Abstract

Theoretical and experimental studies of the electromagnetic coupling between parallel, passive, glass-fiber waveguides and active (Nd3+-doped laser) resonators are reported. Predicted evanescent-wave coupling strengths are verified to within a factor of two. Far-field interference patterns of these phase-locked, optical waveguides manifest a high degree of coherence and give the predicted asymmetry. Coupling of two fiber lasers is also demonstrated through common-cavity end-mirror reflectors; a high-frequency self-Q-switching action is found when the fiber ends are not rigidly mounted.

© 1968 Optical Society of America

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References

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  1. S. E. Miller, Bell System Tech. J. 33, 661 (1954).
    [Crossref]
  2. W. H. Louisell, Coupled Mode and Parametric Electronics (John Wiley& Sons, Inc., New York, 1960).
  3. S. A. Schelkunoff, Electromagnetic Fields (Blaisdell Publishing Co., New York, 1963).
  4. C. C. Johnson, Field and wave Electrodynamics (McGraw–Hill Book Co., New York, 1965).
  5. E. Snitzer, in Advances in Quantum Electronics, J. R. Singer, Ed. (Columbia University Press, New York, 1961), p. 348.
  6. E. Snitzer, in Optical Processing of Information, D. K. Pollock, C. J. Koester, and J. T. Tippett, Eds. (Spartan Books, Inc., Baltimore, 1963), p. 61.
  7. N. S. Kapany, G. M. Burgwald, and J. J. Burke, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh, Eds. (MIT Press, Cambridge, 1965), p. 305.
  8. N. S. Kapany, J. J. Burke, and K. L. Frame, Appl. Opt. 4, 1534 (1965).
    [Crossref]
  9. M. F. Bracey, A. L. Cullen, E. F. F. Gillespie, and J. A. Staniforth, IRE Trans. AP-7, S219 (1959).
  10. A. L. Jones, J. Opt. Soc. Am. 55, 261 (1965)
    [Crossref]
  11. J. J. Burke, J. Opt. Soc. Am. 57, 1056 (1967).
    [Crossref]
  12. C. J. Koester and C. H. Swope, in Ref. 7, p. 253.
  13. E. Snitzer, J. Opt. Soc. Am. 51, 491 (1961).
    [Crossref]
  14. E. Snitzer and H. Osterberg, J. Opt. Am. 51, 499 (1961).
    [Crossref]
  15. N. S. Kapany and J. J. Burke, J. Opt. Am. 51, 1067 (1961).
    [Crossref]
  16. E. Snitzer, J. Appl. Phys. 32, 36 (1961).
    [Crossref]
  17. Snitzer5,6 offers a substantially different interpretation of the same theory for this case, suggesting that the forward direction is either a maximum or a minimum. His published photographic data,5,6 however, may be interpreted as manifesting the kind of asymmetry that we would expect.
  18. Similar clustering was observed by H. C. Nedderman, Y. C. Kiang, and F. C. Unterleitner, Proc. IRE 50, 7 (1962) with a ruby crystal operating in an inhomogeneous magnetic field.

1967 (1)

1965 (2)

1962 (1)

Similar clustering was observed by H. C. Nedderman, Y. C. Kiang, and F. C. Unterleitner, Proc. IRE 50, 7 (1962) with a ruby crystal operating in an inhomogeneous magnetic field.

1961 (4)

E. Snitzer, J. Opt. Soc. Am. 51, 491 (1961).
[Crossref]

E. Snitzer and H. Osterberg, J. Opt. Am. 51, 499 (1961).
[Crossref]

N. S. Kapany and J. J. Burke, J. Opt. Am. 51, 1067 (1961).
[Crossref]

E. Snitzer, J. Appl. Phys. 32, 36 (1961).
[Crossref]

1959 (1)

M. F. Bracey, A. L. Cullen, E. F. F. Gillespie, and J. A. Staniforth, IRE Trans. AP-7, S219 (1959).

1954 (1)

S. E. Miller, Bell System Tech. J. 33, 661 (1954).
[Crossref]

Bracey, M. F.

M. F. Bracey, A. L. Cullen, E. F. F. Gillespie, and J. A. Staniforth, IRE Trans. AP-7, S219 (1959).

Burgwald, G. M.

N. S. Kapany, G. M. Burgwald, and J. J. Burke, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh, Eds. (MIT Press, Cambridge, 1965), p. 305.

Burke, J. J.

J. J. Burke, J. Opt. Soc. Am. 57, 1056 (1967).
[Crossref]

N. S. Kapany, J. J. Burke, and K. L. Frame, Appl. Opt. 4, 1534 (1965).
[Crossref]

N. S. Kapany and J. J. Burke, J. Opt. Am. 51, 1067 (1961).
[Crossref]

N. S. Kapany, G. M. Burgwald, and J. J. Burke, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh, Eds. (MIT Press, Cambridge, 1965), p. 305.

Cullen, A. L.

M. F. Bracey, A. L. Cullen, E. F. F. Gillespie, and J. A. Staniforth, IRE Trans. AP-7, S219 (1959).

Frame, K. L.

Gillespie, E. F. F.

M. F. Bracey, A. L. Cullen, E. F. F. Gillespie, and J. A. Staniforth, IRE Trans. AP-7, S219 (1959).

Johnson, C. C.

C. C. Johnson, Field and wave Electrodynamics (McGraw–Hill Book Co., New York, 1965).

Jones, A. L.

Kapany, N. S.

N. S. Kapany, J. J. Burke, and K. L. Frame, Appl. Opt. 4, 1534 (1965).
[Crossref]

N. S. Kapany and J. J. Burke, J. Opt. Am. 51, 1067 (1961).
[Crossref]

N. S. Kapany, G. M. Burgwald, and J. J. Burke, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh, Eds. (MIT Press, Cambridge, 1965), p. 305.

Kiang, Y. C.

Similar clustering was observed by H. C. Nedderman, Y. C. Kiang, and F. C. Unterleitner, Proc. IRE 50, 7 (1962) with a ruby crystal operating in an inhomogeneous magnetic field.

Koester, C. J.

C. J. Koester and C. H. Swope, in Ref. 7, p. 253.

Louisell, W. H.

W. H. Louisell, Coupled Mode and Parametric Electronics (John Wiley& Sons, Inc., New York, 1960).

Miller, S. E.

S. E. Miller, Bell System Tech. J. 33, 661 (1954).
[Crossref]

Nedderman, H. C.

Similar clustering was observed by H. C. Nedderman, Y. C. Kiang, and F. C. Unterleitner, Proc. IRE 50, 7 (1962) with a ruby crystal operating in an inhomogeneous magnetic field.

Osterberg, H.

E. Snitzer and H. Osterberg, J. Opt. Am. 51, 499 (1961).
[Crossref]

Schelkunoff, S. A.

S. A. Schelkunoff, Electromagnetic Fields (Blaisdell Publishing Co., New York, 1963).

Snitzer, E.

E. Snitzer and H. Osterberg, J. Opt. Am. 51, 499 (1961).
[Crossref]

E. Snitzer, J. Appl. Phys. 32, 36 (1961).
[Crossref]

E. Snitzer, J. Opt. Soc. Am. 51, 491 (1961).
[Crossref]

E. Snitzer, in Advances in Quantum Electronics, J. R. Singer, Ed. (Columbia University Press, New York, 1961), p. 348.

E. Snitzer, in Optical Processing of Information, D. K. Pollock, C. J. Koester, and J. T. Tippett, Eds. (Spartan Books, Inc., Baltimore, 1963), p. 61.

Staniforth, J. A.

M. F. Bracey, A. L. Cullen, E. F. F. Gillespie, and J. A. Staniforth, IRE Trans. AP-7, S219 (1959).

Swope, C. H.

C. J. Koester and C. H. Swope, in Ref. 7, p. 253.

Unterleitner, F. C.

Similar clustering was observed by H. C. Nedderman, Y. C. Kiang, and F. C. Unterleitner, Proc. IRE 50, 7 (1962) with a ruby crystal operating in an inhomogeneous magnetic field.

Appl. Opt. (1)

Bell System Tech. J. (1)

S. E. Miller, Bell System Tech. J. 33, 661 (1954).
[Crossref]

IRE Trans. (1)

M. F. Bracey, A. L. Cullen, E. F. F. Gillespie, and J. A. Staniforth, IRE Trans. AP-7, S219 (1959).

J. Appl. Phys. (1)

E. Snitzer, J. Appl. Phys. 32, 36 (1961).
[Crossref]

J. Opt. Am. (2)

E. Snitzer and H. Osterberg, J. Opt. Am. 51, 499 (1961).
[Crossref]

N. S. Kapany and J. J. Burke, J. Opt. Am. 51, 1067 (1961).
[Crossref]

J. Opt. Soc. Am. (3)

Proc. IRE (1)

Similar clustering was observed by H. C. Nedderman, Y. C. Kiang, and F. C. Unterleitner, Proc. IRE 50, 7 (1962) with a ruby crystal operating in an inhomogeneous magnetic field.

Other (8)

Snitzer5,6 offers a substantially different interpretation of the same theory for this case, suggesting that the forward direction is either a maximum or a minimum. His published photographic data,5,6 however, may be interpreted as manifesting the kind of asymmetry that we would expect.

C. J. Koester and C. H. Swope, in Ref. 7, p. 253.

W. H. Louisell, Coupled Mode and Parametric Electronics (John Wiley& Sons, Inc., New York, 1960).

S. A. Schelkunoff, Electromagnetic Fields (Blaisdell Publishing Co., New York, 1963).

C. C. Johnson, Field and wave Electrodynamics (McGraw–Hill Book Co., New York, 1965).

E. Snitzer, in Advances in Quantum Electronics, J. R. Singer, Ed. (Columbia University Press, New York, 1961), p. 348.

E. Snitzer, in Optical Processing of Information, D. K. Pollock, C. J. Koester, and J. T. Tippett, Eds. (Spartan Books, Inc., Baltimore, 1963), p. 61.

N. S. Kapany, G. M. Burgwald, and J. J. Burke, in Optical and Electro-Optical Information Processing, J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh, Eds. (MIT Press, Cambridge, 1965), p. 305.

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Figures (12)

Fig. 1
Fig. 1

Normalized measured output of excited (solid curve) and unexcited (dashed curve) fibers in coupled pair vs wavelength in nm. Fibers are 9.2 cm long, 4.38-μ diam, and 8.38 μ in center-to-center spacing. Fiber numerical aperture ( 2 n ¯ Δ n ) 1 2 = 0.0822.

Fig. 2
Fig. 2

Normalized measured output of excited and unexcited fibers in coupled pair vs wavelength in nm. Fibers are 2.1 cm long, 4.73-μ diam, and 9.65 μ in center-to-center spacing. N.A.=0.0822.

Fig. 3
Fig. 3

Theoretical prediction of the number of beat lengths per cm vs wavelength for coupled fibers supporting the HE1,1 mode. d=4.73 μ, t=9.65 μ, and N.A.= ( 2 n ¯ Δ n ) 1 2 = 0.0822.

Fig. 4
Fig. 4

Images of ouptut ends of coupled pair (lower photos) and corresponding far-field radiation patterns for successive wavelengths of equipartition of energy alternating with wavelengths of maximum transfer. Dark line is shadow of wire indicating the forward direction. Fiber parameters as in Fig. 2.

Fig. 5
Fig. 5

Photometric traces of far field for successive wavelengths of equipartition (right) and maximum transfer (left) showing asymmetries expected for π/2 phase difference between fibers.

Fig. 6
Fig. 6

Time scale is 20 μsec/cm. Clustered oscillatory behavior in 3.5-μ, dual-fiber resonators. (a) Mode structure of dual fiber under broadband illumination; (b) 166 J Ein, 75-μsec sweep delay; (c) 170 J Ein, 75-μsec sweep delay; (d) 182 J Ein, 80-μsec sweep delay; (e) 196 J Ein, 75-μsec sweep delay; and (f) 202 J Ein, 75-μsec sweep delay.

Fig. 7
Fig. 7

Clustered oscillatory behavior in 3.5-μ single-fiber resonator. (a) 41 J, 20 μsec/cm, 80-μsec sweep delay; and (b) 42 J, 20 μsec/cm, 80-μsec sweep delay.

Fig. 8
Fig. 8

Interference pattern of 3.5-μ dual-fiber resonators from near- to far-field positions (top to bottom, left to right): Focus, 0.1, 0.15, 0.2, 0.3, 0.35, 0.4, and 0.5 mm.

Fig. 9
Fig. 9

Time trace and interference patterns of 3.5-μ, dual-fiber resonator with: (A)–(C) fiber allowed to oscillate; reflector not in contact with fiber; and (D)–(F) fiber not physically oscillating; reflector in contact with fiber. Time base: (A) 10 μsec/cm, 145 J; (B) 5 μsec/cm, 132 J; (D) 10 μsec/cm, 145 J; and (E) 5 μsec/cm, 127 J.

Fig. 10
Fig. 10

Radiation patterns of 3.5-μ, dual-coherent-fiber resonators in phase-locked operation. (A), (C) before and after blocking of the output of one of the fiber cores; and (B) radiation pattern of one of the two fiber cores.

Fig. 11
Fig. 11

Radiation output and time trace of 7-μ, dual resonator with resonator reflector in contact with fiber.

Fig. 12
Fig. 12

Radiation interference patterns and time trace, demonstrating coherent phase-locked output of 7-μ, dual resonator; cavity reflector not in contact with fiber.

Equations (1)

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ψ S = C S [ ψ 0 ( 1 ) + ψ 0 ( 2 ) ] exp [ i ( h 0 + Δ h ) z - i ω 0 t ] ψ A = C A [ ψ 0 ( 1 ) - ψ 0 ( 2 ) ] exp [ i ( h 0 - Δ h ) z - i ω 0 t ] .