STh1F.6.pdfCLEO:2015 © OSA 2015
Demonstration of Distance Emulation for anOrbitalAngularMomentum Beam
Nisar Ahmed
1,*
, Martin P. J. Lavery
1,2
, Peicheng Liao
1
, Guodong Xie
1
, Hao Huang
1
,Long Li
1
, Yongxiong Ren
1
, Yan Yan
1
, Zhe Zhao
1
, Zhe Wang
1
, Nima Ashraﬁ
3,4
,Solyman Ashraﬁ
4
, Roger D. Linquist
4
, Moshe Tur
5
, and Alan E. Willner
1
1
Dept. of Electrical Engineering, University of Southern California, Los Angeles CA 90089, USA.
2
University of Glasgow, Glasgow, G12 8QQ, UK.
3
University of Texas at Dallas, Richardson, TX 75080, USA.
4
NxGen Partners, Dallas, TX 75219, USA.
5
School of Electrical Engineering, Tel Aviv University, Ramat Aviv 69978, ISRAEL.
*
nisarahm@usc.edu
Abstract:
We design and experimentally demonstrate a freespace distance emulator forpropagating OAM beams over long distances in a lab environment. The performance of thesystem is assessed by measuring spot radius and radius of curvature of propagated beams.
© 2015 Optical Society of America
OCIS codes:
080.4865, 350.5500.
1. Introduction
Orbitalangularmomentum (OAM) beams have gained interest over the past several years due partially to the potentialapplications to several ﬁelds, including communications, microscopy and sensing [1–3]. OAM beams can form anorthonormal basis set, such that different beams of various OAM values can be orthogonal to each other [4]. Suchorthogonality enables the efﬁcient multiplexing at a transmitter and demultiplexing at a receiver of several independentbeams. For example, in a communication system in which each beam carries an independent data stream, the totalsystem capacity and spectral efﬁciency can potentially be signiﬁcantly increased [5]. The amount of OAM carried bya beam can be identiﬁed by the number of 2
π
phase shifts,
l
, that occur across the wavefront, such that the phase istwisting in a helical fashion as it propagates [4]. The beam itself has an interesting structure, such that: (i) the intensityforms a doughnut ring with little power in the center and that grows with larger
l
, (ii) the phase changes in an azimuthalfashion according to the
l
number, and (iii) the beam itself diverges faster with a larger
l
. All these properties meanthat the beam is complex and exhibits unique behavior. For some applications, e.g., communications, it is importantto experimentally show how the beam evolves under freespace propagation. Unfortunately, this is difﬁcult in a labenvironment for anything more than a few meters, and yet many important types of experiments require extensive labequipment. Therefore, it is a laudable goal to have a freespace emulator for lab use that can correctly reproduce theintensity and phase characteristics of a propagating beam over longer distances.In this paper, we demonstrate a freespace emulator that can emulate freespace propagation of different distancesforOAMbeams.Toconﬁrmourdesign,wepropagateLaguerreGaussian(LG)beamsofdifferentmodeordersthroughthe emulator and measure the spot size and curvature of the beams at the output.
2. Emulator Design and Experiment Setup
Figs. 1(a)–(b) show the concept of freespace emulator, a system whose output ﬁeld matches both in intensity andphase to a beam propagated over a speciﬁc distance in freespace. Fig. 1(c) shows the experiment setup. We beginwith LG beam (
l
= 0) having a beam waist
w
0
. Due to the divergence, the beam waist at a distance
z
can be givenby
w
(
z
) =
w
0
(
1
+(
z
/
z
r
)
2
)
0
.
5
. We deﬁne the ratio of
w
(
z
)
to
w
0
as the magniﬁcation
M
of the freespace length. Thedivergence angle
θ
of such a beam can be calculated by using the relation
θ
=
2 tan
−
1
(
w
(
z
)
−
w
0
)
/
(
2
z
)
. Using these
M M BS BS Reference Beam Freespace Emulator M d f
1
f
2
SLM 2x
HWP Col.
!
1550
nm
Camera
EDFA
Freespace distance of length L Transmitted OAM Beam Received OAM Beam Freespace Emulator Input OAM Beam Output OAM Beam
(a) (b) (c)
Fig. 1: Concept of freespace emulator and experiment setup. (a) Optical beam propagated in freespace of distance
L
; (b) Abenchtop freespace emulator to perform propagation experiments over long distances; (c) Experiment setup. Col. Collimator;HWP: Halfwave plate; BS: Beamsplitter; SLM: spatial light modulator; M: Mirror; f: lens; L: distance between two lenses.
STh1F.6.pdfCLEO:2015 © OSA 2015
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l
= 0
l
= 1
Crosssection (mm)
X Slice (mm)
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X Slice (mm)
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Distance (m)
0 20 40 60 80 100
00.10.20.30.40.50.60.70.80.91
l
= 0
l
= 1
l
= 2
Before optimizing lens spacing
d
After optimizing lens spacing
d
M o d e P u r i t y ( S i m u l a t e d )
OAM Mode Order
B e a m W a i s t ( m m )
012
246810
Theoretical (L = 5 m)Experiment (L = 5 m)Theoretical (L = 25 m)Experiment (L = 25 m)

6 4 2 0 2 4 6
3210123
ExperimentSimulated

6 4 2 0 2 4 6
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! " # $ % ' ( # ) *
Experiment Simulated
l
= 1
l
= 0
l
= 2
(a) (b) (c) (d) (e) (f) (g)
l
= 0
Fig. 2: (a) Simulation results for mode purity calculations using designed emulator. The spacing between lenses is optimizedto achieve a theoretical mode purity
>
0.99. (b) Theoretical and experimental results for beam waists of different LG beamspropagated over 5 and 25 m. (c)–(e) Intensity ﬁt of measured intensity of different LG beams. (f) Experimentally retrievedphases compared with numerically propagated beams for a distance of 25 m. We measured the effective radius of curvature of the Gaussian beam to be 29.92 m, an error of 0.037%.(g) Crosssection of retrieved phase of Gaussian beam compared withnumerically calculated beam.
relations, we can calculate the focal length of an equivalent lens as
f
ef f
=
w
0
/
θ
. Next, we work out the focal lengthsof two lenses (
f
1
and
f
2
) required to match this system and the spacing
d
between the two lenses. We ﬁx the focallength of the second lens
f
2
and calculate the spacing
d
using the relation:
d
=
f
ef f
f
2
(
M
+
1
)
/
M f
ef f
+
f
2
. Thefocal length of the ﬁrst lens is then given by:
f
1
=
L
/
(
M
+
1
)
. Due to design based on raytrace analysis, a smalladjustment is made in
d
in order to minimize the curvature error, by numerically propagating the beam (under thinlens approximation) using HuygensFresnel diffraction integral to maximize the mode purity. Fig. 2(a) shows thenumerical simulation results for different LG beams using the designed system for different freespace distances. Inorder to validate our design, an experiment was also performed for two distances (5 m and 25 m). For emulating adistance of 5 m, the parameters for
f
1
,
d
(after optimization), and
f
2
are 353 mm, 748 mm , and 400 mm, respectively.A 1550 nm laser is split in two paths to form the two arms of a MachZehnder Interferometer (MZI). In one arm, aphaseonly reﬂective SLM is used to generate LG beams such that the beam waist of
l
= 0 beam at the input of thefreespace emulator is 2.2 mm. The path lengths of the two arms are matched such that in the absence of emulator, aplane wavefront is acquired at the output. We also compensate for system aberrations by digitally applying Zernikepolynomials on the SLM. An InGaAs camera is used to record the intensity and interference proﬁles of the outputbeam. In order to measure the beam waist of the output beam, intensity is ﬁtted to the intensity of the correspondingLG beam (see Fig. 2(b)). The effective radius of curvature of the output beam is estimated by ﬁrst retrieving the phaseof the output beam and then applying equation (17) in [6]. For the 5 m case, we measure an effective radius of curvaturefor Gaussian beam to be 23.57 m, a 0.028 % error. In order to emulate a distance of 25 m, we used 100 mm, 396.8 mm,and 300 mm for
f
1
,
d
and
f
2
. We built a 3x reduction system to image the output plane of the freespace emulatorand accounted for the demagniﬁcation in our calculations. Figs. 2(b–e) show the results for different LG beams atthe output of the emulator setup for 25 m propagation emulation. Fig. 2(f) shows the transverse phase proﬁles of thesimulated and retrieved phases, and Fig. 2(g) shows the crosssection of retrieved phase for the Gaussian beam at theemulator output. For this arrangement, we measured an error of 0.037% for
l
=0 beam curvature.
3. Acknowledgment
Authors would like to thank NxGen Partners for their generous support.
References
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6
, 488–496, (2012).2. B. Harke et al., Optics express,
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341
, 537–540, (2013).4. A. M. Yao et al., Adv. Opt. Photon.,
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, 197–200, (2014).6. A. Siegman, IEEE J. of Quantum Electronics,
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, 1146–1148, (1991).