Abstract

We analyze an on-chip optical isolator based on direction dependent single-mode cutoff, which is described in 1D and 2D momentum space. Isolation is shown using 3D finite difference time domain (FDTD) where the magnetization is represented by imaginary off-diagonal permittivity tensor elements. The isolator designs are optimized using perturbation theory, which successfully predicts increased isolation for rib waveguides and structures with non-magnetic dielectric layers. Our isolators are based on bismuth iron garnet and its compatible substrates; an isolation ratio of 10.7 dB/mm is achieved for TM modes.

© 2009 Optical Society of America

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References

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  1. J. M. Liu, Photonic Devices (Cambridge, New York, 2005).
    [CrossRef]
  2. G. A. Allen, "The Magneto-optic Spectra of Bismuth-substituted Iron Garnets" (Ph.D. Dissertation, Massachusetts Institute of Technology, 1994).
  3. A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
    [CrossRef]
  4. N. Kono and M. Koshiba, "Three-dimensional finite element analysis of nonreciprocal phase shifts in magneto-photonic crystal waveguides," Opt. Express 13, 9155-9166 (2005).
    [CrossRef] [PubMed]
  5. Z. Yu, G. Veronis, Z. Wang, and S. Fan, "One-Way Electromagnetic Waveguide formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal," Phys. Rev. Lett. 100, 023902 (2008).
    [CrossRef] [PubMed]
  6. Y. Shoji, I. W. Hsieh, R. M. Osgood, and T. Mizumoto, "Polarization-Independent Magneto-Optical Waveguide Isolator Using TM-Mode Nonreciprocal Phase Shift," J. Lightwave Technol. 25, 3108-3113 (2007).
    [CrossRef]
  7. T. Amemiya, H. Shimizu, M. Yokoyama, P. N. Hai, M. Tanaka, and Y. Nakano, "1.54-um TM-mode waveguide optical isolator based on the nonreciprocal-loss phenomenon: device design to reduce insertion loss," Appl. Opt. 46, 5784-5791 (2007).
    [CrossRef] [PubMed]
  8. H. Shimizu and Y. Nakano, "Fabrication and characterization of an InGaAs/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation," IEEE J. Lightwave Technol. 24,38-43 (2006).
    [CrossRef]
  9. H. Hemme, H. Dötsch, and P. Hertel, "Integrated optical isolator based on nonreciprocal-mode cut-off," Appl. Opt. 29, 2741-2744 (1990).
    [CrossRef] [PubMed]
  10. V. Priye and M. Tsutsumi, "Nonreciprocal behavior of leaky gyroscopic waveguide," Electron. Lett. 29, 104-105 (1993).
    [CrossRef]
  11. G. Dionne and G. Allen, "Spectra origins of giant Faraday rotation and ellipticity in Bi-substituted magnetic garnets," J. Appl. Phys. 73, 6127-6129 (1993).
    [CrossRef]
  12. T. Amemiya, H. Shimizu, P. N. Hai, M. Yokoyama, M. Tanaka, and Y. Nakano, "Waveguide-based 1.5 µm optical isolator based on magneto-optic effects in ferromagnetic MnAs," Jpn. J. Appl. Phys. 46, 205-210 (2007).
    [CrossRef]
  13. T. Körner, A. Heinrich, M. Weckerle, P. Roocks, and B. Stritzker, "Integration of magneto-optical active bismuth iron garnet on nongarnet substrates," J. Appl. Phys. 103, 07B337 (2008).
    [CrossRef]
  14. K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-614 (2002).
    [PubMed]
  15. L. Tang, S. Drezdzon, and T. Yoshie, "Single-mode waveguide optical isolator based on direction-dependent cutoff frequency," Opt. Express 16, 16202-16207 (2008).
    [CrossRef] [PubMed]

2008 (2)

Z. Yu, G. Veronis, Z. Wang, and S. Fan, "One-Way Electromagnetic Waveguide formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal," Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

L. Tang, S. Drezdzon, and T. Yoshie, "Single-mode waveguide optical isolator based on direction-dependent cutoff frequency," Opt. Express 16, 16202-16207 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (1)

H. Shimizu and Y. Nakano, "Fabrication and characterization of an InGaAs/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation," IEEE J. Lightwave Technol. 24,38-43 (2006).
[CrossRef]

2005 (1)

2002 (1)

2001 (1)

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[CrossRef]

1993 (2)

V. Priye and M. Tsutsumi, "Nonreciprocal behavior of leaky gyroscopic waveguide," Electron. Lett. 29, 104-105 (1993).
[CrossRef]

G. Dionne and G. Allen, "Spectra origins of giant Faraday rotation and ellipticity in Bi-substituted magnetic garnets," J. Appl. Phys. 73, 6127-6129 (1993).
[CrossRef]

1990 (1)

Allen, G.

G. Dionne and G. Allen, "Spectra origins of giant Faraday rotation and ellipticity in Bi-substituted magnetic garnets," J. Appl. Phys. 73, 6127-6129 (1993).
[CrossRef]

Amemiya, T.

T. Amemiya, H. Shimizu, P. N. Hai, M. Yokoyama, M. Tanaka, and Y. Nakano, "Waveguide-based 1.5 µm optical isolator based on magneto-optic effects in ferromagnetic MnAs," Jpn. J. Appl. Phys. 46, 205-210 (2007).
[CrossRef]

T. Amemiya, H. Shimizu, M. Yokoyama, P. N. Hai, M. Tanaka, and Y. Nakano, "1.54-um TM-mode waveguide optical isolator based on the nonreciprocal-loss phenomenon: device design to reduce insertion loss," Appl. Opt. 46, 5784-5791 (2007).
[CrossRef] [PubMed]

Dionne, G.

G. Dionne and G. Allen, "Spectra origins of giant Faraday rotation and ellipticity in Bi-substituted magnetic garnets," J. Appl. Phys. 73, 6127-6129 (1993).
[CrossRef]

Dötsch, H.

Drezdzon, S.

Fan, S.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, "One-Way Electromagnetic Waveguide formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal," Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

Figotin, A.

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Hai, P. N.

T. Amemiya, H. Shimizu, P. N. Hai, M. Yokoyama, M. Tanaka, and Y. Nakano, "Waveguide-based 1.5 µm optical isolator based on magneto-optic effects in ferromagnetic MnAs," Jpn. J. Appl. Phys. 46, 205-210 (2007).
[CrossRef]

T. Amemiya, H. Shimizu, M. Yokoyama, P. N. Hai, M. Tanaka, and Y. Nakano, "1.54-um TM-mode waveguide optical isolator based on the nonreciprocal-loss phenomenon: device design to reduce insertion loss," Appl. Opt. 46, 5784-5791 (2007).
[CrossRef] [PubMed]

Hemme, H.

Hertel, P.

Hsieh, I. W.

Kono, N.

Koshiba, M.

Mizumoto, T.

Nakano, Y.

T. Amemiya, H. Shimizu, M. Yokoyama, P. N. Hai, M. Tanaka, and Y. Nakano, "1.54-um TM-mode waveguide optical isolator based on the nonreciprocal-loss phenomenon: device design to reduce insertion loss," Appl. Opt. 46, 5784-5791 (2007).
[CrossRef] [PubMed]

T. Amemiya, H. Shimizu, P. N. Hai, M. Yokoyama, M. Tanaka, and Y. Nakano, "Waveguide-based 1.5 µm optical isolator based on magneto-optic effects in ferromagnetic MnAs," Jpn. J. Appl. Phys. 46, 205-210 (2007).
[CrossRef]

H. Shimizu and Y. Nakano, "Fabrication and characterization of an InGaAs/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation," IEEE J. Lightwave Technol. 24,38-43 (2006).
[CrossRef]

Osgood, R. M.

Painter, O.

Priye, V.

V. Priye and M. Tsutsumi, "Nonreciprocal behavior of leaky gyroscopic waveguide," Electron. Lett. 29, 104-105 (1993).
[CrossRef]

Shimizu, H.

T. Amemiya, H. Shimizu, P. N. Hai, M. Yokoyama, M. Tanaka, and Y. Nakano, "Waveguide-based 1.5 µm optical isolator based on magneto-optic effects in ferromagnetic MnAs," Jpn. J. Appl. Phys. 46, 205-210 (2007).
[CrossRef]

T. Amemiya, H. Shimizu, M. Yokoyama, P. N. Hai, M. Tanaka, and Y. Nakano, "1.54-um TM-mode waveguide optical isolator based on the nonreciprocal-loss phenomenon: device design to reduce insertion loss," Appl. Opt. 46, 5784-5791 (2007).
[CrossRef] [PubMed]

H. Shimizu and Y. Nakano, "Fabrication and characterization of an InGaAs/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation," IEEE J. Lightwave Technol. 24,38-43 (2006).
[CrossRef]

Shoji, Y.

Srinivasan, K.

Tanaka, M.

T. Amemiya, H. Shimizu, M. Yokoyama, P. N. Hai, M. Tanaka, and Y. Nakano, "1.54-um TM-mode waveguide optical isolator based on the nonreciprocal-loss phenomenon: device design to reduce insertion loss," Appl. Opt. 46, 5784-5791 (2007).
[CrossRef] [PubMed]

T. Amemiya, H. Shimizu, P. N. Hai, M. Yokoyama, M. Tanaka, and Y. Nakano, "Waveguide-based 1.5 µm optical isolator based on magneto-optic effects in ferromagnetic MnAs," Jpn. J. Appl. Phys. 46, 205-210 (2007).
[CrossRef]

Tang, L.

Tsutsumi, M.

V. Priye and M. Tsutsumi, "Nonreciprocal behavior of leaky gyroscopic waveguide," Electron. Lett. 29, 104-105 (1993).
[CrossRef]

Veronis, G.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, "One-Way Electromagnetic Waveguide formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal," Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

Vitebsky, I.

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Wang, Z.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, "One-Way Electromagnetic Waveguide formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal," Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

Yokoyama, M.

T. Amemiya, H. Shimizu, P. N. Hai, M. Yokoyama, M. Tanaka, and Y. Nakano, "Waveguide-based 1.5 µm optical isolator based on magneto-optic effects in ferromagnetic MnAs," Jpn. J. Appl. Phys. 46, 205-210 (2007).
[CrossRef]

T. Amemiya, H. Shimizu, M. Yokoyama, P. N. Hai, M. Tanaka, and Y. Nakano, "1.54-um TM-mode waveguide optical isolator based on the nonreciprocal-loss phenomenon: device design to reduce insertion loss," Appl. Opt. 46, 5784-5791 (2007).
[CrossRef] [PubMed]

Yoshie, T.

Yu, Z.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, "One-Way Electromagnetic Waveguide formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal," Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

Appl. Opt. (2)

Electron. Lett. (1)

V. Priye and M. Tsutsumi, "Nonreciprocal behavior of leaky gyroscopic waveguide," Electron. Lett. 29, 104-105 (1993).
[CrossRef]

IEEE J. Lightwave Technol. (1)

H. Shimizu and Y. Nakano, "Fabrication and characterization of an InGaAs/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation," IEEE J. Lightwave Technol. 24,38-43 (2006).
[CrossRef]

J. Appl. Phys. (1)

G. Dionne and G. Allen, "Spectra origins of giant Faraday rotation and ellipticity in Bi-substituted magnetic garnets," J. Appl. Phys. 73, 6127-6129 (1993).
[CrossRef]

J. Lightwave Technol. (1)

Jpn. J. Appl. Phys. (1)

T. Amemiya, H. Shimizu, P. N. Hai, M. Yokoyama, M. Tanaka, and Y. Nakano, "Waveguide-based 1.5 µm optical isolator based on magneto-optic effects in ferromagnetic MnAs," Jpn. J. Appl. Phys. 46, 205-210 (2007).
[CrossRef]

Opt. Express (3)

Phys. Rev. E (1)

A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

Z. Yu, G. Veronis, Z. Wang, and S. Fan, "One-Way Electromagnetic Waveguide formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal," Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef] [PubMed]

Other (3)

J. M. Liu, Photonic Devices (Cambridge, New York, 2005).
[CrossRef]

G. A. Allen, "The Magneto-optic Spectra of Bismuth-substituted Iron Garnets" (Ph.D. Dissertation, Massachusetts Institute of Technology, 1994).

T. Körner, A. Heinrich, M. Weckerle, P. Roocks, and B. Stritzker, "Integration of magneto-optical active bismuth iron garnet on nongarnet substrates," J. Appl. Phys. 103, 07B337 (2008).
[CrossRef]

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Figures (5)

Fig 1.
Fig 1.

Basic BIG isolator design: (a) Normalized band diagram results for different computational techniques; the GGG light line indicates single-mode cutoff. (b) The B:G structure with its dimensions and coordinate system; light propagates along the z-axis.

Fig. 2.
Fig. 2.

Ey TM mode profiles for different values of a for the un-magnetized B:G structure. (a) The mode is largely cutoff or unguided, providing lower than -150 dB/mm transmission; (b) an intermediate cutoff stage, with -30 dB/mm transmission; and (c) the mode is largely guided, with -3 dB/mm transmission. The black outline defines the BIG guiding region.

Fig. 3.
Fig. 3.

(a) The light cone of a slab waveguide; the dotted line represents cutoff. (b)-(d) 2D Momentum space diagrams for the Fourier transform of Ey measured on an xz-plane in the GGG substrate. The data is from 3D FDTD and corresponds to the first quadrant of a plane in the light cone defined by ω = ω 0. Note that the large isolation ratio (147 dB/mm) is because the value of ε 1″ for BIG is increased by a factor of ten. The total amount of energy in momentum space is lowest for (d) because more radiation is lost to the PML.

Fig. 4.
Fig. 4.

(a) The imaginary part of the electric field overlap for the B:G structure. (b) Result from perturbation theory for the B:G structure. The plot indicates that there is cancellation for Iyz because the components at the top and bottom of the guiding region have the opposite sign.

Fig. 5.
Fig. 5.

(a) Rib waveguide with 7.3 dB/mm isolation ratio. There is still cancellation in the integral Iyz due to the positive contribution near the BIG-GGG interface. (b) Incorporating dielectric materials (TiO2) with BIG; the isolation ratio is 5.41 dB/mm for this T:B:G structure. (c) The B:T:G structure, which has the highest isolation ratio of 10.7 dB/mm.

Tables (1)

Tables Icon

Table 1. 3D FDTD Isolation data for the various waveguide isolator structures.

Equations (2)

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

Δβ=2ω2c2β0 i,jIij ,
Iij=εji(x,y)Im[Ei*(x,y)Ej(x,y)] dxdy .

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