Abstract

We demonstrate a paradigm in absolute laser radiometry where a laser beam’s power can be measured from its radiation pressure. Using an off-the-shelf high-accuracy mass scale, a 530 W Yb-doped fiber laser, and a 92 kW CO2 laser, we present preliminary results of absolute optical power measurements with inaccuracies of better than 7% to 13%. We find negligible contribution from radiometric (thermal) forces. We also identify this scale’s dynamic-force noise floor for a 0.1 Hz modulation frequency as 4μN/Hz1/2 or, as optical power sensitivity, 600W/Hz1/2.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. E. Martin, N. P. Fox, and P. J. Key, Metrologia 21, 147 (1985).
    [CrossRef]
  2. R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, IEEE Trans. Instrum. Meas. 21, 434 (1972).
    [CrossRef]
  3. S. R. Gunn, Rev. Sci. Instrum. 45, 936 (1974).
    [CrossRef]
  4. C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” presented at the 11th Conference on New Developments and Applications in Optical Radiometry, Maui, Hawaii, USA, September19–23, 2011.
  5. J. C. Maxwell, A Treatise on Electricity and Magnetism, 1st ed. (Oxford University, 1873), p. 391.
  6. E. F. Nichols and G. F. Hull, Phys. Rev. 13, 307 (1901).
    [CrossRef]
  7. E. F. Nichols and G. F. Hull, Astrophys. J. 17, 315 (1903).
    [CrossRef]
  8. J. J. Cook, W. L. Flowers, and C. B. Arnold, Proc. IRE 50, 1693 (1962).
  9. M. Stimler, Z. I. Slawsky, and R. E. Grantham, Rev. Scient. Instrum. 35, 311 (1964).
    [CrossRef]
  10. G. Roosen and C. Imbert, Opt. Eng. 20, 203437 (1981).
    [CrossRef]
  11. G. T. Gillies, Fizika 19, 407 (1987).
  12. Y. Yuan, Rev. Sci. Instrum. 61, 1743 (1990).
    [CrossRef]
  13. G. T. Gillies and R. C. Ritter, Rev. Sci. Instrum. 64, 283 (1993).
    [CrossRef]
  14. V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, Metrologia 46, 277 (2009).
    [CrossRef]
  15. F. C. Maring, “High resolution offset electronic weighing devices and methods,” U.S. patent7,315,003 B2 (January1, 2008).
  16. P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, Appl. Phys. Lett., 102, 184103 (2013).
  17. D. J. Wineland and W. M. Itano, Phys. Rev. A 20, 1521 (1979).
    [CrossRef]
  18. A. Dogariu, S. Sukhov, and J. J. Sáenz, Nat. Photonics 7, 24 (2012).
    [CrossRef]
  19. M. Scandurra, “Enhanced radiometric forces,” arXiv: physics/0402011v1 (2004).

2013 (1)

P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, Appl. Phys. Lett., 102, 184103 (2013).

2012 (1)

A. Dogariu, S. Sukhov, and J. J. Sáenz, Nat. Photonics 7, 24 (2012).
[CrossRef]

2009 (1)

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, Metrologia 46, 277 (2009).
[CrossRef]

1993 (1)

G. T. Gillies and R. C. Ritter, Rev. Sci. Instrum. 64, 283 (1993).
[CrossRef]

1990 (1)

Y. Yuan, Rev. Sci. Instrum. 61, 1743 (1990).
[CrossRef]

1987 (1)

G. T. Gillies, Fizika 19, 407 (1987).

1985 (1)

J. E. Martin, N. P. Fox, and P. J. Key, Metrologia 21, 147 (1985).
[CrossRef]

1981 (1)

G. Roosen and C. Imbert, Opt. Eng. 20, 203437 (1981).
[CrossRef]

1979 (1)

D. J. Wineland and W. M. Itano, Phys. Rev. A 20, 1521 (1979).
[CrossRef]

1974 (1)

S. R. Gunn, Rev. Sci. Instrum. 45, 936 (1974).
[CrossRef]

1972 (1)

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, IEEE Trans. Instrum. Meas. 21, 434 (1972).
[CrossRef]

1964 (1)

M. Stimler, Z. I. Slawsky, and R. E. Grantham, Rev. Scient. Instrum. 35, 311 (1964).
[CrossRef]

1962 (1)

J. J. Cook, W. L. Flowers, and C. B. Arnold, Proc. IRE 50, 1693 (1962).

1903 (1)

E. F. Nichols and G. F. Hull, Astrophys. J. 17, 315 (1903).
[CrossRef]

1901 (1)

E. F. Nichols and G. F. Hull, Phys. Rev. 13, 307 (1901).
[CrossRef]

Arnold, C. B.

J. J. Cook, W. L. Flowers, and C. B. Arnold, Proc. IRE 50, 1693 (1962).

Brand, U.

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, Metrologia 46, 277 (2009).
[CrossRef]

Case, W. E.

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, IEEE Trans. Instrum. Meas. 21, 434 (1972).
[CrossRef]

Cook, J. J.

J. J. Cook, W. L. Flowers, and C. B. Arnold, Proc. IRE 50, 1693 (1962).

Cromer, C. L.

C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” presented at the 11th Conference on New Developments and Applications in Optical Radiometry, Maui, Hawaii, USA, September19–23, 2011.

Dogariu, A.

A. Dogariu, S. Sukhov, and J. J. Sáenz, Nat. Photonics 7, 24 (2012).
[CrossRef]

Dowell, M. L.

C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” presented at the 11th Conference on New Developments and Applications in Optical Radiometry, Maui, Hawaii, USA, September19–23, 2011.

Flowers, W. L.

J. J. Cook, W. L. Flowers, and C. B. Arnold, Proc. IRE 50, 1693 (1962).

Fox, N. P.

J. E. Martin, N. P. Fox, and P. J. Key, Metrologia 21, 147 (1985).
[CrossRef]

Frumin, L. L.

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, Metrologia 46, 277 (2009).
[CrossRef]

Gillies, G. T.

G. T. Gillies and R. C. Ritter, Rev. Sci. Instrum. 64, 283 (1993).
[CrossRef]

G. T. Gillies, Fizika 19, 407 (1987).

Grantham, R. E.

M. Stimler, Z. I. Slawsky, and R. E. Grantham, Rev. Scient. Instrum. 35, 311 (1964).
[CrossRef]

Gunn, S. R.

S. R. Gunn, Rev. Sci. Instrum. 45, 936 (1974).
[CrossRef]

Hull, G. F.

E. F. Nichols and G. F. Hull, Astrophys. J. 17, 315 (1903).
[CrossRef]

E. F. Nichols and G. F. Hull, Phys. Rev. 13, 307 (1901).
[CrossRef]

Imbert, C.

G. Roosen and C. Imbert, Opt. Eng. 20, 203437 (1981).
[CrossRef]

Itano, W. M.

D. J. Wineland and W. M. Itano, Phys. Rev. A 20, 1521 (1979).
[CrossRef]

Key, P. J.

J. E. Martin, N. P. Fox, and P. J. Key, Metrologia 21, 147 (1985).
[CrossRef]

Lehman, J. H.

C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” presented at the 11th Conference on New Developments and Applications in Optical Radiometry, Maui, Hawaii, USA, September19–23, 2011.

Li, X.

C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” presented at the 11th Conference on New Developments and Applications in Optical Radiometry, Maui, Hawaii, USA, September19–23, 2011.

Maring, F. C.

F. C. Maring, “High resolution offset electronic weighing devices and methods,” U.S. patent7,315,003 B2 (January1, 2008).

Martin, J. E.

J. E. Martin, N. P. Fox, and P. J. Key, Metrologia 21, 147 (1985).
[CrossRef]

Maxwell, J. C.

J. C. Maxwell, A Treatise on Electricity and Magnetism, 1st ed. (Oxford University, 1873), p. 391.

Mueller, M.

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, Metrologia 46, 277 (2009).
[CrossRef]

Nesterov, V.

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, Metrologia 46, 277 (2009).
[CrossRef]

Nichols, E. F.

E. F. Nichols and G. F. Hull, Astrophys. J. 17, 315 (1903).
[CrossRef]

E. F. Nichols and G. F. Hull, Phys. Rev. 13, 307 (1901).
[CrossRef]

Pratt, J. R.

P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, Appl. Phys. Lett., 102, 184103 (2013).

Rasmussen, A. L.

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, IEEE Trans. Instrum. Meas. 21, 434 (1972).
[CrossRef]

Ritter, R. C.

G. T. Gillies and R. C. Ritter, Rev. Sci. Instrum. 64, 283 (1993).
[CrossRef]

Roosen, G.

G. Roosen and C. Imbert, Opt. Eng. 20, 203437 (1981).
[CrossRef]

Russell, T. W.

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, IEEE Trans. Instrum. Meas. 21, 434 (1972).
[CrossRef]

Sáenz, J. J.

A. Dogariu, S. Sukhov, and J. J. Sáenz, Nat. Photonics 7, 24 (2012).
[CrossRef]

Scandurra, M.

M. Scandurra, “Enhanced radiometric forces,” arXiv: physics/0402011v1 (2004).

Shaw, G. A.

P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, Appl. Phys. Lett., 102, 184103 (2013).

Slawsky, Z. I.

M. Stimler, Z. I. Slawsky, and R. E. Grantham, Rev. Scient. Instrum. 35, 311 (1964).
[CrossRef]

Smith, R. L.

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, IEEE Trans. Instrum. Meas. 21, 434 (1972).
[CrossRef]

Stimler, M.

M. Stimler, Z. I. Slawsky, and R. E. Grantham, Rev. Scient. Instrum. 35, 311 (1964).
[CrossRef]

Sukhov, S.

A. Dogariu, S. Sukhov, and J. J. Sáenz, Nat. Photonics 7, 24 (2012).
[CrossRef]

Wilkinson, P. R.

P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, Appl. Phys. Lett., 102, 184103 (2013).

Wineland, D. J.

D. J. Wineland and W. M. Itano, Phys. Rev. A 20, 1521 (1979).
[CrossRef]

Yuan, Y.

Y. Yuan, Rev. Sci. Instrum. 61, 1743 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, Appl. Phys. Lett., 102, 184103 (2013).

Astrophys. J. (1)

E. F. Nichols and G. F. Hull, Astrophys. J. 17, 315 (1903).
[CrossRef]

Fizika (1)

G. T. Gillies, Fizika 19, 407 (1987).

IEEE Trans. Instrum. Meas. (1)

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, IEEE Trans. Instrum. Meas. 21, 434 (1972).
[CrossRef]

Metrologia (2)

J. E. Martin, N. P. Fox, and P. J. Key, Metrologia 21, 147 (1985).
[CrossRef]

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, Metrologia 46, 277 (2009).
[CrossRef]

Nat. Photonics (1)

A. Dogariu, S. Sukhov, and J. J. Sáenz, Nat. Photonics 7, 24 (2012).
[CrossRef]

Opt. Eng. (1)

G. Roosen and C. Imbert, Opt. Eng. 20, 203437 (1981).
[CrossRef]

Phys. Rev. (1)

E. F. Nichols and G. F. Hull, Phys. Rev. 13, 307 (1901).
[CrossRef]

Phys. Rev. A (1)

D. J. Wineland and W. M. Itano, Phys. Rev. A 20, 1521 (1979).
[CrossRef]

Proc. IRE (1)

J. J. Cook, W. L. Flowers, and C. B. Arnold, Proc. IRE 50, 1693 (1962).

Rev. Sci. Instrum. (3)

S. R. Gunn, Rev. Sci. Instrum. 45, 936 (1974).
[CrossRef]

Y. Yuan, Rev. Sci. Instrum. 61, 1743 (1990).
[CrossRef]

G. T. Gillies and R. C. Ritter, Rev. Sci. Instrum. 64, 283 (1993).
[CrossRef]

Rev. Scient. Instrum. (1)

M. Stimler, Z. I. Slawsky, and R. E. Grantham, Rev. Scient. Instrum. 35, 311 (1964).
[CrossRef]

Other (4)

C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” presented at the 11th Conference on New Developments and Applications in Optical Radiometry, Maui, Hawaii, USA, September19–23, 2011.

J. C. Maxwell, A Treatise on Electricity and Magnetism, 1st ed. (Oxford University, 1873), p. 391.

F. C. Maring, “High resolution offset electronic weighing devices and methods,” U.S. patent7,315,003 B2 (January1, 2008).

M. Scandurra, “Enhanced radiometric forces,” arXiv: physics/0402011v1 (2004).

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 (7)

Fig. 1.
Fig. 1.

Layout of radiation pressure measurement. In this work, the laser beam propagates entirely in a horizontal plane, requiring the scale to operate in a “vertical” orientation with the mirror surface in a vertical plane.

Fig. 2.
Fig. 2.

Scale reading (in force units) for 530 W incident power modulated at 0.1 Hz. The average y-axis value is arbitrary since it includes the initial (nonzero) mass reading of the scale.

Fig. 3.
Fig. 3.

Measured radiation force versus effective laser power (includes mirror reflectivity and angle of incidence). Circles are 1071 nm laser; squares are 10.6 μm laser. The solid line indicates the theoretical force-to-power slope.

Fig. 4.
Fig. 4.

CO2 laser power versus time (92 kW injected power) measured by radiation pressure. The solid curve is scale output corrected for incidence angle and mirror reflectivity; shaded region indicates injection amplitude and duration.

Fig. 5.
Fig. 5.

Scale verification showing error as percent disagreement of scale readings with calibrated masses. Repeated measurements indicate measurement variability.

Fig. 6.
Fig. 6.

Measured force amplitude (solid circles) for various angles of incidence demonstrating expected cosine dependence (solid line).

Fig. 7.
Fig. 7.

Force spectrum from scale with 0.1 Hz modulated laser power, 533 W incident on mirror (black), and 4.6 W incident on absorber (light red). With no signal, we treat the absorber curve as our noise floor.

Equations (2)

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

F=(2P/c)rcos(θ),
Fopt=gπ2m(t)sin(ωt)2+m(t)cos(ωt)2,

Metrics