Abstract

A simple derivation of the cavity dispersion equation for high-gain pulsed lasers, Δλ ≈ Δθ(∂θ/∂λ)−1, is provided by using Dirac’s notation for probability amplitudes as applied to the analysis of dispersive cavities.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. C. Strome, J. P. Webb, “Flashtube-pumped dye laser with multiple-prism tuning,” Appl. Opt. 10, 1348–1353 (1971).
    [CrossRef] [PubMed]
  2. T. W. Hänsch, “Repetitively pulsed tunable dye laser for high resolution spectroscopy,” Appl. Opt. 11, 895–898 (1972).
    [CrossRef] [PubMed]
  3. D. C. Hanna, P. A. Karkkainen, R. Wyatt, “A simple beam expander for frequency narrowing of dye lasers,” Opt. Quantum Electron. 7, 115–119 (1975).
    [CrossRef]
  4. F. P. Schäfer, “Principles of dye laser operation,” in Dye Lasers, F. P. Schäfer, ed. (Springer-Verlag, Berlin, 1990), pp. 1–89.
  5. F. J. Duarte, “Narrow-linewidth pulsed dye laser oscillators,” in Dye Laser Principles, F. J. Duarte, L. W. Hillman, eds. (Academic, New York, 1990), pp. 133–183.
  6. A. F. Bernhardt, P. Rasmussen, “Design criteria and operating characteristics of a single-mode pulsed dye laser,” Appl. Phys. B 26, 141–146 (1981).
    [CrossRef]
  7. F. J. Duarte, J. A. Piper, “Narrow linewidth high prf copper laser-pumped dye-laser oscillators,” Appl. Opt. 23, 1391–1394 (1984).
    [CrossRef] [PubMed]
  8. F. J. Duarte, “Multiple-prism Littrow and grazing-incidence pulsed CO2 lasers,” Appl. Opt. 24, 1244–1245 (1985).
    [CrossRef] [PubMed]
  9. J. K. Robertson, Introduction to Optics: Geometrical and Physical (Van Nostrand, New York, 1955).
  10. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).
  11. J. Meaburn, Detection and Spectrometry of Faint Light (Reidel, Boston, Mass., 1976).
  12. R. Kingslake, Optical System Design (Academic, New York, 1983).
  13. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford, London, 1978).
  14. R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1971), Vol. 3; R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
  15. This probability approaches unity for the special case of Δθ ≈ ΔθD so that the constant is κ1 ≈ λ/(πw) and for all other cases |〈ϕ1,m|s〉|2 < 1.
  16. P. N. Everett, “Flashlamp-excited dye lasers,” in High Power Dye Lasers, F. J. Duarte, ed. (Springer-Verlag, Berlin, 1991), pp. 183–245.
  17. Similar arguments to those used to estimate κ1 can be applied to approximate κ2 and κ3.
  18. F. J. Duarte, “Dispersive dye lasers,” in High Power Dye Lasers, F. J. Duarte, ed. (Springer-Verlag, Berlin, 1991), pp. 7–43.

1985

1984

1981

A. F. Bernhardt, P. Rasmussen, “Design criteria and operating characteristics of a single-mode pulsed dye laser,” Appl. Phys. B 26, 141–146 (1981).
[CrossRef]

1975

D. C. Hanna, P. A. Karkkainen, R. Wyatt, “A simple beam expander for frequency narrowing of dye lasers,” Opt. Quantum Electron. 7, 115–119 (1975).
[CrossRef]

1972

1971

Bernhardt, A. F.

A. F. Bernhardt, P. Rasmussen, “Design criteria and operating characteristics of a single-mode pulsed dye laser,” Appl. Phys. B 26, 141–146 (1981).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

Dirac, P. A. M.

P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford, London, 1978).

Duarte, F. J.

F. J. Duarte, “Multiple-prism Littrow and grazing-incidence pulsed CO2 lasers,” Appl. Opt. 24, 1244–1245 (1985).
[CrossRef] [PubMed]

F. J. Duarte, J. A. Piper, “Narrow linewidth high prf copper laser-pumped dye-laser oscillators,” Appl. Opt. 23, 1391–1394 (1984).
[CrossRef] [PubMed]

F. J. Duarte, “Narrow-linewidth pulsed dye laser oscillators,” in Dye Laser Principles, F. J. Duarte, L. W. Hillman, eds. (Academic, New York, 1990), pp. 133–183.

F. J. Duarte, “Dispersive dye lasers,” in High Power Dye Lasers, F. J. Duarte, ed. (Springer-Verlag, Berlin, 1991), pp. 7–43.

Everett, P. N.

P. N. Everett, “Flashlamp-excited dye lasers,” in High Power Dye Lasers, F. J. Duarte, ed. (Springer-Verlag, Berlin, 1991), pp. 183–245.

Feynman, R. P.

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1971), Vol. 3; R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).

Hanna, D. C.

D. C. Hanna, P. A. Karkkainen, R. Wyatt, “A simple beam expander for frequency narrowing of dye lasers,” Opt. Quantum Electron. 7, 115–119 (1975).
[CrossRef]

Hänsch, T. W.

Karkkainen, P. A.

D. C. Hanna, P. A. Karkkainen, R. Wyatt, “A simple beam expander for frequency narrowing of dye lasers,” Opt. Quantum Electron. 7, 115–119 (1975).
[CrossRef]

Kingslake, R.

R. Kingslake, Optical System Design (Academic, New York, 1983).

Leighton, R. B.

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1971), Vol. 3; R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).

Meaburn, J.

J. Meaburn, Detection and Spectrometry of Faint Light (Reidel, Boston, Mass., 1976).

Piper, J. A.

Rasmussen, P.

A. F. Bernhardt, P. Rasmussen, “Design criteria and operating characteristics of a single-mode pulsed dye laser,” Appl. Phys. B 26, 141–146 (1981).
[CrossRef]

Robertson, J. K.

J. K. Robertson, Introduction to Optics: Geometrical and Physical (Van Nostrand, New York, 1955).

Sands, M.

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1971), Vol. 3; R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).

Schäfer, F. P.

F. P. Schäfer, “Principles of dye laser operation,” in Dye Lasers, F. P. Schäfer, ed. (Springer-Verlag, Berlin, 1990), pp. 1–89.

Strome, F. C.

Webb, J. P.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

Wyatt, R.

D. C. Hanna, P. A. Karkkainen, R. Wyatt, “A simple beam expander for frequency narrowing of dye lasers,” Opt. Quantum Electron. 7, 115–119 (1975).
[CrossRef]

Appl. Opt.

Appl. Phys. B

A. F. Bernhardt, P. Rasmussen, “Design criteria and operating characteristics of a single-mode pulsed dye laser,” Appl. Phys. B 26, 141–146 (1981).
[CrossRef]

Opt. Quantum Electron.

D. C. Hanna, P. A. Karkkainen, R. Wyatt, “A simple beam expander for frequency narrowing of dye lasers,” Opt. Quantum Electron. 7, 115–119 (1975).
[CrossRef]

Other

F. P. Schäfer, “Principles of dye laser operation,” in Dye Lasers, F. P. Schäfer, ed. (Springer-Verlag, Berlin, 1990), pp. 1–89.

F. J. Duarte, “Narrow-linewidth pulsed dye laser oscillators,” in Dye Laser Principles, F. J. Duarte, L. W. Hillman, eds. (Academic, New York, 1990), pp. 133–183.

J. K. Robertson, Introduction to Optics: Geometrical and Physical (Van Nostrand, New York, 1955).

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975).

J. Meaburn, Detection and Spectrometry of Faint Light (Reidel, Boston, Mass., 1976).

R. Kingslake, Optical System Design (Academic, New York, 1983).

P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford, London, 1978).

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1971), Vol. 3; R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).

This probability approaches unity for the special case of Δθ ≈ ΔθD so that the constant is κ1 ≈ λ/(πw) and for all other cases |〈ϕ1,m|s〉|2 < 1.

P. N. Everett, “Flashlamp-excited dye lasers,” in High Power Dye Lasers, F. J. Duarte, ed. (Springer-Verlag, Berlin, 1991), pp. 183–245.

Similar arguments to those used to estimate κ1 can be applied to approximate κ2 and κ3.

F. J. Duarte, “Dispersive dye lasers,” in High Power Dye Lasers, F. J. Duarte, ed. (Springer-Verlag, Berlin, 1991), pp. 7–43.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Schematic of the unfolded dispersive assembly of the cavity integrated by a multiple-prism expander and grating. Single-pass radiation exits the gain medium at s and is incident at an angle ϕ1,m at the prismatic expander. The dispersive assembly A allows emission within a resonant narrow-bandwidth range to exit the prisms at the angle ϕ1,m′. Radiation that exits at this angle proceeds to return to the narrow-band amplification beam axis at the gain medium (s′).

Fig. 2
Fig. 2

Expanded beam (S) illuminates a large number of slits of a transmission grating (J). The photons then proceed to reach X, where interference is observed. Here, the beam expander is assumed to be of a dispersionless design.5

Equations (20)

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

( θ / λ ) = M ( θ / λ ) G + 2 m = 1 r ( ± 1 ) ( j = 1 m k 1 , j ) tan ψ 1 , m ( n m / λ ) ,
M = m = 1 r k 1 , m
L 1 , m = L 2 , ( m - 1 ) + [ 1 - L 2 , ( m - 1 ) ] R 1 , m ,
R 1 , m = tan 2 ( ϕ 1 , m - ψ 1 , m ) / tan 2 ( ϕ 1 , m + ψ 1 , m )
s A s = ϕ 1 , m s ϕ 1 , m ϕ 1 , m A ϕ 1 , m ϕ 1 , m s .
s A s 2 = s ϕ 1 , m 2 ϕ 1 , m A ϕ 1 , m 2 ϕ 1 , m s 2 .
ϕ 1 , m s 2 = κ 1 ( 1 / Δ θ ) .
ϕ 1 , m A ϕ 1 , m 2 = κ 2 ( θ / λ ) .
s ϕ 1 , m 2 1.
s A s 2 = κ 3 ( 1 / Δ λ ) ,
Δ λ = Δ θ ( θ / λ ) - 1
x s = j = 1 N x j j s .
x s 2 = j = 1 N Ψ ( r j ) 2 + 2 j = 1 N Ψ ( r j ) × [ m = j + 1 N Ψ ( r m ) cos ( Ω m - Ω j ) ] ,
1 s = 2 s = 3 s = = N s = Ψ ( r s , j ) exp ( - i θ j ) = 1 ,
x s 2 = j = 1 N Ψ ( r j , x ) 2 + 2 j = 1 N Ψ ( r j , x ) × [ m = j + 1 N Ψ ( r m , x ) cos ( ϕ m - ϕ j ) ] .
cos ( ϕ m - ϕ j ) = cos k · r = cos k L m - L m - 1 ,
L m - L m - 1 = d m sin θ m .
n λ = 2 d sin θ .
n Δ λ 2 d Δ θ { 1 - ( 3 θ 2 / 3 ! ) + ( 5 θ 4 / 5 ! ) . } .
Δ λ Δ θ ( θ / λ ) - 1 { 1 - ( θ 2 / 2 ! ) + ( θ 4 / 4 ! ) } ( 1 / cos θ ) .

Metrics