
[CrossRef]

2007 (1)

2004 (1)

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, Electron. Lett. 40, 1293 (2004).
[CrossRef]

2000 (1)

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

1999 (1)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

1998 (1)

1996 (1)

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photon. Technol. Lett. 8, 903 (1996).
[CrossRef]

1990 (1)

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

1972 (1)

S. Wang, M. Shah, and J. D. Crow, J. Appl. Phys. 43, 1861 (1972).
[CrossRef]

1934 (1)

C. Zener, Proc. R. Soc. A 145, 523 (1934).
[CrossRef]

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Ando, K.

V. Zayets, H. Saito, K. Ando, and S. Yuasa, Materials 5, 857 (2012).
[CrossRef]

Bauters, J.

D. Dai, J. Bauters, and J. E. Bowers, Light: Sci. Applic. 1, 1 (2012).
[CrossRef]

Bhandare, S.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, Electron. Lett. 40, 1293 (2004).
[CrossRef]

Bi, L.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nature Photon. 5, 758 (2011).
[CrossRef]

Bowers, J. E.

Cadieu, F. J.

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photon. Technol. Lett. 8, 903 (1996).
[CrossRef]

Chen, R.

Christodoulides, D. N.

Crow, J. D.

S. Wang, M. Shah, and J. D. Crow, J. Appl. Phys. 43, 1861 (1972).
[CrossRef]

Dai, D.

D. Dai, J. Bauters, and J. E. Bowers, Light: Sci. Applic. 1, 1 (2012).
[CrossRef]

Dionne, G. F.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nature Photon. 5, 758 (2011).
[CrossRef]

Dotsch, H.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

El-Ganainy, R.

Fan, S.

K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
[CrossRef]

Z. Yu and S. Fan, Nature Photon. 3, 91 (2009).
[CrossRef]

H. L. Lira, Z. Yu, M. Lipson, and S. Fan, in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CW1K.5.

Fang, K.

K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
[CrossRef]

Fratello, V. J.

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photon. Technol. Lett. 8, 903 (1996).
[CrossRef]

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Fujita, J.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

Green, W. M. J.

Y. Vlasov, W. M. J. Green, and F. Xia, Nature Photon. 2, 242 (2008).
[CrossRef]

Hao, Y.

Hegde, H.

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photon. Technol. Lett. 8, 903 (1996).
[CrossRef]

Hsieh, I.-W.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

Y. Shoji, I.-W. Hsieh, R. M. Osgood, and T. Mizumoto, J. Lightwave Technol. 25, 3108 (2007).
[CrossRef]

Hu, J.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nature Photon. 5, 758 (2011).
[CrossRef]

Huang, W.-P.

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

Ibrahim, S. K.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, Electron. Lett. 40, 1293 (2004).
[CrossRef]

Jiang, G.

Jiang, P.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nature Photon. 5, 758 (2011).
[CrossRef]

Jiang, X.

Kim, D. H.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nature Photon. 5, 758 (2011).
[CrossRef]

Kimerling, L. C.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nature Photon. 5, 758 (2011).
[CrossRef]

Kip, D.

Kopylov, N.

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Kromer, H.

Kumar, P.

Lederer, F.

Levy, M.

P. Kumar and M. Levy, Opt. Lett. 36, 4359 (2011), and references therein.
[CrossRef]

M. Levy and P. Kumar, Opt. Lett. 35, 3147 (2010).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photon. Technol. Lett. 8, 903 (1996).
[CrossRef]

Lieberman, R. A.

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Lipson, M.

H. L. Lira, Z. Yu, M. Lipson, and S. Fan, in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CW1K.5.

Lira, H. L.

H. L. Lira, Z. Yu, M. Lipson, and S. Fan, in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CW1K.5.

Mizumoto, T.

Morandotti, R.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Mu, J.-W.

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

Noe, R.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, Electron. Lett. 40, 1293 (2004).
[CrossRef]

Osgood, R. M.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

Y. Shoji, I.-W. Hsieh, R. M. Osgood, and T. Mizumoto, J. Lightwave Technol. 25, 3108 (2007).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photon. Technol. Lett. 8, 903 (1996).
[CrossRef]

Pertsch, T.

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Pintus, P.

Ross, C. A.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nature Photon. 5, 758 (2011).
[CrossRef]

Ruter, C. E.

Saito, H.

V. Zayets, H. Saito, K. Ando, and S. Yuasa, Materials 5, 857 (2012).
[CrossRef]

Sandel, D.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, Electron. Lett. 40, 1293 (2004).
[CrossRef]

Scotti, R. E.

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Shah, M.

S. Wang, M. Shah, and J. D. Crow, J. Appl. Phys. 43, 1861 (1972).
[CrossRef]

Shoji, Y.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

Y. Shoji, I.-W. Hsieh, R. M. Osgood, and T. Mizumoto, J. Lightwave Technol. 25, 3108 (2007).
[CrossRef]

Silberberg, Y.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Tien, M.-C.

Vlasov, Y.

Y. Vlasov, W. M. J. Green, and F. Xia, Nature Photon. 2, 242 (2008).
[CrossRef]

Wang, M.

Wang, S.

S. Wang, M. Shah, and J. D. Crow, J. Appl. Phys. 43, 1861 (1972).
[CrossRef]

Wilkens, L.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

Wolfe, R.

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photon. Technol. Lett. 8, 903 (1996).
[CrossRef]

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

Xia, F.

Y. Vlasov, W. M. J. Green, and F. Xia, Nature Photon. 2, 242 (2008).
[CrossRef]

Yang, J.

Yokoi, H.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

Yu, Z.

K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
[CrossRef]

Z. Yu and S. Fan, Nature Photon. 3, 91 (2009).
[CrossRef]

H. L. Lira, Z. Yu, M. Lipson, and S. Fan, in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CW1K.5.

Yuasa, S.

V. Zayets, H. Saito, K. Ando, and S. Yuasa, Materials 5, 857 (2012).
[CrossRef]

Zayets, V.

V. Zayets, H. Saito, K. Ando, and S. Yuasa, Materials 5, 857 (2012).
[CrossRef]

Zener, C.

C. Zener, Proc. R. Soc. A 145, 523 (1934).
[CrossRef]

Zhang, H.

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, Electron. Lett. 40, 1293 (2004).
[CrossRef]

Zhang, W.

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

Zhao, W.

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

Appl. Phys. Lett. (4)

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

R. Wolfe, R. A. Lieberman, V. J. Fratello, R. E. Scotti, and N. Kopylov, Appl. Phys. Lett. 56, 426 (1990).
[CrossRef]

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

Electron. Lett. (1)

S. K. Ibrahim, S. Bhandare, D. Sandel, H. Zhang, and R. Noe, Electron. Lett. 40, 1293 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Levy, R. M. Osgood, H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, IEEE Photon. Technol. Lett. 8, 903 (1996).
[CrossRef]

J. Appl. Phys. (1)

S. Wang, M. Shah, and J. D. Crow, J. Appl. Phys. 43, 1861 (1972).
[CrossRef]

J. Lightwave Technol. (1)

Light: Sci. Applic. (1)

D. Dai, J. Bauters, and J. E. Bowers, Light: Sci. Applic. 1, 1 (2012).
[CrossRef]

Materials (1)

V. Zayets, H. Saito, K. Ando, and S. Yuasa, Materials 5, 857 (2012).
[CrossRef]

Nature Photon. (3)

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nature Photon. 5, 758 (2011).
[CrossRef]

Y. Vlasov, W. M. J. Green, and F. Xia, Nature Photon. 2, 242 (2008).
[CrossRef]

Z. Yu and S. Fan, Nature Photon. 3, 91 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. Lett. (2)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

K. Fang, Z. Yu, and S. Fan, Phys. Rev. Lett. 108, 153901 (2012).
[CrossRef]

Proc. R. Soc. A (1)

C. Zener, Proc. R. Soc. A 145, 523 (1934).
[CrossRef]

Other (1)

H. L. Lira, Z. Yu, M. Lipson, and S. Fan, in CLEO: Science and Innovations, OSA Technical Digest (online) (Optical Society of America, 2012), paper CW1K.5.

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Figures (2)

Fig. 1.
Fig. 1.

(a) Bloch oscillator waveguide array (widths are scaled up and separations scaled down four times to fit in the sketch) and (b) unidirectional BO-based isolator design showing the BO array with damping channels on each side.

Fig. 2.
Fig. 2.

In the FW direction, the beam returns to the central channel after traveling one Bloch period as shown by (a) the intensity plot and (c) the simulation plot; in the BW direction, a diffractive beam spread occurs with the beam reaching the damping channels as depicted by (b) a simulation plot and (d) the corresponding intensity plot. The intensity plots (a) and (d) show the slice output at the Bloch period [highlighted with square boxes in (c) and (b)] in the FW and BW directions, respectively.

Equations (3)

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

idanf,bdz+δβf,bnanf,b+κf,b(an1f,b+an+1f,b)=0,
ε^=(ε0ig0ε0ig0ε).
δβm+1,mfδβm+1,mb=βm+1fβmf(βm+1bβmb)=Δβm+1nrΔβmnr=Δ(Δβnr)m+1,m.

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