Abstract

A technique to measure the spectral distribution in a cross section of a KrF laser beam is described. Two-dimensional distribution, pulse-by-pulse fluctuation, and long term variation of the spectrum of the laser beam are measured with this method.

© 1990 Optical Society of America

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References

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  1. T. J. McKee, “Spectral-Narrowing Techniques for Excimer Laser Oscillators,” Can. J. Phys. 63, 214–219 (1985).
    [CrossRef]
  2. T. Yagi, H. Saito, T. Fujioka, K. Ohta, M. Obara,“Diagnostic Methods and Beam Qualities for the Discharge Pumped ExcimerLaser,” in Proceedings, International Conference on Lasers’88, Lake Tahoe (1988), pp. 127–134.
  3. S. Gidon, G. Behar, “Instantaeous Velocity Field Measurements: Application to Shock Wave Studies,” Appl. Opt. 25, 1429–1433 (1986).
    [CrossRef] [PubMed]
  4. D. Rees, A. H. Greenaway, “Doppler Imaging System; an Optical Device for Measuring Vector Winds. 1: General Principles,” Appl. Opt. 22, 1078–1083 (1983).
    [CrossRef] [PubMed]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 323–333.
  6. T. Yagi, Y. Matsumi, K. Ohta, J. Bachar, H. Saito, M. Obara, T. Fujioka, “Beam Monitoring System for Simultaneous Measurement of Near and Far Field Patterns in High Repetition Rate KrF Lasers,” Appl. Opt. 28, 3775–3778 (1989).
    [CrossRef] [PubMed]
  7. T. Yagi, “Fabry-Perot Interferometer Measurement of the Temperature and Wind at F-Layer Heights,” Ph.D. Thesis, La Trobe U., Melbourne, Australia (1983).
  8. S. F. Fulghum, D. W. Trainor, C. H. Appel, “Transient Refractive Index Measurements in XeF Laser Gas Mixtures,” IEEE J. Quantum Electron. QE-25, 955–962 (1989).
    [CrossRef]
  9. C. A. Brau, “Rare Gas Halogen Excimers,” in Excimer Lasers, C. K. Rhodes, Ed. (Springer-Verlag, New York, 1984), pp. 96–101.
  10. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 286–303.

1989 (2)

1986 (1)

1985 (1)

T. J. McKee, “Spectral-Narrowing Techniques for Excimer Laser Oscillators,” Can. J. Phys. 63, 214–219 (1985).
[CrossRef]

1983 (1)

Appel, C. H.

S. F. Fulghum, D. W. Trainor, C. H. Appel, “Transient Refractive Index Measurements in XeF Laser Gas Mixtures,” IEEE J. Quantum Electron. QE-25, 955–962 (1989).
[CrossRef]

Bachar, J.

Behar, G.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 323–333.

Brau, C. A.

C. A. Brau, “Rare Gas Halogen Excimers,” in Excimer Lasers, C. K. Rhodes, Ed. (Springer-Verlag, New York, 1984), pp. 96–101.

Fujioka, T.

T. Yagi, Y. Matsumi, K. Ohta, J. Bachar, H. Saito, M. Obara, T. Fujioka, “Beam Monitoring System for Simultaneous Measurement of Near and Far Field Patterns in High Repetition Rate KrF Lasers,” Appl. Opt. 28, 3775–3778 (1989).
[CrossRef] [PubMed]

T. Yagi, H. Saito, T. Fujioka, K. Ohta, M. Obara,“Diagnostic Methods and Beam Qualities for the Discharge Pumped ExcimerLaser,” in Proceedings, International Conference on Lasers’88, Lake Tahoe (1988), pp. 127–134.

Fulghum, S. F.

S. F. Fulghum, D. W. Trainor, C. H. Appel, “Transient Refractive Index Measurements in XeF Laser Gas Mixtures,” IEEE J. Quantum Electron. QE-25, 955–962 (1989).
[CrossRef]

Gidon, S.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 286–303.

Greenaway, A. H.

Matsumi, Y.

McKee, T. J.

T. J. McKee, “Spectral-Narrowing Techniques for Excimer Laser Oscillators,” Can. J. Phys. 63, 214–219 (1985).
[CrossRef]

Obara, M.

T. Yagi, Y. Matsumi, K. Ohta, J. Bachar, H. Saito, M. Obara, T. Fujioka, “Beam Monitoring System for Simultaneous Measurement of Near and Far Field Patterns in High Repetition Rate KrF Lasers,” Appl. Opt. 28, 3775–3778 (1989).
[CrossRef] [PubMed]

T. Yagi, H. Saito, T. Fujioka, K. Ohta, M. Obara,“Diagnostic Methods and Beam Qualities for the Discharge Pumped ExcimerLaser,” in Proceedings, International Conference on Lasers’88, Lake Tahoe (1988), pp. 127–134.

Ohta, K.

T. Yagi, Y. Matsumi, K. Ohta, J. Bachar, H. Saito, M. Obara, T. Fujioka, “Beam Monitoring System for Simultaneous Measurement of Near and Far Field Patterns in High Repetition Rate KrF Lasers,” Appl. Opt. 28, 3775–3778 (1989).
[CrossRef] [PubMed]

T. Yagi, H. Saito, T. Fujioka, K. Ohta, M. Obara,“Diagnostic Methods and Beam Qualities for the Discharge Pumped ExcimerLaser,” in Proceedings, International Conference on Lasers’88, Lake Tahoe (1988), pp. 127–134.

Rees, D.

Saito, H.

T. Yagi, Y. Matsumi, K. Ohta, J. Bachar, H. Saito, M. Obara, T. Fujioka, “Beam Monitoring System for Simultaneous Measurement of Near and Far Field Patterns in High Repetition Rate KrF Lasers,” Appl. Opt. 28, 3775–3778 (1989).
[CrossRef] [PubMed]

T. Yagi, H. Saito, T. Fujioka, K. Ohta, M. Obara,“Diagnostic Methods and Beam Qualities for the Discharge Pumped ExcimerLaser,” in Proceedings, International Conference on Lasers’88, Lake Tahoe (1988), pp. 127–134.

Trainor, D. W.

S. F. Fulghum, D. W. Trainor, C. H. Appel, “Transient Refractive Index Measurements in XeF Laser Gas Mixtures,” IEEE J. Quantum Electron. QE-25, 955–962 (1989).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 323–333.

Yagi, T.

T. Yagi, Y. Matsumi, K. Ohta, J. Bachar, H. Saito, M. Obara, T. Fujioka, “Beam Monitoring System for Simultaneous Measurement of Near and Far Field Patterns in High Repetition Rate KrF Lasers,” Appl. Opt. 28, 3775–3778 (1989).
[CrossRef] [PubMed]

T. Yagi, H. Saito, T. Fujioka, K. Ohta, M. Obara,“Diagnostic Methods and Beam Qualities for the Discharge Pumped ExcimerLaser,” in Proceedings, International Conference on Lasers’88, Lake Tahoe (1988), pp. 127–134.

T. Yagi, “Fabry-Perot Interferometer Measurement of the Temperature and Wind at F-Layer Heights,” Ph.D. Thesis, La Trobe U., Melbourne, Australia (1983).

Appl. Opt. (3)

Can. J. Phys. (1)

T. J. McKee, “Spectral-Narrowing Techniques for Excimer Laser Oscillators,” Can. J. Phys. 63, 214–219 (1985).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. F. Fulghum, D. W. Trainor, C. H. Appel, “Transient Refractive Index Measurements in XeF Laser Gas Mixtures,” IEEE J. Quantum Electron. QE-25, 955–962 (1989).
[CrossRef]

Other (5)

C. A. Brau, “Rare Gas Halogen Excimers,” in Excimer Lasers, C. K. Rhodes, Ed. (Springer-Verlag, New York, 1984), pp. 96–101.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 286–303.

T. Yagi, “Fabry-Perot Interferometer Measurement of the Temperature and Wind at F-Layer Heights,” Ph.D. Thesis, La Trobe U., Melbourne, Australia (1983).

T. Yagi, H. Saito, T. Fujioka, K. Ohta, M. Obara,“Diagnostic Methods and Beam Qualities for the Discharge Pumped ExcimerLaser,” in Proceedings, International Conference on Lasers’88, Lake Tahoe (1988), pp. 127–134.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 323–333.

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Figures (7)

Fig. 1
Fig. 1

Optical arrangement of the 2-D Fabry-Perot spectrometer: S1, focal plane of lens L1; S0, conjugate plane to S1; FPI, Fabry-Perot interferometer.

Fig. 2
Fig. 2

Measurement system of the 2-D spectral distribution in the narrowband KrF laser beam.

Fig. 3
Fig. 3

Fringe pattern analysis.

Fig. 4
Fig. 4

Fringe patterns: (a) optimum tuning of the dispersion optics and (b) offset of the wavelength from the optimum point, obtained for the KrF laser at 250-Hz repetition rate.

Fig. 5
Fig. 5

Three-dimensional representation of the wavenumber distribution obtained from the fringe analysis.

Fig. 6
Fig. 6

Fluctuation of the wavenumbers at different shot numbers.

Fig. 7
Fig. 7

Long term variation of the wavenumber distribution.

Equations (23)

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A ( r ) = ( 1 - R ) [ U ( r , l ) + R U ( r , l + 2 h ) + R 2 U ( r , 1 + 4 h ) + ]
= - ( f 1 / f 2 ) U ( x 0 y 0 ) exp [ ( 2 π i / λ ) ( f 1 + f 2 ) ] × exp [ ( π i f 1 / f 2 ) ( 1 / f 1 + 1 / f 2 ) r 2 ] × exp ( 2 π i / λ ) [ 1 - ( 1 / 2 ) ( r / f 2 ) 2 ] l × ( 1 - R ) ( 1 + R exp ( i δ ) + R 2 exp ( 2 i δ ) + ) ,
r = ( x 1 2 + y 1 2 ) 1 / 2 ,
δ = ( 4 π h / λ ) [ 1 - ( 1 / 2 ) ( r / f 2 ) 2 ] ,
δ = ( 4 π h / λ ) cos θ ,
x 0 = - ( f 1 / f 2 ) x 1 ,             y 0 = - ( f 1 / f 2 ) y 1 .
I ( r ) = A A * = ( f 1 / f 2 ) 2 I ( x 0 , y 0 ) ( 1 - R ) 2 / ( 1 - 2 R cos δ + R 2 ) .
ɛ = R 30 ~ 0.0076.
σ 0 = 4 π h σ 0 [ 1 - ( 1 / 2 ) ( r / f 2 ) 2 ] = 2 π m ,
σ ( Q 1 ) = σ 0 + δ σ ~ σ 0 [ 1 + ( r / f 2 2 ) ] δ r ,
Δ r / r = ( cos θ / cos ( θ - γ ) - 1 ) sin θ sin γ ,
δ θ r = [ ( 1 / n ) ( cos θ i / cos θ r ) ] 3 δ θ i ,
2 sin θ = ( m / d ) ( 1 / σ ) ,
δ σ = σ ( cos θ / sin θ ) δ θ r = 0.28 cm - 1 ,
sin ( π / 2 - θ ) = 1 - δ n ,
U ( x 1 , y 1 ) = [ - 1 / ( i λ 2 l 1 l 2 l 3 ) ] exp [ ( 2 π i / λ ) ( l 1 + l 2 + l 3 ) ] × U ( x 0 , y 0 ) exp [ ( π i / λ ) ( 1 / l 1 + 1 / l 2 - 1 / f 1 ) × ( s 1 2 + t 1 2 ) ] exp [ ( π i / λ l 1 ) ( x 0 2 + y 0 2 ) ] × exp [ ( - 2 π i / λ l 1 ) ( x 0 s 1 + y 0 t 1 ) ] × exp [ ( π i / λ ) ( 1 / l 2 + 1 / l 3 - 1 / f 2 ) × ( s 2 2 + t 2 2 ) ] exp [ ( - 2 π i / λ l 2 ) ( s 1 s 2 + t 1 t 2 ) ] × exp [ ( - 2 π i / λ l 3 ) ( s 2 x 1 + t 2 y 1 ) ] × d x 0 d y 0 d s 1 d t 1 d s 2 d t 2 ,
U ( x 1 , y 1 ) = - ( f 1 / f 2 ) U ( x 0 , y 0 ) exp [ ( 2 π i / λ ) ( f 1 + f 2 ) ] × exp [ ( π i / λ ) ( f 1 / f 2 ) ( 1 / f 1 + 1 / f 2 ) r 2 ] × exp { ( 2 π i / λ ) [ 1 - ( 1 / 2 ) ( r / f 2 ) 2 ] l 2 } ,
r = ( x 1 2 + y 1 2 ) 1 / 2 ,
x 0 = - ( f 1 / f 2 ) x 1 ,             y 0 = - ( f 1 / f 2 ) y 1 ,
- exp ( 2 π ikx ) d x = δ ( k ) ,
- exp [ ( π i / λ l ) x 2 ] exp ( 2 π ikx ) d x = ( i λ l ) 1 / 2 exp ( π i λ l k 2 ) .
r 0 2 / f l c ,             f = f 1 ,             f 2 , f 3 ,
r 0 2 / l l c ,             l = l 1 ,             l 2 , l 3 ,

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