Abstract

Our work is focused on the problem of theoretical analysis of paraxial properties of the three-element zoom optical system for laser beam expanders. Equations that enable to calculate mutual axial distances between individual elements of the system based on the axial position of the beam waist of the input Gaussian beam and the desired magnification of the system are derived. Finally, the derived equations are applied on an example of calculation of paraxial parameters of the three-element zoom system for the laser beam expander.

© 2014 Optical Society of America

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References

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  1. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley-Interscience, New York, 2007).
  2. H. Kogelnik and T. Li, “Laser Beams and Resonators,” Appl. Opt. 5(10), 1550–1567 (1966).
    [Crossref] [PubMed]
  3. A. D. Clark, Zoom Lenses (Adam Hilger, London, 1973).
  4. K. Yamaji, Progres in Optics, Vol.VI (North-Holland Publishing Co., Amsterdam 1967).
  5. A. Miks, J. Novák, and P. Novák, “Method of zoom lens design,” Appl. Opt. 47(32), 6088–6098 (2008).
    [Crossref] [PubMed]
  6. 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]
  7. G. Wooters and E. W. Silvertooth, “Optically Compensated Zoom Lens,” J. Opt. Soc. Am. 55(4), 347–351 (1965).
    [Crossref]
  8. T. Kryszczyński, M. Leśniewski, and J. Mikucki, “Use of matrix optics to analyze the complex multi-group zoom systems,” Proc. SPIE 8697, 86970I (2012).
    [Crossref]
  9. S. Pal and L. Hazra, “Ab initio synthesis of linearly compensated zoom lenses by evolutionary programming,” Appl. Opt. 50(10), 1434–1441 (2011).
    [Crossref] [PubMed]
  10. L. Hazra and S. Pal, “A novel approach for structural synthesis of zoom systems,” Proc. SPIE 7786, 778607 (2010).
    [Crossref]
  11. S. Pal and L. Hazra, “Stabilization of pupils in a zoom lens with two independent movements,” Appl. Opt. 52(23), 5611–5618 (2013).
    [Crossref] [PubMed]
  12. S. Pal, “Aberration correction of zoom lenses using evolutionary programming,” Appl. Opt. 52(23), 5724–5732 (2013).
    [Crossref] [PubMed]
  13. A. Miks, Applied Optics (Czech Technical University Press, Prague, 2009).
  14. http://www.edmundoptics.com
  15. W. T. Welford, Aberrations of the Symmetrical Optical Systems, (Academic Press, London, 1974).
  16. W. Smith, Modern optical engineering, 4th Ed., (McGraw-Hill, New York, 2007).
  17. 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]

2013 (3)

2012 (1)

T. Kryszczyński, M. Leśniewski, and J. Mikucki, “Use of matrix optics to analyze the complex multi-group zoom systems,” Proc. SPIE 8697, 86970I (2012).
[Crossref]

2011 (1)

2010 (1)

L. Hazra and S. Pal, “A novel approach for structural synthesis of zoom systems,” Proc. SPIE 7786, 778607 (2010).
[Crossref]

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]

1966 (1)

1965 (1)

Hazra, L.

Kogelnik, H.

Kryszczynski, T.

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]

T. Kryszczyński, M. Leśniewski, and J. Mikucki, “Use of matrix optics to analyze the complex multi-group zoom systems,” Proc. SPIE 8697, 86970I (2012).
[Crossref]

Lesniewski, M.

T. Kryszczyński, M. Leśniewski, and J. Mikucki, “Use of matrix optics to analyze the complex multi-group zoom systems,” Proc. SPIE 8697, 86970I (2012).
[Crossref]

Li, T.

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]

Mikucki, J.

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]

T. Kryszczyński, M. Leśniewski, and J. Mikucki, “Use of matrix optics to analyze the complex multi-group zoom systems,” Proc. SPIE 8697, 86970I (2012).
[Crossref]

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.

Silvertooth, E. W.

Wooters, G.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Opt. Express (1)

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]

Proc. SPIE (2)

T. Kryszczyński, M. Leśniewski, and J. Mikucki, “Use of matrix optics to analyze the complex multi-group zoom systems,” Proc. SPIE 8697, 86970I (2012).
[Crossref]

L. Hazra and S. Pal, “A novel approach for structural synthesis of zoom systems,” Proc. SPIE 7786, 778607 (2010).
[Crossref]

Other (7)

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

K. Yamaji, Progres in Optics, Vol.VI (North-Holland Publishing Co., Amsterdam 1967).

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

A. Miks, Applied Optics (Czech Technical University Press, Prague, 2009).

http://www.edmundoptics.com

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

W. Smith, Modern optical engineering, 4th Ed., (McGraw-Hill, New York, 2007).

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Figures (2)

Fig. 1
Fig. 1

Basic parameters of a Gaussian beam

Fig. 2
Fig. 2

Three-element zoom systems for laser beam expander

Tables (1)

Tables Icon

Table 1 – Example of three-element zoom system for laser beam expansion

Equations (19)

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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.
1/ R 1/R=1/ f ,
G i = f i 2 q i 2 + z 0i 2 = m i 2 1+ m i 2 ( z 0i / f i ) 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 = ( w 0 / w 0 ) 2 = (θ/ θ ) 2 = i=1 i=n G i .
a 2 Δ 2 2 + a 1 Δ 2 + a 0 =0,
a 2 = ( Δ 1 z 01 ) 2 + ( Δ 1 q 1 f 1 2 ) 2 , a 1 =2 f 2 2 [ Δ 1 z 01 2 + q 1 ( Δ 1 q 1 f 1 2 ) ], a 0 = f 2 2 [ ( z 01 f 2 ) 2 + ( q 1 f 2 ) 2 ( f 1 f 3 / m G ) 2 ].
b 2 Δ 1min 2 + b 1 Δ 1min + b 0 =0,
b 2 = f 3 2 ( z 01 2 + q 1 2 ), b 1 =2 q 1 ( f 1 f 3 ) 2 , b 0 = f 1 2 [ ( f 1 f 3 ) 2 ( z 01 f 2 m G ) 2 ].
m G 2 = ( f 3 f 1 f 2 ) 2 [ 1+ ( q 1 z 01 ) 2 ][ ( d 1 f 1 f 2 + q 1 f 1 2 z 01 2 + q 1 2 ) 2 + z 01 2 f 1 4 ( z 01 2 + q 1 2 ) 2 ].
( m G 2 ) aprox [ f 3 ( f 1 + f 2 ) f 1 f 2 d 1 f 3 f 1 f 2 ] 2 = [ f 3 ( f 1 + f 2 d 1 ) f 1 f 2 ] 2 = ( f 3 f 12 ) 2 ,
c 2 f 1min 4 + c 1 f 1min 2 + c 0 =0,
c 2 = f 3 2 , c 1 =2 d 1 q 1 f 3 2 m G 2 z 01 2 f 2 2 , c 0 = d 1 2 f 3 2 ( q 1 2 + z 01 2 ).
f 1min =± m G 2 z 01 2 f 2 2 2 d 1 q 1 f 3 2 ± m G 2 f 2 2 ( m G 2 z 01 2 f 2 2 4 d 1 q 1 f 3 2 )4 d 1 2 f 3 4 2 f 3 2 .
e 2 f 1min 4 + e 1 f 1min 2 + e 0 =0,
e 2 = f 3 2 m G 2 z 01 2 , e 1 =2 d 1 q 1 f 3 2 , e 0 = d 1 2 f 3 2 ( q 1 2 + z 01 2 ).
f 1min =± d 1 q 1 f 3 2 + d 1 f 3 z 01 m G 2 ( q 1 2 + z 01 2 ) f 3 2 m G 2 z 01 2 f 3 2 .
f 1min ± d 1 f 3 / m G .

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