Abstract

The atomic-iodine hyperfine structure is shown to produce anomalous dispersion effects on its hyperfine laser transition at 1.315 µm whenever reasonable small-signal gains are available (~1% cm). This dispersion effect is linearly dependent on the iodine inversion density. Such an anomalous dispersion effect may produce strong phase-induced mode-media interactions for all the lower-gain iodine hyperfine transitions in any low pressure (<50 Torr) atomic-iodine laser. Fortunately, the highest-gain hyperfine transition, <i>F</i>′ = 3 → <i>F</i>″ = 4, has the smallest amount of additional phase shift (or refractivity) introduced by this anomalous dispersion. All the other transitions experience much larger anomalous dispersion effects. This condition should act as an internal frequency discriminator, forcing the iodine to lase on the highest-gain hyperfine transition.

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  1. W. E. McDermott et al., "An electronic transition chemical laser," Appl. Phys. Lett. 32, 469–471 (1978).
  2. D. J. Benard et al., "Efficient operation of a 100-W transverse-flow oxygen-iodine chemical laser," Appl. Phys. Lett. 34, 40–42 (1979).
  3. R. J. Richardson and C. E. Wiswall, "Chemically pumped iodine laser," Appl. Phys. Lett. 35, 138–139 (1979).
  4. W. E. McDermott, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, personal communication.
  5. W. R. Bennett, Jr., "Hole-burning effects in a He—Ne optical maser," Phys. Rev. 126, 580–593 (1962).
  6. A. Y. Cabezas and R. P. Treat, "Effects of spectral hole-burning and cross relaxation on the gain saturation of laser amplifiers," J. Appl. Phys., 37, 3556–3563 (1966).
  7. T. Kan and G. J. Wolga, "Influence of collisions on radiative saturation and Lamb dip formation in CO2 molecular lasers," IEEE J. Quantum Electron. QE-7, 141–150 (1971).
  8. D. H. Close, "Strong-field saturation effects in laser media," Phys. Rev. 153, 360–371 (1967).
  9. R. Ladenburg, "Dispersion in electrically excited gases," Rev. Mod. Phys. 5, 243–256 (1933).
  10. R. Ladenburg, "Untersuchungen ¨ber die Anomale Dispersion Angeregter Gase," Z. Phys. 48, 15–50 (1928); R. Ladenburg and R. Minkowski, "Die Verdamplungswärme des Natriums und die Ubergangswahrssheinlichkeit des Na-Atoms and dem Resonaz in den Normalzustand auf Grund Optischer Messungen," Z. Phys. 6, 153–164 (1921); R. Ladenburg and G. Wolfsohn, "Untersuchungen über die Dispersion von Gasen und Dampfen und ihre Darslellung durch die Dispersion-Theorie," Z. Phys. 63, 616–633 (1930).
  11. R. F. Shea, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, personal communication.
  12. For example, see A. E. Siegman, "Unstable optical resonators for laser applications," Proc. IEEE 53, 277–287 (1965); A. E. Siegman and R. Arrathoon, "Modes in unstable optical resonators and lens waveguides," IEEE J. Quantum Electron. QE-3, 156 (1967); A. E. Siegman, "Stabilizing output with unstable resonators," Laser Focus 7, 42–47 (1971).
  13. J. A. Glaze, "Linewidth parameters from the Lamb dip in a cw HF chemical laser," Appl. Phys. Lett. 23, 300–302 (1973).
  14. N. Skribanowitz et al., "Anisotropic ultrahigh gain emission observed in rotational transitions in optically pumped HF gas," Appl. Phys. Lett. 20, 428–431 (1972).
  15. R. S. Derwent and B. A. Thrush, "The radiative lifetime of the metastable iodine atom I(52P½)," Chèm. Phys. Lett. 9, 591–592 (1971).
  16. V. S. Zuev et al., Investigation of the luminescence spectrum of atomic iodine (2P½-2P3/2) laser transition," Sov. Phys. JETP 35, 870–873 (1972).
  17. I. M. Belousova, V. M. Kiselev, and V. N. Kurzenkov, "Induced emission spectrum of atomic iodine due to the hyperfine structure of the transition 2P½-2P3/2 (7600 cm-1)," Opt. Spectrosc. 33, 112–114 (1972).
  18. G. Herzberg, Atomic Spectra and Atomic Structure (Dover, New York, 1944), p. 195.
  19. Ref. 18, pp. 182–196.
  20. R. M. Eisberg, Fundamentals of Modern Physics (Wiley, New York, 1961), pp. 449–452.
  21. V. Jaccarino et al., "Hyperfine structure of I127. Nuclear magnetic octupole moment," Phys. Rev. 94, 1798–1799 (1954).
  22. E. Luc-Koenig, C. Morillon, and J. Vergés, "Etude experimental et thérique de le lode Atomique," Phys. Scr. 12, 199–207 (1975).
  23. R. Engleman, Jr., R. A. Keller, and B. A. Palmer, "Hyperfine structure and isotope shift of the 1.3 μm transition of 129I," Appl. Opt. 19, 2767–2770 (1980).
  24. A. C. G. Mitchell and M. N. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, New York, 1961), pp. 103–106.
  25. V. N. Faddeyeva and N. M. Terent'ev, Tables of Values of the Function [Equation] for Complex Arguments (Pergamon, New York, 1961).
  26. B. D. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).
  27. Ref. 18, pp. 188–190.
  28. For example, see A. V. Phelps, "Tunable gas lasers utilizing ground state dissociation," JILA Rep. No. 110 (unpublished) (Joint Institute for Laboratory Astrophysics, Boulder, Colo. 1972). Normally, σse is defined by the relation σse = (λ02As)/(8πΔν), with the peak total fractional gain given by G1P = σse [(Nu/gu) - (Nl/gl] × L.
  29. R. de L. Kronig, "On the theory of dispersion of x-rays," J. Opt. Soc. Am. 12, 547–557 (1926).
  30. H. A. Kramers, Atti Congr. Internaz. Fisici Como., 2, 545–561 (1927).
  31. T. D. Padrick and R. E. Palmer, "Pressure broadening of the atomic iodine 52P½-52P3/2 transition," J. Chem. Phys. 62, 3350–3352 (1975).
  32. W. Fuss and K. Hohla, "Pressure broadening of the 1.3 μm iodine laser line," Ipp Rep. No. IV/67 (Max Planck Institute für Plasmaphysik, Munich, 1974). For a somewhat more accessible source, see W. Fuss and K. Hohla, "Pressure broadening of the 1.3 μm iodine laser line," Z. Naturforsch. Teil A 31, 569–581 (1976).
  33. V. A. Katulin, V. Yu Nosach, and A. L. Petrov, "Investigation of the characteristics of the preamplifier stages of a short-pulse iodine laser," Sov. J. Quantum Electron. 9, 169–174 (1979).
  34. S. J. Davis and D. Neumann, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, unpublished. This value is the best estimate at present and is thought to have an upper limit of 10 MHz/Torr.
  35. W. R. Bennett, Jr., "Gaseous optical masers," Appl. Opt. Suppl. 1, 24–61 (1962).
  36. In the chemically pumped atomic iodine laser,2 the chemical O2(1Δg) generator1 produces a large fraction of H2O vapor as a by-product. This H2O vapor is thought to be very detrimental to the atomic-iodine lasing at 1.315 μm since it quenches the excited I 52P½ state readily.37 Cold traps are used to eliminate this H2O vapor before it is mixed with the I2 vapor.1,2 However, it has been reported that large fractions (approximately 40%) exist within the laser cavity and yet the device still operates.38 Although the kinetics of this iodine system obviously are not well understood scientifically, the device still operates. Consequently, since the device still operates with such a large fraction of H2O vapor, the pressure-broadening effects of this molecule are important.
  37. For iodine quenching, see D. R. Kearns, "Physical and chemical properties of singlet molecular oxygen," Chem. Rev. 71, 395–427 (1971). In addition, there exists quenching of excited O2 by H2O. See, for example, F. Stuhland and K. H. Welge, "Deactivation of O(1S) and O2(b1Σg+)," Can. J. Chem. 47, 1870–1871 (1969); R. J. O'Brien, Jr., and G. H. Myers, "Direct flow measurements of O2(b2Σg+) quenching rates," J. Chem. Phys. 53, 3832–3841 (1970); K. H. Becker, W. Groth, and U. Schurath, "The quenching of metastable O2(1Δg) and O2(1Σg+) molecules," Chem. Phys. Lett. 8, 259–262 (1971).
  38. W. E. McDermott, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, personal communication.
  39. D. R. Kearns, "Physical and chemical properties of singlet molecular oxygen," Chem. Rev. 71, 395–427 (1971).
  40. P. W. Morse and H. Feshbach, Methods of the Theoretical Physics (McGraw-Hill, New York, 1953). Another approach deals with the real and imaginary parts of network functions. For example, see H. W. Bode, Network Analysis and Feedback Amplifier Design (Vail Nostrand, Princeton, N.J., 1945), Chap. XIV; S. Seshu and N. Balabanian, Linear Network Analysis (Wiley, New York, 1963), pp. 261–276.
  41. R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1960).
  42. Ref. 24, p. 584.
  43. For example, see W. Kaplan, Advanced Calculus (Addison-Wesley, New York, 1952), p. 193.
  44. H. B. Dwight, Tables of Integrals and Other Mathematical Data (Macmillan, New York, 1964), pp. 235–236.
  45. The integral ∫ 0e-x2/4 sin(wx)dx is evaluated using complex variables. See Ref. 41, p. 171. Also see Ref. 42, p. 584.
  46. The imaginary parts of ZI(w, a) have been expanded previously in a similar manner. See B. H. Armstrong, "Spectrum line profiles: the Voigt function," J. Quantum Spectrosc. Radiat. Transfer 7, 61–88 (1967).
  47. Also see S. A. Korff and G. Breit, "Optical dispersion," Rev. Mod. Phys. 4, 471–503 (1932).
  48. Ref. 24, pp. 95–96.
  49. M. J. Yoder and D. R. Ahouse, "Output flux instabilities in a flowing-gas cw CO2 electric discharge laser," Appl. Phys. Lett. 27, 673–676 (1975).
  50. Yu. A. Dreizin and A. M. Dykhne, "Self-oscillating instability of fast-flow lasers using unstable resonators," JETP Lett. 19, 371 (1974).
  51. M. L. Alme, "Temporal oscillations in the output from a gas dynamic laser with an unstable resonator," in Laser Digest, AFWL-TR-75-229 (Air Force Weapons Laboratory, Kirtland AFB, N.M.) (unpublished), pp. 6−15.
  52. In addition to frequency pulling, there are also frequency pushing effects. See, for example, R. A. McFarlane, "Frequency pushing and frequency pulling in a He-Ne gas optical maser," Phys. Rev. 135, 543 (1964).
  53. H. Kogelnik, "Imaging of optical modes—resonators with internal lenses," Bell Syst. Tech. J. 44, 455 (1965); H. Kogelnik and T. Li, "Laser beams and resonators," Appl. Opt. 5, 1550 (1966).
  54. L. A. Schlie and J. T. Verdeyen, "Radial profile of neon 1s5 atoms in a He-Ne active discharge and their lens effect on lasing at 6401 Å," IEEE J. Quantum Electron. 5, 21 (1969).

1980

1979

D. J. Benard et al., "Efficient operation of a 100-W transverse-flow oxygen-iodine chemical laser," Appl. Phys. Lett. 34, 40–42 (1979).

R. J. Richardson and C. E. Wiswall, "Chemically pumped iodine laser," Appl. Phys. Lett. 35, 138–139 (1979).

V. A. Katulin, V. Yu Nosach, and A. L. Petrov, "Investigation of the characteristics of the preamplifier stages of a short-pulse iodine laser," Sov. J. Quantum Electron. 9, 169–174 (1979).

1978

W. E. McDermott et al., "An electronic transition chemical laser," Appl. Phys. Lett. 32, 469–471 (1978).

1975

E. Luc-Koenig, C. Morillon, and J. Vergés, "Etude experimental et thérique de le lode Atomique," Phys. Scr. 12, 199–207 (1975).

T. D. Padrick and R. E. Palmer, "Pressure broadening of the atomic iodine 52P½-52P3/2 transition," J. Chem. Phys. 62, 3350–3352 (1975).

M. J. Yoder and D. R. Ahouse, "Output flux instabilities in a flowing-gas cw CO2 electric discharge laser," Appl. Phys. Lett. 27, 673–676 (1975).

1974

Yu. A. Dreizin and A. M. Dykhne, "Self-oscillating instability of fast-flow lasers using unstable resonators," JETP Lett. 19, 371 (1974).

1973

J. A. Glaze, "Linewidth parameters from the Lamb dip in a cw HF chemical laser," Appl. Phys. Lett. 23, 300–302 (1973).

1972

N. Skribanowitz et al., "Anisotropic ultrahigh gain emission observed in rotational transitions in optically pumped HF gas," Appl. Phys. Lett. 20, 428–431 (1972).

V. S. Zuev et al., Investigation of the luminescence spectrum of atomic iodine (2P½-2P3/2) laser transition," Sov. Phys. JETP 35, 870–873 (1972).

I. M. Belousova, V. M. Kiselev, and V. N. Kurzenkov, "Induced emission spectrum of atomic iodine due to the hyperfine structure of the transition 2P½-2P3/2 (7600 cm-1)," Opt. Spectrosc. 33, 112–114 (1972).

1971

R. S. Derwent and B. A. Thrush, "The radiative lifetime of the metastable iodine atom I(52P½)," Chèm. Phys. Lett. 9, 591–592 (1971).

T. Kan and G. J. Wolga, "Influence of collisions on radiative saturation and Lamb dip formation in CO2 molecular lasers," IEEE J. Quantum Electron. QE-7, 141–150 (1971).

For iodine quenching, see D. R. Kearns, "Physical and chemical properties of singlet molecular oxygen," Chem. Rev. 71, 395–427 (1971). In addition, there exists quenching of excited O2 by H2O. See, for example, F. Stuhland and K. H. Welge, "Deactivation of O(1S) and O2(b1Σg+)," Can. J. Chem. 47, 1870–1871 (1969); R. J. O'Brien, Jr., and G. H. Myers, "Direct flow measurements of O2(b2Σg+) quenching rates," J. Chem. Phys. 53, 3832–3841 (1970); K. H. Becker, W. Groth, and U. Schurath, "The quenching of metastable O2(1Δg) and O2(1Σg+) molecules," Chem. Phys. Lett. 8, 259–262 (1971).

D. R. Kearns, "Physical and chemical properties of singlet molecular oxygen," Chem. Rev. 71, 395–427 (1971).

1969

L. A. Schlie and J. T. Verdeyen, "Radial profile of neon 1s5 atoms in a He-Ne active discharge and their lens effect on lasing at 6401 Å," IEEE J. Quantum Electron. 5, 21 (1969).

1967

The imaginary parts of ZI(w, a) have been expanded previously in a similar manner. See B. H. Armstrong, "Spectrum line profiles: the Voigt function," J. Quantum Spectrosc. Radiat. Transfer 7, 61–88 (1967).

D. H. Close, "Strong-field saturation effects in laser media," Phys. Rev. 153, 360–371 (1967).

1966

A. Y. Cabezas and R. P. Treat, "Effects of spectral hole-burning and cross relaxation on the gain saturation of laser amplifiers," J. Appl. Phys., 37, 3556–3563 (1966).

1965

H. Kogelnik, "Imaging of optical modes—resonators with internal lenses," Bell Syst. Tech. J. 44, 455 (1965); H. Kogelnik and T. Li, "Laser beams and resonators," Appl. Opt. 5, 1550 (1966).

1964

In addition to frequency pulling, there are also frequency pushing effects. See, for example, R. A. McFarlane, "Frequency pushing and frequency pulling in a He-Ne gas optical maser," Phys. Rev. 135, 543 (1964).

1962

W. R. Bennett, Jr., "Gaseous optical masers," Appl. Opt. Suppl. 1, 24–61 (1962).

W. R. Bennett, Jr., "Hole-burning effects in a He—Ne optical maser," Phys. Rev. 126, 580–593 (1962).

1954

V. Jaccarino et al., "Hyperfine structure of I127. Nuclear magnetic octupole moment," Phys. Rev. 94, 1798–1799 (1954).

1933

R. Ladenburg, "Dispersion in electrically excited gases," Rev. Mod. Phys. 5, 243–256 (1933).

1932

Also see S. A. Korff and G. Breit, "Optical dispersion," Rev. Mod. Phys. 4, 471–503 (1932).

1928

R. Ladenburg, "Untersuchungen ¨ber die Anomale Dispersion Angeregter Gase," Z. Phys. 48, 15–50 (1928); R. Ladenburg and R. Minkowski, "Die Verdamplungswärme des Natriums und die Ubergangswahrssheinlichkeit des Na-Atoms and dem Resonaz in den Normalzustand auf Grund Optischer Messungen," Z. Phys. 6, 153–164 (1921); R. Ladenburg and G. Wolfsohn, "Untersuchungen über die Dispersion von Gasen und Dampfen und ihre Darslellung durch die Dispersion-Theorie," Z. Phys. 63, 616–633 (1930).

1926

Ahouse, D. R.

M. J. Yoder and D. R. Ahouse, "Output flux instabilities in a flowing-gas cw CO2 electric discharge laser," Appl. Phys. Lett. 27, 673–676 (1975).

Alme, M. L.

M. L. Alme, "Temporal oscillations in the output from a gas dynamic laser with an unstable resonator," in Laser Digest, AFWL-TR-75-229 (Air Force Weapons Laboratory, Kirtland AFB, N.M.) (unpublished), pp. 6−15.

Armstrong, B. H.

The imaginary parts of ZI(w, a) have been expanded previously in a similar manner. See B. H. Armstrong, "Spectrum line profiles: the Voigt function," J. Quantum Spectrosc. Radiat. Transfer 7, 61–88 (1967).

Belousova, I. M.

I. M. Belousova, V. M. Kiselev, and V. N. Kurzenkov, "Induced emission spectrum of atomic iodine due to the hyperfine structure of the transition 2P½-2P3/2 (7600 cm-1)," Opt. Spectrosc. 33, 112–114 (1972).

Benard, D. J.

D. J. Benard et al., "Efficient operation of a 100-W transverse-flow oxygen-iodine chemical laser," Appl. Phys. Lett. 34, 40–42 (1979).

Bennett, Jr., W. R.

W. R. Bennett, Jr., "Hole-burning effects in a He—Ne optical maser," Phys. Rev. 126, 580–593 (1962).

W. R. Bennett, Jr., "Gaseous optical masers," Appl. Opt. Suppl. 1, 24–61 (1962).

Breit, G.

Also see S. A. Korff and G. Breit, "Optical dispersion," Rev. Mod. Phys. 4, 471–503 (1932).

Cabezas, A. Y.

A. Y. Cabezas and R. P. Treat, "Effects of spectral hole-burning and cross relaxation on the gain saturation of laser amplifiers," J. Appl. Phys., 37, 3556–3563 (1966).

Churchill, R. V.

R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1960).

Close, D. H.

D. H. Close, "Strong-field saturation effects in laser media," Phys. Rev. 153, 360–371 (1967).

Conte, S. D.

B. D. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

Davis, S. J.

S. J. Davis and D. Neumann, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, unpublished. This value is the best estimate at present and is thought to have an upper limit of 10 MHz/Torr.

Derwent, R. S.

R. S. Derwent and B. A. Thrush, "The radiative lifetime of the metastable iodine atom I(52P½)," Chèm. Phys. Lett. 9, 591–592 (1971).

Dreizin, Yu. A.

Yu. A. Dreizin and A. M. Dykhne, "Self-oscillating instability of fast-flow lasers using unstable resonators," JETP Lett. 19, 371 (1974).

Dwight, H. B.

H. B. Dwight, Tables of Integrals and Other Mathematical Data (Macmillan, New York, 1964), pp. 235–236.

Dykhne, A. M.

Yu. A. Dreizin and A. M. Dykhne, "Self-oscillating instability of fast-flow lasers using unstable resonators," JETP Lett. 19, 371 (1974).

Eisberg, R. M.

R. M. Eisberg, Fundamentals of Modern Physics (Wiley, New York, 1961), pp. 449–452.

Engleman, Jr., R.

Faddeyeva, V. N.

V. N. Faddeyeva and N. M. Terent'ev, Tables of Values of the Function [Equation] for Complex Arguments (Pergamon, New York, 1961).

Feshbach, H.

P. W. Morse and H. Feshbach, Methods of the Theoretical Physics (McGraw-Hill, New York, 1953). Another approach deals with the real and imaginary parts of network functions. For example, see H. W. Bode, Network Analysis and Feedback Amplifier Design (Vail Nostrand, Princeton, N.J., 1945), Chap. XIV; S. Seshu and N. Balabanian, Linear Network Analysis (Wiley, New York, 1963), pp. 261–276.

Fried, B. D.

B. D. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

Fuss, W.

W. Fuss and K. Hohla, "Pressure broadening of the 1.3 μm iodine laser line," Ipp Rep. No. IV/67 (Max Planck Institute für Plasmaphysik, Munich, 1974). For a somewhat more accessible source, see W. Fuss and K. Hohla, "Pressure broadening of the 1.3 μm iodine laser line," Z. Naturforsch. Teil A 31, 569–581 (1976).

Glaze, J. A.

J. A. Glaze, "Linewidth parameters from the Lamb dip in a cw HF chemical laser," Appl. Phys. Lett. 23, 300–302 (1973).

Herzberg, G.

G. Herzberg, Atomic Spectra and Atomic Structure (Dover, New York, 1944), p. 195.

Hohla, K.

W. Fuss and K. Hohla, "Pressure broadening of the 1.3 μm iodine laser line," Ipp Rep. No. IV/67 (Max Planck Institute für Plasmaphysik, Munich, 1974). For a somewhat more accessible source, see W. Fuss and K. Hohla, "Pressure broadening of the 1.3 μm iodine laser line," Z. Naturforsch. Teil A 31, 569–581 (1976).

Jaccarino, V.

V. Jaccarino et al., "Hyperfine structure of I127. Nuclear magnetic octupole moment," Phys. Rev. 94, 1798–1799 (1954).

Kan, T.

T. Kan and G. J. Wolga, "Influence of collisions on radiative saturation and Lamb dip formation in CO2 molecular lasers," IEEE J. Quantum Electron. QE-7, 141–150 (1971).

Kaplan, W.

For example, see W. Kaplan, Advanced Calculus (Addison-Wesley, New York, 1952), p. 193.

Katulin, V. A.

V. A. Katulin, V. Yu Nosach, and A. L. Petrov, "Investigation of the characteristics of the preamplifier stages of a short-pulse iodine laser," Sov. J. Quantum Electron. 9, 169–174 (1979).

Kearns, D. R.

For iodine quenching, see D. R. Kearns, "Physical and chemical properties of singlet molecular oxygen," Chem. Rev. 71, 395–427 (1971). In addition, there exists quenching of excited O2 by H2O. See, for example, F. Stuhland and K. H. Welge, "Deactivation of O(1S) and O2(b1Σg+)," Can. J. Chem. 47, 1870–1871 (1969); R. J. O'Brien, Jr., and G. H. Myers, "Direct flow measurements of O2(b2Σg+) quenching rates," J. Chem. Phys. 53, 3832–3841 (1970); K. H. Becker, W. Groth, and U. Schurath, "The quenching of metastable O2(1Δg) and O2(1Σg+) molecules," Chem. Phys. Lett. 8, 259–262 (1971).

D. R. Kearns, "Physical and chemical properties of singlet molecular oxygen," Chem. Rev. 71, 395–427 (1971).

Keller, R. A.

Kiselev, V. M.

I. M. Belousova, V. M. Kiselev, and V. N. Kurzenkov, "Induced emission spectrum of atomic iodine due to the hyperfine structure of the transition 2P½-2P3/2 (7600 cm-1)," Opt. Spectrosc. 33, 112–114 (1972).

Kogelnik, H.

H. Kogelnik, "Imaging of optical modes—resonators with internal lenses," Bell Syst. Tech. J. 44, 455 (1965); H. Kogelnik and T. Li, "Laser beams and resonators," Appl. Opt. 5, 1550 (1966).

Korff, S. A.

Also see S. A. Korff and G. Breit, "Optical dispersion," Rev. Mod. Phys. 4, 471–503 (1932).

Kramers, H. A.

H. A. Kramers, Atti Congr. Internaz. Fisici Como., 2, 545–561 (1927).

Kronig, R. de L.

Kurzenkov, V. N.

I. M. Belousova, V. M. Kiselev, and V. N. Kurzenkov, "Induced emission spectrum of atomic iodine due to the hyperfine structure of the transition 2P½-2P3/2 (7600 cm-1)," Opt. Spectrosc. 33, 112–114 (1972).

Ladenburg, R.

R. Ladenburg, "Dispersion in electrically excited gases," Rev. Mod. Phys. 5, 243–256 (1933).

R. Ladenburg, "Untersuchungen ¨ber die Anomale Dispersion Angeregter Gase," Z. Phys. 48, 15–50 (1928); R. Ladenburg and R. Minkowski, "Die Verdamplungswärme des Natriums und die Ubergangswahrssheinlichkeit des Na-Atoms and dem Resonaz in den Normalzustand auf Grund Optischer Messungen," Z. Phys. 6, 153–164 (1921); R. Ladenburg and G. Wolfsohn, "Untersuchungen über die Dispersion von Gasen und Dampfen und ihre Darslellung durch die Dispersion-Theorie," Z. Phys. 63, 616–633 (1930).

Luc-Koenig, E.

E. Luc-Koenig, C. Morillon, and J. Vergés, "Etude experimental et thérique de le lode Atomique," Phys. Scr. 12, 199–207 (1975).

McDermott, W. E.

W. E. McDermott et al., "An electronic transition chemical laser," Appl. Phys. Lett. 32, 469–471 (1978).

W. E. McDermott, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, personal communication.

W. E. McDermott, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, personal communication.

McFarlane, R. A.

In addition to frequency pulling, there are also frequency pushing effects. See, for example, R. A. McFarlane, "Frequency pushing and frequency pulling in a He-Ne gas optical maser," Phys. Rev. 135, 543 (1964).

Mitchell, A. C. G.

A. C. G. Mitchell and M. N. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, New York, 1961), pp. 103–106.

Morillon, C.

E. Luc-Koenig, C. Morillon, and J. Vergés, "Etude experimental et thérique de le lode Atomique," Phys. Scr. 12, 199–207 (1975).

Morse, P. W.

P. W. Morse and H. Feshbach, Methods of the Theoretical Physics (McGraw-Hill, New York, 1953). Another approach deals with the real and imaginary parts of network functions. For example, see H. W. Bode, Network Analysis and Feedback Amplifier Design (Vail Nostrand, Princeton, N.J., 1945), Chap. XIV; S. Seshu and N. Balabanian, Linear Network Analysis (Wiley, New York, 1963), pp. 261–276.

Neumann, D.

S. J. Davis and D. Neumann, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, unpublished. This value is the best estimate at present and is thought to have an upper limit of 10 MHz/Torr.

Nosach, V. Yu

V. A. Katulin, V. Yu Nosach, and A. L. Petrov, "Investigation of the characteristics of the preamplifier stages of a short-pulse iodine laser," Sov. J. Quantum Electron. 9, 169–174 (1979).

Padrick, T. D.

T. D. Padrick and R. E. Palmer, "Pressure broadening of the atomic iodine 52P½-52P3/2 transition," J. Chem. Phys. 62, 3350–3352 (1975).

Palmer, B. A.

Palmer, R. E.

T. D. Padrick and R. E. Palmer, "Pressure broadening of the atomic iodine 52P½-52P3/2 transition," J. Chem. Phys. 62, 3350–3352 (1975).

Petrov, A. L.

V. A. Katulin, V. Yu Nosach, and A. L. Petrov, "Investigation of the characteristics of the preamplifier stages of a short-pulse iodine laser," Sov. J. Quantum Electron. 9, 169–174 (1979).

Phelps, A. V.

For example, see A. V. Phelps, "Tunable gas lasers utilizing ground state dissociation," JILA Rep. No. 110 (unpublished) (Joint Institute for Laboratory Astrophysics, Boulder, Colo. 1972). Normally, σse is defined by the relation σse = (λ02As)/(8πΔν), with the peak total fractional gain given by G1P = σse [(Nu/gu) - (Nl/gl] × L.

Richardson, R. J.

R. J. Richardson and C. E. Wiswall, "Chemically pumped iodine laser," Appl. Phys. Lett. 35, 138–139 (1979).

Schlie, L. A.

L. A. Schlie and J. T. Verdeyen, "Radial profile of neon 1s5 atoms in a He-Ne active discharge and their lens effect on lasing at 6401 Å," IEEE J. Quantum Electron. 5, 21 (1969).

Shea, R. F.

R. F. Shea, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, personal communication.

Siegman, A. E.

For example, see A. E. Siegman, "Unstable optical resonators for laser applications," Proc. IEEE 53, 277–287 (1965); A. E. Siegman and R. Arrathoon, "Modes in unstable optical resonators and lens waveguides," IEEE J. Quantum Electron. QE-3, 156 (1967); A. E. Siegman, "Stabilizing output with unstable resonators," Laser Focus 7, 42–47 (1971).

Skribanowitz, N.

N. Skribanowitz et al., "Anisotropic ultrahigh gain emission observed in rotational transitions in optically pumped HF gas," Appl. Phys. Lett. 20, 428–431 (1972).

Terent’ev, N. M.

V. N. Faddeyeva and N. M. Terent'ev, Tables of Values of the Function [Equation] for Complex Arguments (Pergamon, New York, 1961).

Thrush, B. A.

R. S. Derwent and B. A. Thrush, "The radiative lifetime of the metastable iodine atom I(52P½)," Chèm. Phys. Lett. 9, 591–592 (1971).

Treat, R. P.

A. Y. Cabezas and R. P. Treat, "Effects of spectral hole-burning and cross relaxation on the gain saturation of laser amplifiers," J. Appl. Phys., 37, 3556–3563 (1966).

Verdeyen, J. T.

L. A. Schlie and J. T. Verdeyen, "Radial profile of neon 1s5 atoms in a He-Ne active discharge and their lens effect on lasing at 6401 Å," IEEE J. Quantum Electron. 5, 21 (1969).

Vergés, J.

E. Luc-Koenig, C. Morillon, and J. Vergés, "Etude experimental et thérique de le lode Atomique," Phys. Scr. 12, 199–207 (1975).

Wiswall, C. E.

R. J. Richardson and C. E. Wiswall, "Chemically pumped iodine laser," Appl. Phys. Lett. 35, 138–139 (1979).

Wolga, G. J.

T. Kan and G. J. Wolga, "Influence of collisions on radiative saturation and Lamb dip formation in CO2 molecular lasers," IEEE J. Quantum Electron. QE-7, 141–150 (1971).

Yoder, M. J.

M. J. Yoder and D. R. Ahouse, "Output flux instabilities in a flowing-gas cw CO2 electric discharge laser," Appl. Phys. Lett. 27, 673–676 (1975).

Zemansky, M. N.

A. C. G. Mitchell and M. N. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, New York, 1961), pp. 103–106.

Zuev, V. S.

V. S. Zuev et al., Investigation of the luminescence spectrum of atomic iodine (2P½-2P3/2) laser transition," Sov. Phys. JETP 35, 870–873 (1972).

Appl. Opt.

Appl. Opt. Suppl.

W. R. Bennett, Jr., "Gaseous optical masers," Appl. Opt. Suppl. 1, 24–61 (1962).

Appl. Phys. Lett.

W. E. McDermott et al., "An electronic transition chemical laser," Appl. Phys. Lett. 32, 469–471 (1978).

D. J. Benard et al., "Efficient operation of a 100-W transverse-flow oxygen-iodine chemical laser," Appl. Phys. Lett. 34, 40–42 (1979).

R. J. Richardson and C. E. Wiswall, "Chemically pumped iodine laser," Appl. Phys. Lett. 35, 138–139 (1979).

J. A. Glaze, "Linewidth parameters from the Lamb dip in a cw HF chemical laser," Appl. Phys. Lett. 23, 300–302 (1973).

N. Skribanowitz et al., "Anisotropic ultrahigh gain emission observed in rotational transitions in optically pumped HF gas," Appl. Phys. Lett. 20, 428–431 (1972).

M. J. Yoder and D. R. Ahouse, "Output flux instabilities in a flowing-gas cw CO2 electric discharge laser," Appl. Phys. Lett. 27, 673–676 (1975).

Bell Syst. Tech. J.

H. Kogelnik, "Imaging of optical modes—resonators with internal lenses," Bell Syst. Tech. J. 44, 455 (1965); H. Kogelnik and T. Li, "Laser beams and resonators," Appl. Opt. 5, 1550 (1966).

Chèm. Phys. Lett.

R. S. Derwent and B. A. Thrush, "The radiative lifetime of the metastable iodine atom I(52P½)," Chèm. Phys. Lett. 9, 591–592 (1971).

Chem. Rev.

D. R. Kearns, "Physical and chemical properties of singlet molecular oxygen," Chem. Rev. 71, 395–427 (1971).

For iodine quenching, see D. R. Kearns, "Physical and chemical properties of singlet molecular oxygen," Chem. Rev. 71, 395–427 (1971). In addition, there exists quenching of excited O2 by H2O. See, for example, F. Stuhland and K. H. Welge, "Deactivation of O(1S) and O2(b1Σg+)," Can. J. Chem. 47, 1870–1871 (1969); R. J. O'Brien, Jr., and G. H. Myers, "Direct flow measurements of O2(b2Σg+) quenching rates," J. Chem. Phys. 53, 3832–3841 (1970); K. H. Becker, W. Groth, and U. Schurath, "The quenching of metastable O2(1Δg) and O2(1Σg+) molecules," Chem. Phys. Lett. 8, 259–262 (1971).

IEEE J. Quantum Electron.

L. A. Schlie and J. T. Verdeyen, "Radial profile of neon 1s5 atoms in a He-Ne active discharge and their lens effect on lasing at 6401 Å," IEEE J. Quantum Electron. 5, 21 (1969).

T. Kan and G. J. Wolga, "Influence of collisions on radiative saturation and Lamb dip formation in CO2 molecular lasers," IEEE J. Quantum Electron. QE-7, 141–150 (1971).

J. Appl. Phys.

A. Y. Cabezas and R. P. Treat, "Effects of spectral hole-burning and cross relaxation on the gain saturation of laser amplifiers," J. Appl. Phys., 37, 3556–3563 (1966).

J. Chem. Phys.

T. D. Padrick and R. E. Palmer, "Pressure broadening of the atomic iodine 52P½-52P3/2 transition," J. Chem. Phys. 62, 3350–3352 (1975).

J. Opt. Soc. Am.

J. Quantum Spectrosc. Radiat. Transfer

The imaginary parts of ZI(w, a) have been expanded previously in a similar manner. See B. H. Armstrong, "Spectrum line profiles: the Voigt function," J. Quantum Spectrosc. Radiat. Transfer 7, 61–88 (1967).

JETP Lett.

Yu. A. Dreizin and A. M. Dykhne, "Self-oscillating instability of fast-flow lasers using unstable resonators," JETP Lett. 19, 371 (1974).

Opt. Spectrosc.

I. M. Belousova, V. M. Kiselev, and V. N. Kurzenkov, "Induced emission spectrum of atomic iodine due to the hyperfine structure of the transition 2P½-2P3/2 (7600 cm-1)," Opt. Spectrosc. 33, 112–114 (1972).

Phys. Rev.

D. H. Close, "Strong-field saturation effects in laser media," Phys. Rev. 153, 360–371 (1967).

W. R. Bennett, Jr., "Hole-burning effects in a He—Ne optical maser," Phys. Rev. 126, 580–593 (1962).

V. Jaccarino et al., "Hyperfine structure of I127. Nuclear magnetic octupole moment," Phys. Rev. 94, 1798–1799 (1954).

In addition to frequency pulling, there are also frequency pushing effects. See, for example, R. A. McFarlane, "Frequency pushing and frequency pulling in a He-Ne gas optical maser," Phys. Rev. 135, 543 (1964).

Phys. Scr.

E. Luc-Koenig, C. Morillon, and J. Vergés, "Etude experimental et thérique de le lode Atomique," Phys. Scr. 12, 199–207 (1975).

Rev. Mod. Phys.

R. Ladenburg, "Dispersion in electrically excited gases," Rev. Mod. Phys. 5, 243–256 (1933).

Also see S. A. Korff and G. Breit, "Optical dispersion," Rev. Mod. Phys. 4, 471–503 (1932).

Sov. J. Quantum Electron.

V. A. Katulin, V. Yu Nosach, and A. L. Petrov, "Investigation of the characteristics of the preamplifier stages of a short-pulse iodine laser," Sov. J. Quantum Electron. 9, 169–174 (1979).

Sov. Phys. JETP

V. S. Zuev et al., Investigation of the luminescence spectrum of atomic iodine (2P½-2P3/2) laser transition," Sov. Phys. JETP 35, 870–873 (1972).

Z. Phys.

R. Ladenburg, "Untersuchungen ¨ber die Anomale Dispersion Angeregter Gase," Z. Phys. 48, 15–50 (1928); R. Ladenburg and R. Minkowski, "Die Verdamplungswärme des Natriums und die Ubergangswahrssheinlichkeit des Na-Atoms and dem Resonaz in den Normalzustand auf Grund Optischer Messungen," Z. Phys. 6, 153–164 (1921); R. Ladenburg and G. Wolfsohn, "Untersuchungen über die Dispersion von Gasen und Dampfen und ihre Darslellung durch die Dispersion-Theorie," Z. Phys. 63, 616–633 (1930).

Other

R. F. Shea, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, personal communication.

For example, see A. E. Siegman, "Unstable optical resonators for laser applications," Proc. IEEE 53, 277–287 (1965); A. E. Siegman and R. Arrathoon, "Modes in unstable optical resonators and lens waveguides," IEEE J. Quantum Electron. QE-3, 156 (1967); A. E. Siegman, "Stabilizing output with unstable resonators," Laser Focus 7, 42–47 (1971).

W. E. McDermott, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, personal communication.

G. Herzberg, Atomic Spectra and Atomic Structure (Dover, New York, 1944), p. 195.

Ref. 18, pp. 182–196.

R. M. Eisberg, Fundamentals of Modern Physics (Wiley, New York, 1961), pp. 449–452.

S. J. Davis and D. Neumann, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, unpublished. This value is the best estimate at present and is thought to have an upper limit of 10 MHz/Torr.

In the chemically pumped atomic iodine laser,2 the chemical O2(1Δg) generator1 produces a large fraction of H2O vapor as a by-product. This H2O vapor is thought to be very detrimental to the atomic-iodine lasing at 1.315 μm since it quenches the excited I 52P½ state readily.37 Cold traps are used to eliminate this H2O vapor before it is mixed with the I2 vapor.1,2 However, it has been reported that large fractions (approximately 40%) exist within the laser cavity and yet the device still operates.38 Although the kinetics of this iodine system obviously are not well understood scientifically, the device still operates. Consequently, since the device still operates with such a large fraction of H2O vapor, the pressure-broadening effects of this molecule are important.

H. A. Kramers, Atti Congr. Internaz. Fisici Como., 2, 545–561 (1927).

W. Fuss and K. Hohla, "Pressure broadening of the 1.3 μm iodine laser line," Ipp Rep. No. IV/67 (Max Planck Institute für Plasmaphysik, Munich, 1974). For a somewhat more accessible source, see W. Fuss and K. Hohla, "Pressure broadening of the 1.3 μm iodine laser line," Z. Naturforsch. Teil A 31, 569–581 (1976).

A. C. G. Mitchell and M. N. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, New York, 1961), pp. 103–106.

V. N. Faddeyeva and N. M. Terent'ev, Tables of Values of the Function [Equation] for Complex Arguments (Pergamon, New York, 1961).

B. D. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

Ref. 18, pp. 188–190.

For example, see A. V. Phelps, "Tunable gas lasers utilizing ground state dissociation," JILA Rep. No. 110 (unpublished) (Joint Institute for Laboratory Astrophysics, Boulder, Colo. 1972). Normally, σse is defined by the relation σse = (λ02As)/(8πΔν), with the peak total fractional gain given by G1P = σse [(Nu/gu) - (Nl/gl] × L.

Ref. 24, pp. 95–96.

W. E. McDermott, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, personal communication.

P. W. Morse and H. Feshbach, Methods of the Theoretical Physics (McGraw-Hill, New York, 1953). Another approach deals with the real and imaginary parts of network functions. For example, see H. W. Bode, Network Analysis and Feedback Amplifier Design (Vail Nostrand, Princeton, N.J., 1945), Chap. XIV; S. Seshu and N. Balabanian, Linear Network Analysis (Wiley, New York, 1963), pp. 261–276.

R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1960).

Ref. 24, p. 584.

For example, see W. Kaplan, Advanced Calculus (Addison-Wesley, New York, 1952), p. 193.

H. B. Dwight, Tables of Integrals and Other Mathematical Data (Macmillan, New York, 1964), pp. 235–236.

The integral ∫ 0e-x2/4 sin(wx)dx is evaluated using complex variables. See Ref. 41, p. 171. Also see Ref. 42, p. 584.

M. L. Alme, "Temporal oscillations in the output from a gas dynamic laser with an unstable resonator," in Laser Digest, AFWL-TR-75-229 (Air Force Weapons Laboratory, Kirtland AFB, N.M.) (unpublished), pp. 6−15.

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