Abstract

A single-mode-waveguide optical isolator based on propagation direction dependent cut-off frequency is proposed. The isolation bandwidth is the difference between the cut-off frequencies of the lowest forward and backward propagating modes. Perturbation theory is used for analyzing the correlation between the material distribution and the bandwidth. The mode profile determines an appropriate distribution of non-reciprocal materials.

© 2008 Optical Society of America

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  1. M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
    [CrossRef]
  2. 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]
  3. J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dotsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
    [CrossRef]
  4. H. Dotsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, "Applications of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22, 240-253 (2005).
    [CrossRef]
  5. 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]
  6. A. Figotin and I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E 63, 066609 (2001).
    [CrossRef]
  7. A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys.Rev. B 72, 035123 (2005).
    [CrossRef]
  8. Z. Yu, Z. Wang, and S. Fan, "One-way total reflection with one-dimensional magneto-optical photonic crystals," Appl. Phys. Lett. 90, 121133- (2007).
    [CrossRef]
  9. M. J. Steel, M. Levy, and R. M. Osgood, Jr., "High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects," IEEE Photon. Technol. Lett. 12, 1171-1173 (2000).
    [CrossRef]
  10. 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]
  11. F. D. M. Haldane and S. Raghu, "Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry," Phys. Rev. Lett. 100, 013904 (2008).
    [CrossRef] [PubMed]
  12. 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]
  13. W. Zaets and K. Ando, "Optical Waveguide Isolator Based on Nonreciprocal Loss/Gain of Amplifier Covered by Ferromagnetic Layer," IEEE Photon. Technol. Lett. 11, 1012-1014 (1999).
    [CrossRef]
  14. S. Johnson and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [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]

F. D. M. Haldane and S. Raghu, "Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry," Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef] [PubMed]

2007 (2)

2005 (3)

2001 (2)

2000 (2)

M. J. Steel, M. Levy, and R. M. Osgood, Jr., "High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects," IEEE Photon. Technol. Lett. 12, 1171-1173 (2000).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dotsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

1999 (1)

W. Zaets and K. Ando, "Optical Waveguide Isolator Based on Nonreciprocal Loss/Gain of Amplifier Covered by Ferromagnetic Layer," IEEE Photon. Technol. Lett. 11, 1012-1014 (1999).
[CrossRef]

1996 (1)

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Amemiya, T.

Ando, K.

W. Zaets and K. Ando, "Optical Waveguide Isolator Based on Nonreciprocal Loss/Gain of Amplifier Covered by Ferromagnetic Layer," IEEE Photon. Technol. Lett. 11, 1012-1014 (1999).
[CrossRef]

Bahlmann, N.

Baryshev, A. V.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys.Rev. B 72, 035123 (2005).
[CrossRef]

Cadieu, F. J.

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Dotsch, H.

H. Dotsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, "Applications of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22, 240-253 (2005).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dotsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

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]

Z. Yu, Z. Wang, and S. Fan, "One-way total reflection with one-dimensional magneto-optical photonic crystals," Appl. Phys. Lett. 90, 121133- (2007).
[CrossRef]

Figotin, A.

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

Fratello, V. J.

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Fujita, J.

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dotsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

Gerhardt, R.

Granovsky, A. B.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys.Rev. B 72, 035123 (2005).
[CrossRef]

Hai, P. N.

Haldane, F. D. M.

F. D. M. Haldane and S. Raghu, "Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry," Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef] [PubMed]

Hammer, M.

Hegde, H.

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Hertel, P.

Hsieh, I. W.

Inoue, M.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys.Rev. B 72, 035123 (2005).
[CrossRef]

Joannopoulos, J.

Johnson, S.

Khanikaev, A. B.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys.Rev. B 72, 035123 (2005).
[CrossRef]

Kono, N.

Koshiba, M.

Levy, M.

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dotsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

M. J. Steel, M. Levy, and R. M. Osgood, Jr., "High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects," IEEE Photon. Technol. Lett. 12, 1171-1173 (2000).
[CrossRef]

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Mizumoto, T.

Nakano, Y.

Osgood, R. M.

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]

M. J. Steel, M. Levy, and R. M. Osgood, Jr., "High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects," IEEE Photon. Technol. Lett. 12, 1171-1173 (2000).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dotsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Raghu, S.

F. D. M. Haldane and S. Raghu, "Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry," Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef] [PubMed]

Shimizu, H.

Shoji, Y.

Steel, M. J.

M. J. Steel, M. Levy, and R. M. Osgood, Jr., "High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects," IEEE Photon. Technol. Lett. 12, 1171-1173 (2000).
[CrossRef]

Tanaka, M.

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]

Vinogradov, A. P.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys.Rev. B 72, 035123 (2005).
[CrossRef]

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]

Z. Yu, Z. Wang, and S. Fan, "One-way total reflection with one-dimensional magneto-optical photonic crystals," Appl. Phys. Lett. 90, 121133- (2007).
[CrossRef]

Wilkens, L.

H. Dotsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, and P. Hertel, "Applications of magneto-optical waveguides in integrated optics: review," J. Opt. Soc. Am. B 22, 240-253 (2005).
[CrossRef]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dotsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

Wolfe, R.

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

Yokoyama, M.

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]

Z. Yu, Z. Wang, and S. Fan, "One-way total reflection with one-dimensional magneto-optical photonic crystals," Appl. Phys. Lett. 90, 121133- (2007).
[CrossRef]

Zaets, W.

W. Zaets and K. Ando, "Optical Waveguide Isolator Based on Nonreciprocal Loss/Gain of Amplifier Covered by Ferromagnetic Layer," IEEE Photon. Technol. Lett. 11, 1012-1014 (1999).
[CrossRef]

Zhuromskyy, O.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dotsch, "Waveguide optical isolator based on Mach-Zehnder interferometer," Appl. Phys. Lett. 76, 2158-2160 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

M. J. Steel, M. Levy, and R. M. Osgood, Jr., "High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects," IEEE Photon. Technol. Lett. 12, 1171-1173 (2000).
[CrossRef]

W. Zaets and K. Ando, "Optical Waveguide Isolator Based on Nonreciprocal Loss/Gain of Amplifier Covered by Ferromagnetic Layer," IEEE Photon. Technol. Lett. 11, 1012-1014 (1999).
[CrossRef]

M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. Fratello, "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photon. Technol. Lett. 8, 903-905 (1996).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Phys. Rev. E (1)

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

Phys. Rev. Lett. (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]

F. D. M. Haldane and S. Raghu, "Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry," Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef] [PubMed]

Phys.Rev. B (1)

A. B. Khanikaev, A. V. Baryshev, M. Inoue, A. B. Granovsky, and A. P. Vinogradov, "Two-dimensional magnetophotonic crystal: Exactly solvable model," Phys.Rev. B 72, 035123 (2005).
[CrossRef]

Other (1)

Z. Yu, Z. Wang, and S. Fan, "One-way total reflection with one-dimensional magneto-optical photonic crystals," Appl. Phys. Lett. 90, 121133- (2007).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Dispersion curves of the proposed optical waveguide isolator. Solid lines are the lowest and second lowest modes. Dashed lines indicate forward and backward propagating modes for Δε≠0. Only one forward wave is guided within the isolation range Δω̄.

Fig. 2.
Fig. 2.

Optical isolator structures: (a,b) right-left configuration, (c,d) up-down configuration, (e) rib waveguide, and (f) trapezoidal configuration. C is a low-index material, A is a reciprocal material, and B is non-reciprocal material. B+ and B- have anti-parallel magnetizations. The magnetization direction in each non-reciprocal material is indicated by the single-ended arrows.

Fig. 3.
Fig. 3.

(a). Dispersion curves of the optical isolator in Fig. 2(b). where w/a=0.4 and h/a=0.3. The value a is the scaling length. The permittivity tensors are ε 0 [12.25 0 0; 0 12.25∓i; 0 ±i 12.25] for B+ and B-. The substrate C is isotropic (ε=2.13ε 0) where ε 0 is the permittivity of vacuum. We have selected large off-diagonal values so that isolation is clearly shown. (b) Electric field component profiles of the lowest TE and TM modes at |β|a/2π=0.8 for forward and backward directions. “A on C” represents a reciprocal waveguide (Δε=0)-the unperturbed case. “B+B- on C” shows a nonreciprocal isolator waveguide (the perturbed case with magnetic material). The modal field changes are negligible even due to large perturbation, so using perturbation theory is justified.

Fig. 4.
Fig. 4.

Profiles of Im[Ez*Ey] and Im[Ex*Ez]. Im[Ey*Ex] is negligible. (a)TE mode, h/a=0.6 and w/a=0.8. (b) TE mode, h/a=0.6 and w/a=1.2. (c) TM mode, h/a=0.8, w/a=0.6. (d) TM mode, h/a=1.2, w/a=0.6.

Fig. 5.
Fig. 5.

(a). Dispersion curves obtained from perturbation theory and 2D PWE modeling for the structure Fig. 2(b). ε B ±=ε 0 [6.25 0 0; 0 6.25∓0.06i; 0 ±0.06i 6.25]. ε C=2.13ε 0. w=0.8a and h =0.6a. (b). Bandwidth obtained from PWE vs. Iyx+Ixz+Izy. Data from various designs shown in this paper are plotted.

Fig. 6.
Fig. 6.

Profiles of Im[Ez*Ey] and Im[Ex *Ez] for the lowest TE and TM mode. Im[Ey*Ex] is negligible. (a) TE mode, h=0.6a, (total w)=1.2a, wn=2.5=0.8a, wn=1.46=0.2a. (b) TM mode, w=0.6a, (total h)=a, hn=2.5=0.8a, hn=1.46=0.2a.

Tables (1)

Tables Icon

Table 1. Isolation bandwidth of some analyzed isolator examples. Bandwidth is obtained from 2D PWE modeling. ε B ±=ε 0 [6.25 0∓0.06i; 0 6.25 0; ±0.06i 0 6.25]. ε C =2.13ε 0. The value Iyx+Ixz+Izy is evaluated at β̄=0.6.

Equations (8)

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

ε ˜ = ( ε xx ε xy ε xz ε yx ε yy ε yz ε zx ε zy ε zz ) = [ ε xx ε xy ε xz ; ε yx ε yy ε yz ; ε zx ε zy ε zz ] ,
H ̂ 0 n β 2 n
H ̂ 0 = ( t 2 + ω 2 μ 0 ε i 0 i β 0 x 0 t 2 + ω 2 μ 0 ε i i β 0 y 0 0 t 2 + ω 2 μ 0 ε i + β 0 2 )
Δ ̂ ε = ε 0 ( 0 iu xy iu zx iu xy 0 iu yz iu zx iu yz 0 )
β 2 ( ω ) β 0 2 + ω 2 μ 0 n Δ ̂ ε n = β 0 2 { 1 + 2 ( ω c β 0 ) 2 ( I yx + I xz + I zy ) }
or β ( ω ) β 0 + ω 2 μ 0 2 β 0 n Δ ̂ ε n = β 0 { 1 + ( ω c β 0 ) 2 ( I yx + I xz + I zy ) }
I ij = u ji ( x , y ) Im [ E i * ( x , y ) E j ( x , y ) ] didj .
Δ β ( ω ) = 2 ω 2 ( I yx + I xz + I zy ) ( c 2 β 0 ) Δ ω .

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