Abstract

An experimental technique to observe and accurately measure the Gouy phase evolution of Hermite–Gaussian modes is presented. Because of the unique features of spatial mode interference frequency-locking error signals, we are able to readily perform explicit measurement of the Gouy phase in a simple and highly accurate manner. We present these data and discuss the technique and its implications.

© 2004 Optical Society of America

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References

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  1. L. G. Gouy, Acad. Sci. Paris 110, 1251 (1890).
  2. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  3. M. F. Erden and H. M. Ozaktas, J. Opt. Soc. Am. A 14, 2190 (1997).
    [CrossRef]
  4. T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, Opt. Commun. 189, 5 (2001).
    [CrossRef]
  5. S. Feng and H. G. Winful, Opt. Lett. 26, 485 (2001).
    [CrossRef]
  6. A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, Phys. Rev. Lett. 83, 3410 (1999).
    [CrossRef]
  7. T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, Phys. Rev. Lett. 88, 257402 (2002).
    [CrossRef]
  8. G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
    [CrossRef]
  9. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, Appl. Opt. 33, 5037 (1994).
    [CrossRef] [PubMed]
  10. N. Mavalala, D. Sigg, and D. Shoemaker, Appl. Opt. 37, 7743 (1998).
    [CrossRef]
  11. H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Wilke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, J. Hough, and K. Danzmann, Appl. Opt. 43, 1938 (2004).
    [CrossRef] [PubMed]
  12. J. Arlt and M. J. Padgett, Opt. Lett. 25, 191 (2000).
    [CrossRef]
  13. D. A. Shaddock, M. B. Gray, and D. E. McClelland, Opt. Lett. 24, 1499 (1999).
    [CrossRef]
  14. H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]
  15. J. H. Chow, D. Rabeling, M. B. Gray, D. E. McClelland, and G. de Vine, Class. Quantum Grav. 21, S909 (2004).
    [CrossRef]
  16. G. Mueller, Q. Z. Shu, R. Adhikari, D. Tanner, D. Reitze, D. Sigg, N. Mavalala, and J. Camp, Opt. Lett. 25, 266 (2000).
    [CrossRef]

2004

2002

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef]

2001

T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, Opt. Commun. 189, 5 (2001).
[CrossRef]

S. Feng and H. G. Winful, Opt. Lett. 26, 485 (2001).
[CrossRef]

2000

1999

D. A. Shaddock, M. B. Gray, and D. E. McClelland, Opt. Lett. 24, 1499 (1999).
[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, Phys. Rev. Lett. 83, 3410 (1999).
[CrossRef]

1998

1997

1994

1968

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

1966

1890

L. G. Gouy, Acad. Sci. Paris 110, 1251 (1890).

Ackemann, T.

T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, Opt. Commun. 189, 5 (2001).
[CrossRef]

Adhikari, R.

Arlt, J.

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Camp, J.

Casey, M. M.

Chow, J. H.

J. H. Chow, D. Rabeling, M. B. Gray, D. E. McClelland, and G. de Vine, Class. Quantum Grav. 21, S909 (2004).
[CrossRef]

Danzmann, K.

de Vine, G.

J. H. Chow, D. Rabeling, M. B. Gray, D. E. McClelland, and G. de Vine, Class. Quantum Grav. 21, S909 (2004).
[CrossRef]

Erden, M. F.

Feng, S.

S. Feng and H. G. Winful, Opt. Lett. 26, 485 (2001).
[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, Phys. Rev. Lett. 83, 3410 (1999).
[CrossRef]

Feurer, T.

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef]

Freise, A.

Gossler, S.

Gouy, L. G.

L. G. Gouy, Acad. Sci. Paris 110, 1251 (1890).

Gray, M. B.

J. H. Chow, D. Rabeling, M. B. Gray, D. E. McClelland, and G. de Vine, Class. Quantum Grav. 21, S909 (2004).
[CrossRef]

D. A. Shaddock, M. B. Gray, and D. E. McClelland, Opt. Lett. 24, 1499 (1999).
[CrossRef]

Grosse-Nobis, W.

T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, Opt. Commun. 189, 5 (2001).
[CrossRef]

Grote, H.

Heinzel, G.

Hough, J.

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Kogelnik, H.

Li, T.

Lippi, G. L.

T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, Opt. Commun. 189, 5 (2001).
[CrossRef]

Lück, H.

Mavalala, N.

McClelland, D. E.

J. H. Chow, D. Rabeling, M. B. Gray, D. E. McClelland, and G. de Vine, Class. Quantum Grav. 21, S909 (2004).
[CrossRef]

D. A. Shaddock, M. B. Gray, and D. E. McClelland, Opt. Lett. 24, 1499 (1999).
[CrossRef]

Meers, B. J.

Morrison, E.

Mueller, G.

Nelson, K. A.

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef]

Ozaktas, H. M.

Padgett, M. J.

Rabeling, D.

J. H. Chow, D. Rabeling, M. B. Gray, D. E. McClelland, and G. de Vine, Class. Quantum Grav. 21, S909 (2004).
[CrossRef]

Reitze, D.

Robertson, D.

Robertson, D. I.

Rudd, J. V.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, Phys. Rev. Lett. 83, 3410 (1999).
[CrossRef]

Ruffin, A. B.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, Phys. Rev. Lett. 83, 3410 (1999).
[CrossRef]

Shaddock, D. A.

Shoemaker, D.

Shu, Q. Z.

Siegman, A. E.

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

Sigg, D.

Stoyanov, N. S.

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef]

Strain, K. A.

Tanner, D.

Ward, D. W.

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef]

Ward, H.

Whitaker, J. F.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, Phys. Rev. Lett. 83, 3410 (1999).
[CrossRef]

Wilke, B.

Winful, H. G.

S. Feng and H. G. Winful, Opt. Lett. 26, 485 (2001).
[CrossRef]

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, Phys. Rev. Lett. 83, 3410 (1999).
[CrossRef]

Acad. Sci. Paris

L. G. Gouy, Acad. Sci. Paris 110, 1251 (1890).

Appl. Opt.

Class. Quantum Grav.

J. H. Chow, D. Rabeling, M. B. Gray, D. E. McClelland, and G. de Vine, Class. Quantum Grav. 21, S909 (2004).
[CrossRef]

J. Appl. Phys.

G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, Opt. Commun. 189, 5 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, Phys. Rev. Lett. 83, 3410 (1999).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, and K. A. Nelson, Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef]

Other

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

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Figures (4)

Fig. 1
Fig. 1

Theoretical plots of (a) Gouy phase evolution from the waist, with a lens placed 0.6 m after the waist and (b) calculated error signals for various Δφ1,0.

Fig. 2
Fig. 2

Optical layout of the Gouy phase measurement setup. See text for definitions. QPD2 was placed at Δφ1,0=3π/2, and its error signature was monitored and maintained to ensure θ=-π/2, while the Δφ1,0 of QPD1 was varied.

Fig. 3
Fig. 3

(a)–(e) Sample experimental error signatures at various Δφ1,0 as observed from QPD1. (f) Error signature from QPD2, which corresponds to θ=-π/2.

Fig. 4
Fig. 4

Experimental versus calculated plots for (a) spot size and (b) Gouy phase evolution as seen by QPD1. The two data points denoted by circles show the corresponding experimental θ values for M1 and M2.

Equations (5)

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

φnz=n+1arctanλzπω02,
vz,Δν-0u˜0*x,z,Δνu˜1x,zdx-0u˜0*x,z,Δνu˜1x,zdx,
u˜0x,z,Δν=r˜cavΔνexp-jkz-φ0zU˜0x,z,u˜1x,z=exp-jkz-θ-φ1zU˜1x,z,
r˜cavΔν=rcΔνexpjϕcΔν
vz,ΔνrcΔνcosθ+Δφ1,0z+ϕcΔν.

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