A multi-pinhole interferometer for characterizing optical vortices

Jonathan Preston, City College of New York

John Noe and Marty Cohen, Laser Teaching Center, Stony Brook University

We have investigated a simple interferometric method for determining the 
topological charge l of an optical vortex recently described by 
Berkout and Beijersbergen [1]. The method utilizes a multi-pinhole interferometer (MPI), a 
series of small circular apertures equally-spaced around the circumference of 
a circle. An optical vortex beam incident on the apertures creates an 
interference pattern that with an appropriate number of apertures is 
characteristic of l. The method can be applied to vortices of 
arbitrary size and eliminates the need for a reference plane wave or a 
complete sampling of the vortex light field.

MPIs with 5, 6 and 9 apertures were fabricated by drilling 170 micron diameter 
holes into 225 micron thick Al disks 25.4 mm in diameter. In the first two 
devices the apertures were on a circle with radius r = 1.75 mm; for the 9 
aperture device we used r = 2.0 mm to better match the diameter of the 
l = 3 and 4 LG modes. These dimensions were dictated by the available 
collimating lenses and aperture fabrication methods, the overall table 
length, and profile measurements on the collimated LG modes. The 
interference patterns were recorded directly on an Electrim EDC1000N CCD 
camera at distances from 127 to 610 mm. A long opaque tube attached to the 
front of the camera sufficed to block room light. The expected patterns 
were simulated by evaluating Eq. 2 in Ref. [1] in Mathematica. We also created several tools 
with Mathematica to facilitate the use and fabrication of the MPI.

LG modes up to order l = 4 were created using an open cavity He-Ne 
laser followed by an astigmatic mode converter [2]. Only the 9 aperture MPI is 
able to distinguish topological charge up to l=4. The previous work was 
limited to charges up to 2 and no more than 7 apertures [1]. All of the 
patterns we obtained with 5 or 6 apertures were a good visual match to those 
previously reported or predicted [1]. The 9-aperture patterns we observed 
resemble Bessel functions, as anticipated [1]. One unanticipated result was 
that the interference patterns were apparent even when the diffraction 
patterns of the apertures had only very slight overlap. We also observed 
that the interference patterns not from pure LG modes are qualitatively 
different from those that are from pure modes.

We thank Jeff Slechta for fabricating the MPI devices and Giovanni Milione 
for helpful discussions. JK would like to thank the Physics REU program and 
the Laser Teaching Center for financial support.

REFERENCES

[1] G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Letters {101}, 
100801 (2008).

[2] M. Beijersbergen et al., Opt. Commun. {96}, 123-132 (1992).