We demonstrate that a |q|=1/2 plate plus polarization optics can tunably excite all linear combinations of |l|=1 fiber OAM modes with up to ~30 dB purity, enabling switch fabrics in fiber-OAM networks and disentangling of degenerate mode mixing effects in long fibers

Boyd, R.

Gregg, P.

Karimi, E.

Marrucci, L.

Mirhosseini, M.

Ramachandran, S.

Rubano, A.

Caltech Authors - Main

SW4M.3.pdf CLEO:2015 © OSA 2015
Q-plates for Switchable Excitation of Fiber OAM Modes 
 
P. Gregg
1
, M. Mirhosseini
2
, A. Rubano
3
, L. Marrucci
3
, E. Karimi
4
, R. Boyd
2,4
, S. Ramachandran
1
 
1Boston University, 8 Saint Mary’s St, Boston, MA 02215, USA 
2Institute of Optics, University of Rochester, Rochester, NY 14627, USA 
3Dipartimento di Fisica, Università di Napoli Federico II, MSA, via Cintia, 80126 Napoli, Italy 
4Department of Physics, University of Ottawa, 25 Templeton, Ottawa, Ontario, K1N 6N5 Canada 
Author e-mail address:sidr@bu.edu 
 
Abstract: We demonstrate that a |q|=1/2 plate plus polarization optics can tunably excite all linear 
combinations of |l|=1 fiber OAM modes with up to ~30 dB purity, enabling switch fabrics in  
fiber-OAM networks and disentangling of degenerate mode mixing effects in long fibers.  
OCIS codes: (050.4865) Optical vortices, (060.6042) Multiplexing, (260.6042) Singular optics, (260.5430) Polarization. 
 
Orbital angular momentum (OAM) modes [1,2,3] in fibers have recently gained attention for increasing the 
dimensionality of alphabets used in space-division multiplexing (SDM) applications [4]. Methods to (de)multiplex 
such channels currently include spatial light modulators (SLMs) [4], mode sorters [5], and integrated photonic 
devices [6]. Such devices typically generate OAM modes of free space, which are considered sufficient for coupling 
into fiber modes, because fiber and free-space OAM modes have similar phase and polarization distributions.  
However, fiber OAM modes differ from their free-space counterparts in their degeneracies, which has 
implications for mitigating mode mixing effects or building switchable networks. Whereas all four free-space OAM 
modes of given |l| are degenerate, allowing turbulence compensation [7] or data exchange [8] with SLMs or other 
free-space devices, fiber OAM modes come in degenerate pairs of opposing polarizations and opposite signs of l, 
given by (for |l| = 1): 
𝑂𝐴𝑀1,𝑚
± = (?̂?±𝑒±𝑖𝜑)𝐹𝑚(𝑟)𝑒
𝑖𝛽𝑂𝐴𝑀𝑧     (1) 
where ?̂?±  are orthogonal (circular) polarizations, Fm is the field distribution of radial mode order m (hereafter 
assumed 1), and βOAM is the wave-vector of the OAM modes. This two-fold degeneracy parallels the polarization 
degeneracy in single mode fiber (SMF) and it is well known that polarization controllers (polcons) can be realized 
with free-space wave-plates or fiber loops to switch or control polarization. We have shown that loops of OAM-
fiber can act as polcons to “unwind” degenerate state coupling for |l| = 1 [9], but fiber loops may be inefficient for 
higher l [2], cannot be used in a multiplexed fashion for several OAM modes simultaneously, and cannot be 
controlled at high speeds. 
Here we show that q-plates, which couple the spin and orbital angular momentum of light [10], offer the ability 
to create exactly such superpositions. Hence, we demonstrate switching between OAM fiber modes, creation of any 
combination of the |l|=1 OAM modes of fiber with up to ~30-dB purity with respect to other, parasitic mode groups, 
and the ability to disentangle OAM mode coupling in fiber. Such low input-coupling crosstalk is a necessary 
condition for digital signal processing-free SDM in which OAM modes are independent information carriers.   
 
 
Fig. 1 (a) Light with uniform polarization set by the electronic polcon passes through the q-plate, which imparts a Δl of 0 or ±1, followed by 
two rotating quarter-wave plates. The desired superposition of states with |l|=0 or |l|=1 is focused into the vortex fiber. 50/50 tap provides a 
reference beam for interference. (b) Fiber output and (c) interference with a reference beam at 1530nm after 300m of vortex fiber for different 
launch conditions. (d) Input coupling MPI. Each row indicates the same desired mode. LP02 and LP21 exist at 1530nm but are inaccessible with 
the q= –1/2 plate and are considered parasitic.*MPI of TE into LP02/LP21 not resolvable below 13.8dB due to detector impulse response.  
 
SW4M.3.pdf CLEO:2015 © OSA 2015
A q-plate of topological charge q performs the following linear transformation (neglecting a global phase factor): 
𝑞 ∙ (𝐴?̂?+ + 𝐵?̂?−) = 𝐴?̂?−𝑒𝑖2𝑞𝜑 + 𝐵?̂?+𝑒−𝑖2𝑞𝜑    (2)  
that is, a q-plate imparts angular momentum 2q, with sign opposite to the polarization of the incoming beam. This 
exactly mirrors the OAM mode degeneracy in fiber. Thus, by controlling the polarization incident to the q-plate by 
tuning a fiber polcon (see Fig. 1), an arbitrary superposition of states in (1) may be excited. For q = –1/2, or 
alternatively q=1/2 followed by a half-wave plate, these devices in series can access any superposition of 𝑂𝐴𝑀±. 
The half-wave plate is realized here with two quarter-wave-plates in series, allowing for switchable action between 
no retardance, and half-wave retardance. Similarly, the TE and TM modes can be generated with A=±B and a q= 1/2 
plate. l = 0 excitation is achieved by tuning the bias of the q-plate to yield λ retardation, preserving the input beam’s 
mode and polarization [11]. Figure 1b shows experimental images of the output after 300m of vortex fiber [1] sorted 
by ?̂?+ and ?̂?−, for different launch conditions using a CW laser. As expected, if the fiber exhibits negligible mode 
coupling, when an 𝑂𝐴𝑀±  mode is excited, we observe a bright ring in only one polarization. Inclusion of a 
reference beam (Fig. 1c) reveals phase: 𝑂𝐴𝑀±  modes show spirals with a handedness that matches spin. 
Quantitative measurements (Fig. 1d) of the mode purities, conducted with time-of-flight measurements using a 
pulsed laser and fast detector and oscilloscope, indicate the ability to achieve mode purities of at least -18dB, and as 
high as 29.9 dB. Coupling losses at 1530nm were 3.1dB for the fundamental modes, and 2.4dB for the 𝑂𝐴𝑀± 
modes, of which 1.4dB is intrinsic q–plate loss, and the remainder is from beam imperfections or size mismatches. 
Having demonstrated pure mode excitation with q-plates, we excite linear combinations of degenerate OAM 
modes to disentangle degenerate state-mixing effects expected in long length fibers (Fig. 2). If the input polarization 
to the q=–1/2 plate is ?̂?∓, the fiber output is a pure 𝑂𝐴𝑀±, as before (Fig 2a). Once this fiber is subject to bends and 
twists, degenerate state coupling occurs, yielding an OAM mode in both polarizations (Fig. 2b). However, since the 
fiber and q-plate span the same set of OAM modes, introducing a mode of a specific elliptical polarization to the 
q-plate, yields, after fiber mode-mixing, the desired pure OAM
+
 or OAM

 (Fig. 2c). 
In summary, a setup comprising a q-plate and two polarization controllers not only allows 18-30dB pure 
creation of |l|=1 OAM modes in fibers, it also enables creating linear combinations of these modes, hence facilitating 
(a) remote switching between the modes, possibly at ~GHz speeds, by tuning polcons before the transmission fiber 
alone and (b) disentangling of degenerate state mixing that may be unavoidable. Disentangling the effects of the 
fiber propagation is functionality unique to fiber-bend induced polcons and the q-plate system we demonstrate here. 
Between them, the q-plate system is preferable, because it is scalable with the number of OAM modes of fiber, and 
facilitates fast switching. Thus, the q-plate excitation scheme could play a role as vital as the polarization controller 
for SMF, in OAM communications networks that can also incorporate switch fabrics based on OAM modes. 
[1] S. Ramachandran et al, “Generation and propagation of radially polarized beams in optical fibers.” Opt. Lett. 34 (2009) 2525-7. 
[2] P. Gregg et al, “Conservation of orbital angular momentum in air core optical fibers.” arXiv: 1412.1397 (2014). 
[3] C. Brunet et al, “Design, fabrication, and validation of an OAM fiber supporting 36 states.” Opt. Expr. 22 26117 (2014). 
[4] N. Bozinovic et al, “Terabit-scale orbital angular momentum mode division multiplexing in fibers.” Science 340 (2013) 1545-8. 
[5] G.C.G. Berkhout et al, “Efficient sorting of orbital angular momentum states of light.” Phys. Rev. Lett. 105 153601 (2010). 
[6] J. Sun et al, “Generating and identifying optical orbital angular momentum with silicon photonic circuits.” Opt. Lett. 39 (2014) 5977-5980. 
[7] Y. Ren et al, “Adaptive optics compensation of multiple OAM beams prop. through emulated atmospheric turb.” Opt Lett 39 (2014) 2845-8. 
[8] J. Wang et al, “Terabit free-space data transmission employing orbital angular momentum multiplexing.” Nat. Photonics 6 (2012) 488-96. 
[9] N. Bozinovic et al, “Control of orbital angular momentum of light with optical fibers.” Opt. Lett. 37 (2012) 2451-3. 
[10] L. Marrucci et al, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications.” J. Opt. 13 064001 (2011). 
[11] S. Slussarenko et al, “Tunable liquid crystal q-plates with arbitrary topological charge.” Opt. Expr. 19 (2011) 4085-4090. 
 
Fig. 2 OAM transmission schematic and experimental results, using a q=–1/2 plate, in the case of (a) a fiber which maintains OAM states, (b) a 
fiber which mixes degenerate OAM states according to some mixing coefficient, γ, such that |γ|2+|α|2=1, and (c) a fiber which mixes degenerate 
OAM states, but in which said coupling is compensated for, by tuning the input state via polarization control. 
 


Q-plates for Switchable Excitation of Fiber OAM Modes

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