Abstract

We investigate the possibility of stacking light pulses produced by a free-electron laser with wavelengths in the millimeter regime in an external cavity. An aperture in one of the mirrors is used to couple the radiation into the cavity. The field is extracted by means of an optical switch, such as a YAG-illuminated semiconductor slab. Some general design considerations of the cavity are discussed, and results of numerical simulations are shown as verification of the applicability of the principle.

© 1995 Optical Society of America

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  1. J. Burghoorn, J. P. Kaminski, R. C. Strijbos, T. O. Klassen, and W. Th. Wenckebach, "Generation of subnanosecond high power far infrared pulses using a FEL pumped passive resonator," Nucl. Instr. Meth. A 318, 85 (1992).
    [CrossRef]
  2. B. Faatz, E. H. Haselhoff, V. I. Zhulin, and P. W. van Amersfoort, "Pulse Stacking in FELIX," Nucl. Instr. Meth. A 318, 136 ABS (1994).
  3. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  4. D. E. McCumber, "Eigenmodes of a symmetric cylindrical confocal laser resonator and their perturbation by outputcoupling apertures," Bell Syst. Tech. J. 333 (1965).
  5. G. A. Barnett, S. V. Benson, and J. M. J. Madey, "Warm cavity modes of free-electron laser resonators with on-axis holes," IEEE J. Quantum Electron. 27, 2522 (1993).
  6. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, & Winston, New York, 1971), p. 61.
  7. G. Bourianoff, B. Moore, M. Rosenbluth, F. Waelbroeck, H. Waelbroeck, and H. V. Wong, "Adaptive eigenmode expansion for 3-D FEL simulations, Nucl. Inst. Meth. A 272, 340 (1988).
    [CrossRef]
  8. R. W. B. Best and B. Faatz, "Gauss–Laguerre modes in a high-gain FEL" J. Phys. D. 23, 1337 (1990).
    [CrossRef]
  9. R. H. Pantell, J. Feinstein, and A. H. Ho, "Interferometer mirrors with holes on-axis," Nucl. Instr. Meth. A 296, 638 (1990).
    [CrossRef]
  10. B. Faatz, R. W. B. Best, D. Oepts, and P. W. Amersfoort, "Hole coupling in free electron lasers," IEEE J. Quantum Electron. 29, 2229 (1993).
    [CrossRef]
  11. A. A. Andreev, V. I. Zhulin, A. P. Mikhailovsky, and K. Yu. Platonov, "Transverse structure of optical klystron radiation," Quantum Electron. (USSR) 18, 795 (1991).
  12. V. I. Zhulin, "Field transverse structure in free electron resonator with a hole in exit mirror," in Transverse Patterns in Nonlinear Optics, N. N. Rosanov, ed., Proc. Soc. Photo- Opt. Instrum. Eng. 1840, p. 244 (1991).
    [CrossRef]
  13. G. H. C. van Werkhoven, B. Faatz, and T. J. Schep, "Slippage and scattering of light pulses in hole-coupled free-electron lasers," Phys. Rev. E 50, 4063 (1994).
    [CrossRef]

1994 (2)

B. Faatz, E. H. Haselhoff, V. I. Zhulin, and P. W. van Amersfoort, "Pulse Stacking in FELIX," Nucl. Instr. Meth. A 318, 136 ABS (1994).

G. H. C. van Werkhoven, B. Faatz, and T. J. Schep, "Slippage and scattering of light pulses in hole-coupled free-electron lasers," Phys. Rev. E 50, 4063 (1994).
[CrossRef]

1993 (2)

G. A. Barnett, S. V. Benson, and J. M. J. Madey, "Warm cavity modes of free-electron laser resonators with on-axis holes," IEEE J. Quantum Electron. 27, 2522 (1993).

B. Faatz, R. W. B. Best, D. Oepts, and P. W. Amersfoort, "Hole coupling in free electron lasers," IEEE J. Quantum Electron. 29, 2229 (1993).
[CrossRef]

1992 (1)

J. Burghoorn, J. P. Kaminski, R. C. Strijbos, T. O. Klassen, and W. Th. Wenckebach, "Generation of subnanosecond high power far infrared pulses using a FEL pumped passive resonator," Nucl. Instr. Meth. A 318, 85 (1992).
[CrossRef]

1991 (1)

A. A. Andreev, V. I. Zhulin, A. P. Mikhailovsky, and K. Yu. Platonov, "Transverse structure of optical klystron radiation," Quantum Electron. (USSR) 18, 795 (1991).

1990 (2)

R. W. B. Best and B. Faatz, "Gauss–Laguerre modes in a high-gain FEL" J. Phys. D. 23, 1337 (1990).
[CrossRef]

R. H. Pantell, J. Feinstein, and A. H. Ho, "Interferometer mirrors with holes on-axis," Nucl. Instr. Meth. A 296, 638 (1990).
[CrossRef]

1988 (1)

G. Bourianoff, B. Moore, M. Rosenbluth, F. Waelbroeck, H. Waelbroeck, and H. V. Wong, "Adaptive eigenmode expansion for 3-D FEL simulations, Nucl. Inst. Meth. A 272, 340 (1988).
[CrossRef]

1965 (1)

D. E. McCumber, "Eigenmodes of a symmetric cylindrical confocal laser resonator and their perturbation by outputcoupling apertures," Bell Syst. Tech. J. 333 (1965).

Amersfoort, P. W.

B. Faatz, R. W. B. Best, D. Oepts, and P. W. Amersfoort, "Hole coupling in free electron lasers," IEEE J. Quantum Electron. 29, 2229 (1993).
[CrossRef]

Amersfoort, P. W. van

B. Faatz, E. H. Haselhoff, V. I. Zhulin, and P. W. van Amersfoort, "Pulse Stacking in FELIX," Nucl. Instr. Meth. A 318, 136 ABS (1994).

Andreev, A. A.

A. A. Andreev, V. I. Zhulin, A. P. Mikhailovsky, and K. Yu. Platonov, "Transverse structure of optical klystron radiation," Quantum Electron. (USSR) 18, 795 (1991).

Barnett, G. A.

G. A. Barnett, S. V. Benson, and J. M. J. Madey, "Warm cavity modes of free-electron laser resonators with on-axis holes," IEEE J. Quantum Electron. 27, 2522 (1993).

Benson, S. V.

G. A. Barnett, S. V. Benson, and J. M. J. Madey, "Warm cavity modes of free-electron laser resonators with on-axis holes," IEEE J. Quantum Electron. 27, 2522 (1993).

Best, R. W. B.

B. Faatz, R. W. B. Best, D. Oepts, and P. W. Amersfoort, "Hole coupling in free electron lasers," IEEE J. Quantum Electron. 29, 2229 (1993).
[CrossRef]

R. W. B. Best and B. Faatz, "Gauss–Laguerre modes in a high-gain FEL" J. Phys. D. 23, 1337 (1990).
[CrossRef]

Bourianoff, G.

G. Bourianoff, B. Moore, M. Rosenbluth, F. Waelbroeck, H. Waelbroeck, and H. V. Wong, "Adaptive eigenmode expansion for 3-D FEL simulations, Nucl. Inst. Meth. A 272, 340 (1988).
[CrossRef]

Burghoorn, J.

J. Burghoorn, J. P. Kaminski, R. C. Strijbos, T. O. Klassen, and W. Th. Wenckebach, "Generation of subnanosecond high power far infrared pulses using a FEL pumped passive resonator," Nucl. Instr. Meth. A 318, 85 (1992).
[CrossRef]

Faatz, B.

B. Faatz, E. H. Haselhoff, V. I. Zhulin, and P. W. van Amersfoort, "Pulse Stacking in FELIX," Nucl. Instr. Meth. A 318, 136 ABS (1994).

G. H. C. van Werkhoven, B. Faatz, and T. J. Schep, "Slippage and scattering of light pulses in hole-coupled free-electron lasers," Phys. Rev. E 50, 4063 (1994).
[CrossRef]

B. Faatz, R. W. B. Best, D. Oepts, and P. W. Amersfoort, "Hole coupling in free electron lasers," IEEE J. Quantum Electron. 29, 2229 (1993).
[CrossRef]

R. W. B. Best and B. Faatz, "Gauss–Laguerre modes in a high-gain FEL" J. Phys. D. 23, 1337 (1990).
[CrossRef]

Feinstein, J.

R. H. Pantell, J. Feinstein, and A. H. Ho, "Interferometer mirrors with holes on-axis," Nucl. Instr. Meth. A 296, 638 (1990).
[CrossRef]

Haselhoff, E. H.

B. Faatz, E. H. Haselhoff, V. I. Zhulin, and P. W. van Amersfoort, "Pulse Stacking in FELIX," Nucl. Instr. Meth. A 318, 136 ABS (1994).

Ho, A. H.

R. H. Pantell, J. Feinstein, and A. H. Ho, "Interferometer mirrors with holes on-axis," Nucl. Instr. Meth. A 296, 638 (1990).
[CrossRef]

Kaminski, J. P.

J. Burghoorn, J. P. Kaminski, R. C. Strijbos, T. O. Klassen, and W. Th. Wenckebach, "Generation of subnanosecond high power far infrared pulses using a FEL pumped passive resonator," Nucl. Instr. Meth. A 318, 85 (1992).
[CrossRef]

Klassen, T. O.

J. Burghoorn, J. P. Kaminski, R. C. Strijbos, T. O. Klassen, and W. Th. Wenckebach, "Generation of subnanosecond high power far infrared pulses using a FEL pumped passive resonator," Nucl. Instr. Meth. A 318, 85 (1992).
[CrossRef]

Madey, J. M. J.

G. A. Barnett, S. V. Benson, and J. M. J. Madey, "Warm cavity modes of free-electron laser resonators with on-axis holes," IEEE J. Quantum Electron. 27, 2522 (1993).

McCumber, D. E.

D. E. McCumber, "Eigenmodes of a symmetric cylindrical confocal laser resonator and their perturbation by outputcoupling apertures," Bell Syst. Tech. J. 333 (1965).

Mikhailovsky, A. P.

A. A. Andreev, V. I. Zhulin, A. P. Mikhailovsky, and K. Yu. Platonov, "Transverse structure of optical klystron radiation," Quantum Electron. (USSR) 18, 795 (1991).

Moore, B.

G. Bourianoff, B. Moore, M. Rosenbluth, F. Waelbroeck, H. Waelbroeck, and H. V. Wong, "Adaptive eigenmode expansion for 3-D FEL simulations, Nucl. Inst. Meth. A 272, 340 (1988).
[CrossRef]

Oepts, D.

B. Faatz, R. W. B. Best, D. Oepts, and P. W. Amersfoort, "Hole coupling in free electron lasers," IEEE J. Quantum Electron. 29, 2229 (1993).
[CrossRef]

Pantell, R. H.

R. H. Pantell, J. Feinstein, and A. H. Ho, "Interferometer mirrors with holes on-axis," Nucl. Instr. Meth. A 296, 638 (1990).
[CrossRef]

Platonov, K. Yu.

A. A. Andreev, V. I. Zhulin, A. P. Mikhailovsky, and K. Yu. Platonov, "Transverse structure of optical klystron radiation," Quantum Electron. (USSR) 18, 795 (1991).

Rosenbluth, M.

G. Bourianoff, B. Moore, M. Rosenbluth, F. Waelbroeck, H. Waelbroeck, and H. V. Wong, "Adaptive eigenmode expansion for 3-D FEL simulations, Nucl. Inst. Meth. A 272, 340 (1988).
[CrossRef]

Schep, T. J.

G. H. C. van Werkhoven, B. Faatz, and T. J. Schep, "Slippage and scattering of light pulses in hole-coupled free-electron lasers," Phys. Rev. E 50, 4063 (1994).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Strijbos, R. C.

J. Burghoorn, J. P. Kaminski, R. C. Strijbos, T. O. Klassen, and W. Th. Wenckebach, "Generation of subnanosecond high power far infrared pulses using a FEL pumped passive resonator," Nucl. Instr. Meth. A 318, 85 (1992).
[CrossRef]

Waelbroeck, F.

G. Bourianoff, B. Moore, M. Rosenbluth, F. Waelbroeck, H. Waelbroeck, and H. V. Wong, "Adaptive eigenmode expansion for 3-D FEL simulations, Nucl. Inst. Meth. A 272, 340 (1988).
[CrossRef]

Waelbroeck, H.

G. Bourianoff, B. Moore, M. Rosenbluth, F. Waelbroeck, H. Waelbroeck, and H. V. Wong, "Adaptive eigenmode expansion for 3-D FEL simulations, Nucl. Inst. Meth. A 272, 340 (1988).
[CrossRef]

Wenckebach, W. Th.

J. Burghoorn, J. P. Kaminski, R. C. Strijbos, T. O. Klassen, and W. Th. Wenckebach, "Generation of subnanosecond high power far infrared pulses using a FEL pumped passive resonator," Nucl. Instr. Meth. A 318, 85 (1992).
[CrossRef]

Werkhoven, G. H. C. van

G. H. C. van Werkhoven, B. Faatz, and T. J. Schep, "Slippage and scattering of light pulses in hole-coupled free-electron lasers," Phys. Rev. E 50, 4063 (1994).
[CrossRef]

Wong, H. V.

G. Bourianoff, B. Moore, M. Rosenbluth, F. Waelbroeck, H. Waelbroeck, and H. V. Wong, "Adaptive eigenmode expansion for 3-D FEL simulations, Nucl. Inst. Meth. A 272, 340 (1988).
[CrossRef]

Yariv, A.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, & Winston, New York, 1971), p. 61.

Zhulin, V. I.

B. Faatz, E. H. Haselhoff, V. I. Zhulin, and P. W. van Amersfoort, "Pulse Stacking in FELIX," Nucl. Instr. Meth. A 318, 136 ABS (1994).

A. A. Andreev, V. I. Zhulin, A. P. Mikhailovsky, and K. Yu. Platonov, "Transverse structure of optical klystron radiation," Quantum Electron. (USSR) 18, 795 (1991).

V. I. Zhulin, "Field transverse structure in free electron resonator with a hole in exit mirror," in Transverse Patterns in Nonlinear Optics, N. N. Rosanov, ed., Proc. Soc. Photo- Opt. Instrum. Eng. 1840, p. 244 (1991).
[CrossRef]

Bell Syst. Tech. J. (1)

D. E. McCumber, "Eigenmodes of a symmetric cylindrical confocal laser resonator and their perturbation by outputcoupling apertures," Bell Syst. Tech. J. 333 (1965).

IEEE J. Quantum Electron. (2)

G. A. Barnett, S. V. Benson, and J. M. J. Madey, "Warm cavity modes of free-electron laser resonators with on-axis holes," IEEE J. Quantum Electron. 27, 2522 (1993).

B. Faatz, R. W. B. Best, D. Oepts, and P. W. Amersfoort, "Hole coupling in free electron lasers," IEEE J. Quantum Electron. 29, 2229 (1993).
[CrossRef]

J. Phys. D. (1)

R. W. B. Best and B. Faatz, "Gauss–Laguerre modes in a high-gain FEL" J. Phys. D. 23, 1337 (1990).
[CrossRef]

Nucl. Inst. Meth. A (1)

G. Bourianoff, B. Moore, M. Rosenbluth, F. Waelbroeck, H. Waelbroeck, and H. V. Wong, "Adaptive eigenmode expansion for 3-D FEL simulations, Nucl. Inst. Meth. A 272, 340 (1988).
[CrossRef]

Nucl. Instr. Meth. A (3)

R. H. Pantell, J. Feinstein, and A. H. Ho, "Interferometer mirrors with holes on-axis," Nucl. Instr. Meth. A 296, 638 (1990).
[CrossRef]

J. Burghoorn, J. P. Kaminski, R. C. Strijbos, T. O. Klassen, and W. Th. Wenckebach, "Generation of subnanosecond high power far infrared pulses using a FEL pumped passive resonator," Nucl. Instr. Meth. A 318, 85 (1992).
[CrossRef]

B. Faatz, E. H. Haselhoff, V. I. Zhulin, and P. W. van Amersfoort, "Pulse Stacking in FELIX," Nucl. Instr. Meth. A 318, 136 ABS (1994).

Phys. Rev. E (1)

G. H. C. van Werkhoven, B. Faatz, and T. J. Schep, "Slippage and scattering of light pulses in hole-coupled free-electron lasers," Phys. Rev. E 50, 4063 (1994).
[CrossRef]

Quantum Electron. (1)

A. A. Andreev, V. I. Zhulin, A. P. Mikhailovsky, and K. Yu. Platonov, "Transverse structure of optical klystron radiation," Quantum Electron. (USSR) 18, 795 (1991).

Other (3)

V. I. Zhulin, "Field transverse structure in free electron resonator with a hole in exit mirror," in Transverse Patterns in Nonlinear Optics, N. N. Rosanov, ed., Proc. Soc. Photo- Opt. Instrum. Eng. 1840, p. 244 (1991).
[CrossRef]

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, & Winston, New York, 1971), p. 61.

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Figures (5)

Fig. 1
Fig. 1

Layout of the pulse-stacking scheme.

Fig. 2
Fig. 2

Power (solid curve) and power normalized to the input power in the first 10 GL modes (dashed curve) versus the Rayleigh length of the input field. The radius of curvature of both mirrors is 27.6 mm.

Fig. 3
Fig. 3

Total power (filled circles) and power in the dominant mode (open circles) versus the radius of curvature for the case of a symmetrical resonator.

Fig. 4
Fig. 4

Total power (filled circles) and power in the dominant mode (open circles) versus the radius of curvature for the case of a nonsymmetrical resonator.

Fig. 5
Fig. 5

Total power (solid curve) and the power in the dominant L4 mode for the case of δL = 0 (dashed curve) versus the cavity detuning for a nonsymmetrical resonator with R1 = R2 = 77.8 mm.

Tables (2)

Tables Icon

Table 1 ENEA Millimeter-Wave Compact FEL Parameters

Tables Icon

Table 2 Influence of the Input Field Profile in Terms of GL Modes on the Power Enhancement and Normalized Power Enhancement in the Stacker Cavitya

Equations (15)

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0 ξ a e - ξ d ξ ξ a = 2 π R a 2 l 1 / λ s ( l 1 2 + z 1 2 ) ,
z 1 = ( R 2 - L c ) L c R 1 + R 2 - 2 L c ,             l 1 = [ z 1 ( R 1 - z 1 ) ] 1 / 2 .
c p ( z 1 , l 1 ) = ( 2 l 0 l 0 + l 1 + i z 1 ) ( l 1 - l 0 - i z 1 l 0 + l 1 + i z 1 ) p ,
c 0 2 c p 2 = 4 l 0 l 1 ( l 1 + l 0 ) 2 + z 1 2 = 4 l 1 l 0 + ( 2 + π / ξ a ) l 1 ,
k s L c - ( 2 p + 1 ) arctan ( L c - z 1 l 1 ) - ( 2 p + 1 ) arctan ( z 1 l 1 ) = n π ,
( 2 p + 1 ) arctan [ L c l 1 ( R 1 - L c ) z 1 ] = n π .
2 ( 2 p + 1 ) arctan ( L c 2 l 1 ) = n π .
R 1 R 2 = L c ( 1 - cos ϕ ) , ξ a = 2 π R a 2 λ s L c sin ϕ = π l 0 L c sin ϕ ,
R 1 = L c + L c 2 2 κ 2 z 1 ± L c 2 2 κ 2 z 1 ( 1 + 4 κ 2 z 1 L c - 4 κ 2 z 1 2 L c 2 ) 1 / 2 ,
R 1 = - R 2 = L c sin ϕ , z 1 = L c ( sin ϕ + 1 ) 2 sin ϕ , l 1 = L c cos ϕ 2 sin ϕ , ξ a = π l 0 cos ϕ sin ϕ L c ( sin ϕ + 1 )
ξ a = π l 0 cos ϕ sin ϕ L c ( 1 - sin ϕ ) .
a p exp ( - i ζ p ) = q a q exp ( - i ζ q ) 0 ξ a L q ( ξ ) L p ( ξ ) e - ξ d ξ ,
k = 0 p ( p k ) ( - 1 ) k f k , q = ξ p p ! L q ( ξ ) e - ξ d ξ
f p , q = R a R m L q ( ξ ) L p ( ξ ) e - ξ d ξ = k = 0 p - 1 ( p - 1 k ) ( - 1 ) k + p [ ( q p - k p - k ) f k , q - q p f k , q - 1 ] + ( - 1 ) p + 1 x p p ! L q ( ξ ) e - x ξ a ξ m ,
f 0 , q = ξ a ξ m L q ( ξ ) e - ξ d ξ = k = 1 q ( q - 1 q - k ) ( - 1 ) k + 1 ξ k k ! e - ξ ξ a ξ m , f 0 , 0 = ξ a ξ m e - ξ d ξ = - e - ξ ξ a ξ m

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