Abstract

We have implemented the nonreciprocal propagation capabilities into plasmonic waveguides and have simulated the performances. We employed dielectric-loaded surface plasmon polariton waveguide (DLSPPW) and long-range DLSPPW (LR-DLSPPW) configurations, where ferromagnetic-metal Fe is used instead of noble metals in order to obtain nonreciprocal propagations by the transverse magneto-optical (MO) effect. The nonreciprocal performances were characterized by the finite-difference frequency-domain (FDFD) method in terms of the propagation losses in return for the nonreciprocal phase shift (NRPS) and nonreciprocal propagation loss (NRL). The NRPS and NRL of the DLSPPW configuration are larger than those of the previously reported semiconductor waveguide optical isolators owing to the large MO constant of Fe and the field confinement by surface plasmons although the propagation loss for NRL of 1 dB is at least 31 dB and the propagation length is limited to less than 10 μm. To reduce such a large propagation loss, we introduced the LR-DLSPPW configuration composed of Polymethyl methacrylate (PMMA) ridge and Benzocyclobutene (BCB) buffer layer. The Fe layer thickness and width are optimized to 50 nm and 500 nm, respectively, so that sizable MO effect and low propagation loss coexist. The propagation loss for NRL of 1 dB is suppressed to ~10 dB within a waveguide length of ~56 μm. Our comprehensive investigation offers fundamental information on practical magneto-plasmonic waveguides and how much nonreciprocal performances are expected, providing an insight into the integration of magneto-plasmonics with on-chip photonics and electronics.

© 2017 Optical Society of America

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  46. T. Kaihara, H. Shimizu, A. Cebollada, and G. Armelles, “Magnetic field control and wavelength tunability of SPP excitations using Al2O3/SiO2/Fe structures,” Appl. Phys. Lett. 109(11), 111102 (2016).
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  48. V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Magnetization-dependent loss in an (Al,Ga)As optical waveguide with an embedded Fe micromagnet,” Opt. Lett. 35(7), 931–933 (2010).
    [Crossref] [PubMed]

2016 (2)

Y. Shoji, K. Miura, and T. Mizumoto, “Optical nonreciprocal devices based on magneto-optical phase shift in silicon photonics,” J. Opt. 18(1), 013001 (2016).
[Crossref]

T. Kaihara, H. Shimizu, A. Cebollada, and G. Armelles, “Magnetic field control and wavelength tunability of SPP excitations using Al2O3/SiO2/Fe structures,” Appl. Phys. Lett. 109(11), 111102 (2016).
[Crossref]

2015 (1)

2014 (1)

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

2013 (3)

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

E. Ferreiro-Vila, J. M. García-Martín, A. Cebollada, G. Armelles, and M. U. González, “Magnetic modulation of surface plasmon modes in magnetoplasmonic metal-insulator-metal cavities,” Opt. Express 21(4), 4917–4930 (2013).
[Crossref] [PubMed]

G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: Combining Magnetic and Plasmonic Functionalities,” Adv. Optical. Mater. 1(1), 10–35 (2013).
[Crossref]

2012 (3)

S. Randhawa, S. Lachèze, J. Renger, A. Bouhelier, R. E. de Lamaestre, A. Dereux, and R. Quidant, “Performance of electro-optical plasmonic ring resonators at telecom wavelengths,” Opt. Express 20(3), 2354–2362 (2012).
[Crossref] [PubMed]

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
[Crossref]

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
[Crossref]

2011 (3)

2010 (8)

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Magnetization-dependent loss in an (Al,Ga)As optical waveguide with an embedded Fe micromagnet,” Opt. Lett. 35(7), 931–933 (2010).
[Crossref] [PubMed]

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18(2), 1207–1216 (2010).
[Crossref] [PubMed]

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, and H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010).
[Crossref] [PubMed]

A. V. Krasavin and A. V. Zayats, “Electro-optic switching element for dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 97(4), 041107 (2010).
[Crossref]

H. Shimizu, S. Goto, and T. Mori, “Optical isolation using nonreciprocal polarization rotation in Fe–InGaAlAs/InP semiconductor active waveguide optical isolators,” Appl. Phys. Express 3(7), 072201 (2010).
[Crossref]

T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010).
[Crossref] [PubMed]

M. L. Brongersma and V. M. Shalaev, “The case for plasmonics,” Science 328(5977), 440–441 (2010).
[Crossref] [PubMed]

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. M. García-Martín, T. Thomay, A. Leitenstorfer, and R. Bratschitsch, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
[Crossref]

2009 (6)

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9(2), 897–902 (2009).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, and R. Ram, “Surface plasmon isolator based on nonreciprocal coupling,” J. Appl. Phys. 106(2), 023108 (2009).
[Crossref]

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1(3), 484–588 (2009).
[Crossref]

V. Zayets and K. Ando, “High-speed switching of spin polarization for proposed spin-photon memory,” Appl. Phys. Lett. 94(12), 121104 (2009).
[Crossref]

J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9(8), 2935–2939 (2009).
[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(2), 023902 (2008).
[Crossref] [PubMed]

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

2007 (2)

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[Crossref]

M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal corners,” J. Opt. Soc. Am. B 24(9), 2333–2342 (2007).
[Crossref]

2006 (4)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[Crossref] [PubMed]

H. Shimizu and Y. Nakano, “Fabrication and characterization of an InGaAsP/InP active waveguide optical isolator with 14.7 dB/mm TE mode nonreciprocal attenuation,” J. Lightwave Technol. 24(1), 38–43 (2006).
[Crossref]

B. Sepúlveda, L. M. Lechuga, and G. Armelles, “Magnetooptic effects in surface-plasmon-polaritons slab waveguides,” J. Lightwave Technol. 24(2), 945–955 (2006).
[Crossref]

J. B. Khurgin, “Optical isolating action in surface plasmon polaritons,” Appl. Phys. Lett. 89(25), 251115 (2006).
[Crossref]

2005 (2)

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, “Dielectric optical elements for surface plasmons,” Opt. Lett. 30(8), 893–895 (2005).
[Crossref] [PubMed]

J.-N. Hwang, “A compact 2-D FDFD method for modeling microstrip structures with nonuniform grids and perfectly matched layer,” IEEE Trans. Microw. Theory Tech. 53(2), 653–659 (2005).
[Crossref]

2003 (1)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

2001 (1)

P. Bertrand, C. Hermann, G. Lampel, J. Peretti, and V. I. Safarov, “General analytical treatment of optics in layered structures: Application to magneto-optics,” Phys. Rev. B 64(23), 235421 (2001).
[Crossref]

2000 (1)

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000).
[Crossref]

1998 (1)

Y. He, T. Kojima, T. Uno, and S. Adachi, “FDTD analysis of three-dimensional light-beam scattering from the magneto-optical disk structure,” IEICE Trans. Electron. 81(12), 1881–1888 (1998).

1997 (1)

1988 (1)

A. Köck, W. Beinstingl, K. Berthold, and E. Gornik, “Surface plasmon polariton enhanced light emission from Schottky diodes,” Appl. Phys. Lett. 52(14), 1164–1166 (1988).
[Crossref]

1968 (1)

G. S. Krinchik and V. A. Artemjev, “Magneto-optic Properties of Nickel, Iron, and Cobalt,” J. Appl. Phys. 39(2), 1276–1278 (1968).
[Crossref]

Adachi, S.

Y. He, T. Kojima, T. Uno, and S. Adachi, “FDTD analysis of three-dimensional light-beam scattering from the magneto-optical disk structure,” IEICE Trans. Electron. 81(12), 1881–1888 (1998).

Allen, M.

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, and R. Ram, “Surface plasmon isolator based on nonreciprocal coupling,” J. Appl. Phys. 106(2), 023108 (2009).
[Crossref]

Andersen, T. B.

Ando, K.

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
[Crossref]

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
[Crossref]

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Magnetization-dependent loss in an (Al,Ga)As optical waveguide with an embedded Fe micromagnet,” Opt. Lett. 35(7), 931–933 (2010).
[Crossref] [PubMed]

V. Zayets and K. Ando, “High-speed switching of spin polarization for proposed spin-photon memory,” Appl. Phys. Lett. 94(12), 121104 (2009).
[Crossref]

Armelles, G.

T. Kaihara, H. Shimizu, A. Cebollada, and G. Armelles, “Magnetic field control and wavelength tunability of SPP excitations using Al2O3/SiO2/Fe structures,” Appl. Phys. Lett. 109(11), 111102 (2016).
[Crossref]

G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: Combining Magnetic and Plasmonic Functionalities,” Adv. Optical. Mater. 1(1), 10–35 (2013).
[Crossref]

E. Ferreiro-Vila, J. M. García-Martín, A. Cebollada, G. Armelles, and M. U. González, “Magnetic modulation of surface plasmon modes in magnetoplasmonic metal-insulator-metal cavities,” Opt. Express 21(4), 4917–4930 (2013).
[Crossref] [PubMed]

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. M. García-Martín, T. Thomay, A. Leitenstorfer, and R. Bratschitsch, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
[Crossref]

B. Sepúlveda, L. M. Lechuga, and G. Armelles, “Magnetooptic effects in surface-plasmon-polaritons slab waveguides,” J. Lightwave Technol. 24(2), 945–955 (2006).
[Crossref]

Artemjev, V. A.

G. S. Krinchik and V. A. Artemjev, “Magneto-optic Properties of Nickel, Iron, and Cobalt,” J. Appl. Phys. 39(2), 1276–1278 (1968).
[Crossref]

Atwater, H. A.

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, and H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010).
[Crossref] [PubMed]

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Quidant, R.

Ram, R.

J. Montoya, K. Parameswaran, J. Hensley, M. Allen, and R. Ram, “Surface plasmon isolator based on nonreciprocal coupling,” J. Appl. Phys. 106(2), 023108 (2009).
[Crossref]

Randhawa, S.

Renger, J.

Renner, H.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
[Crossref]

Safarov, V. I.

P. Bertrand, C. Hermann, G. Lampel, J. Peretti, and V. I. Safarov, “General analytical treatment of optics in layered structures: Application to magneto-optics,” Phys. Rev. B 64(23), 235421 (2001).
[Crossref]

Saito, H.

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
[Crossref]

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
[Crossref]

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Magnetization-dependent loss in an (Al,Ga)As optical waveguide with an embedded Fe micromagnet,” Opt. Lett. 35(7), 931–933 (2010).
[Crossref] [PubMed]

Sepúlveda, B.

Shalaev, V. M.

M. L. Brongersma and V. M. Shalaev, “The case for plasmonics,” Science 328(5977), 440–441 (2010).
[Crossref] [PubMed]

Shi, X.

Shimizu, H.

T. Kaihara, H. Shimizu, A. Cebollada, and G. Armelles, “Magnetic field control and wavelength tunability of SPP excitations using Al2O3/SiO2/Fe structures,” Appl. Phys. Lett. 109(11), 111102 (2016).
[Crossref]

H. Shimizu, S. Goto, and T. Mori, “Optical isolation using nonreciprocal polarization rotation in Fe–InGaAlAs/InP semiconductor active waveguide optical isolators,” Appl. Phys. Express 3(7), 072201 (2010).
[Crossref]

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[Crossref]

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Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

Shoji, Y.

Y. Shoji, K. Miura, and T. Mizumoto, “Optical nonreciprocal devices based on magneto-optical phase shift in silicon photonics,” J. Opt. 18(1), 013001 (2016).
[Crossref]

Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

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R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

Steinberger, B.

Stepanov, A. L.

Stockman, M. I.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

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J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9(2), 897–902 (2009).
[Crossref] [PubMed]

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

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Taki, H.

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V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. M. García-Martín, T. Thomay, A. Leitenstorfer, and R. Bratschitsch, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
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V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. M. García-Martín, T. Thomay, A. Leitenstorfer, and R. Bratschitsch, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
[Crossref]

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O. Tsilipakos, E. E. Kriezis, and S. I. Bozhevolnyi, “Thermo-optic microring resonator switching elements made of dielectric-loaded plasmonic waveguides,” J. Appl. Phys. 109(7), 073111 (2011).
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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(2), 023902 (2008).
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J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18(2), 1207–1216 (2010).
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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(2), 023902 (2008).
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J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9(8), 2935–2939 (2009).
[Crossref] [PubMed]

Woggon, U.

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. M. García-Martín, T. Thomay, A. Leitenstorfer, and R. Bratschitsch, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
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Yan, M.

Yu, Z.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
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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(2), 023902 (2008).
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V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
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V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Magnetization-dependent loss in an (Al,Ga)As optical waveguide with an embedded Fe micromagnet,” Opt. Lett. 35(7), 931–933 (2010).
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A. V. Krasavin and A. V. Zayats, “Electro-optic switching element for dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 97(4), 041107 (2010).
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V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
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V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Enhancement of the transverse non-reciprocal magneto-optical effect,” J. Appl. Phys. 111(2), 023103 (2012).
[Crossref]

V. Zayets, H. Saito, S. Yuasa, and K. Ando, “Magnetization-dependent loss in an (Al,Ga)As optical waveguide with an embedded Fe micromagnet,” Opt. Lett. 35(7), 931–933 (2010).
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V. Zayets and K. Ando, “High-speed switching of spin polarization for proposed spin-photon memory,” Appl. Phys. Lett. 94(12), 121104 (2009).
[Crossref]

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R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
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O. Tsilipakos, E. E. Kriezis, and S. I. Bozhevolnyi, “Thermo-optic microring resonator switching elements made of dielectric-loaded plasmonic waveguides,” J. Appl. Phys. 109(7), 073111 (2011).
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Y. Shoji, Y. Shirato, and T. Mizumoto, “Silicon Mach–Zehnder interferometer optical isolator having 8 nm bandwidth for over 20 dB isolation,” Jpn. J. Appl. Phys. 53(2), 022202 (2014).
[Crossref]

Materials (Basel) (1)

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical isolator utilizing surface plasmons,” Materials (Basel) 5(5), 857–871 (2012).
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Nano Lett. (4)

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9(2), 897–902 (2009).
[Crossref] [PubMed]

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, and H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010).
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J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9(8), 2935–2939 (2009).
[Crossref] [PubMed]

Nat. Photonics (2)

V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. M. García-Martín, T. Thomay, A. Leitenstorfer, and R. Bratschitsch, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010).
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D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is — and what is not — an optical isolator,” Nat. Photonics 7(8), 579–582 (2013).
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R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

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Figures (12)
Fig. 1
Fig. 1 (a) A schematic diagram of the DLSPPW configurations with Fe. (b) Closeup of the computation domain, in which the meshes represent the non-uniform Yee grid cells. Positive ( + M) or negative (–M) magnetization is applied in the direction indicated by the red or blue arrows, respectively.

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Fig. 2
Fig. 2 The dependence of the nonreciprocal propagation characteristics on the thickness (T) and width (W) of the ridge in the DLSPPW configuration. (a) The real part of the effective refractive index (red and blue solid curves, left axis) and the real part of Δneff (dashed black curves, right axis) related to the NRPS = k0 Re[Δneff]. (b) The propagation length Lspp (red and blue solid curves, left axis) and the NRL (dashed black curves, right axis). The upper insets show the field distributions of the norm of the electric field (TM-like) under the positive magnetization. The aspect ratio of the insets is different from reality for an illustration purpose. The white curve inside indicates the intensity along the vertical direction at the horizontal center.

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Fig. 3
Fig. 3 The dependence of the nonreciprocal propagation characteristics on the refractive index of the ridge (nr) in the DLSPPW configuration of W = 1 μm. (a) Re[neff] (red and blue solid curves, left axis) and Re[Δneff] (dashed black curves, right axis). (b) Lspp (red and blue solid curves, left axis) and NRL (dashed black curves, right axis). The upper insets show the field distributions of the norm of the electric field (TM-like) under the positive magnetization. The aspect ratio of the insets is different from reality for an illustration purpose.

Download Full Size | PPT Slide | PDF

Fig. 4
Fig. 4 Parametric plots of (a) απ/2 NRPS versus Lπ/2 NRPS and (b) α1-dB NRL versus L1-dB NRL for the different widths (black curves) and refractive indices (red curves) of the ridge. The arrows indicate the direction of each trajectory as the thickness of the ridge changes from T = 0.02 μm to 1 μm.

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Fig. 5
Fig. 5 (a) A schematic diagram of the LR-DLSPPW configurations with Fe of variable dimension. (b) Closeup of the computation domain, in which the meshes represent the non-uniform Yee grid cells. Positive ( + M) or negative (–M) magnetization is applied in the direction indicated by the red or blue arrows, respectively.

Download Full Size | PPT Slide | PDF

Fig. 6
Fig. 6 The dependence of the nonreciprocal propagation characteristics on the thickness of the Fe layer (TFe) in the LR-DLSPPW configuration (W x T = 1 x 1 μm, WFe = infinity). (a) Re[neff] (red and blue solid curves, left axis) and Re[Δneff] (dashed black curves, right axis). (b) Lspp (red and blue solid curves, left axis) and NRL (dashed black curves, right axis). The upper insets show the field distributions of the norm of the electric field (TM-like) under the positive magnetization. The aspect ratio of the insets is different from reality for an illustration purpose. The white curve inside indicates the intensity along the vertical direction at the horizontal center.

Download Full Size | PPT Slide | PDF

Fig. 7
Fig. 7 The dependence of the nonreciprocal propagation characteristics on the width of the Fe layer (WFe) in the LR-DLSPPW configuration (W x T = 1 x 1 μm, TFe = 50 nm). (a) Re[neff] (red and blue solid curves, left axis) and Re[Δneff] (dashed black curves, right axis). (b) Lspp (red and blue solid curves, left axis) and NRL (dashed black curves, right axis). The upper insets show the field distributions of the norm of the electric field (TM-like) under the positive magnetization. The aspect ratio of the insets is different from reality for an illustration purpose. The white curve inside indicates the intensity along the vertical direction at the horizontal center.

Download Full Size | PPT Slide | PDF

Fig. 8
Fig. 8 Parametric plots of (a) απ/2 NRPS versus Lπ/2 NRPS and (b) α1-dB NRL versus L1-dB NRL for the different thicknesses with infinite width of the Fe layer (black curves) and different widths with a 50-nm thickness of the Fe layer (red curves). The arrows indicate the direction of each trajectory as the thickness of the buffer layer changes from t = 0.04 μm to 0.5 μm.

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Fig. 9
Fig. 9 The dependence of the nonreciprocal propagation characteristics on the thickness of the ridge (T) in the LR-DLSPPW configuration (WFe x TFe = 500 x 50 nm, W = 1 μm). (a) Re[neff] (red and blue solid curves, left axis) and Re[Δneff] (dashed black curves, right axis). (b) Lspp (red and blue solid curves, left axis) and NRL (dashed black curves, right axis). The upper insets show the field distributions of the norm of the electric field (TM-like) under the positive magnetization. The aspect ratio of the insets is different from reality for an illustration purpose.

Download Full Size | PPT Slide | PDF

Fig. 10
Fig. 10 The dependence of the nonreciprocal propagation characteristics on the width of the ridge (W) in the LR-DLSPPW configuration (WFe x TFe = 500 x 50 nm, T = 1 μm). (a) Re[neff] (red and blue solid curves, left axis) and Re[Δneff] (dashed black curves, right axis). (b) Lspp (red and blue solid curves, left axis) and NRL (dashed black curves, right axis). The upper insets show the field distributions of the norm of the electric field (TM-like) under the positive magnetization. The aspect ratio of the insets is different from reality for an illustration purpose.

Download Full Size | PPT Slide | PDF

Fig. 11
Fig. 11 The dependence of the nonreciprocal propagation characteristics on the refractive index of the buffer layer (nb) in the LR-DLSPPW configuration (WFe x TFe = 500 x 50 nm, W x T = 1 x 1 μm). (a) Re[neff] (red and blue solid curves, left axis) and Re[Δneff] (dashed black curves, right axis). (b) Lspp (red and blue solid curves, left axis) and NRL (dashed black curves, right axis). The upper insets show the field distributions of the norm of the electric field (TM-like) under the positive magnetization. The aspect ratio of the insets is different from reality for an illustration purpose. The white curve inside indicates the intensity along the vertical direction at the horizontal center.

Download Full Size | PPT Slide | PDF

Fig. 12
Fig. 12 Parametric plots of (a) απ/2 NRPS versus Lπ/2 NRPS and (b) α1-dB NRL versus L1-dB NRL for the W x T = 1 x {0.7, 1.3} μm (red curves), W x T = {0.7, 1.3} x 1 μm (blue curves), and W x T = 1 x 1 μm with different refractive indices of the buffer layer (green curves), as compared with W x T = 1 x 1 μm with BCB buffer layer (black curve). The arrows indicate the direction of each trajectory as the thickness of the buffer layer changes from t = 0.04 μm to 0.5 μm.

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Tables (1)

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Table 1 Comparison of nonreciprocal performances.

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Equations (8)

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ε ˜ r =( ε r 0 0 0 ε r − ε MO 0 ε MO ε r ).
Δ n eff = n eff ( +M )− n eff ( −M ).
NRPS= k 0 Re[ Δ n eff ]     [rad/μm].
NRL=−20 k 0 log 10 ( e )  Im[ Δ n eff ]   ​​  [dB/μm].
α π/2 NRPS = π 2 rad×Propagation loss  [ dB/μm ] | NRPS | [ rad/μm ]      [ dB ].
α 1-dB NRL = 1 dB×Propagation loss  [ dB/μm ] | NRL | [ dB/μm ]      [ dB ].
L π/2 NRPS = π 2 rad | NRPS | [ rad/μm ]      [ μm ].
L 1-dB NRL = 1 dB | NRL | [ dB/μm ]      [ μm ].

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