Abstract

We demonstrate vortex array-beam generations from a thin-slice, wide-aperture, solid-state laser with laser-diode end-pumping. Radial and rectangular vortex arrays were found to be formed in a controlled fashion with symmetric and asymmetric pump-beam profiles, respectively. Most of these vortices exhibited single-frequency oscillations arising from a spontaneous process of transverse mode locking of degenerate or nearly degenerate modes assisted by the laser nonlinearity. Single-frequency rectangular array beams consisting of a large number of vortices, e.g., closely packed 25, 36, or 46 vortex pixels, were generated, originating from Ince–Gaussian modes excited by the asymmetric pumping.

© 2008 Optical Society of America

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References

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2007 (2)

2006 (1)

Y. F. Chen, T. H. Lu, and K. F. Huang, Phys. Rev. Lett.  97, 233903 (2006).
[CrossRef]

2004 (2)

2002 (1)

K. Otsuka, J.-Y. Ko, T.-S. Lim, and H. Makino, Phys. Rev. Lett.  87, 083903 (2002).
[CrossRef]

1999 (1)

J. Scheuer and M. Orenstein, Science  285, 230 (1999).
[CrossRef] [PubMed]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun.  112, 321 (1994).
[CrossRef]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun.  96, 123 (1993).
[CrossRef]

1992 (1)

1991 (1)

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A  43, 5090 (1991).
[CrossRef] [PubMed]

1988 (1)

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun.  96, 123 (1993).
[CrossRef]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (CRC Press, 2003), and references therein.
[CrossRef]

Andrews, D.

D. Andrews, Structured Light and Its Applications (Academic, 2008).

Bandres, M.

Bandres, M. A.

Barnett, S. M.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (CRC Press, 2003), and references therein.
[CrossRef]

Battipede, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A  43, 5090 (1991).
[CrossRef] [PubMed]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun.  112, 321 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun.  96, 123 (1993).
[CrossRef]

Brambilla, M.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A  43, 5090 (1991).
[CrossRef] [PubMed]

Chen, Y. F.

T. H. Lu, Y. F. Chen, and K. F. Huang, Phys. Rev. E  75, 026614 (2007).
[CrossRef]

Y. F. Chen, T. H. Lu, and K. F. Huang, Phys. Rev. Lett.  97, 233903 (2006).
[CrossRef]

Chu, S.-C.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun.  112, 321 (1994).
[CrossRef]

Gutierrez-Vega, J. C.

Heckenberg, N. R.

Huang, K. F.

T. H. Lu, Y. F. Chen, and K. F. Huang, Phys. Rev. E  75, 026614 (2007).
[CrossRef]

Y. F. Chen, T. H. Lu, and K. F. Huang, Phys. Rev. Lett.  97, 233903 (2006).
[CrossRef]

Kamikariya, K.

Ko, J.-Y.

K. Otsuka, J.-Y. Ko, T.-S. Lim, and H. Makino, Phys. Rev. Lett.  87, 083903 (2002).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun.  112, 321 (1994).
[CrossRef]

Lim, T.-S.

K. Otsuka, J.-Y. Ko, T.-S. Lim, and H. Makino, Phys. Rev. Lett.  87, 083903 (2002).
[CrossRef]

Lu, T. H.

T. H. Lu, Y. F. Chen, and K. F. Huang, Phys. Rev. E  75, 026614 (2007).
[CrossRef]

Y. F. Chen, T. H. Lu, and K. F. Huang, Phys. Rev. Lett.  97, 233903 (2006).
[CrossRef]

Lugiato, L. A.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A  43, 5090 (1991).
[CrossRef] [PubMed]

L. A. Lugiato, C. Oldano, and L. M. Naruducci, J. Opt. Soc. Am. B  5, 879 (1988).
[CrossRef]

Makino, H.

K. Otsuka, J.-Y. Ko, T.-S. Lim, and H. Makino, Phys. Rev. Lett.  87, 083903 (2002).
[CrossRef]

McDuff, R.

Naruducci, L. M.

Ohtomo, T.

Oldano, C.

Orenstein, M.

J. Scheuer and M. Orenstein, Science  285, 230 (1999).
[CrossRef] [PubMed]

Otsuka, K.

T. Ohtomo, K. Kamikariya, K. Otsuka, and S.-C. Chu, Opt. Express  15, 10705 (2007).
[CrossRef] [PubMed]

K. Otsuka, J.-Y. Ko, T.-S. Lim, and H. Makino, Phys. Rev. Lett.  87, 083903 (2002).
[CrossRef]

K. Otsuka, Nonlinear Dynamics in Optical Complex Systems (Kluwer Academic, 1999) pp. 176–181.

Padgett, M. J.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (CRC Press, 2003), and references therein.
[CrossRef]

Penna, V.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A  43, 5090 (1991).
[CrossRef] [PubMed]

Prati, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A  43, 5090 (1991).
[CrossRef] [PubMed]

Scheuer, J.

J. Scheuer and M. Orenstein, Science  285, 230 (1999).
[CrossRef] [PubMed]

Schwarz, U. T.

Smith, C. P.

Tamm, C.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A  43, 5090 (1991).
[CrossRef] [PubMed]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun.  96, 123 (1993).
[CrossRef]

Weiss, C. O.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A  43, 5090 (1991).
[CrossRef] [PubMed]

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun.  112, 321 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun.  96, 123 (1993).
[CrossRef]

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

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

Opt. Commun. (2)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun.  96, 123 (1993).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun.  112, 321 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, Phys. Rev. A  43, 5090 (1991).
[CrossRef] [PubMed]

Phys. Rev. E (1)

T. H. Lu, Y. F. Chen, and K. F. Huang, Phys. Rev. E  75, 026614 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

K. Otsuka, J.-Y. Ko, T.-S. Lim, and H. Makino, Phys. Rev. Lett.  87, 083903 (2002).
[CrossRef]

Y. F. Chen, T. H. Lu, and K. F. Huang, Phys. Rev. Lett.  97, 233903 (2006).
[CrossRef]

Science (1)

J. Scheuer and M. Orenstein, Science  285, 230 (1999).
[CrossRef] [PubMed]

Other (3)

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (CRC Press, 2003), and references therein.
[CrossRef]

D. Andrews, Structured Light and Its Applications (Academic, 2008).

K. Otsuka, Nonlinear Dynamics in Optical Complex Systems (Kluwer Academic, 1999) pp. 176–181.

Supplementary Material (3)

» Media 1: MOV (138 KB)     
» Media 2: MOV (163 KB)     
» Media 3: MOV (768 KB)     

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Figures (4)

Fig. 1
Fig. 1

(a) Experimental setup. LD, laser diode; SFP, scanning Fabry–Perot interferometer (free spectral range, 2 GHz ; resolution, 6.6 MHz ); DO, digital oscilloscope. (b) LD pump beam profile as a function of LNP position. Ordered transverse patterns were not observed outside the indicated regions. (c) Radial vortex lattice patterns on circular cylindrical coordinates observed with nearly symmetric large-aperture LD pumping. Pump power P; 2 n + l = 1 ( w x = 330 μ m , w y = 300 μ m ), 80 mW ; 2 n + l = 2 ( w x = 330 μ m , w y = 330 μ m ), 105 mW (doughnut); 120 mW (oval), 140 mW (four holes); 2 n + l = 3 ( w x = 330 μ m , w y = 360 μ m ), 160 mW (three holes), 168 mW (five holes).

Fig. 2
Fig. 2

Pump-dependent structural change of vortex arrays with asymmetric large-aperture LD pumping. (a) w x = 300 μ m , w y = 550 μ m . Column (i), P = 177 mW ; (ii), 191 mW ; (iii), 195 mW ; (iv), 198 mW (Media 1). (b) w x = 300 μ m , w y = 570 μ m . Column (i), P = 164 mW ; (ii), 190 mW ; (iii), 207 mW ; (iv), magnified interferogram of six-hole pattern. (c) w x = 300 μ m , w y = 600 μ m . Column (i), P = 156 mW ; (ii), 164 mW ; (iii), 195 mW ; (iv), 201 mW (Media 2).

Fig. 3
Fig. 3

Theoretically reconstructed vortex arrays. Used ellipticity parameters: ε = 50 for the eight-hole array, ε = 30 for the five-hole [ 3 × 2 ] arrays, and ε = 10 for [ 2 × 3 ] , [ 3 × 3 ] arrays. (a) five-hole, IG 3 , 3 o + IG 3 , 1 e ; (b) eight-hole, IG 4 , 2 o + i 0.5 IG 4 , 2 e ; (c) [ 2 × 2 ] , IG 2 , 2 e + i 0.5 IG 3 , 1 e ; (d) [ 3 × 2 ] , IG 3 , 1 o + i 0.33 IG 4 , 2 e ; (e) [ 2 × 3 ] , IG 3 , 3 e + i 0.25 IG 4 , 2 e ; (f) [ 3 × 3 ] , IG 5 , 3 o + i 2 IG 3 , 3 e . Sold circles, clockwise phase rotation; open circles, anticlockwise phase rotation. The starting phases of nearest-neighbor vortices in the same row or column are shifted by π.

Fig. 4
Fig. 4

Pump-dependent structural change of a [ q × r ] vortex array and magnified views observed in the high pump-power region. w x = 300 μ m , w y = 620 μ m . a, P = 233 mW ; b, 267 mW ; c, 284 mW ; d, 430 mW ; e, 498 mW ; f, 515 mW . The four- and five-hole unit-cell structures are indicated in the magnified views (Media 3).

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