Abstract

The problem of the propagation of modes along a moving dielectric interface is considered. Two types of dielectric structures were considered in particular: a moving dielectric slab and a moving dielectric circular cylinder. The characteristic equations for modes along these two types of structures are derived and a detailed discussion concerning these characteristic equations is also given. As a specific example, numerical results for the guide wavelength of the dominant TE wave along a moving dielectric slab as a function of frequency for various values of υz/c, where υz is the velocity of the moving dielectric material and c is the velocity of light in vacuum, were presented. It is found that if υz/c>(1/0)12, the moving dielectric structure can support a forward wave as well as a backward wave and there also exists a high-frequency cutoff for the dominant mode under consideration.

© 1968 Optical Society of America

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References

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  1. L. V. Boffi, “Electrodynamics of Moving Media,” Ph.D. dissertation, Mass. Inst. of Tech., Cambridge (1958).
  2. R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic Fields, Energy and Forces (John Wiley & Sons, Inc., New York, 1960), p. 315.
  3. C. T. Tai, Proc. IEEE 52, 685 (1964).
    [Crossref]
  4. R. S. Elliott, Electromagnetics (McGraw–Hill Book Co., New York, 1966), pp. 98–272.
  5. L. J. Chu, H. A. Haus, and P. Penfield, Proc. IEEE 54, 920 (1966).
    [Crossref]
  6. K. S. Lee and C. H. Papas, J. Math. Phys. 5, 1668 (1964).
    [Crossref]
  7. J. R. Collier and C. T. Tai, IEEE Trans. Microwave Theory Techniques MTT–13, 441 (1965).
    [Crossref]
  8. H. Fujioka, K. Yoshida, and N. Kumagai, IEEE Trans. Microwave Theory Techniques MTT–15, 265 (1967); P. Daly, IEEE Trans. Microwave Theory Techniques MTT–15, 274 (1967).
    [Crossref]
  9. C. T. Tai, Radio Sci. 69D, 401 (1965).
  10. C. Yeh, J. Appl. Phys. 36, 3513 (1965).
    [Crossref]
  11. R. T. Compton, J. Math. Phys. 7, 2145 (1966).
    [Crossref]
  12. C. T. Tai, J. Math. Phys. 8, 646 (1967).
    [Crossref]
  13. R. E. Collins, Field Theory of Guided Waves (McGraw-Hill Book Co., New York, 1960), pp. 470–474.
  14. A. Sommerfeld, Electrodynamics (Academic Press Inc., New York, 1952), p. 120.

1967 (2)

H. Fujioka, K. Yoshida, and N. Kumagai, IEEE Trans. Microwave Theory Techniques MTT–15, 265 (1967); P. Daly, IEEE Trans. Microwave Theory Techniques MTT–15, 274 (1967).
[Crossref]

C. T. Tai, J. Math. Phys. 8, 646 (1967).
[Crossref]

1966 (2)

R. T. Compton, J. Math. Phys. 7, 2145 (1966).
[Crossref]

L. J. Chu, H. A. Haus, and P. Penfield, Proc. IEEE 54, 920 (1966).
[Crossref]

1965 (3)

J. R. Collier and C. T. Tai, IEEE Trans. Microwave Theory Techniques MTT–13, 441 (1965).
[Crossref]

C. T. Tai, Radio Sci. 69D, 401 (1965).

C. Yeh, J. Appl. Phys. 36, 3513 (1965).
[Crossref]

1964 (2)

C. T. Tai, Proc. IEEE 52, 685 (1964).
[Crossref]

K. S. Lee and C. H. Papas, J. Math. Phys. 5, 1668 (1964).
[Crossref]

Adler, R. B.

R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic Fields, Energy and Forces (John Wiley & Sons, Inc., New York, 1960), p. 315.

Boffi, L. V.

L. V. Boffi, “Electrodynamics of Moving Media,” Ph.D. dissertation, Mass. Inst. of Tech., Cambridge (1958).

Chu, L. J.

L. J. Chu, H. A. Haus, and P. Penfield, Proc. IEEE 54, 920 (1966).
[Crossref]

R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic Fields, Energy and Forces (John Wiley & Sons, Inc., New York, 1960), p. 315.

Collier, J. R.

J. R. Collier and C. T. Tai, IEEE Trans. Microwave Theory Techniques MTT–13, 441 (1965).
[Crossref]

Collins, R. E.

R. E. Collins, Field Theory of Guided Waves (McGraw-Hill Book Co., New York, 1960), pp. 470–474.

Compton, R. T.

R. T. Compton, J. Math. Phys. 7, 2145 (1966).
[Crossref]

Elliott, R. S.

R. S. Elliott, Electromagnetics (McGraw–Hill Book Co., New York, 1966), pp. 98–272.

Fano, R. M.

R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic Fields, Energy and Forces (John Wiley & Sons, Inc., New York, 1960), p. 315.

Fujioka, H.

H. Fujioka, K. Yoshida, and N. Kumagai, IEEE Trans. Microwave Theory Techniques MTT–15, 265 (1967); P. Daly, IEEE Trans. Microwave Theory Techniques MTT–15, 274 (1967).
[Crossref]

Haus, H. A.

L. J. Chu, H. A. Haus, and P. Penfield, Proc. IEEE 54, 920 (1966).
[Crossref]

Kumagai, N.

H. Fujioka, K. Yoshida, and N. Kumagai, IEEE Trans. Microwave Theory Techniques MTT–15, 265 (1967); P. Daly, IEEE Trans. Microwave Theory Techniques MTT–15, 274 (1967).
[Crossref]

Lee, K. S.

K. S. Lee and C. H. Papas, J. Math. Phys. 5, 1668 (1964).
[Crossref]

Papas, C. H.

K. S. Lee and C. H. Papas, J. Math. Phys. 5, 1668 (1964).
[Crossref]

Penfield, P.

L. J. Chu, H. A. Haus, and P. Penfield, Proc. IEEE 54, 920 (1966).
[Crossref]

Sommerfeld, A.

A. Sommerfeld, Electrodynamics (Academic Press Inc., New York, 1952), p. 120.

Tai, C. T.

C. T. Tai, J. Math. Phys. 8, 646 (1967).
[Crossref]

J. R. Collier and C. T. Tai, IEEE Trans. Microwave Theory Techniques MTT–13, 441 (1965).
[Crossref]

C. T. Tai, Radio Sci. 69D, 401 (1965).

C. T. Tai, Proc. IEEE 52, 685 (1964).
[Crossref]

Yeh, C.

C. Yeh, J. Appl. Phys. 36, 3513 (1965).
[Crossref]

Yoshida, K.

H. Fujioka, K. Yoshida, and N. Kumagai, IEEE Trans. Microwave Theory Techniques MTT–15, 265 (1967); P. Daly, IEEE Trans. Microwave Theory Techniques MTT–15, 274 (1967).
[Crossref]

IEEE Trans. Microwave Theory Techniques (2)

J. R. Collier and C. T. Tai, IEEE Trans. Microwave Theory Techniques MTT–13, 441 (1965).
[Crossref]

H. Fujioka, K. Yoshida, and N. Kumagai, IEEE Trans. Microwave Theory Techniques MTT–15, 265 (1967); P. Daly, IEEE Trans. Microwave Theory Techniques MTT–15, 274 (1967).
[Crossref]

J. Appl. Phys. (1)

C. Yeh, J. Appl. Phys. 36, 3513 (1965).
[Crossref]

J. Math. Phys. (3)

R. T. Compton, J. Math. Phys. 7, 2145 (1966).
[Crossref]

C. T. Tai, J. Math. Phys. 8, 646 (1967).
[Crossref]

K. S. Lee and C. H. Papas, J. Math. Phys. 5, 1668 (1964).
[Crossref]

Proc. IEEE (2)

L. J. Chu, H. A. Haus, and P. Penfield, Proc. IEEE 54, 920 (1966).
[Crossref]

C. T. Tai, Proc. IEEE 52, 685 (1964).
[Crossref]

Radio Sci. (1)

C. T. Tai, Radio Sci. 69D, 401 (1965).

Other (5)

R. S. Elliott, Electromagnetics (McGraw–Hill Book Co., New York, 1966), pp. 98–272.

L. V. Boffi, “Electrodynamics of Moving Media,” Ph.D. dissertation, Mass. Inst. of Tech., Cambridge (1958).

R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic Fields, Energy and Forces (John Wiley & Sons, Inc., New York, 1960), p. 315.

R. E. Collins, Field Theory of Guided Waves (McGraw-Hill Book Co., New York, 1960), pp. 470–474.

A. Sommerfeld, Electrodynamics (Academic Press Inc., New York, 1952), p. 120.

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Figures (2)

Fig. 1
Fig. 1

(hd/k0d) vs (pd/k0d) for various υz/c with. 1/0 = 2.0; i.e., a plot of Eq. (23).

Fig. 2
Fig. 2

Normalized guide wavelength λ/λ0 as a function of k0d for the dominant TE even mode along a moving-dielectric slab with thickness 2d and 1/0 = 2.0. Note that the scale for k0d in (b) is expanded.

Equations (24)

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E y = { A exp { ( p | x | d ) j β z + j ω t } | x | d A sec ( h d ) cos ( h x ) exp ( j β z + j ω t ) | x | d
E y = { A exp { p ( x d ) j β z + j ω t } x d A csc ( h d ) sin ( h x ) exp ( j β z + j ω t ) | x | d A exp { p ( x + d ) j β z + j ω t } x d
( β d ) 2 = ω 2 μ 0 1 d 2 ( h d ) 2
( β d ) 2 = ω 2 μ 0 0 d 2 + ( p d ) 2 .
p d = h d tan h d
p d = h d cot h d
( p d ) 2 + ( h d ) 2 = [ ( 1 / 0 ) 1 ] ω 2 μ 0 0 d 2 .
E y = { A exp { ( p | x | d ) j β z + j ω t } | x | d A sec ( h d ) cos ( h x ) exp ( j β z + j ω t ) | x | d
p d = h d tan h d
( p d ) 2 + ( h d ) 2 = ( 1 0 1 ) ( k 0 d 2 ) γ 2 × [ 1 + υ z c 1 k 0 d ( k 0 2 d 2 + p d 2 ) 1 2 ] 2
( β d ) 2 = ( k 0 d ) 2 + ( p d ) 2 ,
E y = { A exp { p ( x d ) j β z + j ω t } x d A csc ( h d ) sin ( h x ) exp ( j β z + j ω t ) | x | d A exp { p ( x + d ) j β z + j ω t } x d
p d = h d cot h d
H y = { B cos ( h x ) exp ( j β z + j ω t ) | x | d B cos ( h d ) exp { p ( | x | d ) j β z + j ω t } | x | d
( 1 / 0 ) p d = h d tan ( h d )
( p d ) 2 + ( h d ) 2 = ( 1 0 1 ) ( k 0 d ) 2 γ 2 × [ 1 + υ z c 1 k 0 d ( k 0 2 d 2 + p d 2 ) 1 2 ] 2
( β d ) 2 = ( k 0 d ) 2 + ( p d ) 2 ,
H y = { B exp { p ( x d ) j β z + j ω t } x d B csc ( h d ) sin ( h x ) exp ( j β z + j ω t ) } d x d B exp { p ( x + d ) j β z + j ω t } x d ,
( 1 / 0 ) p d = h d cot ( h d )
E z = { f m ( 1 ) ( r ) exp ( j m θ j β z + j ω t ) r < a f m ( 2 ) ( r ) exp ( j m θ j β z + j ω t ) r > a
H z = { g m ( 1 ) ( r ) exp ( j m θ j β z + j ω t ) r < a g m ( 2 ) ( r ) exp ( j m θ j β z + j ω t ) , r > a ,
[ 1 h d J m ( h d ) J m ( h d ) + 1 p d K m ( p d ) K m ( p d ) ] × [ 1 h d J m ( h d ) J m ( h d ) + 0 1 1 p d K m ( p d ) K m ( p d ) ] = m 2 [ ( h d ) 2 + ( p d ) 2 ] [ ( p d ) 2 + ( h d ) 2 0 / 1 ] ( h d ) 4 ( p d ) 4
( p d ) 2 + ( h d ) 2 = ( 1 0 1 ) ( k 0 d ) 2 γ 2 × [ 1 + υ z c 1 k 0 d ( k 0 2 d 2 + p d 2 ) 1 2 ] 2
( β d ) 2 = ( k 0 d ) 2 + ( p d ) 2 .