Abstract

The group-velocity concept of a complex of modes is investigated, and the findings are related to power and energy. A special case of interest is polarization mode dispersion. This approach permits a generalization of polarization mode dispersion to the case of polarization mixing of multiple modes. Further, it is shown that first- and second-order polarization mode dispersions are related to an energy matrix.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Andresciani, F. Curti, F. Matera, and B. Daĩno, “Measurement of the difference between the principal states of polarization in a low-birefringence terrestrial fiber cable,” Opt. Lett. 12, 844–846 (1987).
    [CrossRef] [PubMed]
  2. C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schultz, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
    [CrossRef]
  3. B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
    [CrossRef]
  4. B. L. Heffner, “Accurate automated measurement of differential group delay dispersion and principal state variation using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 5, 814–817 (1993).
    [CrossRef]
  5. N. Gisin, R. Passy, and J. P. Von der Weid, “Definitions and measurements of polarization mode dispersion: interferometric versus fixed analyzer methods,” IEEE Photon. Technol. Lett. 6, 730–732 (1994).
    [CrossRef]
  6. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford; Addison-Wesley, Reading, Mass., 1960).

1994 (1)

N. Gisin, R. Passy, and J. P. Von der Weid, “Definitions and measurements of polarization mode dispersion: interferometric versus fixed analyzer methods,” IEEE Photon. Technol. Lett. 6, 730–732 (1994).
[CrossRef]

1993 (1)

B. L. Heffner, “Accurate automated measurement of differential group delay dispersion and principal state variation using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 5, 814–817 (1993).
[CrossRef]

1992 (1)

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

1988 (1)

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schultz, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

1987 (1)

Andresciani, D.

Bergano, N. S.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schultz, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Curti, F.

Daino, B.

Gisin, N.

N. Gisin, R. Passy, and J. P. Von der Weid, “Definitions and measurements of polarization mode dispersion: interferometric versus fixed analyzer methods,” IEEE Photon. Technol. Lett. 6, 730–732 (1994).
[CrossRef]

Heffner, B. L.

B. L. Heffner, “Accurate automated measurement of differential group delay dispersion and principal state variation using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 5, 814–817 (1993).
[CrossRef]

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

Matera, F.

Passy, R.

N. Gisin, R. Passy, and J. P. Von der Weid, “Definitions and measurements of polarization mode dispersion: interferometric versus fixed analyzer methods,” IEEE Photon. Technol. Lett. 6, 730–732 (1994).
[CrossRef]

Poole, C. D.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schultz, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Schultz, H. J.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schultz, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Von der Weid, J. P.

N. Gisin, R. Passy, and J. P. Von der Weid, “Definitions and measurements of polarization mode dispersion: interferometric versus fixed analyzer methods,” IEEE Photon. Technol. Lett. 6, 730–732 (1994).
[CrossRef]

Wagner, R. E.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schultz, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

B. L. Heffner, “Accurate automated measurement of differential group delay dispersion and principal state variation using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 5, 814–817 (1993).
[CrossRef]

N. Gisin, R. Passy, and J. P. Von der Weid, “Definitions and measurements of polarization mode dispersion: interferometric versus fixed analyzer methods,” IEEE Photon. Technol. Lett. 6, 730–732 (1994).
[CrossRef]

J. Lightwave Technol. (1)

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schultz, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Opt. Lett. (1)

Other (1)

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford; Addison-Wesley, Reading, Mass., 1960).

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 (1)

Fig. 1
Fig. 1

The Poincaré sphere.

Equations (32)

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

a(ω)(exp[jωt-jβ(ω)z]+exp{j(ω+Δω)t-j[β(ω)t+Δωβz]}),
a(ω)exp[jωt-jβ(ω)z]{1+exp[jΔω(t-βz)]}.
βl=wp=dϕdω,
b=Ta.
TT=TT=1.
b(ω+Δω)=b(ω)+Δω ddωb=b(ω)+ΔωddωTa(ω).
ddωb=dTdωa(ω)=λb=λTa.
T ddωTa=λa.
b(ω+Δω)=exp(-jΔϕ)b(ω),orddωb=-j dϕdωb.
λ=-j dϕdω.
dTdωT+T dTdω=0.
Eω×H*+E*×Hω·dS
=-j H*·μ¯¯+ω μ¯¯ω·H+E*·¯¯+ω ¯¯ω·EdV=-j4w,
w=aWa,
b dbdω=-jaWa.
aT dTdωa=-jaWa.
T dTdω=-jW.
e(i)We(i)=jλ(i)e(i)e(i)=dϕ(i)dωe(i)e(i).
dϕ(i)dω=w(i)p(i).
[λ(1)1+jW]e(1)=1.
[Δλ(1)1+jΔW]e(1)+[λ(1)1+jW]Δe(1)=0.
Δλ(1)=-je(1)ΔWe(1),
je(2)ΔWe(1)+[λ(1)-λ(2)]e(2)Δe(1)=0.
ddωλ(1)=-j d2ϕ(1)dω2=-je(1) dWdωe(1),
e(2) ddωe(1)=j e(2) dWdωe(1)[λ(2)-λ(1)]=e(2) dWdωe(1)dϕ(1)dω-dϕ(2)dω.
Wij=14hi*·μ¯¯+ω μ¯¯ω·hj+ei*·¯¯+ω ¯¯ω·ejdV.
T=e-jθejϕ00e-jϕ,
T=1211-11ejϕ00e-jϕ1-111ejϕ00e-jϕe-2jθ=121+e2jϕ-1+e-2jϕ1-e2jϕ1+e-2jϕe-2jθSe-2jθ.
dTdω=dSdω-2j dθdωSe-2jθ.
T dTdω=S dSdω-2j dθdω1=-jW.
S dSdω=j dϕdω1-e-2jϕ-e2jϕ-1.
-j dWdω=ddωS dSdω=2jdϕdω20e-2jϕ-e2jϕ-0.

Metrics