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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2004

2002

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

2001

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

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

2000

1999

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

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

1998

1997

1994

1986

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

1968

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

1966

H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

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.

H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

Li, T.

H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

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.

H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

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)

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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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