Abstract

We present a relatively simple method for efficiently transforming a single high-order mode into a nearly Gaussian beam of much higher quality. The method is based on dividing the mode into equal parts that are then combined coherently. We illustrate the method by transforming a Hermite–Gaussian (1, 0) mode with Mx2=3 into a nearly Gaussian beam with Mx2=1.045. Experimental results are presented and compared with theoretical results.

© 2002 Optical Society of America

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References

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  1. A. E. Siegman, Proc. SPIE 1224, 2 (1990).
    [CrossRef]
  2. R. Oron, Y. Danziger, N. Davidson, and A. A. Friesem, Appl. Phys. Lett. 74, 1373 (1999).
    [CrossRef]
  3. R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 169, 115 (1999).
    [CrossRef]
  4. R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, Oxford, 2001), Vol. 42, Chap. 6.
  5. A. E. Siegman, Opt. Lett. 18, 675 (1993).
    [CrossRef] [PubMed]
  6. R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Lett. 25, 939 (2000).
    [CrossRef]
  7. R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 193, 227 (2001).
    [CrossRef]
  8. T. Graf and J. E. Balmer, Opt. Commun. 131, 77 (1996).
    [CrossRef]
  9. N. Davidson, A. A. Friesem, and E. Hasman, Appl. Phys. Lett. 61, 381 (1992).
    [CrossRef]
  10. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  11. It seems that the combined summation of two halves is smoother and more symmetric and hence resembles a Gaussian better than each half separately (see Fig. 2).
  12. J. B. Murphy, Opt. Commun. 165, 11 (1999).
    [CrossRef]

2001 (1)

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 193, 227 (2001).
[CrossRef]

2000 (1)

1999 (3)

R. Oron, Y. Danziger, N. Davidson, and A. A. Friesem, Appl. Phys. Lett. 74, 1373 (1999).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 169, 115 (1999).
[CrossRef]

J. B. Murphy, Opt. Commun. 165, 11 (1999).
[CrossRef]

1996 (1)

T. Graf and J. E. Balmer, Opt. Commun. 131, 77 (1996).
[CrossRef]

1993 (1)

1992 (1)

N. Davidson, A. A. Friesem, and E. Hasman, Appl. Phys. Lett. 61, 381 (1992).
[CrossRef]

1990 (1)

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

Balmer, J. E.

T. Graf and J. E. Balmer, Opt. Commun. 131, 77 (1996).
[CrossRef]

Danziger, Y.

R. Oron, Y. Danziger, N. Davidson, and A. A. Friesem, Appl. Phys. Lett. 74, 1373 (1999).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 169, 115 (1999).
[CrossRef]

Davidson, N.

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 193, 227 (2001).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Lett. 25, 939 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 169, 115 (1999).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, and A. A. Friesem, Appl. Phys. Lett. 74, 1373 (1999).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, Appl. Phys. Lett. 61, 381 (1992).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, Oxford, 2001), Vol. 42, Chap. 6.

Friesem, A. A.

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 193, 227 (2001).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Lett. 25, 939 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, and A. A. Friesem, Appl. Phys. Lett. 74, 1373 (1999).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 169, 115 (1999).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, Appl. Phys. Lett. 61, 381 (1992).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, Oxford, 2001), Vol. 42, Chap. 6.

Graf, T.

T. Graf and J. E. Balmer, Opt. Commun. 131, 77 (1996).
[CrossRef]

Hasman, E.

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 193, 227 (2001).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Lett. 25, 939 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 169, 115 (1999).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, Appl. Phys. Lett. 61, 381 (1992).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, Oxford, 2001), Vol. 42, Chap. 6.

Murphy, J. B.

J. B. Murphy, Opt. Commun. 165, 11 (1999).
[CrossRef]

Oron, R.

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 193, 227 (2001).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Lett. 25, 939 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, and A. A. Friesem, Appl. Phys. Lett. 74, 1373 (1999).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 169, 115 (1999).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, Oxford, 2001), Vol. 42, Chap. 6.

Siegman, A. E.

A. E. Siegman, Opt. Lett. 18, 675 (1993).
[CrossRef] [PubMed]

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Appl. Phys. Lett. (2)

R. Oron, Y. Danziger, N. Davidson, and A. A. Friesem, Appl. Phys. Lett. 74, 1373 (1999).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, Appl. Phys. Lett. 61, 381 (1992).
[CrossRef]

Opt. Commun. (4)

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 193, 227 (2001).
[CrossRef]

T. Graf and J. E. Balmer, Opt. Commun. 131, 77 (1996).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 169, 115 (1999).
[CrossRef]

J. B. Murphy, Opt. Commun. 165, 11 (1999).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

Other (3)

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, in Progress in Optics, E. Wolf, ed. (Pergamon, Oxford, 2001), Vol. 42, Chap. 6.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

It seems that the combined summation of two halves is smoother and more symmetric and hence resembles a Gaussian better than each half separately (see Fig. 2).

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Figures (5)

Fig. 1
Fig. 1

Arrangement for obtaining a nearly Gaussian beam from a HG10 mode. The sharp mirror reflects only one spot, whereas the other two mirrors reflect the spots toward the 50% beam splitter where they are combined coherently. The phase tuning plate permits fine adjustment of the relative phases of the two beams to produce the best coherent summation.

Fig. 2
Fig. 2

Coherent summation of the two spots of the HG10 mode. The left-hand spot (dashed curve) is shifted to the right-hand by a shift parameter x0/w=1.6 (see arrow), so it will almost coincide with the right-hand spot (dashed curve) and thereby produce the coherent sum of the two spots (solid curve).

Fig. 3
Fig. 3

(a) Relative power leakage and (b) beam-quality factor M2 as functions of relative shift parameter x0/w. It is evident that the power leakage is minimal at x0/w=1.6. The M2 value obtained at x0/w=1.6 is 1.045.

Fig. 4
Fig. 4

Experimental intensity distributions of the HG10 mode: (a) near field, (b) far field.

Fig. 5
Fig. 5

Experimental intensity distributions of the output high-quality, nearly Gaussian beam: (a) near field, (b) far field. Cross sections in the x and y directions are shown at the bottom and left-hand sides.

Equations (2)

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ΔPP=-U1x-U2x-x02dx2-U12x+U22x-x0dx,
Mx2=4πσxσsx,

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