Abstract

Plane-parallel cavities with Gaussian-reflectivity-profile mirrors as full reflectors were applied to a XeCl laser, and the near- and the far-field characteristics of the laser radiation were analyzed. It is shown that excimer lasers fitted with plane-parallel Gaussian cavities deliver laser radiation with a beam-quality factor M2 that is more than 50% smaller than that of laser beams delivered by conventional plane-parallel cavities. The effect of the Gaussian mirror spot size on M2 was also investigated, and it is shown that the narrowing of the Gaussian mirror spot size reduces the beam-quality-factor value.

© 1997 Optical Society of America

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References

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  1. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 23, p. 913.
  2. A. G. Nikitenko, “Novel design and method of fabrication of inhomogeneous mirrors,” Pure Appl. Opt. 3, 485–490 (1994).
    [CrossRef]
  3. M. Piché, D. Catin, “Enhancement of modal feedback in unstable resonators using mirrors with a phase step,” Opt. Lett. 16, 1135–1137 (1991).
    [CrossRef] [PubMed]
  4. P. A. Belanger, C. Paré, “Unstable laser resonators with a specified output profile by using a graded-reflectivity mirror: geometrical optics limit,” Opt. Commun. 109, 507–517 (1994).
    [CrossRef]
  5. P. Lavigne, N. McCarthy, J.-G. Demers, “Design and characterization of complementary Gaussian reflectivity mirrors,” Appl. Opt. 24, 2581–2586 (1985).
    [CrossRef] [PubMed]
  6. D. M. Walsh, L. V. Knight, “Transverse modes of a laser resonator with Gaussian mirrors,” Appl. Opt. 25, 2947–2954 (1986).
    [CrossRef] [PubMed]
  7. G. Ciccotti, P. DeSantis, G. Guattari, C. Palma, “Propagation of partially coherent beams in a periodic sequence of lenses and Gaussian apertures,” Pure Appl. Opt. 3, 561–571 (1994).
    [CrossRef]
  8. M. R. Perrone, C. Palma, V. Biagini, A. Piegari, D. Flori, S. Scaglione, “Theoretical and experimental determination of single round-trip beam parameters in a XeCl laser,” J. Opt. Soc. Am. A 12, 991–998 (1995).
    [CrossRef]
  9. V. Bagini, A. Mascello, C. Palma, M. R. Perrone, “Transient states analysis of a partially coherent laser beam propagating through a Gaussian cavity,” IEEE J. Quantum Electron. 31, 1572–1578 (1995).
    [CrossRef]
  10. P. De Santis, A. Mascello, C. Palma, M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802–812 (1996).
    [CrossRef]
  11. A. Siegman, M. W. Sasnett, T. F. Johnston, “Choice of the clip level for beam width measurements using knife-edge techniques,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).
    [CrossRef]
  12. J. J. Chang, “Time-resolved beam-quality characterization of copper-vapor lasers with unstable resonators,” Appl. Opt. 33, 2255–2265 (1994).
    [CrossRef] [PubMed]
  13. N. Reng, B. Eppich, “Definition and measurements of high-power laser beam parameters,” Opt. Quantum Electron. 24, S973–S992 (1992).
    [CrossRef]
  14. C. Giuri, M. R. Perrone, V. Piccinno, “Output coupler design of unstable cavities for excimer lasers,” Appl. Opt. 36, 1–6 (1997).
    [CrossRef]
  15. K. Yamada, K. Miyazaki, T. Hasama, T. Sato, “1-ns high-power high-repetitive excimer laser oscillator,” IEEE J. Quantum Electron. 24, 177–182 (1988).
    [CrossRef]
  16. D. Lo, “Electrical characteristics of small active volume (1 cm3) discharge-pumped XeCl laser,” Opt. Quantum Electron. 20, 257–262 (1988).
    [CrossRef]

1997 (1)

C. Giuri, M. R. Perrone, V. Piccinno, “Output coupler design of unstable cavities for excimer lasers,” Appl. Opt. 36, 1–6 (1997).
[CrossRef]

1996 (1)

P. De Santis, A. Mascello, C. Palma, M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802–812 (1996).
[CrossRef]

1995 (2)

V. Bagini, A. Mascello, C. Palma, M. R. Perrone, “Transient states analysis of a partially coherent laser beam propagating through a Gaussian cavity,” IEEE J. Quantum Electron. 31, 1572–1578 (1995).
[CrossRef]

M. R. Perrone, C. Palma, V. Biagini, A. Piegari, D. Flori, S. Scaglione, “Theoretical and experimental determination of single round-trip beam parameters in a XeCl laser,” J. Opt. Soc. Am. A 12, 991–998 (1995).
[CrossRef]

1994 (4)

J. J. Chang, “Time-resolved beam-quality characterization of copper-vapor lasers with unstable resonators,” Appl. Opt. 33, 2255–2265 (1994).
[CrossRef] [PubMed]

G. Ciccotti, P. DeSantis, G. Guattari, C. Palma, “Propagation of partially coherent beams in a periodic sequence of lenses and Gaussian apertures,” Pure Appl. Opt. 3, 561–571 (1994).
[CrossRef]

A. G. Nikitenko, “Novel design and method of fabrication of inhomogeneous mirrors,” Pure Appl. Opt. 3, 485–490 (1994).
[CrossRef]

P. A. Belanger, C. Paré, “Unstable laser resonators with a specified output profile by using a graded-reflectivity mirror: geometrical optics limit,” Opt. Commun. 109, 507–517 (1994).
[CrossRef]

1992 (1)

N. Reng, B. Eppich, “Definition and measurements of high-power laser beam parameters,” Opt. Quantum Electron. 24, S973–S992 (1992).
[CrossRef]

1991 (2)

A. Siegman, M. W. Sasnett, T. F. Johnston, “Choice of the clip level for beam width measurements using knife-edge techniques,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).
[CrossRef]

M. Piché, D. Catin, “Enhancement of modal feedback in unstable resonators using mirrors with a phase step,” Opt. Lett. 16, 1135–1137 (1991).
[CrossRef] [PubMed]

1988 (2)

K. Yamada, K. Miyazaki, T. Hasama, T. Sato, “1-ns high-power high-repetitive excimer laser oscillator,” IEEE J. Quantum Electron. 24, 177–182 (1988).
[CrossRef]

D. Lo, “Electrical characteristics of small active volume (1 cm3) discharge-pumped XeCl laser,” Opt. Quantum Electron. 20, 257–262 (1988).
[CrossRef]

1986 (1)

1985 (1)

Bagini, V.

V. Bagini, A. Mascello, C. Palma, M. R. Perrone, “Transient states analysis of a partially coherent laser beam propagating through a Gaussian cavity,” IEEE J. Quantum Electron. 31, 1572–1578 (1995).
[CrossRef]

Belanger, P. A.

P. A. Belanger, C. Paré, “Unstable laser resonators with a specified output profile by using a graded-reflectivity mirror: geometrical optics limit,” Opt. Commun. 109, 507–517 (1994).
[CrossRef]

Biagini, V.

Catin, D.

Chang, J. J.

Ciccotti, G.

G. Ciccotti, P. DeSantis, G. Guattari, C. Palma, “Propagation of partially coherent beams in a periodic sequence of lenses and Gaussian apertures,” Pure Appl. Opt. 3, 561–571 (1994).
[CrossRef]

De Santis, P.

P. De Santis, A. Mascello, C. Palma, M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802–812 (1996).
[CrossRef]

Demers, J.-G.

DeSantis, P.

G. Ciccotti, P. DeSantis, G. Guattari, C. Palma, “Propagation of partially coherent beams in a periodic sequence of lenses and Gaussian apertures,” Pure Appl. Opt. 3, 561–571 (1994).
[CrossRef]

Eppich, B.

N. Reng, B. Eppich, “Definition and measurements of high-power laser beam parameters,” Opt. Quantum Electron. 24, S973–S992 (1992).
[CrossRef]

Flori, D.

Giuri, C.

C. Giuri, M. R. Perrone, V. Piccinno, “Output coupler design of unstable cavities for excimer lasers,” Appl. Opt. 36, 1–6 (1997).
[CrossRef]

Guattari, G.

G. Ciccotti, P. DeSantis, G. Guattari, C. Palma, “Propagation of partially coherent beams in a periodic sequence of lenses and Gaussian apertures,” Pure Appl. Opt. 3, 561–571 (1994).
[CrossRef]

Hasama, T.

K. Yamada, K. Miyazaki, T. Hasama, T. Sato, “1-ns high-power high-repetitive excimer laser oscillator,” IEEE J. Quantum Electron. 24, 177–182 (1988).
[CrossRef]

Johnston, T. F.

A. Siegman, M. W. Sasnett, T. F. Johnston, “Choice of the clip level for beam width measurements using knife-edge techniques,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).
[CrossRef]

Knight, L. V.

Lavigne, P.

Lo, D.

D. Lo, “Electrical characteristics of small active volume (1 cm3) discharge-pumped XeCl laser,” Opt. Quantum Electron. 20, 257–262 (1988).
[CrossRef]

Mascello, A.

P. De Santis, A. Mascello, C. Palma, M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802–812 (1996).
[CrossRef]

V. Bagini, A. Mascello, C. Palma, M. R. Perrone, “Transient states analysis of a partially coherent laser beam propagating through a Gaussian cavity,” IEEE J. Quantum Electron. 31, 1572–1578 (1995).
[CrossRef]

McCarthy, N.

Miyazaki, K.

K. Yamada, K. Miyazaki, T. Hasama, T. Sato, “1-ns high-power high-repetitive excimer laser oscillator,” IEEE J. Quantum Electron. 24, 177–182 (1988).
[CrossRef]

Nikitenko, A. G.

A. G. Nikitenko, “Novel design and method of fabrication of inhomogeneous mirrors,” Pure Appl. Opt. 3, 485–490 (1994).
[CrossRef]

Palma, C.

P. De Santis, A. Mascello, C. Palma, M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802–812 (1996).
[CrossRef]

V. Bagini, A. Mascello, C. Palma, M. R. Perrone, “Transient states analysis of a partially coherent laser beam propagating through a Gaussian cavity,” IEEE J. Quantum Electron. 31, 1572–1578 (1995).
[CrossRef]

M. R. Perrone, C. Palma, V. Biagini, A. Piegari, D. Flori, S. Scaglione, “Theoretical and experimental determination of single round-trip beam parameters in a XeCl laser,” J. Opt. Soc. Am. A 12, 991–998 (1995).
[CrossRef]

G. Ciccotti, P. DeSantis, G. Guattari, C. Palma, “Propagation of partially coherent beams in a periodic sequence of lenses and Gaussian apertures,” Pure Appl. Opt. 3, 561–571 (1994).
[CrossRef]

Paré, C.

P. A. Belanger, C. Paré, “Unstable laser resonators with a specified output profile by using a graded-reflectivity mirror: geometrical optics limit,” Opt. Commun. 109, 507–517 (1994).
[CrossRef]

Perrone, M. R.

C. Giuri, M. R. Perrone, V. Piccinno, “Output coupler design of unstable cavities for excimer lasers,” Appl. Opt. 36, 1–6 (1997).
[CrossRef]

P. De Santis, A. Mascello, C. Palma, M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802–812 (1996).
[CrossRef]

V. Bagini, A. Mascello, C. Palma, M. R. Perrone, “Transient states analysis of a partially coherent laser beam propagating through a Gaussian cavity,” IEEE J. Quantum Electron. 31, 1572–1578 (1995).
[CrossRef]

M. R. Perrone, C. Palma, V. Biagini, A. Piegari, D. Flori, S. Scaglione, “Theoretical and experimental determination of single round-trip beam parameters in a XeCl laser,” J. Opt. Soc. Am. A 12, 991–998 (1995).
[CrossRef]

Piccinno, V.

C. Giuri, M. R. Perrone, V. Piccinno, “Output coupler design of unstable cavities for excimer lasers,” Appl. Opt. 36, 1–6 (1997).
[CrossRef]

Piché, M.

Piegari, A.

Reng, N.

N. Reng, B. Eppich, “Definition and measurements of high-power laser beam parameters,” Opt. Quantum Electron. 24, S973–S992 (1992).
[CrossRef]

Sasnett, M. W.

A. Siegman, M. W. Sasnett, T. F. Johnston, “Choice of the clip level for beam width measurements using knife-edge techniques,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).
[CrossRef]

Sato, T.

K. Yamada, K. Miyazaki, T. Hasama, T. Sato, “1-ns high-power high-repetitive excimer laser oscillator,” IEEE J. Quantum Electron. 24, 177–182 (1988).
[CrossRef]

Scaglione, S.

Siegman, A.

A. Siegman, M. W. Sasnett, T. F. Johnston, “Choice of the clip level for beam width measurements using knife-edge techniques,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 23, p. 913.

Walsh, D. M.

Yamada, K.

K. Yamada, K. Miyazaki, T. Hasama, T. Sato, “1-ns high-power high-repetitive excimer laser oscillator,” IEEE J. Quantum Electron. 24, 177–182 (1988).
[CrossRef]

Appl. Opt. (4)

IEEE J. Quantum Electron. (4)

K. Yamada, K. Miyazaki, T. Hasama, T. Sato, “1-ns high-power high-repetitive excimer laser oscillator,” IEEE J. Quantum Electron. 24, 177–182 (1988).
[CrossRef]

V. Bagini, A. Mascello, C. Palma, M. R. Perrone, “Transient states analysis of a partially coherent laser beam propagating through a Gaussian cavity,” IEEE J. Quantum Electron. 31, 1572–1578 (1995).
[CrossRef]

P. De Santis, A. Mascello, C. Palma, M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802–812 (1996).
[CrossRef]

A. Siegman, M. W. Sasnett, T. F. Johnston, “Choice of the clip level for beam width measurements using knife-edge techniques,” IEEE J. Quantum Electron. 27, 1098–1104 (1991).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

P. A. Belanger, C. Paré, “Unstable laser resonators with a specified output profile by using a graded-reflectivity mirror: geometrical optics limit,” Opt. Commun. 109, 507–517 (1994).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (2)

N. Reng, B. Eppich, “Definition and measurements of high-power laser beam parameters,” Opt. Quantum Electron. 24, S973–S992 (1992).
[CrossRef]

D. Lo, “Electrical characteristics of small active volume (1 cm3) discharge-pumped XeCl laser,” Opt. Quantum Electron. 20, 257–262 (1988).
[CrossRef]

Pure Appl. Opt. (2)

G. Ciccotti, P. DeSantis, G. Guattari, C. Palma, “Propagation of partially coherent beams in a periodic sequence of lenses and Gaussian apertures,” Pure Appl. Opt. 3, 561–571 (1994).
[CrossRef]

A. G. Nikitenko, “Novel design and method of fabrication of inhomogeneous mirrors,” Pure Appl. Opt. 3, 485–490 (1994).
[CrossRef]

Other (1)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 23, p. 913.

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Figures (14)

Fig. 1
Fig. 1

Cross section of the XeCl laser chamber and schematic diagram of the electrical circuit. R1, charging resistance; H.V., high voltage (see text for discussion of other notation).

Fig. 2
Fig. 2

Squared spot-size values of the laser beam focused by a 50-cm focal-length lens versus the distance z from the focal plane: along the discharge direction (y) (bottom) and along the x direction (top). The circles represent experimental measurements, and the solid curve represents Eq. (1).

Fig. 3
Fig. 3

Experimental setup. I’s, intracavity apertures.

Fig. 4
Fig. 4

Time evolution of the laser pulse provided by the cavity with the 2.2-mm spot-size Gaussian mirror. To represents the time chosen to get the first time-resolved far-field intensity profile.

Fig. 5
Fig. 5

Normalized intensity profile of the laser beam provided by the cavity with the 2.2-mm spot-size Gaussian mirror along the discharge direction (open circles) and along x (filled circles). The solid curve represents the best-fitting super-Gaussian curve when n = 6 and w = 2.2 mm are assumed.

Fig. 6
Fig. 6

Squared spot-size values of the laser beam provided by the cavity with the 2.2-mm spot-size Gaussian mirror focused by a 1.3-m focal-length lens versus the distance z from the focal plane along the discharge direction (y) and along the x direction. The circles represent experimental measurements, and the solid curves represent Eq. (1).

Fig. 7
Fig. 7

Normalized intensity profile of the laser beam at the focal plane of the 1.3-m focusing lens along (a), (b) the x, (c), (d) the y direction for different times (TiTo).

Fig. 8
Fig. 8

Temporal evolution of the divergence of the laser beam provided by (a) the cavity with the 2.2-mm spot-size Gaussian mirror, (b) the conventional plane-parallel cavity as a function of the time (TTo) along the discharge direction (open circles) and along the x direction (filled circles).

Fig. 9
Fig. 9

Time evolution of the laser pulse provided by the conventional plane-parallel cavity with 4.6-mm-diameter intracavity apertures. To represents the time chosen to obtain the first time-resolved far-field intensity profile.

Fig. 10
Fig. 10

Squared spot-size values of the laser beam provided by the plane-parallel cavity with 4.6-mm-diameter intracavity apertures focused by a 1.3 m focal-length lens versus the distance z from the focal plane along the discharge direction y (open circles) and along the x direction. The circles represent experimental measurements, and the solid curves represent Eq. (1).

Fig. 11
Fig. 11

Temporal evolution of the laser pulse extracted by the cavity with the 4.2-mm spot-size Gaussian mirror at Va = 35 kV. To represents the time chosen to obtain the first time-resolved far-field intensity profile.

Fig. 12
Fig. 12

Normalized intensity profile of the laser beam extracted by the cavity with the 4.2-mm spot-size Gaussian mirror along the discharge direction (open circles) and along x (filled circles). The solid curve represents the best-fitting super-Gaussian curve when n = 8 and w = 4.2 mm are assumed.

Fig. 13
Fig. 13

Temporal evolution of the divergence of the laser beam extracted by (a) the cavity with the 4.2-mm spot-size Gaussian mirror, (b) the conventional plane-parallel cavity as a function of the time (TTo) along the discharge direction (open circles) and along the x direction (filled circles).

Fig. 14
Fig. 14

Time evolution of the laser pulse provided by the plane-parallel cavity with 9-mm-diameter intracavity apertures at Va = 35 kV. To represents the time chosen to obtain the first time-resolved far-field intensity profile.

Tables (2)

Tables Icon

Table 1 Comparison between the Parameters of the 2.2-mm Spot-Size Beams

Tables Icon

Table 2 Comparison between the Parameters of the 4.2-mm Spot-Size Beams

Equations (4)

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w x , y 2 ( z ) = w o x , y 2 [ 1 + ( z / Z r x , y ) 2 ] ,
w o x , y = w x , y ( z = 0 ) ,
Z r x , y = π w o x , y 2 / ( λ M x , y 2 ) ,
σ I 2 = [ i r i 2 I ( r i ) ] / [ i I ( r i ) ] ,

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