Abstract

We present a fast and easy technique for measuring the beam propagation ratio, M2, of laser beams using a spatial light modulator. Our technique is based on digitally simulating the free-space propagation of light, thus eliminating the need for the traditional scan in the propagation direction. We illustrate two approaches to achieving this, neither of which requires any information of the laser beam under investigation nor necessitates any moving optical components. The comparison with theoretical predictions reveals excellent agreement and proves the accuracy of the technique.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. E. Siegman, in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues (Optical Society of America, 1998), p. MQ1.
  2. ISO, “ISO 11146-1:2005 Test methods for laser beam widths, divergence angles and beam propagation ratios. Part 1: Stigmatic and simple astigmatic beams” (2005).
  3. ISO, “ISO 11146-2:2005 Test methods for laser beam widths, divergence angles and beam propagation ratios. Part 2: General astigmatic beams” (2005).
  4. J. Strohaber, G. Kaya, N. Kaya, N. Hart, A. A. Kolomenskii, G. G. Paulus, and H. A. Schuessler, Opt. Express 19, 14321 (2011).
    [CrossRef]
  5. B. Neubert, G. Huber, and W.-D. Scharfe, J. Phys. D 34, 2414 (2001).
    [CrossRef]
  6. G. Nemes and A. E. Siegman, J. Opt. Soc. Am. A 11, 2257 (1994).
    [CrossRef]
  7. R. W. Lambert, R. Cortés-Martínez, A. J. Waddie, J. D. Shephard, M. R. Taghizadeh, A. H. Greenaway, and D. P. Hand, Appl. Opt. 43, 5037 (2004).
    [CrossRef]
  8. M. Scaggs and G. Haas, Proc. SPIE 8236, 82360H-1 (2012).
  9. A. Letsch, Charakterisierung allgemein astigmatischer Laserstrahlung mit der Methode der zweiten Momente (Herbert Utz Verlag GmbH, 2009).
  10. D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, and M. Duparré, Appl. Opt. 51, 987 (2012).
    [CrossRef]
  11. O. A. Schmidt, C. Schulze, D. Flamm, R. Brüning, T. Kaiser, S. Schröter, and M. Duparré, Opt. Express 19, 6741 (2011).
    [CrossRef]
  12. P. Kwee, F. Seifert, B. Willke, and K. Danzmann, Rev. Sci. Instrum. 78, 073103 (2007).
    [CrossRef]
  13. J. W. Goodman, Introduction to Fourier Optics(McGraw-Hill Publishing Company, 1968).
  14. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, J. Opt. Soc. Am. A 24, 3500 (2007).
    [CrossRef]
  15. D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré, Opt. Lett. 37, 2478 (2012).
    [CrossRef]
  16. C. Mafusire and A. Forbes, J. Opt. Soc. Am. A 28, 1372 (2011).
    [CrossRef]

2012 (3)

2011 (3)

2007 (2)

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, J. Opt. Soc. Am. A 24, 3500 (2007).
[CrossRef]

2004 (1)

2001 (1)

B. Neubert, G. Huber, and W.-D. Scharfe, J. Phys. D 34, 2414 (2001).
[CrossRef]

1994 (1)

Arrizón, V.

Brüning, R.

Carrada, R.

Cortés-Martínez, R.

Danzmann, K.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Duparré, M.

Flamm, D.

Forbes, A.

González, L. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics(McGraw-Hill Publishing Company, 1968).

Greenaway, A. H.

Haas, G.

M. Scaggs and G. Haas, Proc. SPIE 8236, 82360H-1 (2012).

Hand, D. P.

Hart, N.

Huber, G.

B. Neubert, G. Huber, and W.-D. Scharfe, J. Phys. D 34, 2414 (2001).
[CrossRef]

Kaiser, T.

Kaya, G.

Kaya, N.

Kolomenskii, A. A.

Kwee, P.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Lambert, R. W.

Letsch, A.

A. Letsch, Charakterisierung allgemein astigmatischer Laserstrahlung mit der Methode der zweiten Momente (Herbert Utz Verlag GmbH, 2009).

Mafusire, C.

Naidoo, D.

Nemes, G.

Neubert, B.

B. Neubert, G. Huber, and W.-D. Scharfe, J. Phys. D 34, 2414 (2001).
[CrossRef]

Paulus, G. G.

Ruiz, U.

Scaggs, M.

M. Scaggs and G. Haas, Proc. SPIE 8236, 82360H-1 (2012).

Scharfe, W.-D.

B. Neubert, G. Huber, and W.-D. Scharfe, J. Phys. D 34, 2414 (2001).
[CrossRef]

Schmidt, O. A.

Schröter, S.

Schuessler, H. A.

Schulze, C.

Seifert, F.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Shephard, J. D.

Siegman, A. E.

G. Nemes and A. E. Siegman, J. Opt. Soc. Am. A 11, 2257 (1994).
[CrossRef]

A. E. Siegman, in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues (Optical Society of America, 1998), p. MQ1.

Strohaber, J.

Taghizadeh, M. R.

Waddie, A. J.

Willke, B.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. A (3)

J. Phys. D (1)

B. Neubert, G. Huber, and W.-D. Scharfe, J. Phys. D 34, 2414 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (1)

M. Scaggs and G. Haas, Proc. SPIE 8236, 82360H-1 (2012).

Rev. Sci. Instrum. (1)

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Other (5)

J. W. Goodman, Introduction to Fourier Optics(McGraw-Hill Publishing Company, 1968).

A. Letsch, Charakterisierung allgemein astigmatischer Laserstrahlung mit der Methode der zweiten Momente (Herbert Utz Verlag GmbH, 2009).

A. E. Siegman, in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues (Optical Society of America, 1998), p. MQ1.

ISO, “ISO 11146-1:2005 Test methods for laser beam widths, divergence angles and beam propagation ratios. Part 1: Stigmatic and simple astigmatic beams” (2005).

ISO, “ISO 11146-2:2005 Test methods for laser beam widths, divergence angles and beam propagation ratios. Part 2: General astigmatic beams” (2005).

Supplementary Material (4)

» Media 1: MPEG (196 KB)     
» Media 2: MPEG (240 KB)     
» Media 3: MPEG (204 KB)     
» Media 4: MPEG (252 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Schematic geometry to determine the M2 value by measuring the beam diameter d(f) as a function of different lens focal lengths f: d0, waist diameter; dL, diameter in plane of the lens; and z1,2, distances between waist and lens, and lens and CCD plane, respectively.

Fig. 2.
Fig. 2.

Experimental setup. BS, beam source; SLM, spatial light modulator; L, lens (f=400mm, only present in method B); CCD, CCD camera.

Fig. 3.
Fig. 3.

Digital holograms for three sample beams using method A with a focal length of 400 mm. (a) LG10, (b) LG1±3 (Media 1, Media 2), and (c) LG21. Insets depict resulting measured beam intensities.

Fig. 4.
Fig. 4.

Analysis of a Laguerre–Gaussian LG21 beam using (a) method A: measured beam diameter (me) as a function of programmed lens focal length f, yielding an M2=6.22 by fitting with Eq. 1 (fit). (b) method B: measured beam diameter (me) as a function of propagation distance z (Media 3, Media 4). Hyperbolic fitting (fit) yields an M2=6.04.

Tables (1)

Tables Icon

Table 1. Measured (A, B) and Expected (th) M2 Values and Waist Diameters of the Sample Beams

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

d(f)=2(2λz2M2πdL)2+dL24(1+z2(1RL1f))2,
U(r,z)=F1[F[U(r,0)]exp(ikzz)],

Metrics