Abstract

Beams that possess high-intensity peaks that follow curved paths of propagation under linear diffraction have recently been shown to have a multitude of interesting uses. In this Letter, a family of phase-only masks is derived, and each mask gives rise to multiple accelerating intensity maxima. The curved paths of the peaks can be described by the vertices of a regular polygon that is centered on the optic axis and expands with propagation.

© 2010 Optical Society of America

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References

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  1. J. Davis, M. Mitry, M. Bandres, and D. Cottrell, Opt. Express 16, 12866 (2008).
    [CrossRef] [PubMed]
  2. P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, and D. Christodoulides, Opt. Photon. News 21, 39 (2010).
    [CrossRef]
  3. G. Siviloglou and D. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef] [PubMed]
  4. M. Bandres, Opt. Lett. 33, 1678 (2008).
    [CrossRef] [PubMed]
  5. S. Barwick, “Catastrophes in wavefront-coding spatial-domain design,” Appl. Opt., doc. ID 135579 (posted November 11, 2010, in press).
  6. T. Poston and I. Stewart, Catastrophe Theory and Its Application (Pitman, 1978).
  7. V. Arnol’d, Russ. Math. Surv. 28, 19 (1973).
    [CrossRef]
  8. S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, Proc. SPIE 5108, 1 (2003).
    [CrossRef]

2010

P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, and D. Christodoulides, Opt. Photon. News 21, 39 (2010).
[CrossRef]

2008

2007

2003

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, Proc. SPIE 5108, 1 (2003).
[CrossRef]

1973

V. Arnol’d, Russ. Math. Surv. 28, 19 (1973).
[CrossRef]

Arnol’d, V.

V. Arnol’d, Russ. Math. Surv. 28, 19 (1973).
[CrossRef]

Bandres, M.

Barwick, S.

S. Barwick, “Catastrophes in wavefront-coding spatial-domain design,” Appl. Opt., doc. ID 135579 (posted November 11, 2010, in press).

Christodoulides, D.

P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, and D. Christodoulides, Opt. Photon. News 21, 39 (2010).
[CrossRef]

G. Siviloglou and D. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

Cottrell, D.

Davis, J.

Kolesik, M.

P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, and D. Christodoulides, Opt. Photon. News 21, 39 (2010).
[CrossRef]

Mitry, M.

Moloney, J.

P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, and D. Christodoulides, Opt. Photon. News 21, 39 (2010).
[CrossRef]

Pauca, V.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, Proc. SPIE 5108, 1 (2003).
[CrossRef]

Plemmons, R.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, Proc. SPIE 5108, 1 (2003).
[CrossRef]

Polynkin, P.

P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, and D. Christodoulides, Opt. Photon. News 21, 39 (2010).
[CrossRef]

Poston, T.

T. Poston and I. Stewart, Catastrophe Theory and Its Application (Pitman, 1978).

Prasad, S.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, Proc. SPIE 5108, 1 (2003).
[CrossRef]

Siviloglou, G.

P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, and D. Christodoulides, Opt. Photon. News 21, 39 (2010).
[CrossRef]

G. Siviloglou and D. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

Stewart, I.

T. Poston and I. Stewart, Catastrophe Theory and Its Application (Pitman, 1978).

Torgersen, T.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, Proc. SPIE 5108, 1 (2003).
[CrossRef]

van der Gracht, J.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, Proc. SPIE 5108, 1 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Photon. News

P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, and D. Christodoulides, Opt. Photon. News 21, 39 (2010).
[CrossRef]

Proc. SPIE

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, Proc. SPIE 5108, 1 (2003).
[CrossRef]

Russ. Math. Surv.

V. Arnol’d, Russ. Math. Surv. 28, 19 (1973).
[CrossRef]

Other

S. Barwick, “Catastrophes in wavefront-coding spatial-domain design,” Appl. Opt., doc. ID 135579 (posted November 11, 2010, in press).

T. Poston and I. Stewart, Catastrophe Theory and Its Application (Pitman, 1978).

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Figures (2)

Fig. 1
Fig. 1

(a) Bifurcation set B at z = 4.83 cm , (b) h at z = 4.83 cm , and (c) h at z = 6.13 cm are shown versus ( x i , y i ) mm for the RPBs of order (i) 3, (ii) 5, and (iii) 7 with a plane-wave input. The modulations w of the phase masks were 1.21, 0.6, 0.277 × 10 4 cm ( n 1 ) , respectively. Row (d) is a repeat of (c) for a Gaussian beam input. Note the change in scale for (ii) and (iii) of (d).

Fig. 2
Fig. 2

Product of the peak cusp intensity, and n is plotted versus z cm for the masks in Fig. 1 with a plane-wave input and normalized total beam intensity.

Equations (7)

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h ( s , t , u ) = | Σ exp ( i k F ( x , y , s , t , u ) ) d x d y | 2 ,
ϕ n ( x c ) / x 2 u x c s = 0 , ϕ n ( x c ) / y 2 u y c t = 0.
ϕ n ( x , y ) = w ( k = 0 ( n 1 ) / 2 c k ( x n k y k + x k y n k ) ) ,
det [ 2 ϕ n / x 2 2 u 2 ϕ n / x y 2 ϕ n / x y 2 ϕ n / y 2 2 u ] = 0.
c 2 = n ( n 1 ) 2 , ( n k ) ( n k 1 ) c k + ( k + 2 ) ( k + 1 ) c n k 2 + ( k + 2 ) ( k + 1 ) c k + 2 = 0 ,
x 2 + y 2 = ( 2 u / ( n ( n 1 ) w ) ) 2 / ( n 2 ) = R d 2 .
R cusp = 2 | ( ( 2 1 n / 2 ( n 1 ) ) k c k 2 ) ( 2 n ( n 1 ) w ) 1 / ( n 2 ) u ( n 1 ) / ( n 2 ) | .

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