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).
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    [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]
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    [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 (3)

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]

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]

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,” Elect. 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]

Allen, G. A.

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

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]

Heinrich, A.

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]

Hemme, H.

Hertel, P.

Hsieh, I. W.

Kono, N.

Körner, T.

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]

Koshiba, M.

Liu, J. M.

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

Mizumoto, T.

Nakano, Y.

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]

Osgood, R. M.

Painter, O.

Priye, V.

V. Priye and M. Tsutsumi, “Nonreciprocal behavior of leaky gyroscopic waveguide,” Elect. Lett. 29, 104–105 (1993).
[Crossref]

Roocks, P.

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]

Shimizu, H.

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]

Shoji, Y.

Srinivasan, K.

Stritzker, B.

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]

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,” Elect. 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]

Weckerle, M.

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]

Yokoyama, 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]

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)

Elect. Lett. (1)

V. Priye and M. Tsutsumi, “Nonreciprocal behavior of leaky gyroscopic waveguide,” Elect. 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. (2)

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]

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 (2)

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).

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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.

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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.

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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.

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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.

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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.

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Tables (1)

Tables Icon

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

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Equations (2)

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

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