Abstract

Lens ducts have the potential to couple the output from a laser diode array efficiently into the gain medium of a solid-state laser in an end-pumped configuration. Using a ray-tracing method we investigate different design approaches of lens ducts and demonstrate the possibility to obtain an output beam with a symmetric profile that is insensitive to the small displacement from the output surface of a lens duct.

© 1998 Optical Society of America

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References

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  1. R. J. Beach, “Theory and optimization of lens ducts,” Appl. Opt. 35, 2005–2015 (1996).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  6. T. Taira, T. Kobayshi, “Intracavity frequency doubling and Q-switching in diode-laser-pumped Nd:YVO4 lasers,” Appl. Opt. 34, 4298–4301 (1995).
    [CrossRef] [PubMed]

1996

1995

1993

1985

Balmer, J. E.

Beach, R. J.

Bussac, C.

Byer, R. L.

Dixon, G. J.

Feugnet, G.

Graf, Th.

Juhasz, T.

Kane, T. J.

Kobayshi, T.

Larat, C.

Schwarz, M.

Taira, T.

Turi, L.

Zhou, B.

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Figures (7)

Fig. 1
Fig. 1

Schematic of a lens duct in the slow-axis plane of the laser diode in which r is the radius of the spherical input surface, L is the length of the duct, and H 1 and H 2 are the widths of the input and output surfaces, respectively.

Fig. 2
Fig. 2

Example of ray tracing inside a lens duct with H as the width of the originating surface of the pump beam from a laser diode array with H = 9 mm, r = 50 mm, H 1 = 11 mm, and H 2 = 4.5 mm.

Fig. 3
Fig. 3

Ray-tracing result from the single-reflection approach for a lens duct with H = 10 mm, r = 10 mm, H 1 = 11.6 mm, H 2 = 2.9 mm, and L = 28 mm.

Fig. 4
Fig. 4

Normalized irradiance distribution of the same lens duct as in Fig. 3 except in the slow-axis direction.

Fig. 5
Fig. 5

Ray-tracing results of a lens duct from the converging approach in (a) the slow-axis plane assuming 10° for the divergence angle of the incoming ray bundles and (b) in the fast-axis plane with a 3° divergence angle with H = 10 mm, r = 25 mm, H 1 = 14.4 mm, H 2 = 2.9 mm, and L = 68 mm.

Fig. 6
Fig. 6

Normalized irradiance distribution of the same lens duct as in Fig. 5: (a) in the slow-axis direction with a 10° divergence angle and (b) in the fast-axis direction with a 3° divergence angle.

Fig. 7
Fig. 7

Normalized irradiance distribution of the same lens duct as in Fig. 5 except in the fast-axis direction with a 10° divergence angle.

Equations (9)

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y 1 - y 0 = x 1 - x 0 tan   θ ,
x 1 2 + y 1 2 = r 2 .
n   sin   θ 2 = sin   θ 1 ,
y 2 - y 1 = x 2 - x 1 tan θ 2 - arcsin y 1 / r ,
y 2 - H 1 / 2 x 2 + r 2 - H 1 / 2 2 = H 1 - H 2 / 2 - r 2 - H 1 / 2 2 - ( L - r ) .
θ 3 = - θ 2 - arcsin y 1 / r - 2 α ,
sin   α = H 1 - H 2 2 L - r + 4 r 2 - H 1 2 .
y 3 - y 2 = x 3 - x 2 tan   θ 3 ,
y 3 + H 1 / 2 x 3 + r 2 - H 1 / 2 2 = H 2 - H 1 / 2 r 2 - H 1 / 2 2 - L - r .

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