Abstract

An unexpected phenomenon has been observed which triggered an investigation into the lensing effect of a CO2 laser plasma. This effect, so far thought to be negligible in a conventional CO2 laser of, for example, 2-m length, produces a focal length in the order of magnitude of −20 m. In view of this experimental observation, the focal length of the plasma lens, as well as the stability condition for an optical resonator with a plasma lens within its plane concave mirror system, are determined and expressed in terms of plasma and resonator characteristics as well as of the electrical power dissipated in the plasma. The analysis reveals that the semiconfocal configuration is most adverse for a frequency-stabilized laser. The overall result of this investigation suggests that the optimum configuration of a conventional CO2 laser for maximum output power is obtained when the negative focal power of the plasma lens precisely compensates for the positive focal power of the slightly curved mirror.

© 1970 Optical Society of America

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References

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  1. H. Schardin, Ergeb. exakt. Naturw. 20, 303 (1942). H. Wolter, Handbuch der Physik, S. Fluegge, Ed. (SpringerBerlin, 1956), Vol. 24, pp. 555–645.
    [CrossRef]
  2. D. E. Grey, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1957), pp. 6–21.
  3. M. Jakob, G. A. Hawkins, Elements of Heat Transfer (Wiley, New York, 1957), p. 109.
  4. H. Winston, R. A. Gudmundsen, Appl. Opt. 3, 143 (1964); W. H. Steier, Appl. Opt. 5, 1229 (1966).
    [CrossRef] [PubMed]
  5. E. A. J. Marcatili, Bell System Tech. J. 43, 2887 (1964).
  6. C. Kenty, M. A. Easley, B. T. Barnes, J. Appl. Phys. 22, 1006 (1951); L. A. Schlie, J. T. Verdeyen, IEEE J. Quantum Electron. QE-5, 21, 138 (1969).
    [CrossRef]
  7. (a)H. K. V. Lotsch, Z. Naturforschg. 19a, 1438 (1964); (b)H. K. V. Lotsch, Optik 26, 112, 181 (1967).
  8. M. Bertolotti, Nuovo Cimento (10) 32, 1242 (1964); J. T. Verdeyen, J. B. Gerardo, Appl. Opt. 7, 1467 (1968); I. A. Ramsay, J. J. Degnan, Appl. Opt. 9, 385 (1970).
    [CrossRef] [PubMed]
  9. M. Jakob, Heat Transfer (Wiley, New York, 1949), pp. 185–189.
  10. H. Steffen, F. K. Kneubuehl, IEEE J. Quantum Electron. QE-4, 922 (1968).
  11. D. R. Skinner, Opt. Commun. 1, 57 (1969). D. C. Smith, IEEE J. Quantum Electron. QE-5, 600 (1969).
    [CrossRef]
  12. B. W. McCaul, A. L. Schawlow, “Plasma Refractive Effects in HCN Lasers,” 2nd Conference on Chemical and Molecular Lasers, St. Louis, Missouri, 22–24 May, 1969.

1969

D. R. Skinner, Opt. Commun. 1, 57 (1969). D. C. Smith, IEEE J. Quantum Electron. QE-5, 600 (1969).
[CrossRef]

1968

H. Steffen, F. K. Kneubuehl, IEEE J. Quantum Electron. QE-4, 922 (1968).

1964

H. Winston, R. A. Gudmundsen, Appl. Opt. 3, 143 (1964); W. H. Steier, Appl. Opt. 5, 1229 (1966).
[CrossRef] [PubMed]

E. A. J. Marcatili, Bell System Tech. J. 43, 2887 (1964).

(a)H. K. V. Lotsch, Z. Naturforschg. 19a, 1438 (1964); (b)H. K. V. Lotsch, Optik 26, 112, 181 (1967).

M. Bertolotti, Nuovo Cimento (10) 32, 1242 (1964); J. T. Verdeyen, J. B. Gerardo, Appl. Opt. 7, 1467 (1968); I. A. Ramsay, J. J. Degnan, Appl. Opt. 9, 385 (1970).
[CrossRef] [PubMed]

1951

C. Kenty, M. A. Easley, B. T. Barnes, J. Appl. Phys. 22, 1006 (1951); L. A. Schlie, J. T. Verdeyen, IEEE J. Quantum Electron. QE-5, 21, 138 (1969).
[CrossRef]

1942

H. Schardin, Ergeb. exakt. Naturw. 20, 303 (1942). H. Wolter, Handbuch der Physik, S. Fluegge, Ed. (SpringerBerlin, 1956), Vol. 24, pp. 555–645.
[CrossRef]

Barnes, B. T.

C. Kenty, M. A. Easley, B. T. Barnes, J. Appl. Phys. 22, 1006 (1951); L. A. Schlie, J. T. Verdeyen, IEEE J. Quantum Electron. QE-5, 21, 138 (1969).
[CrossRef]

Bertolotti, M.

M. Bertolotti, Nuovo Cimento (10) 32, 1242 (1964); J. T. Verdeyen, J. B. Gerardo, Appl. Opt. 7, 1467 (1968); I. A. Ramsay, J. J. Degnan, Appl. Opt. 9, 385 (1970).
[CrossRef] [PubMed]

Easley, M. A.

C. Kenty, M. A. Easley, B. T. Barnes, J. Appl. Phys. 22, 1006 (1951); L. A. Schlie, J. T. Verdeyen, IEEE J. Quantum Electron. QE-5, 21, 138 (1969).
[CrossRef]

Gudmundsen, R. A.

Hawkins, G. A.

M. Jakob, G. A. Hawkins, Elements of Heat Transfer (Wiley, New York, 1957), p. 109.

Jakob, M.

M. Jakob, G. A. Hawkins, Elements of Heat Transfer (Wiley, New York, 1957), p. 109.

M. Jakob, Heat Transfer (Wiley, New York, 1949), pp. 185–189.

Kenty, C.

C. Kenty, M. A. Easley, B. T. Barnes, J. Appl. Phys. 22, 1006 (1951); L. A. Schlie, J. T. Verdeyen, IEEE J. Quantum Electron. QE-5, 21, 138 (1969).
[CrossRef]

Kneubuehl, F. K.

H. Steffen, F. K. Kneubuehl, IEEE J. Quantum Electron. QE-4, 922 (1968).

Lotsch, H. K. V.

(a)H. K. V. Lotsch, Z. Naturforschg. 19a, 1438 (1964); (b)H. K. V. Lotsch, Optik 26, 112, 181 (1967).

Marcatili, E. A. J.

E. A. J. Marcatili, Bell System Tech. J. 43, 2887 (1964).

McCaul, B. W.

B. W. McCaul, A. L. Schawlow, “Plasma Refractive Effects in HCN Lasers,” 2nd Conference on Chemical and Molecular Lasers, St. Louis, Missouri, 22–24 May, 1969.

Schardin, H.

H. Schardin, Ergeb. exakt. Naturw. 20, 303 (1942). H. Wolter, Handbuch der Physik, S. Fluegge, Ed. (SpringerBerlin, 1956), Vol. 24, pp. 555–645.
[CrossRef]

Schawlow, A. L.

B. W. McCaul, A. L. Schawlow, “Plasma Refractive Effects in HCN Lasers,” 2nd Conference on Chemical and Molecular Lasers, St. Louis, Missouri, 22–24 May, 1969.

Skinner, D. R.

D. R. Skinner, Opt. Commun. 1, 57 (1969). D. C. Smith, IEEE J. Quantum Electron. QE-5, 600 (1969).
[CrossRef]

Steffen, H.

H. Steffen, F. K. Kneubuehl, IEEE J. Quantum Electron. QE-4, 922 (1968).

Winston, H.

Appl. Opt.

Bell System Tech. J.

E. A. J. Marcatili, Bell System Tech. J. 43, 2887 (1964).

Ergeb. exakt. Naturw.

H. Schardin, Ergeb. exakt. Naturw. 20, 303 (1942). H. Wolter, Handbuch der Physik, S. Fluegge, Ed. (SpringerBerlin, 1956), Vol. 24, pp. 555–645.
[CrossRef]

IEEE J. Quantum Electron.

H. Steffen, F. K. Kneubuehl, IEEE J. Quantum Electron. QE-4, 922 (1968).

J. Appl. Phys.

C. Kenty, M. A. Easley, B. T. Barnes, J. Appl. Phys. 22, 1006 (1951); L. A. Schlie, J. T. Verdeyen, IEEE J. Quantum Electron. QE-5, 21, 138 (1969).
[CrossRef]

Nuovo Cimento (10)

M. Bertolotti, Nuovo Cimento (10) 32, 1242 (1964); J. T. Verdeyen, J. B. Gerardo, Appl. Opt. 7, 1467 (1968); I. A. Ramsay, J. J. Degnan, Appl. Opt. 9, 385 (1970).
[CrossRef] [PubMed]

Opt. Commun.

D. R. Skinner, Opt. Commun. 1, 57 (1969). D. C. Smith, IEEE J. Quantum Electron. QE-5, 600 (1969).
[CrossRef]

Z. Naturforschg.

(a)H. K. V. Lotsch, Z. Naturforschg. 19a, 1438 (1964); (b)H. K. V. Lotsch, Optik 26, 112, 181 (1967).

Other

M. Jakob, Heat Transfer (Wiley, New York, 1949), pp. 185–189.

B. W. McCaul, A. L. Schawlow, “Plasma Refractive Effects in HCN Lasers,” 2nd Conference on Chemical and Molecular Lasers, St. Louis, Missouri, 22–24 May, 1969.

D. E. Grey, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1957), pp. 6–21.

M. Jakob, G. A. Hawkins, Elements of Heat Transfer (Wiley, New York, 1957), p. 109.

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Figures (1)

Fig. 1
Fig. 1

The measured focal length of the CO2 laser plasma lens under investigation is illustrated.

Equations (18)

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n = 1 + n o - 1 1 + ( T - T o ) / T o p p o = 1 + ( n o - 1 ) T o T p p o ,
T = T w + ( P / 4 k ) ( R 2 - r 2 ) ,
n η ( 1 + 1 2 α r 2 ) ,
η = 1 + 4 k T o ( n o - 1 ) p / p o P R 2 + 4 k T w
α = 8 k T o P ( n o - 1 ) p / p o ( P R 2 + 4 k T w ) { P R 2 + 4 k [ T w + T o ( n o - 1 ) p / p o ] } ,
2 r / z 2 = ( 1 / n ) ( n / r ) .
( 2 r / z 2 ) α r .
r = r o at z = 0 :             position of input ray r z = r o at z = 0 :             slope of input ray ,
r = r o cosh [ z ( α 1 2 ) ] + ( r / α 1 2 ) sinh [ z ( α 1 2 ) ]
r = r o ( α 1 2 ) sinh [ z ( α 1 2 ) ] + r o cosh [ z ( α 1 2 ) ] .
f = - 1 / { ( α 1 2 ) sinh [ d ( α 1 2 ) ] } ,
f - 1 α d - ( P R 2 + 4 k T w ) 2 8 k T o P d ( n o - 1 ) p / p o .
( r out r out ) = ( 1 0 - 2 / ρ 1 ) ( cosh [ 2 d ( α 1 2 ) ] ( α - 1 2 ) sinh [ 2 d ( α 1 2 ) ] ( α 1 2 ) sinh [ 2 d ( α 1 2 ) ] cosh [ 2 d ( α 1 2 ) ] ) ( r in r in ) ,
ρ sinh [ 2 d ( α 1 2 ) ] / ( ( α 1 2 ) { cosh [ 2 d ( α 1 2 ) ] - 1 } ) .
ρ 1 α d ( P R 2 + 4 k T w ) 2 8 k T o P d ( n o - 1 ) p / p o .
f ρ f / 2 ,
N = 4 π z / arc cos ( 1 2 trace Γ ) = 4 π z / ( arc cos { cosh [ 2 d ( α 1 2 ) ] - ( 1 / ρ α 1 2 ) sinh [ 2 d ( α 1 2 ) ] } ) ,
N 4 π z / arc cos ( 1 + 2 d / ρ + 2 α d 2 ) .

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