Abstract

We propose and numerically investigate the operation of a novel class of polarization-independent splitters based on the photonic crystal fiber (PCF) technology. The proposed polarization-independent feature of the PCF splitter is realized by uniformly distributed elliptically-shaped airholes in the cladding of a dual-core PCF. The design procedure follows a rigorous synthesis protocol based on exact equations for describing the wavelength de-coupling mechanism, and on full-vectorial finite element as well as beam propagation methods for optical characterization of PCFs. The compact de-coupling lengths as well as the low cross-talk over appreciable optical bandwidths are the main advantages of the proposed PCF splitter. The proposed device can be employed in reconfigurable optical communication systems for performing wavelength de-multiplexing operation, especially for fiber-to-the-home applications, as well as the emerging passive optical network applications.

© 2005 Optical Society of America

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References

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  1. J. A. Buck, Fundamentals of Optical Fibers, Wiley-Interscience (2004).
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light. (Princenton, NJ: Princeton Univ. Press, 1995).
  3. J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
    [CrossRef]
  4. J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
    [CrossRef] [PubMed]
  5. J. C. Knight, T. A. Birks, P.St.J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 484–485 (1996).
    [CrossRef]
  6. H. Kawata, T. Ogawa, and N. Yoshimoto, “Multichannel video and IP signal multiplexing system using CWDM technology,” J. Lightwave Technol. 22, 1454–1462 (2004).
    [CrossRef]
  7. W. Chi, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chi, and J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photonics Technol. Lett. 4, 457–459 (1993).
  8. C. R. Doerr, R. Pafchek, and L. W. Stulz, “Integrated band demultiplexer using waveguide grating routers,” IEEE Photonics Technol. Lett. 15, 1088–1090 (2003).
    [CrossRef]
  9. B. J. Offrein, G. L. Bona, F. Horst, W. M. Salemink, R. Beyeler, and R. Germann, “Wavelength tunable optical add-after-drop filter with flat passband for WDM networks,” IEEE Photonics Technol. Lett. 11, 239–241 (1999).
    [CrossRef]
  10. B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, and A. H. Greenway, “Experimental study of dual core photonic crystal fiber,” Electron. Lett. 36, 1358–1359 (2000).
    [CrossRef]
  11. K. Saitoh, Y. Sato, and M. Koshiba, “Coupling characteristics of dual-core photonic crystal fiber couplers,” Opt. Express 11, 3188–3195 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-24-3188.
    [CrossRef] [PubMed]
  12. L. Zhang and C. Yang, “Polarization-dependent coupling in twin core photonic crystal fibers,” J. Lightwave Technol. 22, 1367–1373 (2004).
    [CrossRef]
  13. K. Saitoh, Y. Sato, and M. Koshiba, “Polarization splitter in three-core photonic crystal fibers,” Opt. Express 12, 3940–3946 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-3940.
    [CrossRef] [PubMed]
  14. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Elencron. 38, 927–933 (2002).
    [CrossRef]
  15. N. A. Issa, M. A. Eijkelenborg, M. Fellew, F. Cox, G. Henry, and C. J. Large, “Fabrication and study of microstructured optical fibers with elliptical holes,” Opt. Lett. 29, 1336–1338 (2004).
    [CrossRef] [PubMed]
  16. S. G. Leon-Saval, T. A. Birks, N.Y. Joly, A. K. George, W. J. Wadsworth, G. Kakarantzas, and P.St.J. Russel, “Splice-free interfacing of photonic crystal fibers,” Opt. Lett. 30, 1629–1631 (2005).
    [CrossRef] [PubMed]
  17. R. A. Forber and E. Marom, “Symmetric directional coupler switches,” IEEE J. Quantum Electron. QE-38, 911–919 (1986).
    [CrossRef]
  18. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic waveguides,” J. Lightwave Technol. 19, 405–413 (2001).
    [CrossRef]
  19. J. C. Knight, T. A. Birks, P. St J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” Opt. Lett. 15, 748–752 (1998).

2005 (1)

2004 (4)

2003 (3)

K. Saitoh, Y. Sato, and M. Koshiba, “Coupling characteristics of dual-core photonic crystal fiber couplers,” Opt. Express 11, 3188–3195 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-24-3188.
[CrossRef] [PubMed]

J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
[CrossRef] [PubMed]

C. R. Doerr, R. Pafchek, and L. W. Stulz, “Integrated band demultiplexer using waveguide grating routers,” IEEE Photonics Technol. Lett. 15, 1088–1090 (2003).
[CrossRef]

2002 (1)

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Elencron. 38, 927–933 (2002).
[CrossRef]

2001 (1)

2000 (1)

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, and A. H. Greenway, “Experimental study of dual core photonic crystal fiber,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

1999 (2)

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

B. J. Offrein, G. L. Bona, F. Horst, W. M. Salemink, R. Beyeler, and R. Germann, “Wavelength tunable optical add-after-drop filter with flat passband for WDM networks,” IEEE Photonics Technol. Lett. 11, 239–241 (1999).
[CrossRef]

1998 (1)

J. C. Knight, T. A. Birks, P. St J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” Opt. Lett. 15, 748–752 (1998).

1996 (1)

J. C. Knight, T. A. Birks, P.St.J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 484–485 (1996).
[CrossRef]

1993 (1)

W. Chi, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chi, and J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photonics Technol. Lett. 4, 457–459 (1993).

1986 (1)

R. A. Forber and E. Marom, “Symmetric directional coupler switches,” IEEE J. Quantum Electron. QE-38, 911–919 (1986).
[CrossRef]

Atkin, D. M.

J. C. Knight, T. A. Birks, P.St.J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 484–485 (1996).
[CrossRef]

Barkou, S. E.

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

Beyeler, R.

B. J. Offrein, G. L. Bona, F. Horst, W. M. Salemink, R. Beyeler, and R. Germann, “Wavelength tunable optical add-after-drop filter with flat passband for WDM networks,” IEEE Photonics Technol. Lett. 11, 239–241 (1999).
[CrossRef]

Birks, T. A.

S. G. Leon-Saval, T. A. Birks, N.Y. Joly, A. K. George, W. J. Wadsworth, G. Kakarantzas, and P.St.J. Russel, “Splice-free interfacing of photonic crystal fibers,” Opt. Lett. 30, 1629–1631 (2005).
[CrossRef] [PubMed]

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, and A. H. Greenway, “Experimental study of dual core photonic crystal fiber,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

J. C. Knight, T. A. Birks, P. St J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” Opt. Lett. 15, 748–752 (1998).

J. C. Knight, T. A. Birks, P.St.J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 484–485 (1996).
[CrossRef]

Bjarklev, A.

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

Bona, G. L.

B. J. Offrein, G. L. Bona, F. Horst, W. M. Salemink, R. Beyeler, and R. Germann, “Wavelength tunable optical add-after-drop filter with flat passband for WDM networks,” IEEE Photonics Technol. Lett. 11, 239–241 (1999).
[CrossRef]

Broeng, J.

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

Buck, J. A.

J. A. Buck, Fundamentals of Optical Fibers, Wiley-Interscience (2004).

Chi, K. D.

W. Chi, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chi, and J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photonics Technol. Lett. 4, 457–459 (1993).

Chi, W.

W. Chi, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chi, and J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photonics Technol. Lett. 4, 457–459 (1993).

Cox, F.

de Sandro, J. P.

J. C. Knight, T. A. Birks, P. St J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” Opt. Lett. 15, 748–752 (1998).

Doerr, C. R.

C. R. Doerr, R. Pafchek, and L. W. Stulz, “Integrated band demultiplexer using waveguide grating routers,” IEEE Photonics Technol. Lett. 15, 1088–1090 (2003).
[CrossRef]

Eijkelenborg, M. A.

Fellew, M.

Forber, R. A.

R. A. Forber and E. Marom, “Symmetric directional coupler switches,” IEEE J. Quantum Electron. QE-38, 911–919 (1986).
[CrossRef]

George, A. K.

Germann, R.

B. J. Offrein, G. L. Bona, F. Horst, W. M. Salemink, R. Beyeler, and R. Germann, “Wavelength tunable optical add-after-drop filter with flat passband for WDM networks,” IEEE Photonics Technol. Lett. 11, 239–241 (1999).
[CrossRef]

Greenway, A. H.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, and A. H. Greenway, “Experimental study of dual core photonic crystal fiber,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

Henry, G.

Horst, F.

B. J. Offrein, G. L. Bona, F. Horst, W. M. Salemink, R. Beyeler, and R. Germann, “Wavelength tunable optical add-after-drop filter with flat passband for WDM networks,” IEEE Photonics Technol. Lett. 11, 239–241 (1999).
[CrossRef]

Issa, N. A.

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light. (Princenton, NJ: Princeton Univ. Press, 1995).

Joly, N.Y.

Kakarantzas, G.

Kawata, H.

Knight, J. C.

J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
[CrossRef] [PubMed]

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, and A. H. Greenway, “Experimental study of dual core photonic crystal fiber,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

J. C. Knight, T. A. Birks, P. St J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” Opt. Lett. 15, 748–752 (1998).

J. C. Knight, T. A. Birks, P.St.J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 484–485 (1996).
[CrossRef]

Koshiba, M.

Large, C. J.

Larocque, C.

W. Chi, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chi, and J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photonics Technol. Lett. 4, 457–459 (1993).

Leon-Saval, S. G.

Mangan, B. J.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, and A. H. Greenway, “Experimental study of dual core photonic crystal fiber,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

Marom, E.

R. A. Forber and E. Marom, “Symmetric directional coupler switches,” IEEE J. Quantum Electron. QE-38, 911–919 (1986).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light. (Princenton, NJ: Princeton Univ. Press, 1995).

Mogilevtsev, D.

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

Offrein, B. J.

B. J. Offrein, G. L. Bona, F. Horst, W. M. Salemink, R. Beyeler, and R. Germann, “Wavelength tunable optical add-after-drop filter with flat passband for WDM networks,” IEEE Photonics Technol. Lett. 11, 239–241 (1999).
[CrossRef]

Ogawa, T.

Pafchek, R.

C. R. Doerr, R. Pafchek, and L. W. Stulz, “Integrated band demultiplexer using waveguide grating routers,” IEEE Photonics Technol. Lett. 15, 1088–1090 (2003).
[CrossRef]

Puetz, N.

W. Chi, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chi, and J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photonics Technol. Lett. 4, 457–459 (1993).

Rolland, C.

W. Chi, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chi, and J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photonics Technol. Lett. 4, 457–459 (1993).

Russel, P. St. J.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, and A. H. Greenway, “Experimental study of dual core photonic crystal fiber,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

Russel, P.St.J.

S. G. Leon-Saval, T. A. Birks, N.Y. Joly, A. K. George, W. J. Wadsworth, G. Kakarantzas, and P.St.J. Russel, “Splice-free interfacing of photonic crystal fibers,” Opt. Lett. 30, 1629–1631 (2005).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P.St.J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 484–485 (1996).
[CrossRef]

Russell, P. St J.

J. C. Knight, T. A. Birks, P. St J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” Opt. Lett. 15, 748–752 (1998).

Saitoh, K.

Salemink, W. M.

B. J. Offrein, G. L. Bona, F. Horst, W. M. Salemink, R. Beyeler, and R. Germann, “Wavelength tunable optical add-after-drop filter with flat passband for WDM networks,” IEEE Photonics Technol. Lett. 11, 239–241 (1999).
[CrossRef]

Sato, Y.

Shepherd, F.

W. Chi, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chi, and J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photonics Technol. Lett. 4, 457–459 (1993).

Stulz, L. W.

C. R. Doerr, R. Pafchek, and L. W. Stulz, “Integrated band demultiplexer using waveguide grating routers,” IEEE Photonics Technol. Lett. 15, 1088–1090 (2003).
[CrossRef]

Wadsworth, W. J.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light. (Princenton, NJ: Princeton Univ. Press, 1995).

Xu, J. M.

W. Chi, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chi, and J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photonics Technol. Lett. 4, 457–459 (1993).

Yang, C.

Yoshimoto, N.

Zhang, L.

Electron. Lett. (1)

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, and A. H. Greenway, “Experimental study of dual core photonic crystal fiber,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. A. Forber and E. Marom, “Symmetric directional coupler switches,” IEEE J. Quantum Electron. QE-38, 911–919 (1986).
[CrossRef]

IEEE J. Quantum Elencron. (1)

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Elencron. 38, 927–933 (2002).
[CrossRef]

IEEE Photonics Technol. Lett. (3)

W. Chi, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chi, and J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photonics Technol. Lett. 4, 457–459 (1993).

C. R. Doerr, R. Pafchek, and L. W. Stulz, “Integrated band demultiplexer using waveguide grating routers,” IEEE Photonics Technol. Lett. 15, 1088–1090 (2003).
[CrossRef]

B. J. Offrein, G. L. Bona, F. Horst, W. M. Salemink, R. Beyeler, and R. Germann, “Wavelength tunable optical add-after-drop filter with flat passband for WDM networks,” IEEE Photonics Technol. Lett. 11, 239–241 (1999).
[CrossRef]

J. Lightwave Technol. (3)

Nature (1)

J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Fiber Technol. (1)

J. Broeng, D. Mogilevtsev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[CrossRef]

Opt. Lett. (4)

J. C. Knight, T. A. Birks, P. St J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” Opt. Lett. 15, 748–752 (1998).

S. G. Leon-Saval, T. A. Birks, N.Y. Joly, A. K. George, W. J. Wadsworth, G. Kakarantzas, and P.St.J. Russel, “Splice-free interfacing of photonic crystal fibers,” Opt. Lett. 30, 1629–1631 (2005).
[CrossRef] [PubMed]

N. A. Issa, M. A. Eijkelenborg, M. Fellew, F. Cox, G. Henry, and C. J. Large, “Fabrication and study of microstructured optical fibers with elliptical holes,” Opt. Lett. 29, 1336–1338 (2004).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P.St.J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 484–485 (1996).
[CrossRef]

Other (2)

J. A. Buck, Fundamentals of Optical Fibers, Wiley-Interscience (2004).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light. (Princenton, NJ: Princeton Univ. Press, 1995).

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Figures (5)

Fig. 1.
Fig. 1.

Topology of a dual-core PCF splitter with uniformly distributed elliptical air-holes in a hexagonal arrangement with pitch number Λ and ellipticity e=dy /dx . By a judicious choice of the geometrical parameters, this PCF structure can exhibit polarization-independent propagation characteristics, at two different wavelength bands.

Fig. 2.
Fig. 2.

Coupling length ratios as functions of the dimensionless parameter dx /Λ, for various values of the hole-ellipticity e=dy /dx , at (a) λ2 = 1.55 μm, (b) at λ1 = 1.3 μm, and (c) for x-polarization at wavelengths λ1, λ2.

Fig. 3.
Fig. 3.

Normalized power distribution in the PCF-splitter for x-polarization (red line), y-polarization (blue line) at wavelengths of (a) λ = 1.3 μm, and (b) λ = 1.55 μm. The coupling length was confirmed by the BPM analysis to be L = 15.4 mm.

Fig. 4.
Fig. 4.

Electric field distributions in the polarization-independent dual core PCF splitter with elliptical air-holes for (a) x-polarization ( Ex ) at λ=1.3 μm and z = 0 mm, (b) x-polarization ( Ex ) at λ=1.3 μm and z = 15.4 mm, (c) y-polarization ( Ey ) at λ=1.3 μm and z = 0 mm, (d) y-polarization ( Ey ) at λ=1.3 μm and z = 15.4 mm, (e) x-polarization ( Ex ) at λ=1.55 μm and z = 0 mm, (f) x-polarization ( Ex ) at λ=1.55 μm and z = 15.4 mm, (g) y-polarization ( Ey ) at λ=1.55 μm and z = 0 mm, and (h) y-polarization ( Ey ) at λ=1.55 μm and z = 15.4 mm.

Fig. 5
Fig. 5

Crosstalk between the two cores of the PCF, and the available optical bandwidths defined at a level of -20 dB for (a) λ d = 1.55 μm, with BW=5.1 nm and (b) λ d = 1.3 μm, with BW=2.7 nm.

Equations (8)

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

P out , A = P in cos 2 ( π 2 z L c ) ,
P out , B = P in sin 2 ( π 2 z L c ) ,
L c x , y ( λ ) = λ 2 ( n even x , y n odd x , y ) .
L = mL c x ( λ 1 ) = ( m + q ) L c y ( λ 1 ) = ( m + q ) L c x ( λ 2 ) = ( m + p + q ) L c y ( λ 2 )
L c x ( λ ) L c y ( λ ) = n even y n odd y n even x n odd x ,
L c x ( 1.3 μm ) L c y ( 1.3 μm ) = 9 7 , L c x ( 1.55 μm ) L c y ( 1.55 μm ) = 9 7 , L c x ( 1.3 μm ) L c x ( 1.55 μm ) = 2 1 .
m p q q ( 7,7,2,4 )
Crosstalk j = 10 log 10 [ P j ( λ u ) P x 2 ( λ d ) + P y 2 ( λ d ) ] [ dB ] , j = x or y polarization

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