Abstract

The spatial coherence and the beam divergence at 248 nm of a KrF excimer laser were obtained experimentally. These results are in good agreement with the theoretical calculations based on a simple pulse-laser model and the van Cittert–Zernike theorem. The relation between the spatial coherence and the beam divergence was obtained theoretically and supported by experimental results. This expression is given as a function of the wavelength of the laser but includes no parameters related to the laser structure. It is shown that these theoretical results are applicable to various kinds of pulse laser.

© 1992 Optical Society of America

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References

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  1. V. Pole, J. H. Bennewits, G. C. Escger, M. Feldma, V. A. Firtion, T. E. Jewell, B. E. Wilcomb, J. T. Clemens, “Excimer laser-based lithography,” in Optical Microlithography V, H. L. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.633, 6–16 (1986).
  2. T. A. Zonotins, “Excimer lasers in microlithography,” Lasers Optron. 7, 55–60 (1988).
  3. T. J. McKee, “Spectral-narrowing techniques for excimer laser oscillators,” Can. J. Phys. 63, 214–219 (1985).
    [CrossRef]
  4. S. Watanabe, T. Sato, H. Kashiwagi, “Amplification characteristics of an efficient discharge-pumped KrF laser,” IEEE J. Quantum Electron. QE-15, 322–327 (1979).
    [CrossRef]
  5. R. Fedosejevs, X. X. Shana, A. A. Offenberger, “Wavelength dependence of gain from 248.2 to 248.4 nm in a KrF discharge laser,” J. Phys. D 20, 912–916 (1987).
    [CrossRef]
  6. T. Shimura, K. Kuroda, M. Chihara, I. Ogura, “Active image formation using a copper vapor laser amplifier,” Jpn. J. Opt. (in Japanese) 14, 359–364 (1985).
  7. K. Jain, C. G. Willson, B. J. Lin, “Ultrafast high-resolution contact lithography with excimer lasers,” IBM J. Res. Dev. 26, 151–159 (1982).
    [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), p. 508.
  9. J. C. Wyant, “Double frequency grating lateral shear interferometer,” Appl. Opt. 12, 2057–2060 (1973).
    [CrossRef] [PubMed]
  10. Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).
  11. M. Born, E. Wolf, Principles of Optics, 5th ed., (Pergamon, Oxford, 1975), p. 360.
  12. M. Cŏpič, M. Zgonik, “On multi-pass Fabry–Perot interferometer,” Opt. Commun. 41, 310–314 (1982).
    [CrossRef]
  13. B. Rückele, P. Lokai, U. Brinkmann, D. Basting, W. Mückenheim, “Tuning ranges of an injection-locked excimer laser,” Opt. Laser Technol. 19, 153–157 (1987).
    [CrossRef]
  14. A. E. Siegman, “Unstable optical resonators,” Appl. Opt. 13, 353–367 (1974).
    [CrossRef] [PubMed]
  15. K. E. Oughstun, “Unstable resonator modes,” in Progress in Optics XXIV, E. Wolf, ed. (Elsevier, Amsterdam, 1987), pp. 165–387.
    [CrossRef]
  16. J. M. Eggleston, “Theory of output beam divergence in pulsed unstable resonators,” IEEE J. Quantum Electron. 24, 1302–1311 (1988).
    [CrossRef]
  17. U. Ganiel, A. Hardy, G. Neunann, D. Treves, “Amplified spontaneous emission and signal amplification in dye-laser systems,” IEEE J. Quantum Electron. QE-11, 881–892 (1975).
    [CrossRef]
  18. M. Watanabe, A. Endoh, N. Sarukura, S. Watanabe, “Property of amplified spontaneous emission and saturable absorber for a terawatt XeCl laser system,” J. Appl. Phys. 65, 428–432 (1989).
    [CrossRef]
  19. J. G. Eden, R. W. Waynant, S. K. Searles, R. Burnham, “New quenching rates applicable to the KrF laser,” Appl. Phys. Lett. 32, 733–735 (1978).
    [CrossRef]
  20. C. A. Brau, “Rare gas halogen excimers,” in Excimer Lasers, C. K. Rhodes, ed. (Springer-Verlag, Berlin, 1984), p. 90.

1989 (1)

M. Watanabe, A. Endoh, N. Sarukura, S. Watanabe, “Property of amplified spontaneous emission and saturable absorber for a terawatt XeCl laser system,” J. Appl. Phys. 65, 428–432 (1989).
[CrossRef]

1988 (2)

J. M. Eggleston, “Theory of output beam divergence in pulsed unstable resonators,” IEEE J. Quantum Electron. 24, 1302–1311 (1988).
[CrossRef]

T. A. Zonotins, “Excimer lasers in microlithography,” Lasers Optron. 7, 55–60 (1988).

1987 (2)

R. Fedosejevs, X. X. Shana, A. A. Offenberger, “Wavelength dependence of gain from 248.2 to 248.4 nm in a KrF discharge laser,” J. Phys. D 20, 912–916 (1987).
[CrossRef]

B. Rückele, P. Lokai, U. Brinkmann, D. Basting, W. Mückenheim, “Tuning ranges of an injection-locked excimer laser,” Opt. Laser Technol. 19, 153–157 (1987).
[CrossRef]

1985 (2)

T. Shimura, K. Kuroda, M. Chihara, I. Ogura, “Active image formation using a copper vapor laser amplifier,” Jpn. J. Opt. (in Japanese) 14, 359–364 (1985).

T. J. McKee, “Spectral-narrowing techniques for excimer laser oscillators,” Can. J. Phys. 63, 214–219 (1985).
[CrossRef]

1984 (1)

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

1982 (2)

M. Cŏpič, M. Zgonik, “On multi-pass Fabry–Perot interferometer,” Opt. Commun. 41, 310–314 (1982).
[CrossRef]

K. Jain, C. G. Willson, B. J. Lin, “Ultrafast high-resolution contact lithography with excimer lasers,” IBM J. Res. Dev. 26, 151–159 (1982).
[CrossRef]

1979 (1)

S. Watanabe, T. Sato, H. Kashiwagi, “Amplification characteristics of an efficient discharge-pumped KrF laser,” IEEE J. Quantum Electron. QE-15, 322–327 (1979).
[CrossRef]

1978 (1)

J. G. Eden, R. W. Waynant, S. K. Searles, R. Burnham, “New quenching rates applicable to the KrF laser,” Appl. Phys. Lett. 32, 733–735 (1978).
[CrossRef]

1975 (1)

U. Ganiel, A. Hardy, G. Neunann, D. Treves, “Amplified spontaneous emission and signal amplification in dye-laser systems,” IEEE J. Quantum Electron. QE-11, 881–892 (1975).
[CrossRef]

1974 (1)

1973 (1)

Basting, D.

B. Rückele, P. Lokai, U. Brinkmann, D. Basting, W. Mückenheim, “Tuning ranges of an injection-locked excimer laser,” Opt. Laser Technol. 19, 153–157 (1987).
[CrossRef]

Bennewits, J. H.

V. Pole, J. H. Bennewits, G. C. Escger, M. Feldma, V. A. Firtion, T. E. Jewell, B. E. Wilcomb, J. T. Clemens, “Excimer laser-based lithography,” in Optical Microlithography V, H. L. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.633, 6–16 (1986).

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), p. 508.

M. Born, E. Wolf, Principles of Optics, 5th ed., (Pergamon, Oxford, 1975), p. 360.

Brau, C. A.

C. A. Brau, “Rare gas halogen excimers,” in Excimer Lasers, C. K. Rhodes, ed. (Springer-Verlag, Berlin, 1984), p. 90.

Brinkmann, U.

B. Rückele, P. Lokai, U. Brinkmann, D. Basting, W. Mückenheim, “Tuning ranges of an injection-locked excimer laser,” Opt. Laser Technol. 19, 153–157 (1987).
[CrossRef]

Burnham, R.

J. G. Eden, R. W. Waynant, S. K. Searles, R. Burnham, “New quenching rates applicable to the KrF laser,” Appl. Phys. Lett. 32, 733–735 (1978).
[CrossRef]

Chihara, M.

T. Shimura, K. Kuroda, M. Chihara, I. Ogura, “Active image formation using a copper vapor laser amplifier,” Jpn. J. Opt. (in Japanese) 14, 359–364 (1985).

Clemens, J. T.

V. Pole, J. H. Bennewits, G. C. Escger, M. Feldma, V. A. Firtion, T. E. Jewell, B. E. Wilcomb, J. T. Clemens, “Excimer laser-based lithography,” in Optical Microlithography V, H. L. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.633, 6–16 (1986).

Copic, M.

M. Cŏpič, M. Zgonik, “On multi-pass Fabry–Perot interferometer,” Opt. Commun. 41, 310–314 (1982).
[CrossRef]

Eden, J. G.

J. G. Eden, R. W. Waynant, S. K. Searles, R. Burnham, “New quenching rates applicable to the KrF laser,” Appl. Phys. Lett. 32, 733–735 (1978).
[CrossRef]

Eggleston, J. M.

J. M. Eggleston, “Theory of output beam divergence in pulsed unstable resonators,” IEEE J. Quantum Electron. 24, 1302–1311 (1988).
[CrossRef]

Endoh, A.

M. Watanabe, A. Endoh, N. Sarukura, S. Watanabe, “Property of amplified spontaneous emission and saturable absorber for a terawatt XeCl laser system,” J. Appl. Phys. 65, 428–432 (1989).
[CrossRef]

Escger, G. C.

V. Pole, J. H. Bennewits, G. C. Escger, M. Feldma, V. A. Firtion, T. E. Jewell, B. E. Wilcomb, J. T. Clemens, “Excimer laser-based lithography,” in Optical Microlithography V, H. L. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.633, 6–16 (1986).

Fedosejevs, R.

R. Fedosejevs, X. X. Shana, A. A. Offenberger, “Wavelength dependence of gain from 248.2 to 248.4 nm in a KrF discharge laser,” J. Phys. D 20, 912–916 (1987).
[CrossRef]

Feldma, M.

V. Pole, J. H. Bennewits, G. C. Escger, M. Feldma, V. A. Firtion, T. E. Jewell, B. E. Wilcomb, J. T. Clemens, “Excimer laser-based lithography,” in Optical Microlithography V, H. L. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.633, 6–16 (1986).

Firtion, V. A.

V. Pole, J. H. Bennewits, G. C. Escger, M. Feldma, V. A. Firtion, T. E. Jewell, B. E. Wilcomb, J. T. Clemens, “Excimer laser-based lithography,” in Optical Microlithography V, H. L. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.633, 6–16 (1986).

Ganiel, U.

U. Ganiel, A. Hardy, G. Neunann, D. Treves, “Amplified spontaneous emission and signal amplification in dye-laser systems,” IEEE J. Quantum Electron. QE-11, 881–892 (1975).
[CrossRef]

Hardy, A.

U. Ganiel, A. Hardy, G. Neunann, D. Treves, “Amplified spontaneous emission and signal amplification in dye-laser systems,” IEEE J. Quantum Electron. QE-11, 881–892 (1975).
[CrossRef]

Jain, K.

K. Jain, C. G. Willson, B. J. Lin, “Ultrafast high-resolution contact lithography with excimer lasers,” IBM J. Res. Dev. 26, 151–159 (1982).
[CrossRef]

Jewell, T. E.

V. Pole, J. H. Bennewits, G. C. Escger, M. Feldma, V. A. Firtion, T. E. Jewell, B. E. Wilcomb, J. T. Clemens, “Excimer laser-based lithography,” in Optical Microlithography V, H. L. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.633, 6–16 (1986).

Kashiwagi, H.

S. Watanabe, T. Sato, H. Kashiwagi, “Amplification characteristics of an efficient discharge-pumped KrF laser,” IEEE J. Quantum Electron. QE-15, 322–327 (1979).
[CrossRef]

Kuroda, K.

T. Shimura, K. Kuroda, M. Chihara, I. Ogura, “Active image formation using a copper vapor laser amplifier,” Jpn. J. Opt. (in Japanese) 14, 359–364 (1985).

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

Lin, B. J.

K. Jain, C. G. Willson, B. J. Lin, “Ultrafast high-resolution contact lithography with excimer lasers,” IBM J. Res. Dev. 26, 151–159 (1982).
[CrossRef]

Liu, Z. B.

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

Lokai, P.

B. Rückele, P. Lokai, U. Brinkmann, D. Basting, W. Mückenheim, “Tuning ranges of an injection-locked excimer laser,” Opt. Laser Technol. 19, 153–157 (1987).
[CrossRef]

McKee, T. J.

T. J. McKee, “Spectral-narrowing techniques for excimer laser oscillators,” Can. J. Phys. 63, 214–219 (1985).
[CrossRef]

Mückenheim, W.

B. Rückele, P. Lokai, U. Brinkmann, D. Basting, W. Mückenheim, “Tuning ranges of an injection-locked excimer laser,” Opt. Laser Technol. 19, 153–157 (1987).
[CrossRef]

Neunann, G.

U. Ganiel, A. Hardy, G. Neunann, D. Treves, “Amplified spontaneous emission and signal amplification in dye-laser systems,” IEEE J. Quantum Electron. QE-11, 881–892 (1975).
[CrossRef]

Offenberger, A. A.

R. Fedosejevs, X. X. Shana, A. A. Offenberger, “Wavelength dependence of gain from 248.2 to 248.4 nm in a KrF discharge laser,” J. Phys. D 20, 912–916 (1987).
[CrossRef]

Ogura, I.

T. Shimura, K. Kuroda, M. Chihara, I. Ogura, “Active image formation using a copper vapor laser amplifier,” Jpn. J. Opt. (in Japanese) 14, 359–364 (1985).

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

Oughstun, K. E.

K. E. Oughstun, “Unstable resonator modes,” in Progress in Optics XXIV, E. Wolf, ed. (Elsevier, Amsterdam, 1987), pp. 165–387.
[CrossRef]

Pole, V.

V. Pole, J. H. Bennewits, G. C. Escger, M. Feldma, V. A. Firtion, T. E. Jewell, B. E. Wilcomb, J. T. Clemens, “Excimer laser-based lithography,” in Optical Microlithography V, H. L. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.633, 6–16 (1986).

Rückele, B.

B. Rückele, P. Lokai, U. Brinkmann, D. Basting, W. Mückenheim, “Tuning ranges of an injection-locked excimer laser,” Opt. Laser Technol. 19, 153–157 (1987).
[CrossRef]

Sarukura, N.

M. Watanabe, A. Endoh, N. Sarukura, S. Watanabe, “Property of amplified spontaneous emission and saturable absorber for a terawatt XeCl laser system,” J. Appl. Phys. 65, 428–432 (1989).
[CrossRef]

Sato, T.

S. Watanabe, T. Sato, H. Kashiwagi, “Amplification characteristics of an efficient discharge-pumped KrF laser,” IEEE J. Quantum Electron. QE-15, 322–327 (1979).
[CrossRef]

Searles, S. K.

J. G. Eden, R. W. Waynant, S. K. Searles, R. Burnham, “New quenching rates applicable to the KrF laser,” Appl. Phys. Lett. 32, 733–735 (1978).
[CrossRef]

Shana, X. X.

R. Fedosejevs, X. X. Shana, A. A. Offenberger, “Wavelength dependence of gain from 248.2 to 248.4 nm in a KrF discharge laser,” J. Phys. D 20, 912–916 (1987).
[CrossRef]

Shimura, T.

T. Shimura, K. Kuroda, M. Chihara, I. Ogura, “Active image formation using a copper vapor laser amplifier,” Jpn. J. Opt. (in Japanese) 14, 359–364 (1985).

Siegman, A. E.

Treves, D.

U. Ganiel, A. Hardy, G. Neunann, D. Treves, “Amplified spontaneous emission and signal amplification in dye-laser systems,” IEEE J. Quantum Electron. QE-11, 881–892 (1975).
[CrossRef]

Watanabe, M.

M. Watanabe, A. Endoh, N. Sarukura, S. Watanabe, “Property of amplified spontaneous emission and saturable absorber for a terawatt XeCl laser system,” J. Appl. Phys. 65, 428–432 (1989).
[CrossRef]

Watanabe, S.

M. Watanabe, A. Endoh, N. Sarukura, S. Watanabe, “Property of amplified spontaneous emission and saturable absorber for a terawatt XeCl laser system,” J. Appl. Phys. 65, 428–432 (1989).
[CrossRef]

S. Watanabe, T. Sato, H. Kashiwagi, “Amplification characteristics of an efficient discharge-pumped KrF laser,” IEEE J. Quantum Electron. QE-15, 322–327 (1979).
[CrossRef]

Waynant, R. W.

J. G. Eden, R. W. Waynant, S. K. Searles, R. Burnham, “New quenching rates applicable to the KrF laser,” Appl. Phys. Lett. 32, 733–735 (1978).
[CrossRef]

Wilcomb, B. E.

V. Pole, J. H. Bennewits, G. C. Escger, M. Feldma, V. A. Firtion, T. E. Jewell, B. E. Wilcomb, J. T. Clemens, “Excimer laser-based lithography,” in Optical Microlithography V, H. L. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.633, 6–16 (1986).

Willson, C. G.

K. Jain, C. G. Willson, B. J. Lin, “Ultrafast high-resolution contact lithography with excimer lasers,” IBM J. Res. Dev. 26, 151–159 (1982).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), p. 508.

M. Born, E. Wolf, Principles of Optics, 5th ed., (Pergamon, Oxford, 1975), p. 360.

Wyant, J. C.

Xie, J. P.

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

Zgonik, M.

M. Cŏpič, M. Zgonik, “On multi-pass Fabry–Perot interferometer,” Opt. Commun. 41, 310–314 (1982).
[CrossRef]

Zonotins, T. A.

T. A. Zonotins, “Excimer lasers in microlithography,” Lasers Optron. 7, 55–60 (1988).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. G. Eden, R. W. Waynant, S. K. Searles, R. Burnham, “New quenching rates applicable to the KrF laser,” Appl. Phys. Lett. 32, 733–735 (1978).
[CrossRef]

Can. J. Phys. (1)

T. J. McKee, “Spectral-narrowing techniques for excimer laser oscillators,” Can. J. Phys. 63, 214–219 (1985).
[CrossRef]

IBM J. Res. Dev. (1)

K. Jain, C. G. Willson, B. J. Lin, “Ultrafast high-resolution contact lithography with excimer lasers,” IBM J. Res. Dev. 26, 151–159 (1982).
[CrossRef]

IEEE J. Quantum Electron. (3)

S. Watanabe, T. Sato, H. Kashiwagi, “Amplification characteristics of an efficient discharge-pumped KrF laser,” IEEE J. Quantum Electron. QE-15, 322–327 (1979).
[CrossRef]

J. M. Eggleston, “Theory of output beam divergence in pulsed unstable resonators,” IEEE J. Quantum Electron. 24, 1302–1311 (1988).
[CrossRef]

U. Ganiel, A. Hardy, G. Neunann, D. Treves, “Amplified spontaneous emission and signal amplification in dye-laser systems,” IEEE J. Quantum Electron. QE-11, 881–892 (1975).
[CrossRef]

J. Appl. Phys. (1)

M. Watanabe, A. Endoh, N. Sarukura, S. Watanabe, “Property of amplified spontaneous emission and saturable absorber for a terawatt XeCl laser system,” J. Appl. Phys. 65, 428–432 (1989).
[CrossRef]

J. Phys. D (1)

R. Fedosejevs, X. X. Shana, A. A. Offenberger, “Wavelength dependence of gain from 248.2 to 248.4 nm in a KrF discharge laser,” J. Phys. D 20, 912–916 (1987).
[CrossRef]

Jpn. J. Opt. (in Japanese) (1)

T. Shimura, K. Kuroda, M. Chihara, I. Ogura, “Active image formation using a copper vapor laser amplifier,” Jpn. J. Opt. (in Japanese) 14, 359–364 (1985).

Lasers Optron. (1)

T. A. Zonotins, “Excimer lasers in microlithography,” Lasers Optron. 7, 55–60 (1988).

Opt. Commun. (1)

M. Cŏpič, M. Zgonik, “On multi-pass Fabry–Perot interferometer,” Opt. Commun. 41, 310–314 (1982).
[CrossRef]

Opt. Laser Technol. (1)

B. Rückele, P. Lokai, U. Brinkmann, D. Basting, W. Mückenheim, “Tuning ranges of an injection-locked excimer laser,” Opt. Laser Technol. 19, 153–157 (1987).
[CrossRef]

Seisan Kenkyu (1)

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

Other (5)

M. Born, E. Wolf, Principles of Optics, 5th ed., (Pergamon, Oxford, 1975), p. 360.

K. E. Oughstun, “Unstable resonator modes,” in Progress in Optics XXIV, E. Wolf, ed. (Elsevier, Amsterdam, 1987), pp. 165–387.
[CrossRef]

V. Pole, J. H. Bennewits, G. C. Escger, M. Feldma, V. A. Firtion, T. E. Jewell, B. E. Wilcomb, J. T. Clemens, “Excimer laser-based lithography,” in Optical Microlithography V, H. L. Stover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.633, 6–16 (1986).

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), p. 508.

C. A. Brau, “Rare gas halogen excimers,” in Excimer Lasers, C. K. Rhodes, ed. (Springer-Verlag, Berlin, 1984), p. 90.

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Figures (11)

Fig. 1
Fig. 1

Equivalent cavity model of a KrF excimer laser. Cavity length L is equal to nl, where n/2 is the number of round trips and l is a real cavity length, respectively. F(ξ) (at Y = 0) and f(x) (at Y = nl) are intensity-distribution functions. I(θ) is the angular intensity distribution. θd is the beam divergence of the laser.

Fig. 2
Fig. 2

Schematic diagram of a spectral narrowed KrF laser cavity with étalons.

Fig. 3
Fig. 3

Temporal output pulses for each cavity: a, cavity I; b, cavity II; c, cavity VI (the normal output of the Lambda Physik EGM 103MSC with internal mirrors); d, cavity III; e, cavity IV; f, cavity V. Delays of the peaks of traces e and f are approximately 7 ns and approximately 14 ns from the peak of trace d, respectively.

Fig. 4
Fig. 4

Schematic showing a beam-divergence measurement. The beam divergence is defined as θd = d/F, where d denotes the distance between two e−2 points of u CCD output.

Fig. 5
Fig. 5

Schematic of a shearing interferometer by using double gratings for the measurement of the degree of spatial coherence of the laser; shear, Δx′ = λϕz/D.

Fig. 6
Fig. 6

Experimental data points from the measurement of the visibility of interferograms by the shearing interferometer shown in Fig. 5 as a function of shear Δx′ for five cavity systems: (a) cavity I; (b) cavity II; (c) long-axis direction of the laser beam pattern for cavity III (open circles), cavity IV (triangles), and cavity V (filled circles); (d) short-axis direction for the coherence length xC is defined as a value of Δx′, where visibility declines to e−2.

Fig. 7
Fig. 7

Spatial coherence length xC versus beam radius a for various KrF spectrally narrowed lasers: cavity IV (open triangles) and cavity V (filled circles) with étalon, cavity VII (squares) and cavity VIII (filled triangles) with grating, cavity IX (crosses) with prisms, cavity III (open circles), and cavity III (filled circles with open centers; the cavity length l is changed to 1.5 m). Data were obtained in both directions of the long axis and the short axis of the laser-beam profiles, s denotes the short-axis direction.

Fig. 8
Fig. 8

Spatial coherence length xC versus beam divergence θd. The same symbols in Fig. 6 are used for a data plot. Solid curves represent the theoretical curves for the top-hat profile (xCθd = 1.55λ) and the Gaussian profile (xCθd = 1.97λ). s denotes the short-axis direction of the laser-beam profiles.

Fig. 9
Fig. 9

Schematic of an equivalent-cavity model of a confocal unstable resonator. M is the magnification factor. l is the cavity length.

Fig. 10
Fig. 10

Calculated ASE evolution and gain depletion in cavity I along the gain distance.

Fig. 11
Fig. 11

Ratio of the light source contribution to the ASE intensity at the output window at a distance of 80 cm in Fig. 10. The light source at the opposite end contributes predominantly.

Tables (2)

Tables Icon

Table I Output Data Obtained with Each Cavity

Tables Icon

Table II Experimental and Theoretical Values of Laser Output I t m

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

L = 2 ( 1 l ) n ,
f h ( x ) = { 1 , | x | a 0 , | x | > a ( top-hat type ) ,
f g ( x ) = exp [ 2 ( x / a ) 2 ] ( Gaussian type ) ,
F h ( ξ ) = { 1 , | ξ | a 0 , | ξ | > a ( top-hat type ) ,
F g ( ξ ) = exp [ 2 ( ξ / a ) 2 ] ( Gaussian type ) .
θ d = 4 a / L .
I ( θ ) = a L tan θ a L tan θ d ξ I 0 F ( ξ ) exp [ 0 L g ( ξ , y ) cos θ d y ] , = a L tan θ a L tan θ d ξ I 0 F ( ξ ) exp ( 0 L g 0 d y cos θ ) ,
θ d h = 3 . 53 a / L ( top-hat type ) ,
θ d g = 3 . 1 a / L ( Gaussian type ) .
μ = const F ( ξ ) exp ( i k ξ p ) d ξ / F ( ξ ) d ξ ,
μ h = sin ( k p a ) / k p a ( top-hat type ) ,
μ g = exp [ 2 ( k p a / 4 ) 2 ] ( Gaussian type ) .
x C h = 0 . 44 λ L / a ( top-hat type ) ,
x C g = 2 λ L / π a ( Gaussian type ) .
x C 0 = λ L / 2 a .
x C h θ d h = ( 0 . 44 λ L / a ) ( 3 . 53 a / L ) = 1 . 55 λ ( top-hat type ) ,
x C g θ d g = ( 2 λ L / π a ) ( 3 . 1 a / L ) = 1 . 97 λ ( Gaussian type ) .
x C 0 θ d = ( λ L / 2 a ) ( 4 a / L ) = 2 λ .
θ d = d / F ( rad ) .
Δ x = λ D ϕ z ,
x C = Δ x e 2 ,
x C 1 / a .
L = l 1 m , a = 5 mm x C I = 3 . 2 × 10 2 mm .
L = 3 m , a = 5 mm x C II = 9 . 5 × 10 2 mm .
I t m / I i = const . [ 1 1 + F sin 2 ( δ 1 / 2 ) × 1 1 + F sin 2 ( δ 2 / 2 ) ] m ,
δ 1 = 4 πλ 1 n d cos ( θ e + θ s ) cos θ L + 2 ϕ , δ 2 = 4 πλ 1 n d cos ( θ e θ s ) cos θ L + 2 ϕ ,
x C 1 / a ,
x CIL = M x OC ,
θ I = θ O / M ,
x O C θ O 2 λ,
x CIL θ I = M x OC θ O / M = x OC θ O 2 λ .
x CIL = M x C = 10 ( mm ) , θ I = θ O / M = 0 . 05 ( mrad ) .
V = 0 . 88 × 0 . 9 = 0 . 79 .
x C β = 2 λ l / π a = 1 . 54 × 10 1 ( mm ) , θ d β = 3 . 1 a / l = 3 . 1 ( mrad ) .
x C u = M x C β = 1 . 54 ( mm ) , θ d u = θ d β / M 0 . 3 ( mrad ) .

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