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Invariants and coherent states in fiber optics

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Lie Methods in Optics

Part of the book series: Lecture Notes in Physics ((LNP,volume 250))

Abstract

The aim of this chapter is to review recent results in the quantum mechanics of nonstationary systems, and to demonstrate how they are applied in paraxial fiber optics.

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References

  1. M. Leontovich and V. Fock, Solution of the problem of electromagnetic waves along the earth suface by the method of parabolic equations, Sov. J. Phys. 10, 13 (1946).

    Google Scholar 

  2. L.M. Brechovskih, Waves in Slab Media (in Russian), (Nauka, Moscow, 1973).

    Google Scholar 

  3. J.A. Hudson, A parabolic approximation for elastic waves, Wave Motion 2, 207 (1980).

    Google Scholar 

  4. D. Marcuse, Light Transmission Optics, (Van Nostrand, New York, 1972).

    Google Scholar 

  5. J.A. Arnaud, Beam and Fiber Optics, (Academic Press, New York, 1976).

    Google Scholar 

  6. I.A. Malkin and V.I. Man'ko, Coherent states and excitation of n-dimensional non-stationary forced oscillator, Phys. Lett. 32A, 243 (1970).

    Google Scholar 

  7. I.A. Malkin, V.I. Man'ko, and D.A. Trifonov, Linear adiabatic invariants and coherent states, J. Math. Phys. 14, 576 (1973).

    Google Scholar 

  8. V.V. Dodonov, I.A. Malkin, and V.I. Man'ko, Integrals of the motion, Green function and coherent states of dynamical systems, Intern. J. Theor. Phys. 14, 37 (1975).

    Google Scholar 

  9. V.V. Dodonov and V.I. Man'ko, Coherent states and the resonance of a quantum damped oscillator, Phys. Rev. A20, 550 (1979).

    Google Scholar 

  10. I.A. Malkin and V.I. Man'ko, Dynamical Symmetries and Coherent States of Quantum Mechanics (in Russian), (Nauka, Moscow, 1979).

    Google Scholar 

  11. V.I. Man'ko, Invariants and symmetries of dynamical systems, In Proceedings of the Second International Colloquium on Group Theoretical Methods in Physics. Vol. 1, (University of Nijmegen, The Netherlands, June 25–29, 1973); pp. A107 et seq.

    Google Scholar 

  12. V.I. Man'ko, Possible applications of the integrals of the motion and coherent state methods for dynamical systems. In Quantum Electrodynamics with Outer Fields (in Russian), (Tomsk State University and Tomsk Pedagogical Institute, publishers; Tomsk, USSR, 1977); pp. 101–120.

    Google Scholar 

  13. R. Glauber, Coherent states of the quantum oscillator, Phys. Rev. Lett. 10, 84 (1963).

    Google Scholar 

  14. I.A. Malkin, V.I. Man'ko, and D.A. Trifonov, Coherent states and excitation charge moving in a time-dependent electromagnetic field, Phys. Rev. 2D, 1370 (1970).

    Google Scholar 

  15. I.A. Malkin and V.I. Man'ko, Coherent states of the charged oscillator in a nonstationary magnetic field, Zhurn. Exper. i Teor. Fiz. 59, 1746 (1970).

    Google Scholar 

  16. V.V. Dodonov and V.I. Man'ko, Integrals of the motion and dynamics of general nonstationary quadratic Fermi-Bose systems (in Russian), P.N. Lebedev Inst. Trudy 152, 145–193 (1983).

    Google Scholar 

  17. I.A. Malkin, V.I. Man'ko, and D.A. Trifonov, Dynamical symmetries of nonstationary systems, Nuovo Cimento 4A, 773 (1971).

    Google Scholar 

  18. J.A. Arnaud, Hamilton theory of beam mode propagation. In Progress in Optics, Vol. XI (North Holland, 1973); pp. 249–302.

    Google Scholar 

  19. J.A. Arnaud, Nonorthogonal optical waveguides and resonators, BSTJ 49, 2311 (1970).

    Google Scholar 

  20. H. Kogelnik, On the propagation of gaussian beams of light through lenslike media incuding those with a loss or gain variation, Applied Optics 4, 1562–1569 (1965).

    Google Scholar 

  21. J.A. Arnaud, Mode coupling in first-order optics, J. Opt. Soc. Amer. 61, 751 (1971).

    Google Scholar 

  22. E.E. Bergmann, Optical resonators with paraxial modes, Applied Optics 11, 113 (1972).

    Google Scholar 

  23. S.G. Krivoshlykov, N.I. Petrov, and I.N. Sissakian, Coherent properties of optical fields in nonhomogeneous media. In Proceedings of the Second International Seminar on Group Theoretical Methods in Physics, Vol. nuII (Zvenigorod, USSR, 1980); pp. 235 et seq.

    Google Scholar 

  24. S.G. Krivoshlykov, E.V. Kurmyshev, and I.N. Sissakian, Correlated coherent states in the problems of wave propagations in nonhomogeneous quadratic media. In Proceedings of the Second International Seminar on Group Theoretical Methods in Physics, Vol. II (Zvenigorod, USSR, 1980); pp. 226 et seq.

    Google Scholar 

  25. S.G. Krivoshlykov and I.N. Sissakian, Quantum mechanical theory of optical beam propagation in inhomogeneous media, P.N. Lebedev Institute preprint # 117 (1979).

    Google Scholar 

  26. S.G. Krivoshlykov and I.N. Sissakian, Mode coupling between two connected multimode parabolic-index optical waveguides, Opt. Quant. Electr. 11, 393–405 (1979).

    Google Scholar 

  27. S.G. Krivoshlykov and I.N. Sissakian, Coherent states and light propagation in inhomogeneous media (in Russian), Kvantovaîa Elektronika 7, 553–564 (1980).

    Google Scholar 

  28. S.G. Krivoshlykov, N.I. Petrov, and I.N. Sissakian, Spatial coherence of the light source with cosm ϑ diagram in continuous-inhomogeneous media with quadratic refraction index profile (in Russian), Pis'ma Zh. Teor. Fiz. 9, 1489–1494 (1980).

    Google Scholar 

  29. S.G. Krivoshlykov, N.I. Petrov, and I.N. Sissakian, Density matrix formalism in problems of propagation of optical fields in weakly inhomogeneous media (in Russian), Institute of General Physics preprint # 10 (1985), to be published in Optical and Quantum Electronics.

    Google Scholar 

  30. M. A. Man'ko, Analogue of the Franck-Condon principle for heterolasers (in Russian), Kvantovaîa Elektronika (1985, in press).

    Google Scholar 

  31. M. A. Man'ko, Analogue of the Ramsauer effect for heterolasers (in Russian), Kvantovaía Elektronika (1985, in press).

    Google Scholar 

  32. M. A. Man'ko, Modes in heterolasers, P.N. Lebedev Inst. Trudy 166 (1986, in press).

    Google Scholar 

  33. H. Bacry and M. Cadilhac, Metaplectic group and Fourier optics, Phys. Rev. A23, 2533–2536 (1981).

    Google Scholar 

  34. H. Bacry, Group theory and paraxial optics. In Proceedings of the XIII th International Co11oquium on Group Theoretical Methods in Physics (College Park, Maryland, 21–25 May, 1984), W.W. Zachary, Ed. (World Scientific Publ., Singapore, 1984); pp. 215–224.

    Google Scholar 

  35. A. Dragt, Lie algebraic theory of geometrical optics and optical aberrations, J. Opt. Soc. Amer. 72, 372–379 (1982).

    Google Scholar 

  36. K.B. Wolf, A group-theoretic treatment of gaussian optics and third-order aberrations. In Proceedings of the XII th International Colloquium on Group Theoretical Methods in Physics (Trieste, Italy, 5–10 Sept. 1983). Lecture Notes in Physics # 201, (Springer Verlag, 1984); pp. 133–136.

    Google Scholar 

  37. M. Navarro-Saad and K.B. Wolf, Factorization of the phase-space transformation produced by an arbitrary refracting surface. Preprint CINVESTAV, Mexico (April 1984); to appear in J. Opt. Soc. America.

    Google Scholar 

  38. K.B. Wolf, Group theoretical methods in aberrating systems. In Proceedings of the XIII th International Colloquium on Group Theoretical Methods in Physics (College Park, Maryland, 21–25 May, 1984), W.W. Zachary, Ed. (World Scientific Publ., Singapore, 1984); pp. 111–114.

    Google Scholar 

  39. M. Navarro-Saad and K.B. Wolf, Application of a factorization theorem for ninth-order aberration optics. Comunicaciones Técnicas IIMAS preprint (Desarrollo) # 41, (February 1985). To appear in Journal of Symbolic Computation.

    Google Scholar 

  40. K.B. Wolf, Symmetry in Lie optics. Reporte de Investigación, Depto. de Matemáticas, Universidad Autónoma Metropolitana, 4, # 1 (1985); submitted for publication.

    Google Scholar 

  41. M. Navarro-Saad and K.B. Wolf, The group theoretical treatment of aberrating systems. I. Aligned lens systems in third aberration order. Comunicaciones Técnicas IIMAS preprint # 363 (1984); K.B. Wolf, ibid. II. Axis-symmetric inhomogeneous systems and fiber optics in third aberration order. Comunicaciones Técnicas IIMAS preprint # 366 (1984). To appear in J. Math. Phys.

    Google Scholar 

  42. V.I. Man'ko and K.B. Wolf, The influence of aberrations in the optics of gaussian beam propagation. Reporte de Investigación del Depto. de Matemáticas, Universidad Autónoma Metropolitana, 4, # 3 (1985).

    Google Scholar 

  43. E.V. Doktorov, I.A. Malkin, and V.I. Man'ko, Dynamical symmetry and the Franck-Condon principle for polydimensional molecules (in Russian), P.N. Lebedev Inst. Trudy 152, 202 (1983).

    Google Scholar 

  44. J.R. Klauder, Continuous representation theory. II. Generalized relation between quantum and classical dynamics, J. Math. Phys. 5, 177–1187 (1964).

    Google Scholar 

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Authors
  1. Vladimir I. Man'ko
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J. Sánchez Mondragón K. B. Wolf

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© 1986 Springer-Verlag

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Man'ko, V.I. (1986). Invariants and coherent states in fiber optics. In: Sánchez Mondragón, J., Wolf, K.B. (eds) Lie Methods in Optics. Lecture Notes in Physics, vol 250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16471-5_7

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  • DOI: https://doi.org/10.1007/3-540-16471-5_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16471-5

  • Online ISBN: 978-3-540-39811-0

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