Abstract

The coupling of optical energy from a lamp into a laser rod using a spherical mirror enclosure has been analyzed using geometrical optics. The calculations indicate that about 75% coupling can be obtained for typical sized laser rods and spheres. Experimental results for a 3 mm × 30 mm Nd:Cr:YAG rod are given. Using external resonators, a slope efficiency of 1.15% and an output power of 3.4 W were observed for an input power of 870 W.

© 1967 Optical Society of America

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References

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  1. L. F. Johnson, G. D. Boyd, K. Nassau, R. R. Soden, Phys. Rev. 126, 1406 (1962).
    [CrossRef]
  2. D. Roess, Microwaves 4, 29 (1965).
  3. V. Evtuhov, J. K. Neeland, Appl. Phys. Letters 6, 75 (1965).
    [CrossRef]
  4. R. C. Duncan, Z. J. Kiss, Appl. Phys. Letters 3, 236 (1963).
    [CrossRef]
  5. J. E. Geusic, NEREM Record 8, 192 (1966).
  6. Yu. A. Ananev, Instr. Exp. Tech. 2, 400 (1964).
  7. See, for example, the following references on the elliptical reflector: T. Li, S. O. Sims, Proc. Inst. Radio Engrs. 50, 464 (1962); S. B. Schuldt, R. L. Aagard, Appl. Opt. 2, 509 (1963); J. A. Ackerman, Proc. IEEE 51, 1032 (1963); C. Bowness, Appl. Opt. 4, 103 (1965); K. Kamiryo, T. Kano, H. Matsozawa, Japan. J. Appl. Phys. 5, 1217 (1966).
    [CrossRef]

1966

J. E. Geusic, NEREM Record 8, 192 (1966).

1965

D. Roess, Microwaves 4, 29 (1965).

V. Evtuhov, J. K. Neeland, Appl. Phys. Letters 6, 75 (1965).
[CrossRef]

1964

Yu. A. Ananev, Instr. Exp. Tech. 2, 400 (1964).

1963

R. C. Duncan, Z. J. Kiss, Appl. Phys. Letters 3, 236 (1963).
[CrossRef]

1962

See, for example, the following references on the elliptical reflector: T. Li, S. O. Sims, Proc. Inst. Radio Engrs. 50, 464 (1962); S. B. Schuldt, R. L. Aagard, Appl. Opt. 2, 509 (1963); J. A. Ackerman, Proc. IEEE 51, 1032 (1963); C. Bowness, Appl. Opt. 4, 103 (1965); K. Kamiryo, T. Kano, H. Matsozawa, Japan. J. Appl. Phys. 5, 1217 (1966).
[CrossRef]

L. F. Johnson, G. D. Boyd, K. Nassau, R. R. Soden, Phys. Rev. 126, 1406 (1962).
[CrossRef]

Ananev, Yu. A.

Yu. A. Ananev, Instr. Exp. Tech. 2, 400 (1964).

Boyd, G. D.

L. F. Johnson, G. D. Boyd, K. Nassau, R. R. Soden, Phys. Rev. 126, 1406 (1962).
[CrossRef]

Duncan, R. C.

R. C. Duncan, Z. J. Kiss, Appl. Phys. Letters 3, 236 (1963).
[CrossRef]

Evtuhov, V.

V. Evtuhov, J. K. Neeland, Appl. Phys. Letters 6, 75 (1965).
[CrossRef]

Geusic, J. E.

J. E. Geusic, NEREM Record 8, 192 (1966).

Johnson, L. F.

L. F. Johnson, G. D. Boyd, K. Nassau, R. R. Soden, Phys. Rev. 126, 1406 (1962).
[CrossRef]

Kiss, Z. J.

R. C. Duncan, Z. J. Kiss, Appl. Phys. Letters 3, 236 (1963).
[CrossRef]

Li, T.

See, for example, the following references on the elliptical reflector: T. Li, S. O. Sims, Proc. Inst. Radio Engrs. 50, 464 (1962); S. B. Schuldt, R. L. Aagard, Appl. Opt. 2, 509 (1963); J. A. Ackerman, Proc. IEEE 51, 1032 (1963); C. Bowness, Appl. Opt. 4, 103 (1965); K. Kamiryo, T. Kano, H. Matsozawa, Japan. J. Appl. Phys. 5, 1217 (1966).
[CrossRef]

Nassau, K.

L. F. Johnson, G. D. Boyd, K. Nassau, R. R. Soden, Phys. Rev. 126, 1406 (1962).
[CrossRef]

Neeland, J. K.

V. Evtuhov, J. K. Neeland, Appl. Phys. Letters 6, 75 (1965).
[CrossRef]

Roess, D.

D. Roess, Microwaves 4, 29 (1965).

Sims, S. O.

See, for example, the following references on the elliptical reflector: T. Li, S. O. Sims, Proc. Inst. Radio Engrs. 50, 464 (1962); S. B. Schuldt, R. L. Aagard, Appl. Opt. 2, 509 (1963); J. A. Ackerman, Proc. IEEE 51, 1032 (1963); C. Bowness, Appl. Opt. 4, 103 (1965); K. Kamiryo, T. Kano, H. Matsozawa, Japan. J. Appl. Phys. 5, 1217 (1966).
[CrossRef]

Soden, R. R.

L. F. Johnson, G. D. Boyd, K. Nassau, R. R. Soden, Phys. Rev. 126, 1406 (1962).
[CrossRef]

Appl. Phys. Letters

V. Evtuhov, J. K. Neeland, Appl. Phys. Letters 6, 75 (1965).
[CrossRef]

R. C. Duncan, Z. J. Kiss, Appl. Phys. Letters 3, 236 (1963).
[CrossRef]

Instr. Exp. Tech.

Yu. A. Ananev, Instr. Exp. Tech. 2, 400 (1964).

Microwaves

D. Roess, Microwaves 4, 29 (1965).

NEREM Record

J. E. Geusic, NEREM Record 8, 192 (1966).

Phys. Rev.

L. F. Johnson, G. D. Boyd, K. Nassau, R. R. Soden, Phys. Rev. 126, 1406 (1962).
[CrossRef]

Proc. Inst. Radio Engrs.

See, for example, the following references on the elliptical reflector: T. Li, S. O. Sims, Proc. Inst. Radio Engrs. 50, 464 (1962); S. B. Schuldt, R. L. Aagard, Appl. Opt. 2, 509 (1963); J. A. Ackerman, Proc. IEEE 51, 1032 (1963); C. Bowness, Appl. Opt. 4, 103 (1965); K. Kamiryo, T. Kano, H. Matsozawa, Japan. J. Appl. Phys. 5, 1217 (1966).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Geometry of the spherical reflector.

Fig. 2
Fig. 2

Ray tracing in the spherical reflector.

Fig. 3
Fig. 3

Geometrical efficiency of spherical reflector.

Fig. 4
Fig. 4

Laser power conversion.

Tables (1)

Tables Icon

Table I Theoretical Coupling Efficiency of Radiation of Equal Size Lamps and Laser Rods for Various Size Spheres and Laser Rods

Equations (14)

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u 2 = r 2 + d 1 2 - 2 r d 1 cos θ ,
v 2 = r 2 + d 2 2 - 2 r d 2 cos ( 180 - θ ) .
d 1 / sin φ = u / sin θ ,
d 2 / sin φ = v / sin ( 180 - θ ) = v / sin θ ,
d 1 / d 2 = u / v .
d 1 2 d 2 2 = r 2 + d 1 2 - 2 r d 1 cos θ r 2 + d 2 2 + 2 r d 2 cos θ .
d 2 / d 1 = 1 + ( 2 d 2 / r ) cos θ = 1 / 1 - ( 2 d 1 / r ) cos θ .
A = π c 2 - 2 c a - b .
Δ V = A Δ X = [ π c 2 - 2 c a - b ] Δ X ,
b = a d 2 / d 1 ,
Δ V = [ π c 2 - 2 a c | 1 - 1 1 - [ 2 ( x 2 + a 2 ) ½ / r ] cos θ | ] Δ X .
η = 1 ( 4 π r 2 ) ( π c 2 L / 2 ) 0 L / 2 θ v 180 - θ v A 2 π r 2 sin θ d θ d x ,
η = 1 π c 2 L 0 L / 2 θ v 180 - θ v [ π c 2 - 2 a c | 1 - 1 1 - 2 [ ( x 2 + a 2 ) ½ / r ] cos θ | ] sin θ d θ d x ,
η = cos θ v + ( a r / π c L ) 0 L / 2 ln [ 1 - ( 4 / r 2 ) ( x 2 + a 2 ) cos 2 θ v ] d x ( x 2 + a 2 ) ½ .

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