## 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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### Equations (8)

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(1)
$${k}_{r}=\left(n-1\right)k\gamma .$$
(2)
$${z}_{\text{max}}=\frac{a}{\gamma \left(n-1\right)}.$$
(3)
$${t}_{\text{CL}}=\text{exp}\left(-i\text{\hspace{0.17em}}\frac{k{x}^{2}}{2f}\right),$$
(4)
$$\Phi \left(x,y\right)\cong \pm \frac{k{x}^{2}}{2f}+{k}_{r}\sqrt{{x}^{2}+{y}^{2}}+\frac{\pi}{4},$$
(5)
$${x}_{c}=\pm f\delta =\pm f\gamma \left(n-1\right)\text{.}$$
(6)
$$x=\frac{{a}^{2}-{b}^{2}}{a}\text{\hspace{0.17em}}{\text{cos}}^{3}\text{\hspace{0.17em}}\theta \text{,}y=\frac{{b}^{2}-{a}^{2}}{b}\text{\hspace{0.17em}}{\text{sin}}^{3}\text{\hspace{0.17em}}\theta \text{,}$$
(7)
$${\left(ax\right)}^{2/3}+{\left(by\right)}^{2/3}={\left({a}^{2}-{b}^{2}\right)}^{2/3}.$$
(8)
$${z}_{\text{rec}}=\frac{R}{\gamma \left(n-1\right)},$$