Abstract

It is well known that Bessel beams and the other families of propagation-invariant optical fields have the property of self-healing when obstructed by an opaque object. Here it is shown that there exists another kind of field distribution that can have an analog property. In particular, we demonstrate that a class of caustic wave fields, whose transverse intensity patterns change on propagation, when perturbed by an opaque object can reappear at a further plane as if they had not been obstructed. The physics of the phenomenon is fully explained and shown to be related to that of self-healing propagation invariant optical fields.

© 2007 Optical Society of America

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References

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2007 (1)

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, "Conical dynamics of Bessel beams," Opt. Eng. 46, 078001 (2007).
[Crossref]

2004 (1)

2001 (1)

1999 (1)

S. Chávez-Cerda, "A new approach to Bessel beams," J. Mod. Optic. 46, 923-930 (1999).

1992 (1)

G. Scott and N. McArdle, "Efficient generation of nearly diffraction-free beams using an axicon," Opt. Eng. 31, 2640-2643 (1992).
[Crossref]

1987 (2)

J. Durnin, "Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987).
[Crossref]

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[Crossref] [PubMed]

1970 (1)

1962 (1)

1958 (1)

1954 (1)

J. Mod. Optic. (1)

S. Chávez-Cerda, "A new approach to Bessel beams," J. Mod. Optic. 46, 923-930 (1999).

J. Opt. Soc. Am. (4)

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

Opt. Eng. (2)

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, "Conical dynamics of Bessel beams," Opt. Eng. 46, 078001 (2007).
[Crossref]

G. Scott and N. McArdle, "Efficient generation of nearly diffraction-free beams using an axicon," Opt. Eng. 31, 2640-2643 (1992).
[Crossref]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[Crossref] [PubMed]

Other (1)

T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Pitman Publishing, 1976).

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Figures (7)

Fig. 1
Fig. 1

(Color online) Phases of Hankel functions to represent conical waves.

Fig. 2
Fig. 2

Numerical solution of the Helmholtz equation using an incoming conical Hankel wave H 0 ( 2 ) ( k r r ) as the initial condition.

Fig. 3
Fig. 3

Plots of the resulting wavefront for a cylindrical wave (a) convergent case and (b) divergent case.

Fig. 4
Fig. 4

Numerical simulation of caustic beams for positive cylindrical wave illumination:(a) z = 0.5 normalized units, (b) 1.5 normalized units; for negative cylindrical wave illumination, (c) z = 0.5 normalized units, (d) 1.5 normalized units.

Fig. 5
Fig. 5

Self-healing of a caustic beam for positive cylindrical wave illumination:(a) z = 0.5 normalized units, (b) 1.5 normalized units; for negative cylindrical wave illumination, (c) z = 0.5 normalized units, (d) 1.5 normalized units.

Fig. 6
Fig. 6

Evolution of the caustic beam in the plane:(a) xz (focusing) and (b) yz (defocusing).

Fig. 7
Fig. 7

Numerical simulation of a caustic beams off axis obstructed for positive cylindrical wave illumination:(a) z = 0.5 normalized units, (b) 1.5 normalized units; for negative cylindrical wave illumination, (c) z = 0.5 normalized units, (d) 1.5 normalized units.

Equations (8)

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k r = ( n - 1 ) k γ .
z max = a γ ( n - 1 ) .
t CL = exp ( i k x 2 2 f ) ,
Φ ( x , y ) ± k x 2 2 f + k r x 2 + y 2 + π 4 ,
x c = ± f δ = ± f γ ( n - 1 ) .
x = a 2 - b 2 a cos 3 θ , y = b 2 - a 2 b sin 3 θ ,
( a x ) 2 / 3 + ( b y ) 2 / 3 = ( a 2 - b 2 ) 2 / 3 .
z rec = R γ ( n - 1 ) ,

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