Abstract

The paper is focused on the problem of a theoretical analysis of paraxial imaging properties and initial optical design of the three-element zoom optical system for laser beam expanders using lenses with a tunable focal length. Equations which allow calculation of required optical powers of individual elements of the three-element zoom optical system for laser beam expander depending on the value of the axial position of the beam waist of the input Gaussian beam and the required magnification of the system are derived.

© 2015 Optical Society of America

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References

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  7. A. Donges and R. Noll, Laser Measurement Technology (Springer, 2015).
  8. A. Mikš and P. Novák, “Paraxial properties of three-element zoom systems for laser beam expanders,” Opt. Express 22(18), 21535–21540 (2014).
    [Crossref] [PubMed]
  9. A. D. Clark, Zoom Lenses (Adam Hilger, 1973).
  10. A. Miks, J. Novák, and P. Novák, “Method of zoom lens design,” Appl. Opt. 47(32), 6088–6098 (2008).
    [Crossref] [PubMed]
  11. T. Kryszczyński and J. Mikucki, “Structural optical design of the complex multi-group zoom systems by means of matrix optics,” Opt. Express 21(17), 19634–19647 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  15. A. Miks and J. Novak, “Propagation of Gaussian beam in optical system with aberrations, ” Optik, International Journal for Light and Electron Optics 114(10), 437–440 (2003).
    [Crossref]
  16. W. T. Welford, Aberrations of the Symmetrical Optical Systems (Academic, 1974).
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2014 (1)

2013 (2)

2011 (1)

2008 (1)

2003 (1)

A. Miks and J. Novak, “Propagation of Gaussian beam in optical system with aberrations, ” Optik, International Journal for Light and Electron Optics 114(10), 437–440 (2003).
[Crossref]

1986 (1)

1966 (1)

Hazra, L.

Kogelnik, H.

Kryszczynski, T.

Li, T.

Mahajan, V. N.

Miks, A.

A. Miks, J. Novák, and P. Novák, “Method of zoom lens design,” Appl. Opt. 47(32), 6088–6098 (2008).
[Crossref] [PubMed]

A. Miks and J. Novak, “Propagation of Gaussian beam in optical system with aberrations, ” Optik, International Journal for Light and Electron Optics 114(10), 437–440 (2003).
[Crossref]

Mikš, A.

Mikucki, J.

Novak, J.

A. Miks and J. Novak, “Propagation of Gaussian beam in optical system with aberrations, ” Optik, International Journal for Light and Electron Optics 114(10), 437–440 (2003).
[Crossref]

Novák, J.

Novák, P.

Pal, S.

Appl. Opt. (4)

J. Opt. Soc. Am. A (1)

Opt. Express (2)

Optik, International Journal for Light and Electron Optics (1)

A. Miks and J. Novak, “Propagation of Gaussian beam in optical system with aberrations, ” Optik, International Journal for Light and Electron Optics 114(10), 437–440 (2003).
[Crossref]

Other (10)

W. T. Welford, Aberrations of the Symmetrical Optical Systems (Academic, 1974).

M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter & Co., 1970).

S. F. Ray, Applied Photographic Optics (Focal, 2002).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed. (Wiley-Interscience, 2007).

A. D. Clark, Zoom Lenses (Adam Hilger, 1973).

A. E. Siegman, Lasers (University Science Book, 1986).

F. Trager, ed., Springer Handbook of Lasers and Optics (Springer, 2007).

N. Hodgson and H. Weber, Laser Resonators and Beam Propagation (Springer, 2005).

C. E. Webb and J. D. C. Jones, Handbook of Laser Technology and Applications (IOP, 2004, Vol. I – III).

A. Donges and R. Noll, Laser Measurement Technology (Springer, 2015).

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Figures (2)

Fig. 1
Fig. 1

Basic parameters of a Gaussian beam, F and F' are front and back focus of the optical system.

Fig. 2
Fig. 2

Three-element optical system for transformation of a Gaussian beam

Tables (1)

Tables Icon

Table 1 Example of three-element zoom system for laser beam expansion based on tunable-focus lenses

Equations (15)

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u= w 0 w exp( x 2 + y 2 w 2 )exp( ikz+iψik x 2 + y 2 2R ),
R(z)=z(1+ z 0 2 / z 2 ), w 2 (z)= w 0 2 (1+ z 2 / z 0 2 ),ψ(z)=arctan(z/ z 0 ), z 0 =k w 0 2 /2,
w 0 θ=λ/π.
G i = f i 2 q i 2 + z 0i 2 , q i = q i G i , z 0i+1 = z 0i G i , Δ i = f i + f i+1 d i , q i+1 = q i + Δ i
s i = q i f i , s i = q i + f i ,
m G 2 = i=1 i=p G i .
s 1 + d 1 + s 2 =L=konst.
a 2 f 1 2 + a 1 f 1 + a 0 =0,
a 2 =( d 1 s 1 f 2 )[ ( d 1 s 1 ) 2 L( d 1 s 1 f 2 )]+ z 01 2 ( d 1 s 1 + f 2 L), a 1 =2L s 1 ( d 1 f 2 ) 2 +2( d 1 f 2 )[ s 1 ( d 1 2 + s 1 2 )+L( s 1 2 + z 01 2 )] + z 01 2 [2 d 1 ( s 1 d 1 )+ f 2 ( f 2 2 s 1 )] s 1 2 (2 d 1 f 2 ) 2 , a 0 =( s 1 2 + z 01 2 )( d 1 f 2 )[ d 1 2 ( d 1 f 2 )(L+ s 1 )].
m G12 2 = f 3 2 z 01 2 m G 2
b 2 f 1 2 + b 1 f 1 + b 0 =0
b 2 = f 2 2 m G12 2 ( f 2 d 1 + s 1 ) 2 m G12 2 z 01 2 , b 1 =2 m G12 2 ( d 1 f 2 )[ s 1 ( f 2 d 1 )+ s 1 2 + z 01 2 ], b 0 = m G12 2 ( s 1 2 + z 01 2 ) ( d 1 f 2 ) 2 .
R=| a 2 a 1 a 0 0 0 a 2 a 1 a 0 b 2 b 1 b 0 0 0 b 2 b 1 b 0 |.
c 4 f 2 4 + c 3 f 2 3 + c 2 f 2 2 + c 1 f 2 + c 0 =0,
c 4 =α[ z 01 2 m G12 2 ( m G12 2 1) m G12 2 s 1 2 + β 2 ], c 3 =2 d 1 α[ z 01 2 m G12 2 (12 m G12 2 )+ m G12 2 s 1 2 2 β 2 + d 1 β ], c 2 = d 1 2 α[ z 01 2 m G12 2 (6 m G12 2 1) m G12 2 s 1 2 +6 β 2 6 d 1 β+ d 1 2 ], c 1 =2 d 1 3 α[2 z 01 2 m G12 4 +2 β 2 3 d 1 β+ d 1 2 ], c 0 = d 1 4 α[ z 01 2 m G12 4 + (β d 1 ) 2 ], α= ( s 1 2 + z 01 2 ) 2 ,β=L+ s 1 .

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