Abstract

We present an approach for efficient conversion of a single-high-order-mode distribution from a laser to a nearly Gaussian distribution and vice versa. It is based on dividing the high-order mode distribution into equal parts that are then combined together coherently. We implement our approach with several optical arrangements that include a combination of discrete elements and some with single interferometric elements. These arrangements are analyzed and experimentally evaluated for converting the TEM01 mode distribution with M x 2 = 3 to a nearly Gaussian beam with M x 2 = 1.045 or M x 2 = 1.15. The basic principle, design, and experimental results obtained with several conversion arrangements are presented. The results reveal that conversion efficiency is typically greater than 90%, compared with theoretical ones. In addition, some arrangement is exploited for converting the fundamental Gaussian-beam distribution into the TEM01 mode distribution.

© 2004 Optical Society of America

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  1. R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–385 (2001).
    [CrossRef]
  2. A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” J. Quantum Electron. 39, 74–82 (2003).
    [CrossRef]
  3. A. A. Napartovich, N. N. Elkin, V. N. Troschieva, D. V. Vysotsky, J. R. Leger, “Simplified intracavity phase plates for increasing laser-mode discrimination,” Appl. Opt. 38, 3025–3029 (1999).
    [CrossRef]
  4. M. Gerber, T. Graf, “Generation of super-Gaussian modes in Nd:YAG lasers with graded-phase mirrors,” in Proceedings of International Conference on Advanced Laser Technologies, 15–20 September 2002, Adelboden, Switzerland, pp. 3–4.
  5. T. Graf, J. E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
    [CrossRef]
  6. P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 20, 3545–3553 (1980).
    [CrossRef]
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    [CrossRef]
  8. M. T. Eismann, A. M. Tai, J. N. Cederquist, “Iterative design of a holographic beamformer,” Appl. Opt. 28, 2641–2650 (1989).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. G. Machavariani, N. Davidson, A. A. Ishaaya, A. A. Friesem, E. Hasman, “Efficient formation of a high-quality beam from a pure high-order Hermite-Gaussian mode,” Opt. Lett. 27, 1501–1503 (2002).
    [CrossRef]
  11. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
    [CrossRef]
  12. J. B. Murphy, “Phase space conservation and selection rules for astigmatic mode converters,” Opt. Commun. 165, 11–18 (1999).
    [CrossRef]
  13. A. A. Ishaaya, G. Machavariani, N. Davidson, A. A. Friesem, E. Hasman, “Conversion of a high-order mode beam into a nearly Gaussian beam using a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
    [CrossRef] [PubMed]

2003 (2)

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

A. A. Ishaaya, G. Machavariani, N. Davidson, A. A. Friesem, E. Hasman, “Conversion of a high-order mode beam into a nearly Gaussian beam using a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–385 (2001).
[CrossRef]

1999 (2)

1996 (1)

T. Graf, J. E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[CrossRef]

1992 (1)

N. Davidson, A. A. Friesem, E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

1989 (1)

1980 (1)

P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 20, 3545–3553 (1980).
[CrossRef]

1974 (1)

Balmer, J. E.

T. Graf, J. E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[CrossRef]

Bryngdahl, O.

Cederquist, J. N.

Davidson, N.

A. A. Ishaaya, G. Machavariani, N. Davidson, A. A. Friesem, E. Hasman, “Conversion of a high-order mode beam into a nearly Gaussian beam using a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
[CrossRef] [PubMed]

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

G. Machavariani, N. Davidson, A. A. Ishaaya, A. A. Friesem, E. Hasman, “Efficient formation of a high-quality beam from a pure high-order Hermite-Gaussian mode,” Opt. Lett. 27, 1501–1503 (2002).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–385 (2001).
[CrossRef]

N. Davidson, A. A. Friesem, E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

Eismann, M. T.

Elkin, N. N.

Friesem, A. A.

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

A. A. Ishaaya, G. Machavariani, N. Davidson, A. A. Friesem, E. Hasman, “Conversion of a high-order mode beam into a nearly Gaussian beam using a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
[CrossRef] [PubMed]

G. Machavariani, N. Davidson, A. A. Ishaaya, A. A. Friesem, E. Hasman, “Efficient formation of a high-quality beam from a pure high-order Hermite-Gaussian mode,” Opt. Lett. 27, 1501–1503 (2002).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–385 (2001).
[CrossRef]

N. Davidson, A. A. Friesem, E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

Gerber, M.

M. Gerber, T. Graf, “Generation of super-Gaussian modes in Nd:YAG lasers with graded-phase mirrors,” in Proceedings of International Conference on Advanced Laser Technologies, 15–20 September 2002, Adelboden, Switzerland, pp. 3–4.

Graf, T.

T. Graf, J. E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[CrossRef]

M. Gerber, T. Graf, “Generation of super-Gaussian modes in Nd:YAG lasers with graded-phase mirrors,” in Proceedings of International Conference on Advanced Laser Technologies, 15–20 September 2002, Adelboden, Switzerland, pp. 3–4.

Hasman, E.

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

A. A. Ishaaya, G. Machavariani, N. Davidson, A. A. Friesem, E. Hasman, “Conversion of a high-order mode beam into a nearly Gaussian beam using a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
[CrossRef] [PubMed]

G. Machavariani, N. Davidson, A. A. Ishaaya, A. A. Friesem, E. Hasman, “Efficient formation of a high-quality beam from a pure high-order Hermite-Gaussian mode,” Opt. Lett. 27, 1501–1503 (2002).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–385 (2001).
[CrossRef]

N. Davidson, A. A. Friesem, E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

Ishaaya, A. A.

Leger, J. R.

Machavariani, G.

Murphy, J. B.

J. B. Murphy, “Phase space conservation and selection rules for astigmatic mode converters,” Opt. Commun. 165, 11–18 (1999).
[CrossRef]

Napartovich, A. A.

Oron, R.

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–385 (2001).
[CrossRef]

Rhodes, P. W.

P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 20, 3545–3553 (1980).
[CrossRef]

Shealy, D. L.

P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 20, 3545–3553 (1980).
[CrossRef]

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

Tai, A. M.

Troschieva, V. N.

Vysotsky, D. V.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

N. Davidson, A. A. Friesem, E. Hasman, “Diffractive elements for annular laser beam transformation,” Appl. Phys. Lett. 61, 381–383 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Quantum Electron. (1)

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

Opt. Commun. (2)

J. B. Murphy, “Phase space conservation and selection rules for astigmatic mode converters,” Opt. Commun. 165, 11–18 (1999).
[CrossRef]

T. Graf, J. E. Balmer, “Laser beam quality, entropy and the limits of beam shaping,” Opt. Commun. 131, 77–83 (1996).
[CrossRef]

Opt. Lett. (2)

Prog. Opt. (1)

R. Oron, N. Davidson, A. A. Friesem, E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–385 (2001).
[CrossRef]

Other (2)

M. Gerber, T. Graf, “Generation of super-Gaussian modes in Nd:YAG lasers with graded-phase mirrors,” in Proceedings of International Conference on Advanced Laser Technologies, 15–20 September 2002, Adelboden, Switzerland, pp. 3–4.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Arrangements for converting a TEM01 mode distribution to nearly Gaussian distributions: (a) modified Mach-Zehnder interferometer arrangement with nonsymmetrical folding; (b) arrangement for symmetrical folding that allows exact matching of the individual lobes; (c) arrangement for nonsymmetrical folding that includes orthogonal polarizations.

Fig. 2
Fig. 2

Compact arrangements for obtaining a nearly Gaussian beam from a TEM01 mode: (a) compact single-plate mode converter; (b) compact-prism mode converter.

Fig. 3
Fig. 3

Calculated conversion efficiency as function of the relative shift parameter x 0/w: (a), efficiency for the nonsymmetrical folding arrangements in Figs. 1(a) and 1(c); (b), efficiency for the symmetrical folding arrangement in Fig. 1(b). The maximal efficiency obtained for nonsymmetrical folding is 98.5% (x 0/w = 1.62), while for the symmetrical folding it is 100% (x 0/w = 1.41).

Fig. 4
Fig. 4

Calculated beam-quality factor M x 2 as a function of the relative shift parameter x 0/w: (a), nonsymmetrical folding arrangements in Figs. 1(a) and 1(c); (b), symmetrical folding arrangement in Fig. 1(b).

Fig. 5
Fig. 5

Experimental results obtained with the arrangement in Fig. 1(a): (a), (b) near-field and far-field intensity distributions of the incident TEM01 beam derived from a cw Nd:YAG laser; (c), (d) near-field and far-field intensity distributions of the high-quality, nearly Gaussian output beam. The cross sections in x and y directions are shown at the bottom and left sides.

Fig. 6
Fig. 6

Experimental results obtained with the arrangement in Fig. 2(a): (a), (b) near-field and far-field intensity distributions of the incident TEM01 beam derived from a pulsed Nd:YAG laser; (c), (d) near-field and far-field intensity distributions of the combined nearly Gaussian output beam.

Fig. 7
Fig. 7

Experimental results obtained with the arrangement in Fig. 2(b): (a), (b) near-field and far-field intensity distributions of the incident TEM01 beam derived from a pulsed Nd:YAG laser; (c), (d) near-field and far-field intensity distributions of the output nearly Gaussian beam.

Fig. 8
Fig. 8

Conversion of a Gaussian distribution into a TEM01 mode distribution by using the single-interferometric-element arrangement in Fig. 2(a): (a), (b) near-field and far-field intensity distributions of the incident Gaussian beam; (c) near-field intensity distribution of the TEM01 output beam; (d) far-field intensity distribution of the TEM01 output beam when the phase of each lobe in the near field is the same; (e) far-field intensity distribution of the TEM01 output beam with a conventional TEM01 phase distribution.

Equations (3)

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2d tanarcsin12n=2x0,
C=1-- |U1x-U2x-x0|2dx2 - {|U1x|2+|U2x-x0|2}dx,
Mx2=4πσxσsx,

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