Publication: Neutron fibres: a three-dimensional analysis of bending losses
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The confined propagation of slow neutrons along waveguides of a small cross section (fibres), discussed theoretically some time ago and demonstrated experimentally by other authors later, is analysed further. Motivated by those experiments, a three-dimensional quantum-mechanical treatment of the associated bending losses is presented. An approximate (two-parameter) formula is derived for the transmission coefficient Upsilon of the curved fibre, which displays its explicit dependence on the curvature radius Rcu, for 0<Rcu< + ∞. By adjusting one of the parameters (b), consistently with the theoretical analysis, and by fitting the other, the approximate formula describes all measured data for Upsilon. The parameter b (which accounts for the experimental data for Upsilon at large Rcu) allows the estimation of the number of effectively excited modes in the fibre.
© 2000 IOP Publishing Ltd. The author is grateful to Dr. W. M. Gibson (Center for X-ray Optics, State University of New York at Albany) for an interesting correspondence and comments regarding guided neutron beams, capillary optics and neutron fibres, and to Mr. Gabriel F. Calvo for some computational help when fitting the data. The constructive criticisms of the (anonymous) referees are acknowledged. This work is dedicated to the memory of Dr. Gustavo Torres-Cisneros.
1. Álvarez-Estrada R F and Calvo M L 1984 J. Phys. D: Appl. Phys. 17 475. 2. Bacon G E 1962 Neutron Diffraction (Oxford: Clarendon). 3. Berry M V and Mount K E 1972 Rep. Prog. Phys. 35 315. 4. Born M and Wolf E 1999 Principles of Optics 7 edn, ch X (Cambridge: Cambridge University Press). 5. Calvo M L and Alvarez-Estrada R F 1986 J. Phys. D: Appl. Phys. 19 957. 6. Calvo M L and Alvarez-Estrada R F 1987 J. Opt. Soc. Am. A 4 683. 7. Chen H, Downing R G, Mildner D F R, Gibson W M, Kumakhov M A, Ponomarev I Yu and Gubarev M V 1992 Nature 357 391. 8. Glauber R J 1959 Lectures in Theoretical Physics vol 1 (New York: InterScience). 9. Jacrot B 1970 Proc. Symp. Instrumentation for Neutron Inelastic Scattering Research (Vienna 1969) (Vienna: IAEA). 10. Kumakhov M A and Komarov F F 1990 Phys. Rep. 191 289. 11. Kumakhov M A and Sharov V A 1992 Nature 357 390. 12. Marcatili E A J 1969 Bell Syst. Tech. J. 48 2103. 13. Marcuse D 1972 Light Transmission Optics (New York: Van Nostrand-Reinhold). 14. Marcuse D 1974 Theory of Dielectric Optical Waveguides (New York: Academic). 15. Marcuse D 1976 J. Opt. Soc. Am. 66 216. 16. Martin A 1972 Helv. Phys. Acta 45 140. 17. Messiah A 1961 Quantum Mechanics vol I (Amsterdam: North-Holland). 18. Schaerpf O and Eichler D 1973 J. Phys. E: Sci. Instrum. 6 774. 19. Sears V F 1989 Neutron Optics (New York: Oxford University Press). 20. Snyder A W and Love J D 1983 Optical Waveguide Theory ch 23 (London: Chapman and Hall).