Abstract

An optical resonator simulation code based on the idea of a partially coherent optical field has been developed and used to optimize the design parameters of an unstable resonator with a stable core. The resonator was intended for use with low-gain, large-bore lasers, such as the chemical oxygen–iodine laser (COIL). First the design parameters of the resonator were optimized by the simulation code; then a set of mirrors was fabricated for a small-scale COIL. A 14-W output with M 2 = 29 was obtained. The experimentally obtained results were in good agreement with calculations.

© 1999 Optical Society of America

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References

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  1. A. G. Fox, T. Li, “Resonator modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
    [CrossRef]
  2. E. A. Sziklas, A. E. Siegman, “Mode calculations in unstable resonators with flowing saturable gain. 2. Fast Fourier transform method,” Appl. Opt. 14, 1874–1889 (1975).
    [CrossRef] [PubMed]
  3. P. W. Milonni, A. H. Paxton, “Model for the unstable-resonator carbon monoxide electric-discharge laser,” J. Appl. Phys. 49, 1012–1027 (1978).
    [CrossRef]
  4. A. Bhowmik, “Closed-cavity solutions with partially coherent fields in the space-frequency domain,” Appl. Opt. 22, 3338–3346 (1983).
    [CrossRef] [PubMed]
  5. V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Control of the output power of a laser with an active unstable resonator,” Sov. J. Quantum Electron. 21, 325–330 (1991).
    [CrossRef]
  6. V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Transparency and mode selectivity of variable-configuration resonators for control of laser radiation power,” Sov. J. Quantum Electron. 22, 550–557 (1992).
    [CrossRef]
  7. K. Nanri, M. Matsumura, S. Yamaguchi, T. Fujioka, “An experimental investigation of the novel unstable resonator with a stable resonator core,” Jpn. J. Appl. Phys. 37, 3972–3976 (1998).
    [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 380–381.
  9. Ref. 8, p. 509.
  10. D. A. Copeland, A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. 29, 2525–2539 (1993).
    [CrossRef]
  11. D. R. Hall, P. E. Jackson, The Physics and Technology of Laser Resonators (IPP, Bristol, UK, 1975), pp. 132–142.
  12. D. Sugimoto, M. Endo, K. Nanri, S. Takeda, T. Fujioka, “Output power stabilization of a chemical oxygen–iodine laser with an external magnetic field,” IEEE J. Quantum Electron. 34, 1526–1532 (1998).
    [CrossRef]

1998 (2)

K. Nanri, M. Matsumura, S. Yamaguchi, T. Fujioka, “An experimental investigation of the novel unstable resonator with a stable resonator core,” Jpn. J. Appl. Phys. 37, 3972–3976 (1998).
[CrossRef]

D. Sugimoto, M. Endo, K. Nanri, S. Takeda, T. Fujioka, “Output power stabilization of a chemical oxygen–iodine laser with an external magnetic field,” IEEE J. Quantum Electron. 34, 1526–1532 (1998).
[CrossRef]

1993 (1)

D. A. Copeland, A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. 29, 2525–2539 (1993).
[CrossRef]

1992 (1)

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Transparency and mode selectivity of variable-configuration resonators for control of laser radiation power,” Sov. J. Quantum Electron. 22, 550–557 (1992).
[CrossRef]

1991 (1)

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Control of the output power of a laser with an active unstable resonator,” Sov. J. Quantum Electron. 21, 325–330 (1991).
[CrossRef]

1983 (1)

1978 (1)

P. W. Milonni, A. H. Paxton, “Model for the unstable-resonator carbon monoxide electric-discharge laser,” J. Appl. Phys. 49, 1012–1027 (1978).
[CrossRef]

1975 (1)

1961 (1)

A. G. Fox, T. Li, “Resonator modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[CrossRef]

Apollonov, V. V.

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Transparency and mode selectivity of variable-configuration resonators for control of laser radiation power,” Sov. J. Quantum Electron. 22, 550–557 (1992).
[CrossRef]

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Control of the output power of a laser with an active unstable resonator,” Sov. J. Quantum Electron. 21, 325–330 (1991).
[CrossRef]

Bauer, A. H.

D. A. Copeland, A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. 29, 2525–2539 (1993).
[CrossRef]

Bhowmik, A.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 380–381.

Chetkin, S. A.

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Transparency and mode selectivity of variable-configuration resonators for control of laser radiation power,” Sov. J. Quantum Electron. 22, 550–557 (1992).
[CrossRef]

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Control of the output power of a laser with an active unstable resonator,” Sov. J. Quantum Electron. 21, 325–330 (1991).
[CrossRef]

Copeland, D. A.

D. A. Copeland, A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. 29, 2525–2539 (1993).
[CrossRef]

Endo, M.

D. Sugimoto, M. Endo, K. Nanri, S. Takeda, T. Fujioka, “Output power stabilization of a chemical oxygen–iodine laser with an external magnetic field,” IEEE J. Quantum Electron. 34, 1526–1532 (1998).
[CrossRef]

Fox, A. G.

A. G. Fox, T. Li, “Resonator modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[CrossRef]

Fujioka, T.

D. Sugimoto, M. Endo, K. Nanri, S. Takeda, T. Fujioka, “Output power stabilization of a chemical oxygen–iodine laser with an external magnetic field,” IEEE J. Quantum Electron. 34, 1526–1532 (1998).
[CrossRef]

K. Nanri, M. Matsumura, S. Yamaguchi, T. Fujioka, “An experimental investigation of the novel unstable resonator with a stable resonator core,” Jpn. J. Appl. Phys. 37, 3972–3976 (1998).
[CrossRef]

Hall, D. R.

D. R. Hall, P. E. Jackson, The Physics and Technology of Laser Resonators (IPP, Bristol, UK, 1975), pp. 132–142.

Jackson, P. E.

D. R. Hall, P. E. Jackson, The Physics and Technology of Laser Resonators (IPP, Bristol, UK, 1975), pp. 132–142.

Kislov, V. I.

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Transparency and mode selectivity of variable-configuration resonators for control of laser radiation power,” Sov. J. Quantum Electron. 22, 550–557 (1992).
[CrossRef]

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Control of the output power of a laser with an active unstable resonator,” Sov. J. Quantum Electron. 21, 325–330 (1991).
[CrossRef]

Li, T.

A. G. Fox, T. Li, “Resonator modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[CrossRef]

Matsumura, M.

K. Nanri, M. Matsumura, S. Yamaguchi, T. Fujioka, “An experimental investigation of the novel unstable resonator with a stable resonator core,” Jpn. J. Appl. Phys. 37, 3972–3976 (1998).
[CrossRef]

Milonni, P. W.

P. W. Milonni, A. H. Paxton, “Model for the unstable-resonator carbon monoxide electric-discharge laser,” J. Appl. Phys. 49, 1012–1027 (1978).
[CrossRef]

Nanri, K.

K. Nanri, M. Matsumura, S. Yamaguchi, T. Fujioka, “An experimental investigation of the novel unstable resonator with a stable resonator core,” Jpn. J. Appl. Phys. 37, 3972–3976 (1998).
[CrossRef]

D. Sugimoto, M. Endo, K. Nanri, S. Takeda, T. Fujioka, “Output power stabilization of a chemical oxygen–iodine laser with an external magnetic field,” IEEE J. Quantum Electron. 34, 1526–1532 (1998).
[CrossRef]

Paxton, A. H.

P. W. Milonni, A. H. Paxton, “Model for the unstable-resonator carbon monoxide electric-discharge laser,” J. Appl. Phys. 49, 1012–1027 (1978).
[CrossRef]

Prokhorov, A. M.

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Transparency and mode selectivity of variable-configuration resonators for control of laser radiation power,” Sov. J. Quantum Electron. 22, 550–557 (1992).
[CrossRef]

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Control of the output power of a laser with an active unstable resonator,” Sov. J. Quantum Electron. 21, 325–330 (1991).
[CrossRef]

Siegman, A. E.

Sugimoto, D.

D. Sugimoto, M. Endo, K. Nanri, S. Takeda, T. Fujioka, “Output power stabilization of a chemical oxygen–iodine laser with an external magnetic field,” IEEE J. Quantum Electron. 34, 1526–1532 (1998).
[CrossRef]

Sziklas, E. A.

Takeda, S.

D. Sugimoto, M. Endo, K. Nanri, S. Takeda, T. Fujioka, “Output power stabilization of a chemical oxygen–iodine laser with an external magnetic field,” IEEE J. Quantum Electron. 34, 1526–1532 (1998).
[CrossRef]

Vdovin, G. V.

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Transparency and mode selectivity of variable-configuration resonators for control of laser radiation power,” Sov. J. Quantum Electron. 22, 550–557 (1992).
[CrossRef]

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Control of the output power of a laser with an active unstable resonator,” Sov. J. Quantum Electron. 21, 325–330 (1991).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 380–381.

Yamaguchi, S.

K. Nanri, M. Matsumura, S. Yamaguchi, T. Fujioka, “An experimental investigation of the novel unstable resonator with a stable resonator core,” Jpn. J. Appl. Phys. 37, 3972–3976 (1998).
[CrossRef]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

A. G. Fox, T. Li, “Resonator modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. Sugimoto, M. Endo, K. Nanri, S. Takeda, T. Fujioka, “Output power stabilization of a chemical oxygen–iodine laser with an external magnetic field,” IEEE J. Quantum Electron. 34, 1526–1532 (1998).
[CrossRef]

D. A. Copeland, A. H. Bauer, “Optical saturation and extraction from the chemical oxygen-iodine laser medium,” IEEE J. Quantum Electron. 29, 2525–2539 (1993).
[CrossRef]

J. Appl. Phys. (1)

P. W. Milonni, A. H. Paxton, “Model for the unstable-resonator carbon monoxide electric-discharge laser,” J. Appl. Phys. 49, 1012–1027 (1978).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Nanri, M. Matsumura, S. Yamaguchi, T. Fujioka, “An experimental investigation of the novel unstable resonator with a stable resonator core,” Jpn. J. Appl. Phys. 37, 3972–3976 (1998).
[CrossRef]

Sov. J. Quantum Electron. (2)

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Control of the output power of a laser with an active unstable resonator,” Sov. J. Quantum Electron. 21, 325–330 (1991).
[CrossRef]

V. V. Apollonov, G. V. Vdovin, V. I. Kislov, A. M. Prokhorov, S. A. Chetkin, “Transparency and mode selectivity of variable-configuration resonators for control of laser radiation power,” Sov. J. Quantum Electron. 22, 550–557 (1992).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), pp. 380–381.

Ref. 8, p. 509.

D. R. Hall, P. E. Jackson, The Physics and Technology of Laser Resonators (IPP, Bristol, UK, 1975), pp. 132–142.

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Figures (15)

Fig. 1
Fig. 1

Schematic drawing of the resonator system and definition of coordinates.

Fig. 2
Fig. 2

Schematic drawing of the correlation measurement between two points irradiated by the reflected beam.

Fig. 3
Fig. 3

Intensity distribution of the random-frequency-modulated beam on the focal plane along the x axis.

Fig. 4
Fig. 4

Mutual coherence |μ12| measured along the x axis. Conditions are the same as for Fig. 3.

Fig. 5
Fig. 5

Change in the spatial-frequency component of the optical field distribution on mirror 1.

Fig. 6
Fig. 6

Schematic drawing of the multistage amplification model.

Fig. 7
Fig. 7

Comparison of the calculated intensity and phase distribution for the same conditions: (a) Ref. 2, (b) this work.

Fig. 8
Fig. 8

Change in integrated intensity as a function of iteration number.

Fig. 9
Fig. 9

Change in instant intensity distribution on mirror 1 taken 20 iterations apart. The average intensity distribution is also shown (bottom).

Fig. 10
Fig. 10

Schematic drawing of the unstable resonator with a stable core.

Fig. 11
Fig. 11

Output power and M 2 as a function of the flat part diameter, F, of the resonator.

Fig. 12
Fig. 12

Output power as a function of misalignment angle. Flat-part diameter F is varied as a parameter.

Fig. 13
Fig. 13

Output power as a function of misalignment angle. The flat-part diameter F is varied as a parameter. The flat-part curvature is 150 m.

Fig. 14
Fig. 14

Schematic drawing of the small-scale COIL and beam-quality measurement system. Attn., author define.

Fig. 15
Fig. 15

Near-field pattern of the experimentally obtained oscillation of the novel unstable resonator. The calculated result for the same condition is also shown.

Tables (3)

Tables Icon

Table 1 Parameters Used in Calculations of the Novel Unstable Resonator

Tables Icon

Table 2 Specifications of the Four Resonators

Tables Icon

Table 3 Comparison of Output Power and Beam Quality of the Four Resonators

Equations (16)

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

gxo, yo=expjkljλl P1 fxy, yi×expjk2lxi-xo2+yi-yo2dxidyi,
gxo, yo=gxo, yoexp2jkΔzxo, yo,
Δzxo, yo=xo2+yo22R.
fqxi, yifq+1xi, yi,
fxi, yi=E0 expjπrndxi, yi-1/2K,
μ12Δx, Δy=expjkϕP1 |fxi, yi|2 expjklx1-x2xi+y1-y2yidxidyiP1 |fxi, yi|2dxidyi,
N=1.1×3846×4=16,922.
Ii+˜=1-αi=0q αiIi+q-i,
Ii-˜=1-αi=0q αiIi-q-i,
gix, y=gi0x, y11+Ii+˜x, y-Ii+˜x, yIsx, y,
fioutx, y=fiinx, yexp1/2gix, yd.
Pint=0c2P1 |Ex, y|2dxdy.
ω0=λ/π1/2lR-l1/4,
ω1=λl/π1/2R2lR-l1/4,
θ=λπω M2,  M=ω/ω0,
M22λπd0=D2l,

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