Abstract

The motion of a charged particle in a space- and time-dependent potential and the motion of an optical pulse in an inhomogeneous anisotropic medium coincide when the dispersion surfaces are the same. For the trajectories in space to coincide, it is sufficient that the wave vectors be proportional. It follows from the general expression of the average stress-energy density (∂<i>L¯</i>/∂<i>K⃗</i>)<i>K⃗</i>, where <i>L¯</i> denotes the average lagrangian density and <i>K⃗</i> denotes the 4 wave vector, that radiation forces are proportional to wave vectors for charged particles as well as for optical pulses. Because of these relations, many results in mechanics are applicable to optics. In particular, the constancy of the horizontal component of the velocity of a bullet on earth has, as a counterpart in optics, the constancy of the axial component of the group velocity of optical pulses propagating in thick tapered dielectric slabs. It follows from this observation that thick tapered dielectric slabs are not suited for long-distance communication, because of the large pulse spreading that they introduce. Slabs with moderate thickness, however, may exhibit low pulse spreading.

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  1. V. A. Fock, Bull. Acad. Sci. l'URSS, Ser. Phys. 14, 70 (1950), translated in V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, Oxford, 1965), Ch. 14.
  2. G. B. Whitham, J. Fluid Mech. 44, 373 (1970).
  3. O. Costa de Beauregard, C. R. Acad. Sci. (Paris) B 274, 164 (1972); Nuovo Cimento, Ser. 10 63B, 611 (1969).
  4. P. Penfield and H. A. Haus, Electrodynamics of Moving Media (M.I.T. Press, Cambridge, 1967), p. 211.
  5. S. R. De Groot and L. G. Suttorp, Foundations of Electrodynamics (North–Holland, Amsterdam, 1972).
  6. H. A. Haus, Physica 43, 77 (1969).
  7. J. A. Arnaud, (a) Electr. Lett. 8, 541 (1972); (b) Opt. Commun. 7, 313 (1973); (c) Am. J. Phys. 42, 71 (1974).
  8. J. P. Gordon, Phys. Rev. A 8, 14 (1973).
  9. W. B. Joyce, Phys. Rev. D 9, 3234 (1974).
  10. R. Lucas, in Louis de Broglie, sa Conception du Monde Physique (Gauthier-Villars, Paris, 1973).
  11. A. Kastler, C. R. Acad. Sci. (Paris) B 278, 1013 (1974).
  12. D. Marcuse, Engineering Quantum Electrodynami cs (Harcourt, Brace and World, New York, 1970), p. 80.
  13. D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972), p. 100.
  14. R. V. Jones and J. C. S. Richard, Proc. R. Soc. (Lond.) A 221, 480 (1954).
  15. A. Ashkin, Appl. Phys. Lett. 19, 283 (1971); A. Ashkin and J. M. Diedzic, Phys. Rev. Lett. 30, 139 (1973).
  16. T. H. Boyer, Phys. Rev. D 8, 1669 (1973).
  17. J. A. Arnaud, J. Opt. Soc. Am. 62, 290 (1972) and J. A. Arnaud, in Progress in Optics, Vol. 11, edited by E. Wolf (North–Holland, Amsterdam, 1973), p. 247.
  18. K. Husini, Prog. Theor. Phys. 9, 381 (1953).
  19. J. A. Arnaud, Bell Syst. Tech. J. 49, 2311 (1970).
  20. J. M. Kelso, Radio Ray Propagation in the Ionosphere (McGraw-Hill, New York, 1964), p. 220.
  21. J. A. Arnaud, Bell Syst. Tech. J. 53, 1599 (1974).
  22. E. A. J. Marcatili, Bell Syst. Tech. J. 53, 645 (1974).

Ashkin, A.

A. Ashkin, Appl. Phys. Lett. 19, 283 (1971); A. Ashkin and J. M. Diedzic, Phys. Rev. Lett. 30, 139 (1973).

de Beauregard, O. Costa

O. Costa de Beauregard, C. R. Acad. Sci. (Paris) B 274, 164 (1972); Nuovo Cimento, Ser. 10 63B, 611 (1969).

De Groot, S. R.

S. R. De Groot and L. G. Suttorp, Foundations of Electrodynamics (North–Holland, Amsterdam, 1972).

Fock, V. A.

V. A. Fock, Bull. Acad. Sci. l'URSS, Ser. Phys. 14, 70 (1950), translated in V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, Oxford, 1965), Ch. 14.

Arnaud, J. A.

J. A. Arnaud, Bell Syst. Tech. J. 49, 2311 (1970).

J. A. Arnaud, J. Opt. Soc. Am. 62, 290 (1972) and J. A. Arnaud, in Progress in Optics, Vol. 11, edited by E. Wolf (North–Holland, Amsterdam, 1973), p. 247.

J. A. Arnaud, (a) Electr. Lett. 8, 541 (1972); (b) Opt. Commun. 7, 313 (1973); (c) Am. J. Phys. 42, 71 (1974).

J. A. Arnaud, Bell Syst. Tech. J. 53, 1599 (1974).

Boyer, T. H.

T. H. Boyer, Phys. Rev. D 8, 1669 (1973).

Gordon, J. P.

J. P. Gordon, Phys. Rev. A 8, 14 (1973).

Haus, H. A.

P. Penfield and H. A. Haus, Electrodynamics of Moving Media (M.I.T. Press, Cambridge, 1967), p. 211.

H. A. Haus, Physica 43, 77 (1969).

Husini, K.

K. Husini, Prog. Theor. Phys. 9, 381 (1953).

Jones, R. V.

R. V. Jones and J. C. S. Richard, Proc. R. Soc. (Lond.) A 221, 480 (1954).

Joyce, W. B.

W. B. Joyce, Phys. Rev. D 9, 3234 (1974).

Kastler, A.

A. Kastler, C. R. Acad. Sci. (Paris) B 278, 1013 (1974).

Kelso, J. M.

J. M. Kelso, Radio Ray Propagation in the Ionosphere (McGraw-Hill, New York, 1964), p. 220.

Lucas, R.

R. Lucas, in Louis de Broglie, sa Conception du Monde Physique (Gauthier-Villars, Paris, 1973).

Marcatili, E. A. J.

E. A. J. Marcatili, Bell Syst. Tech. J. 53, 645 (1974).

Marcuse, D.

D. Marcuse, Engineering Quantum Electrodynami cs (Harcourt, Brace and World, New York, 1970), p. 80.

D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972), p. 100.

Penfield, P.

P. Penfield and H. A. Haus, Electrodynamics of Moving Media (M.I.T. Press, Cambridge, 1967), p. 211.

Richard, J. C. S.

R. V. Jones and J. C. S. Richard, Proc. R. Soc. (Lond.) A 221, 480 (1954).

Suttorp, L. G.

S. R. De Groot and L. G. Suttorp, Foundations of Electrodynamics (North–Holland, Amsterdam, 1972).

Whitham, G. B.

G. B. Whitham, J. Fluid Mech. 44, 373 (1970).

Other

V. A. Fock, Bull. Acad. Sci. l'URSS, Ser. Phys. 14, 70 (1950), translated in V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, Oxford, 1965), Ch. 14.

G. B. Whitham, J. Fluid Mech. 44, 373 (1970).

O. Costa de Beauregard, C. R. Acad. Sci. (Paris) B 274, 164 (1972); Nuovo Cimento, Ser. 10 63B, 611 (1969).

P. Penfield and H. A. Haus, Electrodynamics of Moving Media (M.I.T. Press, Cambridge, 1967), p. 211.

S. R. De Groot and L. G. Suttorp, Foundations of Electrodynamics (North–Holland, Amsterdam, 1972).

H. A. Haus, Physica 43, 77 (1969).

J. A. Arnaud, (a) Electr. Lett. 8, 541 (1972); (b) Opt. Commun. 7, 313 (1973); (c) Am. J. Phys. 42, 71 (1974).

J. P. Gordon, Phys. Rev. A 8, 14 (1973).

W. B. Joyce, Phys. Rev. D 9, 3234 (1974).

R. Lucas, in Louis de Broglie, sa Conception du Monde Physique (Gauthier-Villars, Paris, 1973).

A. Kastler, C. R. Acad. Sci. (Paris) B 278, 1013 (1974).

D. Marcuse, Engineering Quantum Electrodynami cs (Harcourt, Brace and World, New York, 1970), p. 80.

D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972), p. 100.

R. V. Jones and J. C. S. Richard, Proc. R. Soc. (Lond.) A 221, 480 (1954).

A. Ashkin, Appl. Phys. Lett. 19, 283 (1971); A. Ashkin and J. M. Diedzic, Phys. Rev. Lett. 30, 139 (1973).

T. H. Boyer, Phys. Rev. D 8, 1669 (1973).

J. A. Arnaud, J. Opt. Soc. Am. 62, 290 (1972) and J. A. Arnaud, in Progress in Optics, Vol. 11, edited by E. Wolf (North–Holland, Amsterdam, 1973), p. 247.

K. Husini, Prog. Theor. Phys. 9, 381 (1953).

J. A. Arnaud, Bell Syst. Tech. J. 49, 2311 (1970).

J. M. Kelso, Radio Ray Propagation in the Ionosphere (McGraw-Hill, New York, 1964), p. 220.

J. A. Arnaud, Bell Syst. Tech. J. 53, 1599 (1974).

E. A. J. Marcatili, Bell Syst. Tech. J. 53, 645 (1974).

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