Abstract

Generation of both scalar and vector hollow beams was demonstrated by using a mirror with a low-reflectivity spot to suppress the oscillation of lower order transverse modes. As scalar beams, several hollow Laguerre–Gaussian beams have been observed from a side-pumped Nd:yttrium aluminum garnet laser cavity. The intensity profiles were in an excellent agreement with theoretical ones. The phase front variation around the optical axis was verified to be spiral. Furthermore, both Laguerre–Gaussian and Bessel–Gaussian vector beams have been also observed from the identical cavity. In addition to the verification of intensity profiles, polarization pattern measurement confirmed that the beams had revolving polarization distributions along the azimuthal direction as theoretically predicted.

© 2010 Optical Society of America

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2010 (1)

2009 (3)

2008 (2)

2007 (2)

2005 (2)

V. Garbin, D. Cojoc, E. Ferrari, R. Z. Proietti, S. Cabrini, and E. D. Fabrizio, “Optical micro-manipulation using Laguerre–Gaussian beams,” Jpn. J. Appl. Phys., Part 1 44, 5773–5776 (2005).
[CrossRef]

J.-F. Bisson, Yu. Senatsky, and K. Ueda, “Generation of Laguerre–Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2, 327–333 (2005).
[CrossRef]

2001 (2)

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

Y. F. Chen and Y. P. Lan, “Dynamics of the Laguerre Gaussian TEM0,J∗ mode in a solid-state laser,” Phys. Rev. A 63, 063807 (2001).
[CrossRef]

1999 (1)

R. Oron, Y. Danziger, N. Davidson, A. A. Fresem, and E. Hasman, “Laser mode discrimination with intra-cavity spiral phase elements,” Opt. Commun. 169, 115–121 (1999).
[CrossRef]

1998 (1)

1996 (1)

1994 (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. Harris, C. A. Hill, and J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

1992 (1)

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
[CrossRef]

Barnett, S. M.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Bisson, J. -F.

J.-F. Bisson, Yu. Senatsky, and K. Ueda, “Generation of Laguerre–Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2, 327–333 (2005).
[CrossRef]

Cabrini, S.

V. Garbin, D. Cojoc, E. Ferrari, R. Z. Proietti, S. Cabrini, and E. D. Fabrizio, “Optical micro-manipulation using Laguerre–Gaussian beams,” Jpn. J. Appl. Phys., Part 1 44, 5773–5776 (2005).
[CrossRef]

Chen, Y. F.

Y. F. Chen and Y. P. Lan, “Dynamics of the Laguerre Gaussian TEM0,J∗ mode in a solid-state laser,” Phys. Rev. A 63, 063807 (2001).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Cojoc, D.

V. Garbin, D. Cojoc, E. Ferrari, R. Z. Proietti, S. Cabrini, and E. D. Fabrizio, “Optical micro-manipulation using Laguerre–Gaussian beams,” Jpn. J. Appl. Phys., Part 1 44, 5773–5776 (2005).
[CrossRef]

Danziger, Y.

R. Oron, Y. Danziger, N. Davidson, A. A. Fresem, and E. Hasman, “Laser mode discrimination with intra-cavity spiral phase elements,” Opt. Commun. 169, 115–121 (1999).
[CrossRef]

Davidson, N.

R. Oron, Y. Danziger, N. Davidson, A. A. Fresem, and E. Hasman, “Laser mode discrimination with intra-cavity spiral phase elements,” Opt. Commun. 169, 115–121 (1999).
[CrossRef]

Dubik, B.

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

Fabrizio, E. D.

V. Garbin, D. Cojoc, E. Ferrari, R. Z. Proietti, S. Cabrini, and E. D. Fabrizio, “Optical micro-manipulation using Laguerre–Gaussian beams,” Jpn. J. Appl. Phys., Part 1 44, 5773–5776 (2005).
[CrossRef]

Ferrari, E.

V. Garbin, D. Cojoc, E. Ferrari, R. Z. Proietti, S. Cabrini, and E. D. Fabrizio, “Optical micro-manipulation using Laguerre–Gaussian beams,” Jpn. J. Appl. Phys., Part 1 44, 5773–5776 (2005).
[CrossRef]

Fresem, A. A.

R. Oron, Y. Danziger, N. Davidson, A. A. Fresem, and E. Hasman, “Laser mode discrimination with intra-cavity spiral phase elements,” Opt. Commun. 169, 115–121 (1999).
[CrossRef]

Garbin, V.

V. Garbin, D. Cojoc, E. Ferrari, R. Z. Proietti, S. Cabrini, and E. D. Fabrizio, “Optical micro-manipulation using Laguerre–Gaussian beams,” Jpn. J. Appl. Phys., Part 1 44, 5773–5776 (2005).
[CrossRef]

Hall, D. G.

Harris, M.

M. Harris, C. A. Hill, and J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

Hasman, E.

R. Oron, Y. Danziger, N. Davidson, A. A. Fresem, and E. Hasman, “Laser mode discrimination with intra-cavity spiral phase elements,” Opt. Commun. 169, 115–121 (1999).
[CrossRef]

Heckenberg, N. R.

Hill, C. A.

M. Harris, C. A. Hill, and J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

Ito, A.

Itoh, M.

Kozawa, Y.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Lan, Y. P.

Y. F. Chen and Y. P. Lan, “Dynamics of the Laguerre Gaussian TEM0,J∗ mode in a solid-state laser,” Phys. Rev. A 63, 063807 (2001).
[CrossRef]

Li, C. -F.

Masajada, J.

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

McDuff, R.

Miyamoto, K.

Okida, M.

Omatsu, T.

Oron, R.

R. Oron, Y. Danziger, N. Davidson, A. A. Fresem, and E. Hasman, “Laser mode discrimination with intra-cavity spiral phase elements,” Opt. Commun. 169, 115–121 (1999).
[CrossRef]

Padgett, M. J.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
[CrossRef]

Proietti, R. Z.

V. Garbin, D. Cojoc, E. Ferrari, R. Z. Proietti, S. Cabrini, and E. D. Fabrizio, “Optical micro-manipulation using Laguerre–Gaussian beams,” Jpn. J. Appl. Phys., Part 1 44, 5773–5776 (2005).
[CrossRef]

Sato, S.

Senatsky, Yu.

J.-F. Bisson, Yu. Senatsky, and K. Ueda, “Generation of Laguerre–Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2, 327–333 (2005).
[CrossRef]

Seshadri, S. R.

Smith, C. P.

Tanaka, Y.

Tovar, A. A.

Ueda, K.

J.-F. Bisson, Yu. Senatsky, and K. Ueda, “Generation of Laguerre–Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2, 327–333 (2005).
[CrossRef]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Vaughan, J. M.

M. Harris, C. A. Hill, and J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Yatagai, T.

Zhan, Q.

Adv. Opt. Photon. (1)

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

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys., Part 1 (1)

V. Garbin, D. Cojoc, E. Ferrari, R. Z. Proietti, S. Cabrini, and E. D. Fabrizio, “Optical micro-manipulation using Laguerre–Gaussian beams,” Jpn. J. Appl. Phys., Part 1 44, 5773–5776 (2005).
[CrossRef]

Laser Phys. Lett. (1)

J.-F. Bisson, Yu. Senatsky, and K. Ueda, “Generation of Laguerre–Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2, 327–333 (2005).
[CrossRef]

Opt. Commun. (5)

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. Harris, C. A. Hill, and J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Fresem, and E. Hasman, “Laser mode discrimination with intra-cavity spiral phase elements,” Opt. Commun. 169, 115–121 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (1)

Y. F. Chen and Y. P. Lan, “Dynamics of the Laguerre Gaussian TEM0,J∗ mode in a solid-state laser,” Phys. Rev. A 63, 063807 (2001).
[CrossRef]

Other (1)

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Spatial polarization patterns of the LG vector beams with the Laguerre polynomial of degree zero and order q = m ± 1 . “Upper” and “lower” in the figure correspond to the upper and lower parts of the last parentheses of Eq. (1), respectively.

Fig. 2
Fig. 2

Examples of calculated total intensity and polarization patterns of the Bessel–Gaussian vector beam.

Fig. 3
Fig. 3

A schematic diagram of an experimental setup. A laser gain medium is a Nd:YAG rod. The cavity consists of two mirrors, an output coupler, and a rear mirror. The rear mirror has a small spot with low reflectivity.

Fig. 4
Fig. 4

Intensity distributions of scalar LG beams observed. In the top row, the total intensity distributions are shown. In the middle row, the measured intensity profiles are plotted by dotted curves. Solid curves correspond to theoretical profiles of the LG beam of the order of m, which are indicated in the bottom row.

Fig. 5
Fig. 5

Observed intensity distributions of linearly polarized LG beams for m = 1 , 2, and 3. In the top row, the total intensity distributions are shown. In the middle row, the interference patterns of the LG beam with a spherical reference beam are depicted.

Fig. 6
Fig. 6

Intensity distributions of observed vector LG beams. On the left column, total intensity distributions are shown. Other four images in each row correspond to intensity distributions after passing through a linear polarizer. The direction of the linear polarizer is indicated by an arrow.

Fig. 7
Fig. 7

Observed and calculated intensity patterns of vector Bessel–Gaussian beams of m = 6 and 7. On the left-hand column, the total intensity distributions are shown. Other two images in each row are the intensity distributions after passing through a linear polarizer, namely, horizontal and vertical polarization components. The direction of the polarizer is indicated by an arrow.

Equations (5)

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E LG ( s ) ( r , ϕ , z ) = E 0 ω 0 ω ( z ) [ 2 r ω ( z ) ] | m | exp [ i ( | m | + 1 ) ψ ( z ) ] exp { r 2 [ 1 ω 2 ( z ) + i k 2 R ( z ) ] } exp ( i m ϕ ) ,
E LG ( v ) ( r , ϕ , z ) = E 0 ω 0 ω ( z ) [ 2 r ω ( z ) ] | m ± 1 | exp [ i k z + i ( | m ± 1 | + 1 ) ψ ( z ) ] exp { r 2 [ 1 ω 2 ( z ) + i k 2 R ( z ) ] } { cos ( m ϕ ) i ϕ sin ( m ϕ ) i r ± sin ( m ϕ ) i ϕ + cos ( m ϕ ) i r } ,
E BG ( v ) ( r , ϕ , z ) = E 0 ω 0 ω ( z ) exp [ i k z + i ψ ( z ) ] exp { r 2 [ 1 ω 2 ( z ) + i k 2 R ( z ) ] } Q ( z ) T ( r , ϕ , z ) ,
T e ( r , ϕ , z ) = [ J m 1 ( u ) J m + 1 ( u ) ] [ sin ( m ϕ ) cos ( m ϕ ) ] i ϕ + [ J m 1 ( u ) + J m + 1 ( u ) ] [ cos ( m ϕ ) sin ( m ϕ ) ] i r ,
T m ( r , ϕ , z ) = [ J m 1 ( u ) + J m + 1 ( u ) ] [ cos ( m ϕ ) sin ( m ϕ ) ] i ϕ + [ J m 1 ( u ) J m + 1 ( u ) ] [ sin ( m ϕ ) cos ( m ϕ ) ] i r ,

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