Abstract

The transmission of a 10.6-μm TEM00 beam through a hollow circular-cross-section waveguide is modeled in terms of the excitation and propagation of the two lowest-order circularly symmetric EH1n modes. At points along the guide axis where the modes are in phase the TEM00 input field is shown to be regenerated, but midway between these points, transverse-mode profiles that have a doughnut shape are produced. It is proposed that these dramatic field variations should cause variations in the effective attenuation coefficient along the length of the waveguide. The first direct experimental measurements to our knowledge of the guide-length-dependent attenuation characteristics of a 1.0-mm-bore hollow silica waveguide support this hypothesis by revealing a strong periodic component in addition to the anticipated exponential decay.

© 1992 Optical Society of America

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References

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  1. F. P. Roullard, M. Bass, “Transverse mode control in high gain, millimeter bore, waveguide lasers,” IEEE J. Quantum. Electron. QE-13, 813–818 (1977).
    [CrossRef]
  2. R. M. Jenkins, R. W. J. Devereux, Defence Research Agency, Royal Signals and Radar Establishment, Malvern, Worcestershire WR14 3PS, England, UK (personal communication).
  3. R. M. Jenkins, R. W. J. Devereux, “Phase characteristics of the modes of hollow dielectric waveguides,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper TUM1.
  4. A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increases in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
    [CrossRef]
  5. S. Karasawa, M. Miyagi, S. Nishida, “Temperature distribution along oversized hollow-core waveguides for infrared radiation,” Appl. Opt. 26, 4581–4586 (1987).
    [CrossRef] [PubMed]
  6. E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1808 (1964).
  7. R. M. Jenkins, R. W. J. Devereux, “Transmission characteristics of a hollow core silica waveguide in the 9–11 μm waveband,” in Active Infrared Systems and Technology, V. G. Roper, ed., Proc. Soc. Photo-Opt. Instrum. Eng.806, 51–61 (1987).
  8. R. M. Jenkins, R. W. J. Devereux, “Dispersion phenomena in hollow alumina waveguides,” IEEE J. Quantum Electron. QE-21, 1722–1727 (1985).
    [CrossRef]
  9. See, for example, D. Marcuse, “Theory of dielectric optical waveguides,” in Theory of Dielectric Optical Waveguides, Y-H Pao, ed. (Academic, New York, 1974).
  10. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  11. R. Gerlach, D. Wei, N. M. Amer, “Coupling efficiencies of waveguide laser resonators formed by flat mirrors: analysis and experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
    [CrossRef]
  12. K. D. Laakmann, W. H. Steier, “Waveguides: characteristic modes of hollow rectangular waveguides,” Appl. Opt. 15, 1334–1340 (1976).
    [CrossRef] [PubMed]
  13. C. A. Hill, “Transverse modes of plane-mirror waveguide resonators,” IEEE J. Quantum Electron. 24, 1936–1946 (1988).
    [CrossRef]

1988 (1)

C. A. Hill, “Transverse modes of plane-mirror waveguide resonators,” IEEE J. Quantum Electron. 24, 1936–1946 (1988).
[CrossRef]

1987 (2)

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increases in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

S. Karasawa, M. Miyagi, S. Nishida, “Temperature distribution along oversized hollow-core waveguides for infrared radiation,” Appl. Opt. 26, 4581–4586 (1987).
[CrossRef] [PubMed]

1985 (1)

R. M. Jenkins, R. W. J. Devereux, “Dispersion phenomena in hollow alumina waveguides,” IEEE J. Quantum Electron. QE-21, 1722–1727 (1985).
[CrossRef]

1984 (1)

R. Gerlach, D. Wei, N. M. Amer, “Coupling efficiencies of waveguide laser resonators formed by flat mirrors: analysis and experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
[CrossRef]

1977 (1)

F. P. Roullard, M. Bass, “Transverse mode control in high gain, millimeter bore, waveguide lasers,” IEEE J. Quantum. Electron. QE-13, 813–818 (1977).
[CrossRef]

1976 (1)

1964 (1)

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1808 (1964).

Amer, N. M.

R. Gerlach, D. Wei, N. M. Amer, “Coupling efficiencies of waveguide laser resonators formed by flat mirrors: analysis and experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
[CrossRef]

Bass, M.

F. P. Roullard, M. Bass, “Transverse mode control in high gain, millimeter bore, waveguide lasers,” IEEE J. Quantum. Electron. QE-13, 813–818 (1977).
[CrossRef]

Devereux, R. W. J.

R. M. Jenkins, R. W. J. Devereux, “Dispersion phenomena in hollow alumina waveguides,” IEEE J. Quantum Electron. QE-21, 1722–1727 (1985).
[CrossRef]

R. M. Jenkins, R. W. J. Devereux, Defence Research Agency, Royal Signals and Radar Establishment, Malvern, Worcestershire WR14 3PS, England, UK (personal communication).

R. M. Jenkins, R. W. J. Devereux, “Phase characteristics of the modes of hollow dielectric waveguides,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper TUM1.

R. M. Jenkins, R. W. J. Devereux, “Transmission characteristics of a hollow core silica waveguide in the 9–11 μm waveband,” in Active Infrared Systems and Technology, V. G. Roper, ed., Proc. Soc. Photo-Opt. Instrum. Eng.806, 51–61 (1987).

Gerlach, R.

R. Gerlach, D. Wei, N. M. Amer, “Coupling efficiencies of waveguide laser resonators formed by flat mirrors: analysis and experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
[CrossRef]

Hill, C. A.

C. A. Hill, “Transverse modes of plane-mirror waveguide resonators,” IEEE J. Quantum Electron. 24, 1936–1946 (1988).
[CrossRef]

Hongo, A.

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increases in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

Jenkins, R. M.

R. M. Jenkins, R. W. J. Devereux, “Dispersion phenomena in hollow alumina waveguides,” IEEE J. Quantum Electron. QE-21, 1722–1727 (1985).
[CrossRef]

R. M. Jenkins, R. W. J. Devereux, “Transmission characteristics of a hollow core silica waveguide in the 9–11 μm waveband,” in Active Infrared Systems and Technology, V. G. Roper, ed., Proc. Soc. Photo-Opt. Instrum. Eng.806, 51–61 (1987).

R. M. Jenkins, R. W. J. Devereux, “Phase characteristics of the modes of hollow dielectric waveguides,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper TUM1.

R. M. Jenkins, R. W. J. Devereux, Defence Research Agency, Royal Signals and Radar Establishment, Malvern, Worcestershire WR14 3PS, England, UK (personal communication).

Karasawa, S.

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increases in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

S. Karasawa, M. Miyagi, S. Nishida, “Temperature distribution along oversized hollow-core waveguides for infrared radiation,” Appl. Opt. 26, 4581–4586 (1987).
[CrossRef] [PubMed]

Laakmann, K. D.

Marcatili, E. A. J.

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1808 (1964).

Marcuse, D.

See, for example, D. Marcuse, “Theory of dielectric optical waveguides,” in Theory of Dielectric Optical Waveguides, Y-H Pao, ed. (Academic, New York, 1974).

Miyagi, M.

S. Karasawa, M. Miyagi, S. Nishida, “Temperature distribution along oversized hollow-core waveguides for infrared radiation,” Appl. Opt. 26, 4581–4586 (1987).
[CrossRef] [PubMed]

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increases in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

Nishida, S.

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increases in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

S. Karasawa, M. Miyagi, S. Nishida, “Temperature distribution along oversized hollow-core waveguides for infrared radiation,” Appl. Opt. 26, 4581–4586 (1987).
[CrossRef] [PubMed]

Roullard, F. P.

F. P. Roullard, M. Bass, “Transverse mode control in high gain, millimeter bore, waveguide lasers,” IEEE J. Quantum. Electron. QE-13, 813–818 (1977).
[CrossRef]

Sakamoto, K.

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increases in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

Schmeltzer, R. A.

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1808 (1964).

Steier, W. H.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Wei, D.

R. Gerlach, D. Wei, N. M. Amer, “Coupling efficiencies of waveguide laser resonators formed by flat mirrors: analysis and experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
[CrossRef]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1808 (1964).

IEEE J. Quantum Electron. (3)

R. M. Jenkins, R. W. J. Devereux, “Dispersion phenomena in hollow alumina waveguides,” IEEE J. Quantum Electron. QE-21, 1722–1727 (1985).
[CrossRef]

R. Gerlach, D. Wei, N. M. Amer, “Coupling efficiencies of waveguide laser resonators formed by flat mirrors: analysis and experiment,” IEEE J. Quantum Electron. QE-20, 948–963 (1984).
[CrossRef]

C. A. Hill, “Transverse modes of plane-mirror waveguide resonators,” IEEE J. Quantum Electron. 24, 1936–1946 (1988).
[CrossRef]

IEEE J. Quantum. Electron. (1)

F. P. Roullard, M. Bass, “Transverse mode control in high gain, millimeter bore, waveguide lasers,” IEEE J. Quantum. Electron. QE-13, 813–818 (1977).
[CrossRef]

Opt. Laser Technol. (1)

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increases in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

Other (5)

See, for example, D. Marcuse, “Theory of dielectric optical waveguides,” in Theory of Dielectric Optical Waveguides, Y-H Pao, ed. (Academic, New York, 1974).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

R. M. Jenkins, R. W. J. Devereux, Defence Research Agency, Royal Signals and Radar Establishment, Malvern, Worcestershire WR14 3PS, England, UK (personal communication).

R. M. Jenkins, R. W. J. Devereux, “Phase characteristics of the modes of hollow dielectric waveguides,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper TUM1.

R. M. Jenkins, R. W. J. Devereux, “Transmission characteristics of a hollow core silica waveguide in the 9–11 μm waveband,” in Active Infrared Systems and Technology, V. G. Roper, ed., Proc. Soc. Photo-Opt. Instrum. Eng.806, 51–61 (1987).

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Figures (5)

Fig. 1
Fig. 1

Radial dependence of field amplitude profiles for (a) EH11; (b) EH12; (c) EH11 + EH12 (in phase), shown by the solid curve, and TEM00 with w = 0.44a, shown by dotted curve; (d) EH11 + EH12 (out of phase).

Fig. 2
Fig. 2

Calculations of power coupling coefficients for the EH1n modes as a function of the ratio of the beam waist to the guide radius, w/a.

Fig. 3
Fig. 3

Predictions of axial variations in the transverse field profile for a 10.6-μm TEM00 beam of waist w = 0.4a that propagates in a lossless 1.0-mm-i.d. hollow-core waveguide.

Fig. 4
Fig. 4

Schematic of the experimental setup used for making mode excitation and transmission measurements.

Fig. 5
Fig. 5

Measurements of the guide-length-dependent attenuation characteristics of a 1.0-mm-i.d. hollow-core silica waveguide made with a 10.6-μm TEM00 input beam of waist w = 0.4a at the guide entrance.

Equations (5)

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EH 1 n ( r , z ) = J 0 ( u 1 n r a ) exp i γ 1 n z ,
E TEM ( 00 ) = A 1 n E H 1 n
β 1 n = 2 π λ { 1 - 1 2 ( u 1 n λ 2 a ) 2 [ 1 + Im ( ν λ π a ) ] } ,
I ( r , z ) = [ A 11 J 0 ( u 11 r a ) exp ( - α 11 z ) ] 2 + [ A 12 J 0 ( u 12 r a ) exp ( - α 12 z ) ] 2 + 2 A 11 A 12 J 0 ( u 11 r a ) J 0 ( u 12 r a ) × exp [ - ( α 11 + α 12 ) z ] cos [ ( β 11 - β 12 ) z ] .
z 2 π = 8 π 2 a 2 λ ( u 12 2 - u 11 2 ) .

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