Abstract

The angular dispersion of spatially Gaussian laser pulses, unlike for plane waves, changes with the distance between the disperser and the observer and between the beam waist and the disperser. The formula that is derived is experimentally verified by use of a high-precision measurement technique. Because the angular dispersion of a Gaussian beam is substantially different from that of a plane wave after the same disperser, the phenomenon may be of special interest for short-pulsed laser systems, for which alignment of the stretcher–compressor system for zero residual angular dispersion is essential.

© 2002 Optical Society of America

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References

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  1. R. L. Fork, O. E. Martinez, and J. P. Gordon, Opt. Lett. 9, 150 (1984).
    [Crossref] [PubMed]
  2. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1996), Chap. 2.
  3. A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
    [Crossref]
  4. O. E. Martinez, Opt. Soc. Am. B 3, 929 (1986).
    [Crossref]
  5. O. E. Martinez, Opt. Commun. 59, 229 (1986).
    [Crossref]
  6. F. A. Jenkins and H. A. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976).
  7. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  8. Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
    [Crossref]
  9. K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, Appl. Phys. B 74, S259 (2002).
    [Crossref]
  10. Z. Bor, B. Rácz, G. Szabó, M. Hilbert, and H. A. Hazim, Opt. Eng. 32, 2501 (1993).
    [Crossref]
  11. J. Hebling, Opt. Quantum Electron. 28, 1759 (1996).
    [Crossref]
  12. K. Osvay and I. N. Ross, Opt. Commun. 105, 271 (1994).
    [Crossref]
  13. K. Osvay and I. N. Ross, Opt. Commun. 154, 390 (1998).
    [Crossref]
  14. C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, IEEE J. Quantum Electron. 30, 1662 (1994).
    [Crossref]

2002 (1)

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, Appl. Phys. B 74, S259 (2002).
[Crossref]

1998 (1)

K. Osvay and I. N. Ross, Opt. Commun. 154, 390 (1998).
[Crossref]

1996 (1)

J. Hebling, Opt. Quantum Electron. 28, 1759 (1996).
[Crossref]

1995 (1)

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[Crossref]

1994 (2)

K. Osvay and I. N. Ross, Opt. Commun. 105, 271 (1994).
[Crossref]

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, IEEE J. Quantum Electron. 30, 1662 (1994).
[Crossref]

1993 (2)

Z. Bor, B. Rácz, G. Szabó, M. Hilbert, and H. A. Hazim, Opt. Eng. 32, 2501 (1993).
[Crossref]

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[Crossref]

1986 (2)

O. E. Martinez, Opt. Soc. Am. B 3, 929 (1986).
[Crossref]

O. E. Martinez, Opt. Commun. 59, 229 (1986).
[Crossref]

1984 (1)

Benkö, Z.

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[Crossref]

Blanchot, N.

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, IEEE J. Quantum Electron. 30, 1662 (1994).
[Crossref]

Bor, Z.

Z. Bor, B. Rácz, G. Szabó, M. Hilbert, and H. A. Hazim, Opt. Eng. 32, 2501 (1993).
[Crossref]

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Diels, J.-C.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1996), Chap. 2.

Fiorini, C.

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, IEEE J. Quantum Electron. 30, 1662 (1994).
[Crossref]

Fork, R. L.

Gordon, J. P.

Hazim, H. A.

Z. Bor, B. Rácz, G. Szabó, M. Hilbert, and H. A. Hazim, Opt. Eng. 32, 2501 (1993).
[Crossref]

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[Crossref]

Hebling, J.

J. Hebling, Opt. Quantum Electron. 28, 1759 (1996).
[Crossref]

Hilbert, M.

Z. Bor, B. Rácz, G. Szabó, M. Hilbert, and H. A. Hazim, Opt. Eng. 32, 2501 (1993).
[Crossref]

Horváth, Z. L.

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[Crossref]

Jenkins, F. A.

F. A. Jenkins and H. A. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976).

Kovács, A. P.

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, Appl. Phys. B 74, S259 (2002).
[Crossref]

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[Crossref]

Kurdi, G.

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, Appl. Phys. B 74, S259 (2002).
[Crossref]

Martinez, O. E.

O. E. Martinez, Opt. Soc. Am. B 3, 929 (1986).
[Crossref]

O. E. Martinez, Opt. Commun. 59, 229 (1986).
[Crossref]

R. L. Fork, O. E. Martinez, and J. P. Gordon, Opt. Lett. 9, 150 (1984).
[Crossref] [PubMed]

Migus, A.

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, IEEE J. Quantum Electron. 30, 1662 (1994).
[Crossref]

Osvay, K.

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, Appl. Phys. B 74, S259 (2002).
[Crossref]

K. Osvay and I. N. Ross, Opt. Commun. 154, 390 (1998).
[Crossref]

K. Osvay and I. N. Ross, Opt. Commun. 105, 271 (1994).
[Crossref]

Rácz, B.

Z. Bor, B. Rácz, G. Szabó, M. Hilbert, and H. A. Hazim, Opt. Eng. 32, 2501 (1993).
[Crossref]

Ross, I. N.

K. Osvay and I. N. Ross, Opt. Commun. 154, 390 (1998).
[Crossref]

K. Osvay and I. N. Ross, Opt. Commun. 105, 271 (1994).
[Crossref]

Rouyer, C.

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, IEEE J. Quantum Electron. 30, 1662 (1994).
[Crossref]

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1996), Chap. 2.

Sauteret, C.

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, IEEE J. Quantum Electron. 30, 1662 (1994).
[Crossref]

Seznec, S.

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, IEEE J. Quantum Electron. 30, 1662 (1994).
[Crossref]

Szabó, G.

Z. Bor, B. Rácz, G. Szabó, M. Hilbert, and H. A. Hazim, Opt. Eng. 32, 2501 (1993).
[Crossref]

Varjú, K.

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, Appl. Phys. B 74, S259 (2002).
[Crossref]

Weiner, A. M.

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[Crossref]

White, H. A.

F. A. Jenkins and H. A. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Appl. Phys. B (1)

K. Varjú, A. P. Kovács, G. Kurdi, and K. Osvay, Appl. Phys. B 74, S259 (2002).
[Crossref]

IEEE J. Quantum Electron. (1)

C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, IEEE J. Quantum Electron. 30, 1662 (1994).
[Crossref]

Opt. Commun. (3)

K. Osvay and I. N. Ross, Opt. Commun. 105, 271 (1994).
[Crossref]

K. Osvay and I. N. Ross, Opt. Commun. 154, 390 (1998).
[Crossref]

O. E. Martinez, Opt. Commun. 59, 229 (1986).
[Crossref]

Opt. Eng. (2)

Z. Bor, B. Rácz, G. Szabó, M. Hilbert, and H. A. Hazim, Opt. Eng. 32, 2501 (1993).
[Crossref]

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[Crossref]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

J. Hebling, Opt. Quantum Electron. 28, 1759 (1996).
[Crossref]

Opt. Soc. Am. B (1)

O. E. Martinez, Opt. Soc. Am. B 3, 929 (1986).
[Crossref]

Prog. Quantum Electron. (1)

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[Crossref]

Other (3)

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1996), Chap. 2.

F. A. Jenkins and H. A. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

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Figures (4)

Fig. 1
Fig. 1

Angular dispersion in a beam gives rise to nonparallel phase fronts of different wavelengths.

Fig. 2
Fig. 2

The angle between the phase fronts ΔΘ is different from the angle of propagation ΔΘ. (Angles are exaggerated for clarity.)

Fig. 3
Fig. 3

Notation for a Gaussian beam incident upon a prism: BW, beam waist.

Fig. 4
Fig. 4

Measured (symbols) and calculated (dashed curves) values of angular dispersion θ/λ as functions of incidence angle at (a) three values of d at s=0.6 m and (b) three values of s at d=4.5 m, w0=120 µm, λ0=800 nm.

Equations (7)

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ΔΘ=αΔγ+ηΔλ,
qd=q0+d,  qd+s=q0+d+s.
qd+s=d+α2s+iLR/α2.
w0=w0/α,
d=d/α2.
R=d+s+LR2d+s=1α2d+α2s+LR2d+α2s.
ΔΘ=ΔΘ1-sR=ΔΘdd+α2s+LR2d+α2s2+LR2.

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