Abstract

In this paper, we present two four-port optical circulators for TE and TM modes, respectively. Exploiting the recent technological development concerning Ce:YIG pulse laser deposition on silicon nitride platform, we design two integrated circulators, which can be used to implement several functions in integrated optics, such as de-interleavers, input/output amplifier isolators and output laser isolators. The proposed devices combine the benefit of low loss silicon nitride waveguides with the non-reciprocal properties of magneto-optical materials. The ring cross-section has been optimized in order to maximize the non-reciprocal phase shift and finally the scattering coefficients have been computed using the transfer matrix method. The material stability and refractive index regularity of silicon nitride, the small micro-ring footprint, and the high wavelength selectivity make these devices particularly attractive.

© 2013 OSA

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2012 (2)

D. D. John, M. J. R. Heck, J. F. Bauters, R. Moreira, J. S. Barton, J. E. Bowers, and D. J. Blumenthal, “Multilayer platform for ultra-low-loss waveguide applications,” IEEE Photon. Technol. Lett.24(11), 876–878 (2012).
[CrossRef]

M. Sekhar, M. R. Singh, S. Basu, and S. Pinnepalli, “Giant Faraday rotation in BixCe3-xFe5O12 epitaxial garnet films,” Opt. Express20(9), 9624–9639 (2012).
[CrossRef] [PubMed]

2011 (4)

2010 (4)

R. Takei and T. Mizumoto, “Design and simulation of silicon waveguide optical circulator employing nonreciprocal phase shift,” Jpn. J. Appl. Phys.49(5), 052203 (2010).
[CrossRef]

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett.96(8), 081112 (2010).
[CrossRef]

W. Śmigaj, J. Romero-Vivas, B. Gralak, L. Magdenko, B. Dagens, and M. Vanwolleghem, “Magneto-optical circulator designed for operation in a uniform external magnetic field,” Opt. Lett.35(4), 568–570 (2010).
[CrossRef] [PubMed]

2009 (1)

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

2008 (1)

2007 (3)

2005 (3)

2001 (2)

T. Sekijima, H. Itoh, T. Fujii, K. Wakino, and M. Okada, “Influence of growth atmosphere on solubility limit of Ce3+ ions in Ce-substituted fibrous yttrium iron garnet single crystals,” J. Cryst. Growth229(1-4), 409–414 (2001).
[CrossRef]

O. Zhuromskyy, H. Dötsch, M. Lohmeyer, L. Wilkens, and P. Hertel, “Magnetooptical waveguides with polarization-independent nonreciprocal phaseshift,” J. Lightwave Technol.19(2), 214–221 (2001).
[CrossRef]

1999 (1)

1998 (1)

Y.-Q. Li, M. Cherif, J. Huang, W. Liu, and Q. Chen, “Metalorganic chemical vapor deposition of magneto-optical Ce:YIG thin films,” MRS Proceedings517, 449 (1998).
[CrossRef]

1997 (1)

1991 (1)

M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” J. Appl. Phys.70(11), 7065 (1991).
[CrossRef]

1977 (1)

A. Konrad, “High-order triangular finite elements for electromagnetic waves in anisotropic media,” IEEE Trans. Microw. Theory Tech.25(5), 353–360 (1977).
[CrossRef]

1965 (1)

G. J. Gabriel and M. E. Brodwin, “The solution of guided waves in inhomogeneous anisotropic media by perturbation and variational method,” IEEE Trans. Microw. Theory Tech.13(3), 364–370 (1965).
[CrossRef]

Abe, M.

M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” J. Appl. Phys.70(11), 7065 (1991).
[CrossRef]

Bahlmann, N.

Barton, J. S.

D. D. John, M. J. R. Heck, J. F. Bauters, R. Moreira, J. S. Barton, J. E. Bowers, and D. J. Blumenthal, “Multilayer platform for ultra-low-loss waveguide applications,” IEEE Photon. Technol. Lett.24(11), 876–878 (2012).
[CrossRef]

J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R.-G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express19(4), 3163–3174 (2011).
[CrossRef] [PubMed]

Basu, S.

Bauters, J. F.

D. D. John, M. J. R. Heck, J. F. Bauters, R. Moreira, J. S. Barton, J. E. Bowers, and D. J. Blumenthal, “Multilayer platform for ultra-low-loss waveguide applications,” IEEE Photon. Technol. Lett.24(11), 876–878 (2012).
[CrossRef]

J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R.-G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express19(4), 3163–3174 (2011).
[CrossRef] [PubMed]

Bi, L.

L. Bi, J. Hu, D.-H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical isolators,” Nat. Photonics5(12), 758–762 (2011).
[CrossRef]

Blumenthal, D. J.

D. D. John, M. J. R. Heck, J. F. Bauters, R. Moreira, J. S. Barton, J. E. Bowers, and D. J. Blumenthal, “Multilayer platform for ultra-low-loss waveguide applications,” IEEE Photon. Technol. Lett.24(11), 876–878 (2012).
[CrossRef]

J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R.-G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express19(4), 3163–3174 (2011).
[CrossRef] [PubMed]

Bowers, J. E.

Brodwin, M. E.

G. J. Gabriel and M. E. Brodwin, “The solution of guided waves in inhomogeneous anisotropic media by perturbation and variational method,” IEEE Trans. Microw. Theory Tech.13(3), 364–370 (1965).
[CrossRef]

Canciamilla, A.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett.96(8), 081112 (2010).
[CrossRef]

Capmany, J.

Cheben, P.

Chen, Q.

Y.-Q. Li, M. Cherif, J. Huang, W. Liu, and Q. Chen, “Metalorganic chemical vapor deposition of magneto-optical Ce:YIG thin films,” MRS Proceedings517, 449 (1998).
[CrossRef]

Cherif, M.

Y.-Q. Li, M. Cherif, J. Huang, W. Liu, and Q. Chen, “Metalorganic chemical vapor deposition of magneto-optical Ce:YIG thin films,” MRS Proceedings517, 449 (1998).
[CrossRef]

Chu, S. T.

Dagens, B.

Dai, D.

De La Rue, R. M.

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett.96(8), 081112 (2010).
[CrossRef]

Delâge, A.

Densmore, A.

Di Pasquale, F.

Dionne, G. F.

L. Bi, J. Hu, D.-H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical isolators,” Nat. Photonics5(12), 758–762 (2011).
[CrossRef]

Domenech, J. D.

Dötsch, H.

Fan, S.

Ferrari, C.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

Ferrera, M.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Fujii, T.

T. Sekijima, H. Itoh, T. Fujii, K. Wakino, and M. Okada, “Influence of growth atmosphere on solubility limit of Ce3+ ions in Ce-substituted fibrous yttrium iron garnet single crystals,” J. Cryst. Growth229(1-4), 409–414 (2001).
[CrossRef]

Furuyama, H.

M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” J. Appl. Phys.70(11), 7065 (1991).
[CrossRef]

Gabriel, G. J.

G. J. Gabriel and M. E. Brodwin, “The solution of guided waves in inhomogeneous anisotropic media by perturbation and variational method,” IEEE Trans. Microw. Theory Tech.13(3), 364–370 (1965).
[CrossRef]

Gerhardt, R.

Gomi, M.

M. Gomi, H. Furuyama, and M. Abe, “Strong magneto-optical enhancement in highly Ce-substituted iron garnet films prepared by sputtering,” J. Appl. Phys.70(11), 7065 (1991).
[CrossRef]

Gralak, B.

Guo, X.

Hammer, M.

Harnagea, C.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Heck, M. J. R.

D. D. John, M. J. R. Heck, J. F. Bauters, R. Moreira, J. S. Barton, J. E. Bowers, and D. J. Blumenthal, “Multilayer platform for ultra-low-loss waveguide applications,” IEEE Photon. Technol. Lett.24(11), 876–878 (2012).
[CrossRef]

J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R.-G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express19(4), 3163–3174 (2011).
[CrossRef] [PubMed]

Heideman, R.-G.

Hertel, P.

Hu, J.

L. Bi, J. Hu, D.-H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical isolators,” Nat. Photonics5(12), 758–762 (2011).
[CrossRef]

Huang, J.

Y.-Q. Li, M. Cherif, J. Huang, W. Liu, and Q. Chen, “Metalorganic chemical vapor deposition of magneto-optical Ce:YIG thin films,” MRS Proceedings517, 449 (1998).
[CrossRef]

Hwang, J.-Y.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Itoh, H.

T. Sekijima, H. Itoh, T. Fujii, K. Wakino, and M. Okada, “Influence of growth atmosphere on solubility limit of Ce3+ ions in Ce-substituted fibrous yttrium iron garnet single crystals,” J. Cryst. Growth229(1-4), 409–414 (2001).
[CrossRef]

Janz, S.

John, D.

John, D. D.

D. D. John, M. J. R. Heck, J. F. Bauters, R. Moreira, J. S. Barton, J. E. Bowers, and D. J. Blumenthal, “Multilayer platform for ultra-low-loss waveguide applications,” IEEE Photon. Technol. Lett.24(11), 876–878 (2012).
[CrossRef]

Kakihara, K.

Kim, D.-H.

L. Bi, J. Hu, D.-H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical isolators,” Nat. Photonics5(12), 758–762 (2011).
[CrossRef]

Kimerling, L. C.

L. Bi, J. Hu, D.-H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical isolators,” Nat. Photonics5(12), 758–762 (2011).
[CrossRef]

Kono, N.

Konrad, A.

A. Konrad, “High-order triangular finite elements for electromagnetic waves in anisotropic media,” IEEE Trans. Microw. Theory Tech.25(5), 353–360 (1977).
[CrossRef]

Koshiba, M.

Kromer, H.

Laine, J.-P.

Lamontagne, B.

Lapointe, J.

Leinse, A.

Li, Y.-Q.

Y.-Q. Li, M. Cherif, J. Huang, W. Liu, and Q. Chen, “Metalorganic chemical vapor deposition of magneto-optical Ce:YIG thin films,” MRS Proceedings517, 449 (1998).
[CrossRef]

Linzon, Y.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Little, B. E.

Liu, W.

Y.-Q. Li, M. Cherif, J. Huang, W. Liu, and Q. Chen, “Metalorganic chemical vapor deposition of magneto-optical Ce:YIG thin films,” MRS Proceedings517, 449 (1998).
[CrossRef]

Lohmeyer, M.

Magdenko, L.

Martinelli, M.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett.96(8), 081112 (2010).
[CrossRef]

Melloni, A.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett.96(8), 081112 (2010).
[CrossRef]

Mizumoto, T.

M.-C. Tien, T. Mizumoto, P. Pintus, H. Kromer, and J. E. Bowers, “Silicon ring isolators with bonded nonreciprocal magneto-optic garnets,” Opt. Express19(12), 11740–11745 (2011).
[CrossRef] [PubMed]

R. Takei and T. Mizumoto, “Design and simulation of silicon waveguide optical circulator employing nonreciprocal phase shift,” Jpn. J. Appl. Phys.49(5), 052203 (2010).
[CrossRef]

Morandotti, R.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Moreira, R.

D. D. John, M. J. R. Heck, J. F. Bauters, R. Moreira, J. S. Barton, J. E. Bowers, and D. J. Blumenthal, “Multilayer platform for ultra-low-loss waveguide applications,” IEEE Photon. Technol. Lett.24(11), 876–878 (2012).
[CrossRef]

Morichetti, F.

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett.96(8), 081112 (2010).
[CrossRef]

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett.104(3), 033902 (2010).
[CrossRef] [PubMed]

Muñoz, P.

Muriel, M. A.

Okada, M.

T. Sekijima, H. Itoh, T. Fujii, K. Wakino, and M. Okada, “Influence of growth atmosphere on solubility limit of Ce3+ ions in Ce-substituted fibrous yttrium iron garnet single crystals,” J. Cryst. Growth229(1-4), 409–414 (2001).
[CrossRef]

Pignolet, A.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Pinnepalli, S.

Pintus, P.

Popkov, A. F.

Post, E.

Qi, X.

S.-Y. Sung, X. Qi, and B. J. Stadler, “Integrating yttrium iron garnet onto nongarnet substrates with faster deposition rates and high reliability,” Appl. Phys. Lett.87(12), 121111 (2005).
[CrossRef]

Ram, R. J.

Razzari, L.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic structure of the TE-mode four-port optical circulator, Top view (a) and cross-section (b).

Fig. 2
Fig. 2

Ring-cross section and external magnetic field direction for the TE-mode circulator (a) and TM-mode circulator (b).

Fig. 3
Fig. 3

Resonance wavelength split for the TE-circulator as a function of the silicon nitride (wSiN) and the magneto-optical material width (wCe:YIG). Figures 3(a) and 3(b) refer to a 300nm and 400nm thick waveguide, respectively.

Fig. 4
Fig. 4

Resonance wavelength split for the TM-circulator as a function of the silicon nitride (hSiN) and the magneto-optical material thickness (hCe:YIG). Figure 4(a) and 4(b) refer to a 850nm and 1.15μm large waveguide, respectively.

Fig. 5
Fig. 5

Magnetic field profile of the principal component for TE-mode (a) and TM-mode (b) in the two circulators, respectively.

Fig. 6
Fig. 6

Scattering coefficients as a function of wavelength λ and power coupling coefficients κ.

Fig. 7
Fig. 7

Scattering coefficients at CW resonant frequency as a function of κ (αrr = 1dB/cm) for R = 25μm.

Fig. 8
Fig. 8

Scattering coefficients at CW resonant frequency as a function of κ (αrr = 1dB/cm)) for R = 300μm.

Tables (3)

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Table 1 TE-circulator scattering coefficients at CW ring resonance

Tables Icon

Table 2 TM-circulator scattering coefficients at CW ring resonance

Tables Icon

Table 3 TE-circulator fabricated with BixCe3-xFe5O12 instead of Ce:YIG (θF = 11000deg/cm [12])

Equations (10)

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

ε r ¯ ¯ = n Ce:YIG 2 ( 1 0 0 0 1 0 0 0 1 )+K( 0 M z M y M z 0 M x M y M x 0 ),
K M j = 2 θ F j n Ce:YIG k 0 ,
Δ β TE 2ω ε 0 β TE N K M y E x * x E x dxdyandΔ β TM 2ω ε 0 β TM N K M x E y * y E y dxdy,
N= 1 2 [ E ¯ × H ¯ * + E ¯ * × H ¯ ] z dxdy.
E ¯ =[ E x (x,y) i ¯ x + E y (x,y) i ¯ y +j E z (x,y) i ¯ z ] e jωtjβz ,
H ¯ =[ H x (x,y) i ¯ x + H y (x,y) i ¯ y +j H z (x,y) i ¯ z ] e jωtjβz ,
×( ε r ¯ ¯ 1 × H ¯ ) k 0 2 H ¯ =0.
( A 1 A 2 A 3 A 4 )=( S 11 S 12 S 13 S 14 S 21 S 22 S 23 S 24 S 31 S 32 S 33 S 34 S 41 S 42 S 43 S 44 )( A 1 + A 2 + A 3 + A 4 + ).
( A 1 A 2 A 3 A 4 )=( 0 S 12 0 S 14 S 43 0 S 41 0 0 S 14 0 S 12 S 41 0 S 43 0 )( A 1 + A 2 + A 3 + A 4 + )
FSR= λ 2 2π R n g 2 ΔλR λ 2 4π Δλ n g .

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