Abstract

States of two-level systems (systems with two eigenstates, such as optical propagation of polarized light or spin 1/2) are conventionally represented by 2 $\times$ 1 complex vectors or real 3 $\times$ 1 geometric vectors. A limitation of geometrical representations is an inability to represent overall phase, important in optical and quantum interference applications. We propose an extension of the usual geometrical representation for such systems, representing the overall phase as an additional, internal, spin of the geometric state vector. We generalize the earlier representations to include this phase, establish rules for its representation and calculation, and illustrate our model by analyzing an optical interferometer.

© 2009 USGov

PDF Article

References

  • View by:
  • |
  • |

  1. C. P. Slichter, Principles of Magnetic Resonance (Springer, 1978).
  2. R. P. Feynman, F. L. Vernon Jr., R. W. Hellwarth, "Geometrical representation of the Schrodinger equation for solving maser problems," J. Appl. Phys. 28, 49-52 (1957).
  3. R. Ulrich, "Representation of codirectional coupled waves," Opt. Lett. 1, 109-111 (1977).
  4. R. Ulrich, A. Simon, "Polarization optics of twisted single-mode fibers," Appl. Opt. 18, 2241-2251 (1979).
  5. H. Kogelnik, R. M. Jopson, L. E. Nelson, Optical Fiber Telecommunications IVB (Academic Press, 2002).
  6. N. J. Frigo, "A generalized geometrical representation of coupled mode theory," IEEE J. Quantum Electron. QE-22, 2131-2139 (1986).
  7. J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. Nat. Acad. Sci. 97, 4541-4550 (2002).
  8. J. N. Damask, Polarization Optics in Telecommunications .
  9. A. D. Kersey, M. J. Marrone, A. Dandridge, "Analysis of input-polarization-induced phase noise in interferometric fiber-optic sensors and its reduction using polarization scrambling," J. Lightw. Technol. 8, 838-845 (1990).
  10. M. V. Berry, "The adiabatic phase and Pancharatnam's phase for polarized light," J. Mod. Opt. 34, 1401-1407 (1987).
  11. S.-I. Tomonaga, The Story of Spin (Univ. Chicago Press, 1997).
  12. K. Hoffman, R. Kunze, Linear Algebra (Prentice-Hall, 1971).
  13. H. Goldstein, C. P. Poole, J. L. Safko, Classical Mechanics (Addison-Wesley, 2002).
  14. M. Karlsson, "Quaternion approach to PMD and PDL phenomena in optical fiber systems," J. Lightw. Technol. 22, 1137-1146 (2004).
  15. R. C. Jones, "A new calculus for the treatment of optical systems. VII. Properties of the N-matrices," J. Opt. Soc. Amer. 38, 671-685 (1948).

2004

M. Karlsson, "Quaternion approach to PMD and PDL phenomena in optical fiber systems," J. Lightw. Technol. 22, 1137-1146 (2004).

2002

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. Nat. Acad. Sci. 97, 4541-4550 (2002).

1990

A. D. Kersey, M. J. Marrone, A. Dandridge, "Analysis of input-polarization-induced phase noise in interferometric fiber-optic sensors and its reduction using polarization scrambling," J. Lightw. Technol. 8, 838-845 (1990).

1987

M. V. Berry, "The adiabatic phase and Pancharatnam's phase for polarized light," J. Mod. Opt. 34, 1401-1407 (1987).

1986

N. J. Frigo, "A generalized geometrical representation of coupled mode theory," IEEE J. Quantum Electron. QE-22, 2131-2139 (1986).

1979

1977

1957

R. P. Feynman, F. L. Vernon Jr., R. W. Hellwarth, "Geometrical representation of the Schrodinger equation for solving maser problems," J. Appl. Phys. 28, 49-52 (1957).

1948

R. C. Jones, "A new calculus for the treatment of optical systems. VII. Properties of the N-matrices," J. Opt. Soc. Amer. 38, 671-685 (1948).

Appl. Opt.

IEEE J. Quantum Electron.

N. J. Frigo, "A generalized geometrical representation of coupled mode theory," IEEE J. Quantum Electron. QE-22, 2131-2139 (1986).

J. Appl. Phys.

R. P. Feynman, F. L. Vernon Jr., R. W. Hellwarth, "Geometrical representation of the Schrodinger equation for solving maser problems," J. Appl. Phys. 28, 49-52 (1957).

J. Lightw. Technol.

A. D. Kersey, M. J. Marrone, A. Dandridge, "Analysis of input-polarization-induced phase noise in interferometric fiber-optic sensors and its reduction using polarization scrambling," J. Lightw. Technol. 8, 838-845 (1990).

M. Karlsson, "Quaternion approach to PMD and PDL phenomena in optical fiber systems," J. Lightw. Technol. 22, 1137-1146 (2004).

J. Mod. Opt.

M. V. Berry, "The adiabatic phase and Pancharatnam's phase for polarized light," J. Mod. Opt. 34, 1401-1407 (1987).

J. Opt. Soc. Amer.

R. C. Jones, "A new calculus for the treatment of optical systems. VII. Properties of the N-matrices," J. Opt. Soc. Amer. 38, 671-685 (1948).

Opt. Lett.

Proc. Nat. Acad. Sci.

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. Nat. Acad. Sci. 97, 4541-4550 (2002).

Other

J. N. Damask, Polarization Optics in Telecommunications .

C. P. Slichter, Principles of Magnetic Resonance (Springer, 1978).

H. Kogelnik, R. M. Jopson, L. E. Nelson, Optical Fiber Telecommunications IVB (Academic Press, 2002).

S.-I. Tomonaga, The Story of Spin (Univ. Chicago Press, 1997).

K. Hoffman, R. Kunze, Linear Algebra (Prentice-Hall, 1971).

H. Goldstein, C. P. Poole, J. L. Safko, Classical Mechanics (Addison-Wesley, 2002).

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.