Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices

doi:10.1364/OE.20.009396

Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices

Tiehui Su, Ryan P. Scott, Stevan S. Djordjevic, Nicolas K. Fontaine, David J. Geisler, Xinran Cai, and S. J. B. Yoo »View Author Affiliations

Optics Express, Vol. 20, Issue 9, pp. 9396-9402 (2012)
http://dx.doi.org/10.1364/OE.20.009396

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▸ Article Outline
– Abstract
1. Introduction
2. Device design and fabrication
3. Device characterization
4. Transmission experiment
5. Conclusion
– References and links

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Abstract

We propose and demonstrate silicon photonic integrated circuits (PICs) for free-space spatial-division-multiplexing (SDM) optical transmission with multiplexed orbital angular momentum (OAM) states over a topological charge range of −2 to +2. The silicon PIC fabricated using a CMOS-compatible process exploits tunable-phase arrayed waveguides with vertical grating couplers to achieve space division multiplexing and demultiplexing. The experimental results utilizing two silicon PICs achieve SDM mux/demux bit-error-rate performance for 1‑b/s/Hz, 10-Gb/s binary phase shifted keying (BPSK) data and 2-b/s/Hz, 20-Gb/s quadrature phase shifted keying (QPSK) data for individual and two simultaneous OAM states.

1. Introduction

Since the initial work of Allen et al. [1

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]

], the orbital angular momentum (OAM) of light has generated significant interest in multiple areas of research, including cold atom confinement [2

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008). [CrossRef]

], nonlinear optics [3

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011). [CrossRef]

], and communications [4

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). [CrossRef] [PubMed]

–9

P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett. 47(17), 972–973 (2011). [CrossRef]

]. Figure 1(a) shows examples of a light beam with different OAM states which have an azimuthal (i.e., in the transverse plane) phase variation of

φ (r, φ) = \exp (i ℓ φ)

, where

i^{2} = - 1

, φ is the azimuthal (angular) coordinate and ℓ can be any positive or negative integer value (known as the topological charge) [3

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011). [CrossRef]

]. This type of beam has helical phase fronts, where the handedness (direction of twist) depends on the sign of ℓ and the number of intertwined helices depends on the magnitude of ℓ (i.e., the number of 2π phase shifts that occur in one revolution of the azimuthal angle φ). In beams with OAM, the electromagnetic field that is transverse to the phase fronts will have axial components. Consequently, the Poynting vector, which is always perpendicular to these phase fronts, has an azimuthal component around the beam and hence an angular momentum along the beam axis equal to ℓħ [1

]. The helical phase of a beam with nonzero OAM (i.e., ℓ ≠ 0) leads to a phase singularity on the beam axis, and therefore the intensity has to vanish and the beam will have a dark central spot [10

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997). [CrossRef]

Fig. 1 (a) Visualization of the electric field of OAM beams. (b) Illustration showing how a beam encoded with an OAM state is sampled and demultiplexed by a circular arrangement of apertures, length-matched waveguides and a star coupler.

Using OAM for encoding, transfer, and decoding of information was suggested by Gibson et al. [4

] in 2004. The OAM-division multiplexing technique is especially useful for improving the photon efficiency or spectral efficiency of free-space optical links such as those used in space-based systems and also short-range terrestrial links. Beams with the same wavelength and polarization, but different OAM eigenstates, are orthogonal [2

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008). [CrossRef]

]. Thus, by using separate OAM channels, it is possible to simultaneously transmit information on collinear beams that otherwise have the same properties. In principle, the possible number of OAM states is infinite, implying that the spectral efficiency is limited only by the achievable signal-to-noise ratio [11

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).

]. However, OAM-multiplexed communication channels have only been demonstrated by using bulk-optic encoders such as those based on holograms or spatial light modulators and bulk-optic decoders [5

J. Lin, X. C. Yuan, S. H. Tao, and R. E. Burge, “Multiplexing free-space optical signals using superimposed collinear orbital angular momentum states,” Appl. Opt. 46(21), 4680–4685 (2007). [CrossRef] [PubMed]

P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett. 47(17), 972–973 (2011). [CrossRef]

,12

R. Čelechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys. 9(9), 328 (2007). [CrossRef]

]. These implementations limit the practical application of OAM-multiplexing because of their instability, large size, weight and power.

In this paper, we describe and demonstrate a photonic integrated circuit (PIC) that is capable of demultiplexing (or multiplexing) free-space optical beams with multiple OAM states near 1550 nm into (or from) single-mode waveguides. As such, it easily connects with high-speed telecommunication components like modulators and photodetectors. Further, the device is fabricated using a CMOS-compatible silicon fabrication process, allowing future integration with on-chip modulators, detectors and possibly even lasers. Working as a demux (i.e., OAM state decoder), Fig. 1(b) shows how a circular array of waveguide grating couplers [13

C. R. Doerr and L. L. Buhl, “Circular grating coupler for creating focused azimuthally and radially polarized beams,” Opt. Lett. 36(7), 1209–1211 (2011). [CrossRef] [PubMed]

] are used to sample areas (dashed circles) of an incoming beam encoded with an OAM state (e.g., ℓ = 1) into a corresponding array of single-mode waveguides. Careful waveguide layout ensures that they have identical optical path lengths. Thus, at the input of the free-propagation region (FPR), the azimuthally varying phase of the OAM state is converted into a linear phase front with a tilt angle determined by the incoming beam’s topological charge. The circular placement of the array waveguides at the input of the FPR focuses the light [14

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2006).

], and the tilt of the linear phase front directs it to a corresponding output. Using the PIC as a mux is as simple as reversing the light’s propagation direction. This device is akin to one recently described by Doerr et al. [15

C. R. Doerr, N. K. Fontaine, M. Hirano, T. Sasaki, L. L. Buhl, and P. J. Winzer, “Silicon photonic integrated circuit for coupling to a ring-core multimode fiber for space-division multiplexing,” in European Conference on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.A.3.

] that enabled achieving space-division multiplexing (SDM) into a ring-core multimode fiber. This paper demonstrates a full coherent optical communication link including a pair of silicon photonic OAM mux/demux devices.

2. Device design and fabrication

Figure 2(a) shows the device’s waveguide layout which is designed for a silicon-on-insulator (SOI) material platform, is optimized for TE polarization, and uses a 1-µm-wide silicon rib waveguides (effective index of 3.27). The upper inset of Fig. 2(a) shows a quarter of the circular grating which is formed by concentric etched circles that have a grating period of 0.47 μm, a 50% duty cycle, and an outer radius of 25 μm. The circular grating converts the vertically incident optical beam (azimuthal polarization) into a horizontally propagating beam. Sixteen tapered waveguides surround and capture the light from the grating and send it to length-matched waveguides (20-mm long) that terminate at the FPR [lower inset of Fig. 2(a)]. Depending on the OAM state of the input beam, the 16 guided modes will have a specific linear phase variation. Since the FPR is designed based on the Rowland circle principle, it focuses the 16 beams onto five waveguide outputs according to the linearly varying phase associated with the five different OAM states (labeled as ℓ = +2, +1, 0, −1, −2). The five waveguide outputs are tapered to a 3-µm width at the edge of the chip and have 250-µm spacing. The device also includes aluminum contact pads and traces that connect to sixteen Ti/Pt heaters. The heaters, located just above the waveguides, thermo-optically change the local index of refraction to compensate for optical phase errors (<π rad) in the waveguides.

Fig. 2 (a) Waveguide layout of silicon OAM device for multiplexing five OAM modes ( ℓ = +2, +1,0,−1,−2). (b) Fabricated silicon OAM device. Inset shows SEM photo of grating.

Figure 2(b) shows the OAM device fabricated on a 6-inch silicon-on-insulator (SOI) wafer with a top silicon layer thickness of 0.5 µm, and buried oxide (BOX) layer thickness of 3 µm. The waveguide layer was patterned using deep-UV ASML stepper with 248 nm KrF excimer source and 4:1 reduction, then transferred to the silicon layer by a 250-nm deep highly anisotropic HBr TCP reactive ion etch. The subsequent stepper lithography and etching process was similar to the previous steps and defined the circular grating layer with an etching depth of 200 nm. The inset of Fig. 2(b) shows a scanning electron microscope (SEM) image of the fabricated grating. Next, the wafer was clad with 1-µm thick SiO₂ by low pressure chemical vapor deposition (LPCVD) and then annealed for densification at 900°C for 40 minutes in an inert atmosphere. The LPCVD SiO₂ coating isolates the waveguide mode from the surface metal layer, eliminating the loss due to metal absorption. Ti/Pt heaters were deposited with an e-beam evaporator and defined through liftoff. The heaters provide phase control on the length-matched waveguides. As a final step, aluminum electrodes were deposited and defined with another liftoff process.

3. Device characterization

Initial device characterization was performed on straight waveguides fabricated on the same silicon chip. The Fabry–Pérot resonance measurement method yielded the straight waveguide loss of 1.9 dB/cm. Figure 3(a) shows a simulation of the near-field intensity pattern of the circular grating output when light is coupled into the ℓ = 0 input. Figure 3(b) is the near-field intensity pattern imaged by an infrared vidicon camera for comparison. The 16 radial stripes indicate that the beam coupled from the waveguides to air as expected. Each radial stripe shows a periodic dark-bright pattern which is caused by interference from light that leaks across the center of the grating from the opposing waveguides. Figure 3(c) shows a simulation of the far-field intensity pattern for ℓ = 0. For comparison, Fig. 3(d) shows the measured far-field pattern with no phase-error correction (PEC) and Fig. 3(e) shows the more evenly distributed far-field pattern after applying appropriate PEC.

Fig. 3 Intensity of near-field output from the OAM device (input port 0) from (a) a simulation and (b) measurement. Intensity of far-field output from OAM device for ℓ = 0 for (c) a simulation, (d) measured without phase-error correction (PEC), and (e) with PEC.

As an initial test of a single OAM device’s performance, we used an objective [20 × , 0.57 numerical aperture (NA)] to collect the light from the grating output, followed by a gold-coated mirror that retro-reflected the OAM mode back through the objective and into the OAM device. Thus, the same OAM device acts as both a transmitter and a receiver. In this retro-reflection configuration, when light is coupled into the +l port, the reflected beam is directed to −l port; similarly the input on the +2 port gives output on the −2 port. Using this configuration to measure the crosstalk performance, we coupled light into the +2 port and measured output ports −2, −1, and 0. The crosstalk without PEC from the −2 port to the −1 port was only −3 dB and −5 dB for the 0 port. After PEC was applied, the crosstalk improved significantly, the −2 port to the −1 port was −10.5 dB and −12 dB for the 0 port.

4. Transmission experiment

Figure 4(a) shows the experimental arrangement for a SDM coherent optical communication link using two OAM devices as an OAM mux/demux. The digital coherent transmitter consists of a continuous-wave (cw) laser centered at 1540 nm, followed by an erbium-doped fiber amplifier (EDFA), an I/Q modulator, and another EDFA. The I/Q modulator was driven by an electronic arbitrary waveform generator at 12 GSa/s (5.5 GHz of analog bandwidth). Using digital signal processing (DSP) implemented in MATLAB, the digital coherent transmitter created data waveforms in either a 1-b/s/Hz, 10-Gb/s binary phase shifted keying (BPSK) format or a 2-b/s/Hz, 20-Gb/s quadrature phase shifted keying (QPSK) format. Both data waveform formats consisted of a pseudorandom bit sequence (PRBS) of length 2⁷−1. An acousto-optic modulator frequency shifted a sample of the unmodulated cw laser by 35 MHz to provide a reference (LO) signal for the digital coherent receiver. An EDFA amplified the signal before it was split and sent to the OAM mux (OAM #1). The output beam from OAM #1 was then collected with an objective (20 × , 0.57 NA) and directed to OAM demux (OAM #2), where a second identical objective was used to focus the beam onto the 50-µm diameter grating. Figure 4(b) shows a photo of the free-space optics and OAM devices, where the total beam path length was 0.5 m. An EDFA and 1-nm bandpass filter (BPF) immediately amplified the demuxed signal from OAM #2 before an attenuator and power meter tap that were used to measure the bit-error-rate (BER) performance. The signal passed through a second EDFA and 1-nm BPF before the return fiber link and detection by the digital coherent receiver [16

G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photonics 1(2), 279–307 (2009). [CrossRef]

]. Offline DSP enabled computing the BER performance. All measurements used TE-polarization, which is transformed into azimuthal polarization by the OAM devices.

Fig. 4 (a) Experimental arrangement using two silicon PICs to achieve OAM multiplexing and demultiplexing for up to two simultaneous channels.(b) Photo of OAM PICs and optics.

The BER performance for both BPSK and QPSK data were separately measured on each of the five OAM channels ( ℓ = −2, −1, 0, 1, 2) by removing the power splitter and sending only one input signal to OAM #1. Figure 5(a) presents the BER versus received power at the input of the link EDFA. A total of 14,986 bits, limited by the memory, were recorded and analyzed at each power level. The back-to-back data were taken without the OAM devices and instead a fiber attenuator provided an output power of −45 dBm (i.e., the highest OAM device output). For the 10-Gb/s BPSK data, all OAM channels in repeated experiments were error free for the 14,986 bits tested. The 3 to 6-dB power penalty with respect to the back-to-back case likely arises from fiber coupling loss variations for each port. For the 20-Gb/s QPSK data, there is a ~6-dB power penalty (BER = 10⁻³) for the back-to-back case (with respect to BPSK back-to-back) and an error floor at a BER of ~10⁻⁴. Since the symbol rates are the same for the BPSK and QPSK data, 3 dB of the power penalty is expected. However, the origin of the excess 3-dB penalty is not understood at this time. The error floor is likely due to the limited signal-to-noise ratio of the amplified −45 dBm signal from OAM #2. Figure 5(b) shows the 10-Gb/s BPSK BER performance in the presence of a second active channel (interferer) with equal power. Due to the additional loss from the splitter, the single-channel BER has a ~4-dB power penalty (BER = 10⁻³) compared to Fig. 5(a). The addition of an interferer when ℓ = −2 only impacts the BER below ~10⁻³, while the introduction of an interferer when ℓ = −1, causes a ~7-dB power penalty. This is likely due to the difference in crosstalk between the OAM channels used in the two measurements (−10 dB versus −6 dB). Preliminary measurements made by imaging the outputs onto an IR vidicon camera indicate that the crosstalk of the adjacent channels are not particularly worse than the other channels.

Fig. 5 (a) Single-channel BER performance of the OAM mux/demux 10 Gb/s for BPSK and 20 Gb/s for QPSK. The legend lists the device input port number (i.e., ℓ). (b) BER performance for the ℓ = −2 and ℓ = +1 channel without, and with, an interferer with 10 Gb/s BPSK data.

The fiber-to-fiber loss for the free-space communication link was estimated at ~55 dB which included (a) 8 dB fiber coupling loss comprised of 1 dB silica fiber tip reflection, 5 dB mode mismatch, and 2.4 dB silicon facet reflection, (b) 4 dB waveguide propagation loss, (c) 4.5 dB grating-to-air loss, (d) 2 dB objective lens loss (non-optimal AR coating designed for visible), (e) repeat of (d), (f) ~21 dB air-to-grating loss from wavefront errors (spherical aberration, residual quadratic spatial phase, etc.) and mode mismatch for the beam as it enters the circular grating, repeat of (b) and (a) for the demux device. Using a true 4-f imaging system is expected to reduce (f), but a full analysis of the beam relay optics is necessary. Additional device optimizations include reducing the fiber-to-waveguide coupling loss with an inverse taper at the waveguide outputs, reducing crosstalk across the grating center with a trench, and decreasing the grating-to-air loss by increasing the grating diameter and the total number of grating periods. A larger grating diameter also allows more waveguides around the grating to support multiplexing OAM states with a larger topological charge.

Although not investigated here, similar to most free-space OAM implementations [2

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008). [CrossRef]

J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. 47(13), 2414–2429 (2008). [CrossRef] [PubMed]

I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010). [CrossRef] [PubMed]

], misalignments between the demonstrated OAM device pair result in increased signal losses and increased crosstalk between demultiplexed states. A full analysis of the free-space beam and optics will provide insight into the specific sensitivities of these OAM devices in a realistic free-space communications system.

5. Conclusion

We fabricated silicon PICs and demonstrated free-space SDM coherent optical transmission using OAM state multiplexing and demultiplexing. The device design allows operation as either an OAM multiplexer or demultiplexer for a topological charge range of −2 to +2 and easily interfaces with fiber-pigtailed components. The single-channel BER statistics for both 10-Gb/s BPSK data and 20-Gb/s QPSK data indicated similar performance for all topological charges. In all cases, the BER was well below the forward error correction (FEC) limit of 2 × 10⁻³ (RS(255,239) coding [17

T. Mizuochi, “Forward error correction,” in High Spectral Density Optical Communication Technologies, M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds. (Springer, 2010), 303–333.

]), even for the two simultaneous channels with crosstalk suffering a significant power penalty. Future work includes reducing coupling and on-chip losses, increasing the addressable number of OAM states, and improving the free-space optical system used to relay the OAM encoded beam between devices.

Acknowledgments

This work was supported in part by DARPA DSO under the contract HR0011-11-1-0005.

References and links

1.	L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]
2.	S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008). [CrossRef]
3.	A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011). [CrossRef]
4.	G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). [CrossRef] [PubMed]
5.	J. Lin, X. C. Yuan, S. H. Tao, and R. E. Burge, “Multiplexing free-space optical signals using superimposed collinear orbital angular momentum states,” Appl. Opt. 46(21), 4680–4685 (2007). [CrossRef] [PubMed]
6.	J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. 47(13), 2414–2429 (2008). [CrossRef] [PubMed]
7.	I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010). [CrossRef] [PubMed]
8.	S. Slussarenko, E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, “Efficient generation and control of different-order orbital angular momentum states for communication links,” J. Opt. Soc. Am. A 28(1), 61–65 (2011). [CrossRef] [PubMed]
9.	P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett. 47(17), 972–973 (2011). [CrossRef]
10.	M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997). [CrossRef]
11.	C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
12.	R. Čelechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys. 9(9), 328 (2007). [CrossRef]
13.	C. R. Doerr and L. L. Buhl, “Circular grating coupler for creating focused azimuthally and radially polarized beams,” Opt. Lett. 36(7), 1209–1211 (2011). [CrossRef] [PubMed]
14.	K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2006).
15.	C. R. Doerr, N. K. Fontaine, M. Hirano, T. Sasaki, L. L. Buhl, and P. J. Winzer, “Silicon photonic integrated circuit for coupling to a ring-core multimode fiber for space-division multiplexing,” in European Conference on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.A.3.
16.	G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photonics 1(2), 279–307 (2009). [CrossRef]
17.	T. Mizuochi, “Forward error correction,” in High Spectral Density Optical Communication Technologies, M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds. (Springer, 2010), 303–333.

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.4230) Fiber optics and optical communications : Multiplexing
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 6, 2012
Revised Manuscript: March 26, 2012
Manuscript Accepted: March 26, 2012
Published: April 9, 2012

Citation
Tiehui Su, Ryan P. Scott, Stevan S. Djordjevic, Nicolas K. Fontaine, David J. Geisler, Xinran Cai, and S. J. B. Yoo, "Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices," Opt. Express 20, 9396-9402 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-9396

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References

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45(11), 8185–8189 (1992). [CrossRef] [PubMed]
S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev.2(4), 299–313 (2008). [CrossRef]
A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics3(2), 161–204 (2011). [CrossRef]
G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12(22), 5448–5456 (2004). [CrossRef] [PubMed]
J. Lin, X. C. Yuan, S. H. Tao, and R. E. Burge, “Multiplexing free-space optical signals using superimposed collinear orbital angular momentum states,” Appl. Opt.46(21), 4680–4685 (2007). [CrossRef] [PubMed]
J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt.47(13), 2414–2429 (2008). [CrossRef] [PubMed]
I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express18(24), 24722–24728 (2010). [CrossRef] [PubMed]
S. Slussarenko, E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, “Efficient generation and control of different-order orbital angular momentum states for communication links,” J. Opt. Soc. Am. A28(1), 61–65 (2011). [CrossRef] [PubMed]
P. Martelli, A. Gatto, P. Boffi, and M. Martinelli, “Free-space optical transmission with orbital angular momentum division multiplexing,” Electron. Lett.47(17), 972–973 (2011). [CrossRef]
M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A56(5), 4064–4075 (1997). [CrossRef]
C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J.27, 379–423 (1948).
R. Čelechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys.9(9), 328 (2007). [CrossRef]
C. R. Doerr and L. L. Buhl, “Circular grating coupler for creating focused azimuthally and radially polarized beams,” Opt. Lett.36(7), 1209–1211 (2011). [CrossRef] [PubMed]
K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2006).
C. R. Doerr, N. K. Fontaine, M. Hirano, T. Sasaki, L. L. Buhl, and P. J. Winzer, “Silicon photonic integrated circuit for coupling to a ring-core multimode fiber for space-division multiplexing,” in European Conference on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.A.3.
G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photonics1(2), 279–307 (2009). [CrossRef]
T. Mizuochi, “Forward error correction,” in High Spectral Density Optical Communication Technologies, M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds. (Springer, 2010), 303–333.

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