## Abstract

Nondiffracting beams are of interest for optical metrology applications because the size and shape of the beams do not change as the beams propagate. We have created a generating pattern consisting of a linear combination of two nondiffracting patterns. This pattern forms a nondiffracting interference pattern that appears as a circular array of nondiffracting spots. More complicated multiplexed arrays are also constructed that simultaneously yield two different nondiffracting patterns. We generate these Bessel function arrays with a programmable spatial light modulator. Such arrays would be useful for angular alignment and for optical interconnection applications.

© 1996 Optical Society of America

Full Article |

PDF Article
### Equations (7)

Equations on this page are rendered with MathJax. Learn more.

(1)
$${T}_{n}\phantom{\rule{0.2em}{0ex}}(r,\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}})=exp(in\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}})exp(-i2\phantom{\rule{0em}{0ex}}\pi \phantom{\rule{0em}{0ex}}r/{r}_{0})\phantom{\rule{0.2em}{0ex}},$$
(2)
$$E\phantom{\rule{0.2em}{0ex}}(\rho ,\phantom{\rule{0em}{0ex}}\varphi \phantom{\rule{0em}{0ex}})\approx {J}_{n}\phantom{\rule{0.2em}{0ex}}\left(\frac{2\phantom{\rule{0em}{0ex}}\pi \phantom{\rule{0em}{0ex}}\rho \phantom{\rule{0em}{0ex}}}{{r}_{0}}\right)exp(in\phantom{\rule{0.1em}{0ex}}\varphi \phantom{\rule{0em}{0ex}})\phantom{\rule{0.2em}{0ex}}.$$
(3)
$${T}_{n}\phantom{\rule{0.1em}{0ex}}(r,\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}})=\{exp[\text{i}\phantom{\rule{0.2em}{0ex}}(n\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}}+\alpha )]+\text{exp}\phantom{\rule{0.2em}{0ex}}[-i(n\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}}-\alpha )]\}\times exp(-i2\phantom{\rule{0em}{0ex}}\pi \phantom{\rule{0em}{0ex}}r\phantom{\rule{0em}{0ex}}/{r}_{0})\phantom{\rule{0.2em}{0ex}},$$
(4)
$$E(\rho ,\varphi )\approx {J}_{n}\phantom{\rule{0.2em}{0ex}}\left(\frac{2\pi \rho}{{r}_{0}}\right)\{exp[i\phantom{\rule{0.2em}{0ex}}(n\varphi +\alpha )]+exp[-i\phantom{\rule{0.2em}{0ex}}(n\varphi -\alpha )]\}\phantom{\rule{0.2em}{0ex}}.$$
(5)
$$I\phantom{\rule{0.2em}{0ex}}(\phantom{\rule{0em}{0ex}}\rho \phantom{\rule{0em}{0ex}},\phantom{\rule{0em}{0ex}}\varphi \phantom{\rule{0em}{0ex}})\approx {{J}_{n}}^{2}\phantom{\rule{0.2em}{0ex}}\left(\frac{2\phantom{\rule{0em}{0ex}}\pi \phantom{\rule{0em}{0ex}}\rho \phantom{\rule{0em}{0ex}}}{{r}_{0}}\right){cos}^{2}\phantom{\rule{0.2em}{0ex}}(n\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}}+\alpha )\phantom{\rule{0.2em}{0ex}}.$$
(6)
$${T}_{1}\phantom{\rule{0.2em}{0ex}}(r,{r}_{0A},\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}})+{T}_{n}\phantom{\rule{0.2em}{0ex}}(r,{r}_{0B},\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}})=\chi exp(i\phantom{\rule{0.1em}{0ex}}\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}})exp(-i2\pi r/{r}_{0A})+\eta [exp(in\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}})+exp(-in\phantom{\rule{0em}{0ex}}\theta \phantom{\rule{0em}{0ex}})]exp(-i2\pi r/{r}_{0B})\phantom{\rule{0.2em}{0ex}},$$
(7)
$$I\phantom{\rule{0.2em}{0ex}}(\rho ,\varphi )\approx {\chi}^{2}{{J}_{1}}^{2}\phantom{\rule{0.2em}{0ex}}\left(\frac{2\pi \rho}{{r}_{0A}}\right)+{\eta}^{2}\phantom{\rule{0.2em}{0ex}}{{J}_{n}}^{2}\phantom{\rule{0.2em}{0ex}}\left(\frac{2\pi \rho}{{r}_{0B}}\right){cos}^{2}\phantom{\rule{0.2em}{0ex}}(n\varphi )\phantom{\rule{0.2em}{0ex}}.$$