Abstract

The miniaturization of Faraday rotator elements is of interest in optical telecommunications for the production of small isolator components. Here we discuss the fabrication of bias-magnet-free-waveguide Faraday rotators for ultrasmall planar device applications. Photonic-crystal structures on magnetic films can yield a significant enhancement in magneto-optic rotation efficiency and an overall reduction in device dimensions. By introducing single-domain magnetic nanoparticles as defects in the photonic bandgap, we show that one can maintain a high degree of coercivity in the Faraday rotator, thus obviating the need for external magnets. We present a theoretical discussion of the formation of single-domain particles in magnetic garnet films, their reversal field characteristics, and the waveguide properties and magneto-optic response of photonic crystals with single-domain defects.

© 2005 Optical Society of America

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  1. V. J. Fratello, S. J. Licht, and C. D. Brandle, "Innovative improvements in bismuth-doped, rare-earth, iron garnet Faraday rotators," IEEE Trans. Magn. 32, 4102-4107 (1996).
    [CrossRef]
  2. M. Levy, H. Hegde, F. J. Cadieu, R. Wolfe, V. J. Fratello, and R. M. Osgood, Jr., "Integrated optical isolators with sputter-deposited thin-film magnets," IEEE Photonics Technol. Lett. 8, 903-905 (1996).
    [CrossRef]
  3. M. J. Steel, M. Levy, and R. M. Osgood, Jr., "Photonic bandgaps with defects and the enhancement of Faraday rotation," J. Lightwave Technol. 18, 1297-1308 (2000).
    [CrossRef]
  4. M. J. Steel, M. Levy, and R. M. Osgood, Jr., "High transmission enhanced Faraday rotation in one-dimensional photonic crystals with defects," IEEE Photonics Technol. Lett. 12, 1171-1173 (2000).
    [CrossRef]
  5. M. Levy, H. C. Yang, M. J. Steel, and J. Fujita, "Flat top response in one-dimensional magnetic photonic band gap structures with Faraday rotation enhancement," J. Lightwave Technol. 19, 1964-1969 (2001).
    [CrossRef]
  6. M. Pardavi-Horvath and G. Vertesy, "Field dependence of the switching field for nonellipsoidal single-domain particles," J. Appl. Phys. 91, 7050-7052 (2002).
    [CrossRef]
  7. Soshin Chikazumi, Physics of Magnetism (Wiley, New York, 1964).
  8. V. K. Vlasko-Vlasov, L. M. Dedukh, and V. I. Nikitenko, "Domain structure of yttrium-iron-garnet single crystals," Sov. Phys. JETP 44, 1208-1214 (1976).
  9. H. Meyer and A. B. Harris, "Specific heat of some rare earth iron garnets and YIG at low temperatures," J. Appl. Phys., Suppl. 31, 49S-50S (1960).
    [CrossRef]
  10. R. L. Douglas, "Spin-wave spectrum of yttrium iron garnet," Phys. Rev. 120, 1612-1614 (1960).
    [CrossRef]
  11. E. E. Anderson, "Molecular field model and the magnetization of YIG," Phys. Rev. 134, A1581-A1585 (1964).
    [CrossRef]
  12. Physics of Magnetic Garnets, Enrico Fermi International Summer School of Physics: Course LXX, L. Paoletti, ed. (Elsevier, Amsterdam, 1978), p. 413.
  13. G. F. Dionne, "Molecular field coefficients of substituted yttrium iron garnets," J. Appl. Phys. 41, 4874-4880 (1970).
    [CrossRef]
  14. H. Schmidt and R. J. Ram, "Coherent magnetization reversal of nanoparticles with crystal and shape anisotropy," J. Appl. Phys. 89, 507-513 (2001).
    [CrossRef]
  15. A. Aharoni, "Angular dependence of nucleation by curling in a prolate spheroid," J. Appl. Phys. 82, 1281-1287 (1997).
    [CrossRef]
  16. W. H. Press, S. A. Teukolsky, W. A. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran - The Art of Scientific Computing , 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  17. V. J. Fratello and R. Wolfe, "Epitaxial garnet films for nonreciprocal magneto-optic devices," in Handbook of Thin Films, Vol. 4, Magnetic Thin Film Devices , M. H. Francombe, ed. (Academic, New York, 2000), Chap. 3.
  18. RSoft, Inc., Ossining, New York, 10562.
  19. M. J. Steel, M. Levy, and R. M. Osgood, Jr., "Large magneto-optical Kerr rotation with high reflectivity from photonic bandgap structures with defects," J. Lightwave Technol. 18, 1289-1296 (2000).
    [CrossRef]

2002 (1)

M. Pardavi-Horvath and G. Vertesy, "Field dependence of the switching field for nonellipsoidal single-domain particles," J. Appl. Phys. 91, 7050-7052 (2002).
[CrossRef]

2001 (2)

2000 (3)

1997 (1)

A. Aharoni, "Angular dependence of nucleation by curling in a prolate spheroid," J. Appl. Phys. 82, 1281-1287 (1997).
[CrossRef]

1996 (2)

V. J. Fratello, S. J. Licht, and C. D. Brandle, "Innovative improvements in bismuth-doped, rare-earth, iron garnet Faraday rotators," IEEE Trans. Magn. 32, 4102-4107 (1996).
[CrossRef]

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

1976 (1)

V. K. Vlasko-Vlasov, L. M. Dedukh, and V. I. Nikitenko, "Domain structure of yttrium-iron-garnet single crystals," Sov. Phys. JETP 44, 1208-1214 (1976).

1970 (1)

G. F. Dionne, "Molecular field coefficients of substituted yttrium iron garnets," J. Appl. Phys. 41, 4874-4880 (1970).
[CrossRef]

1964 (1)

E. E. Anderson, "Molecular field model and the magnetization of YIG," Phys. Rev. 134, A1581-A1585 (1964).
[CrossRef]

1960 (2)

H. Meyer and A. B. Harris, "Specific heat of some rare earth iron garnets and YIG at low temperatures," J. Appl. Phys., Suppl. 31, 49S-50S (1960).
[CrossRef]

R. L. Douglas, "Spin-wave spectrum of yttrium iron garnet," Phys. Rev. 120, 1612-1614 (1960).
[CrossRef]

Aharoni, A.

A. Aharoni, "Angular dependence of nucleation by curling in a prolate spheroid," J. Appl. Phys. 82, 1281-1287 (1997).
[CrossRef]

Anderson, E. E.

E. E. Anderson, "Molecular field model and the magnetization of YIG," Phys. Rev. 134, A1581-A1585 (1964).
[CrossRef]

Brandle, C. D.

V. J. Fratello, S. J. Licht, and C. D. Brandle, "Innovative improvements in bismuth-doped, rare-earth, iron garnet Faraday rotators," IEEE Trans. Magn. 32, 4102-4107 (1996).
[CrossRef]

Cadieu, F. J.

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

Dedukh, L. M.

V. K. Vlasko-Vlasov, L. M. Dedukh, and V. I. Nikitenko, "Domain structure of yttrium-iron-garnet single crystals," Sov. Phys. JETP 44, 1208-1214 (1976).

Dionne, G. F.

G. F. Dionne, "Molecular field coefficients of substituted yttrium iron garnets," J. Appl. Phys. 41, 4874-4880 (1970).
[CrossRef]

Douglas, R. L.

R. L. Douglas, "Spin-wave spectrum of yttrium iron garnet," Phys. Rev. 120, 1612-1614 (1960).
[CrossRef]

Fratello, V. J.

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

V. J. Fratello, S. J. Licht, and C. D. Brandle, "Innovative improvements in bismuth-doped, rare-earth, iron garnet Faraday rotators," IEEE Trans. Magn. 32, 4102-4107 (1996).
[CrossRef]

Fujita, J.

Harris, A. B.

H. Meyer and A. B. Harris, "Specific heat of some rare earth iron garnets and YIG at low temperatures," J. Appl. Phys., Suppl. 31, 49S-50S (1960).
[CrossRef]

Hegde, H.

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

Levy, M.

Licht, S. J.

V. J. Fratello, S. J. Licht, and C. D. Brandle, "Innovative improvements in bismuth-doped, rare-earth, iron garnet Faraday rotators," IEEE Trans. Magn. 32, 4102-4107 (1996).
[CrossRef]

Meyer , H.

H. Meyer and A. B. Harris, "Specific heat of some rare earth iron garnets and YIG at low temperatures," J. Appl. Phys., Suppl. 31, 49S-50S (1960).
[CrossRef]

Nikitenko, V. I.

V. K. Vlasko-Vlasov, L. M. Dedukh, and V. I. Nikitenko, "Domain structure of yttrium-iron-garnet single crystals," Sov. Phys. JETP 44, 1208-1214 (1976).

Osgood, R. M.

M. J. Steel, M. Levy, and R. M. Osgood, Jr., "Large magneto-optical Kerr rotation with high reflectivity from photonic bandgap structures with defects," J. Lightwave Technol. 18, 1289-1296 (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 Photonics Technol. Lett. 12, 1171-1173 (2000).
[CrossRef]

M. J. Steel, M. Levy, and R. M. Osgood, Jr., "Photonic bandgaps with defects and the enhancement of Faraday rotation," J. Lightwave Technol. 18, 1297-1308 (2000).
[CrossRef]

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

Pardavi-Horvath , M.

M. Pardavi-Horvath and G. Vertesy, "Field dependence of the switching field for nonellipsoidal single-domain particles," J. Appl. Phys. 91, 7050-7052 (2002).
[CrossRef]

Ram, R. J.

H. Schmidt and R. J. Ram, "Coherent magnetization reversal of nanoparticles with crystal and shape anisotropy," J. Appl. Phys. 89, 507-513 (2001).
[CrossRef]

Schmidt , H.

H. Schmidt and R. J. Ram, "Coherent magnetization reversal of nanoparticles with crystal and shape anisotropy," J. Appl. Phys. 89, 507-513 (2001).
[CrossRef]

Steel, M. J.

Vertesy, G.

M. Pardavi-Horvath and G. Vertesy, "Field dependence of the switching field for nonellipsoidal single-domain particles," J. Appl. Phys. 91, 7050-7052 (2002).
[CrossRef]

Vlasko-Vlasov, V. K.

V. K. Vlasko-Vlasov, L. M. Dedukh, and V. I. Nikitenko, "Domain structure of yttrium-iron-garnet single crystals," Sov. Phys. JETP 44, 1208-1214 (1976).

Wolfe, R.

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

Yang, H. C.

IEEE Photonics Technol. Lett. (2)

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

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

IEEE Trans. Magn. (1)

V. J. Fratello, S. J. Licht, and C. D. Brandle, "Innovative improvements in bismuth-doped, rare-earth, iron garnet Faraday rotators," IEEE Trans. Magn. 32, 4102-4107 (1996).
[CrossRef]

J. Appl. Phys. (4)

M. Pardavi-Horvath and G. Vertesy, "Field dependence of the switching field for nonellipsoidal single-domain particles," J. Appl. Phys. 91, 7050-7052 (2002).
[CrossRef]

G. F. Dionne, "Molecular field coefficients of substituted yttrium iron garnets," J. Appl. Phys. 41, 4874-4880 (1970).
[CrossRef]

H. Schmidt and R. J. Ram, "Coherent magnetization reversal of nanoparticles with crystal and shape anisotropy," J. Appl. Phys. 89, 507-513 (2001).
[CrossRef]

A. Aharoni, "Angular dependence of nucleation by curling in a prolate spheroid," J. Appl. Phys. 82, 1281-1287 (1997).
[CrossRef]

J. Appl. Phys., Suppl. (1)

H. Meyer and A. B. Harris, "Specific heat of some rare earth iron garnets and YIG at low temperatures," J. Appl. Phys., Suppl. 31, 49S-50S (1960).
[CrossRef]

J. Lightwave Technol. (3)

Phys. Rev. (2)

R. L. Douglas, "Spin-wave spectrum of yttrium iron garnet," Phys. Rev. 120, 1612-1614 (1960).
[CrossRef]

E. E. Anderson, "Molecular field model and the magnetization of YIG," Phys. Rev. 134, A1581-A1585 (1964).
[CrossRef]

Sov. Phys. JETP (1)

V. K. Vlasko-Vlasov, L. M. Dedukh, and V. I. Nikitenko, "Domain structure of yttrium-iron-garnet single crystals," Sov. Phys. JETP 44, 1208-1214 (1976).

Other (5)

Soshin Chikazumi, Physics of Magnetism (Wiley, New York, 1964).

Physics of Magnetic Garnets, Enrico Fermi International Summer School of Physics: Course LXX, L. Paoletti, ed. (Elsevier, Amsterdam, 1978), p. 413.

W. H. Press, S. A. Teukolsky, W. A. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran - The Art of Scientific Computing , 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

V. J. Fratello and R. Wolfe, "Epitaxial garnet films for nonreciprocal magneto-optic devices," in Handbook of Thin Films, Vol. 4, Magnetic Thin Film Devices , M. H. Francombe, ed. (Academic, New York, 2000), Chap. 3.

RSoft, Inc., Ossining, New York, 10562.

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Figures (5)

Fig. 1
Fig. 1

Schematic depiction of a photonic crystal structure on a ridge waveguide with a single quarter-wave phase shift or defect. The defect consists of single-domain magnetic particles aligned longitudinally along the waveguide axis.

Fig. 2
Fig. 2

Nucleation field for magnetization reversal calculated on the basis of the coherent rotation model. The diamonds correspond to YIG particles and the squares to (YBiPb)3Fe4.16Ga0.84O12. The horizontal axis is the ratio of long to short axis lengths in prolate spheroid particles.

Fig. 3
Fig. 3

Double-channel YIG waveguide.

Fig. 4
Fig. 4

TE and TM mode profiles corresponding to a double channel with 550-nm-wide channels and a 450-nm gap between them. The modes have the same fundamental mode effective index and the profiles were computed by semivectorial BPM analysis.

Fig. 5
Fig. 5

Transmission and Faraday rotation characteristics of a two-defect magnetic photonic crystal with single-domain particle defects. The refractive index of the quarter phase-shift region used in these calculations is that of the fundamental waveguide mode index of a 550-nm×647-nm channel pair separated by 450 nm. The photonic crystal is 42.6 µm long and the defects are each 2.33 µm long.

Tables (2)

Tables Icon

Table 1 Magnetic Domain Parametersa

Tables Icon

Table 2 Multiple-Channel Waveguide Parametersa

Equations (8)

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γ=20π(AEC)1/2dφ.
A=5/16(5Jad-8Jaa-3Jdd)(4S/l).
EC=K0+K1(α12α22+α22α32+α12α32)+K2α12α22α32.
Jad=Jda=5.02×10-15(1-0.125x-0.127y)ergs,
Jdd=2.36×10-15(1-0.43x)ergs,
Jaa=1.68×10-15(1-0.42y)ergs.
EM=-HMS cos ϕ,
ES=1/4(Na+Nc)MS2-1/4(Na-Nc)MS2 cos 2ϕ.

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