Abstract

Polarization mode coupling in circularly birefringent gratings is analyzed. It is numerically found that efficient LP01x-LP02y mode coupling (where LP is linear polarization) is possible in a 50-cm-long circularly birefringent fiber grating formed in a terbium-doped borosilicate glass fiber and that complete LP01x-LP02y and LP01x-LP03y mode couplings result after a few-centimeter-long circularly birefringent grating that is formed in a bismuth-substitute iron garnet waveguide. Various parameters of polarization mode coupling in a number of circularly birefringent gratings are also computed.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Erdogan, J. Sipe, “Tilted fiber phase gratings,” J. Opt. Soc. Am. A 13, 296–313 (1996).
    [CrossRef]
  2. A. Vengsarkar, R. Pedrazzani, J. Judkins, P. Lemaire, N. Bergano, C. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 339–337 (1996).
    [CrossRef]
  3. D. Stegall, T. Erdogan, “Dispersion control with use of long-period fiber grating,” J. Opt. Soc. Am. A 17, 304–312 (2000).
    [CrossRef]
  4. C. Poole, J. Wiesenfeld, D. Digiovanni, A. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes new cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
    [CrossRef]
  5. K. Hill, B. Malo, K. Vineberg, F. Bilodo, D. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
    [CrossRef]
  6. K. S. Lee, T. Erdogan, “Transmissive tilted gratings for LP01-to-LP11 mode coupling,” IEEE Photon. Technol. Lett. 11, 1286–1288 (1999).
    [CrossRef]
  7. K. S. Lee, T. Erdogan, “Fiber mode coupling in transmissive and reflective tilted fiber gratings,” Appl. Opt. 39, 1394–1404 (2000).
    [CrossRef]
  8. K. S. Lee, T. Erdogan, “Fiber mode conversion with tilted gratings in optical fiber,” J. Opt. Soc. Am. A 18, 1176–1185 (2001).
    [CrossRef]
  9. K. S. Lee, “Mode coupling in tilted planar waveguide gratings,” Appl. Opt. 39, 6144–6149 (2000).
    [CrossRef]
  10. K. S. Lee, T. Erdogan, “Mode coupling in spiral fibre gratings,” Electron. Lett. 37, 156–157 (2001).
    [CrossRef]
  11. C. Poole, C. Townsend, K. Nelson, “Helical grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 589–604 (1991).
    [CrossRef]
  12. K. S. Lee, J. Y. Cho, “Polarization-mode coupling in birefringent fiber gratings,” J. Opt. Soc. Am. A 19, 1621–1631 (2002).
    [CrossRef]
  13. K. S. Lee, “New compensation method for bulk optical sensors with multiple birefringences,” Appl. Opt. 28, 2001–2011 (1989).
    [CrossRef] [PubMed]
  14. Z. Ren, Y. Wang, P. Robert, “Faraday rotation and its temperature dependence measurements in low-birefringence fibers,” J. Lightwave Technol. 7, 1275–1278 (1989).
    [CrossRef]
  15. J. Krumme, V. Doormann, H. Meyer, W. Radtke, B. Strocka, “Sputter epitaxy of iron-garnet waveguides,” Electro-Optic and Magneto-Optic Materials, J.-P. Huignard, ed., Proc. SPIE1018, 109–114 (1988).
    [CrossRef]
  16. M. Levy, “The on-chip integration of magnetooptic waveguide isolators,” IEEE J. Sel. Top. Quantum Electron. 8, 1300–1306 (2002).
    [CrossRef]
  17. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
    [CrossRef]
  18. K. Shiraishi, S. Sugaya, S. Kawakami, “Fiber Faraday rotator,” Appl. Opt. 23, 1103–1106 (1984).
    [CrossRef] [PubMed]
  19. D. Wilson, “Optical isolators adapt to communication needs,” Laser Focus World, 175–180 (April1991).
  20. J. Ballato, E. Snitzer, “Fabrication of fibers with high rare-earth concentrations for Faraday isolator applications,” Appl. Opt. 34, 6848–6854 (1995).
    [CrossRef] [PubMed]

2002 (2)

M. Levy, “The on-chip integration of magnetooptic waveguide isolators,” IEEE J. Sel. Top. Quantum Electron. 8, 1300–1306 (2002).
[CrossRef]

K. S. Lee, J. Y. Cho, “Polarization-mode coupling in birefringent fiber gratings,” J. Opt. Soc. Am. A 19, 1621–1631 (2002).
[CrossRef]

2001 (2)

K. S. Lee, T. Erdogan, “Fiber mode conversion with tilted gratings in optical fiber,” J. Opt. Soc. Am. A 18, 1176–1185 (2001).
[CrossRef]

K. S. Lee, T. Erdogan, “Mode coupling in spiral fibre gratings,” Electron. Lett. 37, 156–157 (2001).
[CrossRef]

2000 (3)

1999 (1)

K. S. Lee, T. Erdogan, “Transmissive tilted gratings for LP01-to-LP11 mode coupling,” IEEE Photon. Technol. Lett. 11, 1286–1288 (1999).
[CrossRef]

1996 (2)

1995 (1)

1994 (1)

C. Poole, J. Wiesenfeld, D. Digiovanni, A. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes new cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[CrossRef]

1991 (2)

C. Poole, C. Townsend, K. Nelson, “Helical grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 589–604 (1991).
[CrossRef]

D. Wilson, “Optical isolators adapt to communication needs,” Laser Focus World, 175–180 (April1991).

1990 (1)

K. Hill, B. Malo, K. Vineberg, F. Bilodo, D. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

1989 (2)

Z. Ren, Y. Wang, P. Robert, “Faraday rotation and its temperature dependence measurements in low-birefringence fibers,” J. Lightwave Technol. 7, 1275–1278 (1989).
[CrossRef]

K. S. Lee, “New compensation method for bulk optical sensors with multiple birefringences,” Appl. Opt. 28, 2001–2011 (1989).
[CrossRef] [PubMed]

1984 (1)

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

Ballato, J.

Bergano, N.

Bilodo, F.

K. Hill, B. Malo, K. Vineberg, F. Bilodo, D. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Cho, J. Y.

Davidson, C.

Digiovanni, D.

C. Poole, J. Wiesenfeld, D. Digiovanni, A. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes new cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[CrossRef]

Doormann, V.

J. Krumme, V. Doormann, H. Meyer, W. Radtke, B. Strocka, “Sputter epitaxy of iron-garnet waveguides,” Electro-Optic and Magneto-Optic Materials, J.-P. Huignard, ed., Proc. SPIE1018, 109–114 (1988).
[CrossRef]

Erdogan, T.

Hill, K.

K. Hill, B. Malo, K. Vineberg, F. Bilodo, D. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Johnson, D.

K. Hill, B. Malo, K. Vineberg, F. Bilodo, D. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Judkins, J.

Kawakami, S.

Krumme, J.

J. Krumme, V. Doormann, H. Meyer, W. Radtke, B. Strocka, “Sputter epitaxy of iron-garnet waveguides,” Electro-Optic and Magneto-Optic Materials, J.-P. Huignard, ed., Proc. SPIE1018, 109–114 (1988).
[CrossRef]

Lee, K. S.

Lemaire, P.

Levy, M.

M. Levy, “The on-chip integration of magnetooptic waveguide isolators,” IEEE J. Sel. Top. Quantum Electron. 8, 1300–1306 (2002).
[CrossRef]

Malo, B.

K. Hill, B. Malo, K. Vineberg, F. Bilodo, D. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Meyer, H.

J. Krumme, V. Doormann, H. Meyer, W. Radtke, B. Strocka, “Sputter epitaxy of iron-garnet waveguides,” Electro-Optic and Magneto-Optic Materials, J.-P. Huignard, ed., Proc. SPIE1018, 109–114 (1988).
[CrossRef]

Nelson, K.

C. Poole, C. Townsend, K. Nelson, “Helical grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 589–604 (1991).
[CrossRef]

Pedrazzani, R.

Poole, C.

C. Poole, J. Wiesenfeld, D. Digiovanni, A. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes new cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[CrossRef]

C. Poole, C. Townsend, K. Nelson, “Helical grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 589–604 (1991).
[CrossRef]

Radtke, W.

J. Krumme, V. Doormann, H. Meyer, W. Radtke, B. Strocka, “Sputter epitaxy of iron-garnet waveguides,” Electro-Optic and Magneto-Optic Materials, J.-P. Huignard, ed., Proc. SPIE1018, 109–114 (1988).
[CrossRef]

Ren, Z.

Z. Ren, Y. Wang, P. Robert, “Faraday rotation and its temperature dependence measurements in low-birefringence fibers,” J. Lightwave Technol. 7, 1275–1278 (1989).
[CrossRef]

Robert, P.

Z. Ren, Y. Wang, P. Robert, “Faraday rotation and its temperature dependence measurements in low-birefringence fibers,” J. Lightwave Technol. 7, 1275–1278 (1989).
[CrossRef]

Shiraishi, K.

Sipe, J.

Skinner, I.

K. Hill, B. Malo, K. Vineberg, F. Bilodo, D. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Snitzer, E.

Stegall, D.

Strocka, B.

J. Krumme, V. Doormann, H. Meyer, W. Radtke, B. Strocka, “Sputter epitaxy of iron-garnet waveguides,” Electro-Optic and Magneto-Optic Materials, J.-P. Huignard, ed., Proc. SPIE1018, 109–114 (1988).
[CrossRef]

Sugaya, S.

Townsend, C.

C. Poole, C. Townsend, K. Nelson, “Helical grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 589–604 (1991).
[CrossRef]

Vengsarkar, A.

A. Vengsarkar, R. Pedrazzani, J. Judkins, P. Lemaire, N. Bergano, C. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 339–337 (1996).
[CrossRef]

C. Poole, J. Wiesenfeld, D. Digiovanni, A. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes new cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[CrossRef]

Vineberg, K.

K. Hill, B. Malo, K. Vineberg, F. Bilodo, D. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Wang, Y.

Z. Ren, Y. Wang, P. Robert, “Faraday rotation and its temperature dependence measurements in low-birefringence fibers,” J. Lightwave Technol. 7, 1275–1278 (1989).
[CrossRef]

Wiesenfeld, J.

C. Poole, J. Wiesenfeld, D. Digiovanni, A. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes new cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[CrossRef]

Wilson, D.

D. Wilson, “Optical isolators adapt to communication needs,” Laser Focus World, 175–180 (April1991).

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

Appl. Opt. (5)

Electron. Lett. (2)

K. Hill, B. Malo, K. Vineberg, F. Bilodo, D. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fibre using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

K. S. Lee, T. Erdogan, “Mode coupling in spiral fibre gratings,” Electron. Lett. 37, 156–157 (2001).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Levy, “The on-chip integration of magnetooptic waveguide isolators,” IEEE J. Sel. Top. Quantum Electron. 8, 1300–1306 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. S. Lee, T. Erdogan, “Transmissive tilted gratings for LP01-to-LP11 mode coupling,” IEEE Photon. Technol. Lett. 11, 1286–1288 (1999).
[CrossRef]

J. Lightwave Technol. (3)

Z. Ren, Y. Wang, P. Robert, “Faraday rotation and its temperature dependence measurements in low-birefringence fibers,” J. Lightwave Technol. 7, 1275–1278 (1989).
[CrossRef]

C. Poole, J. Wiesenfeld, D. Digiovanni, A. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes new cutoff,” J. Lightwave Technol. 12, 1746–1758 (1994).
[CrossRef]

C. Poole, C. Townsend, K. Nelson, “Helical grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 589–604 (1991).
[CrossRef]

J. Opt. Soc. Am. A (4)

Laser Focus World (1)

D. Wilson, “Optical isolators adapt to communication needs,” Laser Focus World, 175–180 (April1991).

Opt. Lett. (1)

Other (1)

J. Krumme, V. Doormann, H. Meyer, W. Radtke, B. Strocka, “Sputter epitaxy of iron-garnet waveguides,” Electro-Optic and Magneto-Optic Materials, J.-P. Huignard, ed., Proc. SPIE1018, 109–114 (1988).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Circularly birefringent fiber grating formed by periodic magnetic field B with period Λ g .

Fig. 2
Fig. 2

Circularly birefringent fiber grating formed by periodic microsolenoids with length l and current I.

Fig. 3
Fig. 3

(a) Coupling coefficients as a function of wavelength for the LP01x -LP02y polarization mode coupling in the circularly birefringent fiber gratings formed in a terbium-doped borosilicate fiber by the periodic microsolenoids with various currents I(a = 10 μm, n 2 = 1.45, Δ = 0.005, and N = 100 cm-1). (b) Coupling coefficients as a function of wavelength for the LP01x -LP03y polarization mode coupling in the circularly birefringent fiber gratings formed in a terbium-doped borosilicate fiber by periodic microsolenoids with various currents I(a = 10 μm, n 2 = 1.45, Δ = 0.005, and N = 100 cm-1).

Fig. 4
Fig. 4

Transmission spectra of the LP01 mode in the circularly birefringent fiber gratings formed in a terbium-doped borosilicate fiber by periodic microsolenoids with three different solenoid currents (Λ g = 1.8 cm, a = 10 μm, n 2 = 1.45, Δ = 0.005, N = 100 cm-1, and L g = 50 cm). The grating is designed for LP01x -LP02y polarization mode coupling at 0.75 μm.

Fig. 5
Fig. 5

(a) Coupled powers of the LP01x and LP02y modes after the circularly birefringent gratings formed in a BIG waveguide under a periodic magnetic field B = 0.1 mT for LP01x -LP02y polarization mode coupling (Λ g = 2.1 mm, a = 5 μm, n 2 = 2.32, Δ = 0.005, and L g = 3.4 cm). (b) The coupled powers of the LP01x and LP03y modes after the circularly birefringent gratings formed in a BIG waveguide under a periodic magnetic field B = 2 mT for LP01x -LP03y polarization mode coupling (Λ g = 210 μm, a = 5 μm, n 2 = 2.32, Δ = 0.005, and L g = 1.3 cm).

Fig. 6
Fig. 6

Transmission spectra of the LP01 mode in the circularly birefringent gratings formed in a BIG waveguide under three different periodic magnetic fields (Λ g = 2.1 mm, a = 5 μm, n 2 = 2.32, Δ = 0.005, and L g = 3 cm).

Tables (2)

Tables Icon

Table 1 Coupling Coefficients of the LP01x -LP 02y Polarization Mode Coupling (B = 1 mT, Δ = 0.005, a = 1 μm)

Tables Icon

Table 2 Coupling Coefficients of the LP01x -LP 03y Polarization Mode Coupling (B = 20 mT, Δ = 0.005, a = 10 μm)

Equations (3)

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

Δεxy=Δεxy¯fz=-2iε0niVdBfz/k0
dA01x/dz=iA0myG0 exp-2iδz,
dA0my/dz=iA01xG0 exp2iδz,

Metrics