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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 23 — Nov. 18, 2013
  • pp: 28794–28800
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Mode multiplexed single-photon and classical channels in a few-mode fiber

Joel Carpenter, Chunle Xiong, Matthew J. Collins, Juntao Li, Thomas F. Krauss, Benjamin J. Eggleton, Alex S. Clark, and Jochen Schröder  »View Author Affiliations


Optics Express, Vol. 21, Issue 23, pp. 28794-28800 (2013)
http://dx.doi.org/10.1364/OE.21.028794


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Abstract

We classically measure the entire propagation matrix of a few-mode fiber and use a spatial light modulator to undo modal mixing and recover single-photons launched onto each of the eigenmodes of the fiber at one end, but arriving as mixed modal superpositions at the other. We exploit the orthogonality of these modal channels to improve the isolation between a quantum and classical channel launched onto different spatial and polarization modes at different wavelengths. The spatial diversity of the channels provides an additional 35dB of isolation in addition to that provided by polarization and wavelength.

© 2013 Optical Society of America

1. Introduction

Classical communication based on RSA encryption is inherently insecure to attacks from a future quantum computer. Secure communication can be provided through the use of quantum key distribution (QKD) [1

1. N. Gisin and R. Thew, “Quantum communications,” Nat. Photonics 1(3), 165–171 (2007). [CrossRef]

]. QKD can be used to generate symmetric secret keys and distribute them between two users via a quantum mechanical link. QKD has the advantage that the secret key can be distributed with absolute certainty that it was not intercepted. Typically photons are used, as their quantum properties remain intact over the large distances required for useful communication. Fiber optics provides the ideal channel for transmitting QKD photons and building a secure key. If a photon is intercepted in flight by a malicious third party and the result is re-sent in the measured basis then the eavesdropper can be readily detected and communication ceased [2

2. C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” International Conference on Computers, Systems and Signal Processing, 175–179 (1984).

4

4. C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68(21), 3121–3124 (1992). [CrossRef] [PubMed]

]. The information-theoretic security and eavesdropper detection makes QKD a promising route to future-proof global information security. Typically quantum signals are sent in a dark fiber [5

5. P. Eraerds, N. Walenta, M. Legre, N. Gisin, and H. Zbinden, “Quantum key distribution and 1gbps data encryption over a single fiber,” New J. Phys. 12(6), 063027 (2010). [CrossRef]

] or in free-space [6

6. T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007). [CrossRef] [PubMed]

8

8. A. Fedrizzi, R. Ursin, T. Herbst, M. Nespoli, R. Prevedel, T. Scheidl, F. Tiefenbacher, T. Jennewein, and A. Zeilinger, “High-fidelity transmission of entanglement over a high-loss free-space channel,” Nat. Phys. 5(6), 389–392 (2009). [CrossRef]

] for QKD demonstrations; however one would like to carry both quantum and classical signals in fiber simultaneously to make use of the full global fiber optic infrastructure. Previously, quantum and classical signals have been transmitted in the same single-mode fiber by way of wavelength division multiplexing [9

9. P. D. Townsend, “Simultaneous quantum cryptographic key distribution and conventional data transmission over installed fiber using wavelength-division multiplexing,” Electron. Lett. 33(3), 188–190 (1997). [CrossRef]

,10

10. T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. 11(10), 105001 (2009). [CrossRef]

] or polarization multiplexing, or a combination of the two [11

11. N. A. Peters, P. Toliver, T. E. Chapuran, R. J. Runser, S. R. McNown, C. G. Peterson, D. Rosenberg, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, and K. T. Tyagi, “Dense wavelength multiplexing of 1550 nm QKD with strong classical channels in reconfigurable networking environments,” New J. Phys. 11(4), 045012 (2009). [CrossRef]

].

2. Experiment

2.1 Experimental overview

Fig. 1 Wavelength, polarization and spatial mode multiplexing system for single-photon and classical signals. ECL: external cavity laser; SPS: single-photon source; AWG: arrayed waveguide grating; BPF: band-pass filter; PC: polarization controller; MMUX: mode-multiplexer; FMF: few-mode fiber; CWDM: coarse wavelength division multiplexer; PM: power meter; POL: polarizer; SSPD: superconducting single-photon detector.
The spatial light modulator (SLM) based mode multiplexing system (MMUX) [19

19. J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012). [CrossRef]

] of Fig. 1, in combination with a polarization controller (PC) has the ability to couple light from each of its input single-mode fibers (SMFs) independently into arbitrary spatial and polarization modes of the few-mode fiber (FMF). In the reverse direction, this system can be used to detect an arbitrary spatial and polarization mode at the other end of the FMF as a mode demultiplexer. The fiber in this case is a 2 m length of step-index fiber which supports a total of six spatial and polarization modes, which in the weak-guidance approximation [20

20. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

] correspond to the degenerate horizontally and vertically polarized fundamental Gaussian modes (0H, 0V) and the degenerate positive and negative topological charge orbital angular momentum (OAM) modes in both polarizations ( + 1H, + 1V, −1H, −1V).

2.2 Spatial light modulator mode multiplexing system

Fig. 2 (a) Spatial light modulator based arbitrary mode/polarization multiplexing system. (b) Example transmit phase mask. (c) Example receive phase mask.
Figure 2(a) illustrates the mode multiplexing/demultiplexing system that is used at either side of the fiber to transmit/receive arbitrary mode/polarization states [19

19. J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012). [CrossRef]

]. The SLM is shown as if it were a transmissive device for clarity, but in reality it is reflective and the optics on either side of the SLM in Fig. 2(a) are positioned on-top of one another, rather than in the same plane. The multiplexer consists of an array of input/output single-mode fibers, each representing an independent channel to be launched into the fiber. The beams from the fiber array enter polarisation diversity optics which creates two beams representing orthogonal polarisations, but which are both aligned to the polarisation axis required by the liquid crystals of the SLM. The two beams reflect off the left and right side of the SLM respectively, allowing each polarisation to be addressed independently by the device. The two polarisations are then recombined and focused into the FMF.

2.3 Heralded single-photon source

Single-photon measurements were performed using a silicon photonic crystal waveguide single-photon source [21

21. C. Xiong, C. Monat, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. F. Krauss, J. G. Rarity, and B. J. Eggleton, “Slow-light enhanced correlated photon pair generation in a silicon photonic crystal waveguide,” Opt. Lett. 36(17), 3413–3415 (2011). [CrossRef] [PubMed]

,22

22. C. Xiong, C. Monat, M. J. Collins, L. Tranchant, D. Petiteau, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Characteristics of correlated photon pairs generated in ultra-compact silicon slow-light photonic crystal waveguides,” IEEE J. Sel. Top. Quantum Electron. 18(6), 1676–1683 (2012). [CrossRef]

] (SPS) of Fig. 1. The source setup is shown schematically in Fig. 3(a).
Fig. 3 A schematic of spontaneous four-wave mixing. (a) a pulse enters the photonic crystal waveguide and is slowed, causing an increase in peak power and interaction time in the waveguide. Two photons from the pump are annihilated to create signal and idler photons of higher and lower energy, as described by the arrows in (b). The photons and residual pump then exit the waveguide.
A wavelength-tunable pulsed pump laser set to 1556 nm was coupled to the photonic crystal waveguide using polymer access waveguides and inverse tapers, resulting in a 5 dB per facet loss. Two photons from the pump pulse were annihilated to create signal and idler photons of higher and lower energy through the process of spontaneous four-wave mixing (SFWM), as shown in Fig. 3(b). The photonic crystal was dispersion engineered by shifting the two rows of holes closest to the waveguide creating a slow light region over 15 nm wide [23

23. J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008). [CrossRef] [PubMed]

]. This region had a slow-down factor S ≈10, defined as the ratio of the group index inside the waveguide over the group index of bulk silicon. The nonlinearity of the waveguide is enhanced by S2, thereby enhancing the SFWM efficiency by S4. The generated photons were separated using an arrayed waveguide grating (AWG) before passing through 0.5 nm bandpass filters (BPF). The idler photon at 1561 nm was then detected using a superconducting single-photon detector (SSPD) and heralds the presence of the signal photon at 1551 nm which can then be forwarded to the MMUX system.

3. Results and analysis

3.1 Propagation matrix

3.2 Mode multiplexed single-photon and classical channels

A classical information channel was simulated using a 1531 nm external cavity laser (ECL) which passed through a 0.5 nm BPF to reduce spectral noise before passing into MMUX1 where it was assigned to a vertically polarized higher-order OAM mode, as shown in Fig. 1. The heralded single-photon channel again originated from the SPS and was coupled into the other port of MMUX1 and assigned to the horizontally polarized fundamental mode of the fiber. At the other end of the FMF, MMUX2 demultiplexed the two spatial channels to two separate output fibers. The leakage of the classical channel into the single-photon channel output fiber immediately after MMUX2 was measured to be approximately −35 dB. This isolation is provided by the spatial and polarization filtering the MMUX2 system provides and is the isolation between the channels as measured at the point after MMUX2 but before the CWDM of Fig. 1. The single-photon channel then passed through a coarse-wavelength division demultiplexer (CWDM) and a 0.5 nm BPF before passing through a PC and a polarizer (POL) which is aligned with the polarization axis of the SSPD via one final PC. The loss from the SMF inputs of the transmit MMUX1 to the SMF outputs of the receive MMUX2 where measured to be 9.5 dB, with approximately 6 dB of that due to the reflectivity of the two SLMs with the remaining 3.5 dB due to coupling and other MMUX component losses such as lenses, beam-splitters and waveplates. The receiver wavelength and polarization components gave an additional 5.6 dB loss.

Fig. 5 The extracted heralded single-photon rate (blue squares) did not vary significantly as the power was increased in the classical channel and was close to the rate when no power is present (blue dashed line). The measured CAR (black circles) and trend (red line) show values comparable to the classical channel off (black dotted line). Errors are from Poissonian statistics.
The coincidence-to-accidental ratio (CAR) was measured for several classical channel received powers, shown in Fig. 5 as black circles, from −10 dBm, sufficient for error-free operation using direct-detection schemes even without pre-amplification, down to −40 dBm, likely be too little power for error-free operation even using coherent techniques. With the ECL turned off, a CAR of 31.9 ± 1.6 was measured, given by the dotted black line of Fig. 5. At −10 dBm of received power the CAR drops slightly to 29.2 ± 1.4, with a fit to the data suggesting a minor drop as the classical power was increased (red line). However the trend is weak and the CAR remains consistent from no ECL power all the way up to −10dBm to within experimental error. A test was also performed where the classical and single-photon channels were launched onto the same spatial and polarization mode (fundamental mode, horizontally polarized). In this case the CAR approached zero and became immeasurable. The extracted heralded photon rate, shown as blue squares, remains constant and comparable to the case with the ECL turned off, shown as a blue dashed line.

To further prove the usefulness of this scheme it must be scaled up to longer fiber lengths of the order of a few kilometers to be compatible with short-range communication and datacenters. Similar MMUX techniques have been demonstrated over kilometers of fiber [19

19. J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012). [CrossRef]

] where the tracking of mode evolution is possible in real-time and can be corrected using the deMMUX SLM. It will also be important in the future to demonstrate the building of a secure key via QKD through this system, with measurements of key rates and quantum bit error rates as the classical channel power is increased.

4. Conclusion

We have shown that classical and single-photon channels can be successfully multiplexed onto different spatial modes of the same few-mode fiber. This demonstrates that the orthogonality between the modes of a fiber can be used to isolate multiple channels for simultaneous quantum and classical communication, enabling quantum communications in multimode fibers which is especially suited to use in datacenters and short-haul local networks.

Acknowledgments

We acknowledge the Linkage (LP120100661), Laureate Fellowship (FL120100029), Centre of Excellence (CUDOS, CE110001018), and DECRA (DE130101148, DE120101329 and DE120100226) programs of the Australian Research Council and the EPSRC UK Silicon Photonics project (EP/F001428/1) for support.

References and links

1.

N. Gisin and R. Thew, “Quantum communications,” Nat. Photonics 1(3), 165–171 (2007). [CrossRef]

2.

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” International Conference on Computers, Systems and Signal Processing, 175–179 (1984).

3.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991). [CrossRef] [PubMed]

4.

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68(21), 3121–3124 (1992). [CrossRef] [PubMed]

5.

P. Eraerds, N. Walenta, M. Legre, N. Gisin, and H. Zbinden, “Quantum key distribution and 1gbps data encryption over a single fiber,” New J. Phys. 12(6), 063027 (2010). [CrossRef]

6.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007). [CrossRef] [PubMed]

7.

Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J. W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Express 18(8), 8587–8594 (2010). [CrossRef] [PubMed]

8.

A. Fedrizzi, R. Ursin, T. Herbst, M. Nespoli, R. Prevedel, T. Scheidl, F. Tiefenbacher, T. Jennewein, and A. Zeilinger, “High-fidelity transmission of entanglement over a high-loss free-space channel,” Nat. Phys. 5(6), 389–392 (2009). [CrossRef]

9.

P. D. Townsend, “Simultaneous quantum cryptographic key distribution and conventional data transmission over installed fiber using wavelength-division multiplexing,” Electron. Lett. 33(3), 188–190 (1997). [CrossRef]

10.

T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. 11(10), 105001 (2009). [CrossRef]

11.

N. A. Peters, P. Toliver, T. E. Chapuran, R. J. Runser, S. R. McNown, C. G. Peterson, D. Rosenberg, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, and K. T. Tyagi, “Dense wavelength multiplexing of 1550 nm QKD with strong classical channels in reconfigurable networking environments,” New J. Phys. 11(4), 045012 (2009). [CrossRef]

12.

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, S. Bickham, H. Tam, C. Lu, M. Li, S. Ten, A. P. T. Lau, V. Tse, G. Peng, C. Montero, X. Prieto, and G. Li, “88x3x112-Gb/s WDM transmission over 50-km of three-mode fiber with inline multimode fiber amplifier,” in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (Optical Society of America, 2011), paper Th.13.C.2. [CrossRef]

13.

A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s CO-OFDM signal over a two-mode fiber,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC),2011and the National Fiber Optic Engineers Conference, pp. 1, 3, 6–10 March 2011.

14.

G. B. Xavier and J. P. von der Weid, “Limitations for transmission of photonic qubits in optical fibers carrying telecom traffic,” Electron. Lett. 46(15), 1071–1072 (2010). [CrossRef]

15.

R. H. Stolen, “Relation between the effective area of a single-mode fiber and the capture fraction of spontaneous Raman scattering,” J. Opt. Soc. Am. B 19(3), 498–501 (2002). [CrossRef]

16.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001). [CrossRef] [PubMed]

17.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012). [CrossRef] [PubMed]

18.

W. Löffler, T. G. Euser, E. R. Eliel, M. Scharrer, P. St. J. Russell, and J. P. Woerdman, “Fiber transport of spatially entangled photons,” Phys. Rev. Lett. 106(24), 240505 (2011). [CrossRef] [PubMed]

19.

J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012). [CrossRef]

20.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

21.

C. Xiong, C. Monat, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. F. Krauss, J. G. Rarity, and B. J. Eggleton, “Slow-light enhanced correlated photon pair generation in a silicon photonic crystal waveguide,” Opt. Lett. 36(17), 3413–3415 (2011). [CrossRef] [PubMed]

22.

C. Xiong, C. Monat, M. J. Collins, L. Tranchant, D. Petiteau, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Characteristics of correlated photon pairs generated in ultra-compact silicon slow-light photonic crystal waveguides,” IEEE J. Sel. Top. Quantum Electron. 18(6), 1676–1683 (2012). [CrossRef]

23.

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008). [CrossRef] [PubMed]

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(270.0270) Quantum optics : Quantum optics
(270.5565) Quantum optics : Quantum communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 17, 2013
Revised Manuscript: October 28, 2013
Manuscript Accepted: October 28, 2013
Published: November 15, 2013

Virtual Issues
Nonlinear Optics (2013) Optics Express

Citation
Joel Carpenter, Chunle Xiong, Matthew J. Collins, Juntao Li, Thomas F. Krauss, Benjamin J. Eggleton, Alex S. Clark, and Jochen Schröder, "Mode multiplexed single-photon and classical channels in a few-mode fiber," Opt. Express 21, 28794-28800 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-28794


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References

  1. N. Gisin and R. Thew, “Quantum communications,” Nat. Photonics1(3), 165–171 (2007). [CrossRef]
  2. C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” International Conference on Computers, Systems and Signal Processing, 175–179 (1984).
  3. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67(6), 661–663 (1991). [CrossRef] [PubMed]
  4. C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett.68(21), 3121–3124 (1992). [CrossRef] [PubMed]
  5. P. Eraerds, N. Walenta, M. Legre, N. Gisin, and H. Zbinden, “Quantum key distribution and 1gbps data encryption over a single fiber,” New J. Phys.12(6), 063027 (2010). [CrossRef]
  6. T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett.98(1), 010504 (2007). [CrossRef] [PubMed]
  7. Y. Liu, T.-Y. Chen, J. Wang, W.-Q. Cai, X. Wan, L.-K. Chen, J.-H. Wang, S.-B. Liu, H. Liang, L. Yang, C.-Z. Peng, K. Chen, Z.-B. Chen, and J. W. Pan, “Decoy-state quantum key distribution with polarized photons over 200 km,” Opt. Express18(8), 8587–8594 (2010). [CrossRef] [PubMed]
  8. A. Fedrizzi, R. Ursin, T. Herbst, M. Nespoli, R. Prevedel, T. Scheidl, F. Tiefenbacher, T. Jennewein, and A. Zeilinger, “High-fidelity transmission of entanglement over a high-loss free-space channel,” Nat. Phys.5(6), 389–392 (2009). [CrossRef]
  9. P. D. Townsend, “Simultaneous quantum cryptographic key distribution and conventional data transmission over installed fiber using wavelength-division multiplexing,” Electron. Lett.33(3), 188–190 (1997). [CrossRef]
  10. T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys.11(10), 105001 (2009). [CrossRef]
  11. N. A. Peters, P. Toliver, T. E. Chapuran, R. J. Runser, S. R. McNown, C. G. Peterson, D. Rosenberg, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, and K. T. Tyagi, “Dense wavelength multiplexing of 1550 nm QKD with strong classical channels in reconfigurable networking environments,” New J. Phys.11(4), 045012 (2009). [CrossRef]
  12. E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, S. Bickham, H. Tam, C. Lu, M. Li, S. Ten, A. P. T. Lau, V. Tse, G. Peng, C. Montero, X. Prieto, and G. Li, “88x3x112-Gb/s WDM transmission over 50-km of three-mode fiber with inline multimode fiber amplifier,” in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (Optical Society of America, 2011), paper Th.13.C.2. [CrossRef]
  13. A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s CO-OFDM signal over a two-mode fiber,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC),2011and the National Fiber Optic Engineers Conference, pp. 1, 3, 6–10 March 2011.
  14. G. B. Xavier and J. P. von der Weid, “Limitations for transmission of photonic qubits in optical fibers carrying telecom traffic,” Electron. Lett.46(15), 1071–1072 (2010). [CrossRef]
  15. R. H. Stolen, “Relation between the effective area of a single-mode fiber and the capture fraction of spontaneous Raman scattering,” J. Opt. Soc. Am. B19(3), 498–501 (2002). [CrossRef]
  16. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001). [CrossRef] [PubMed]
  17. R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science338(6107), 640–643 (2012). [CrossRef] [PubMed]
  18. W. Löffler, T. G. Euser, E. R. Eliel, M. Scharrer, P. St. J. Russell, and J. P. Woerdman, “Fiber transport of spatially entangled photons,” Phys. Rev. Lett.106(24), 240505 (2011). [CrossRef] [PubMed]
  19. J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol.30(24), 3946–3952 (2012). [CrossRef]
  20. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  21. C. Xiong, C. Monat, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. F. Krauss, J. G. Rarity, and B. J. Eggleton, “Slow-light enhanced correlated photon pair generation in a silicon photonic crystal waveguide,” Opt. Lett.36(17), 3413–3415 (2011). [CrossRef] [PubMed]
  22. C. Xiong, C. Monat, M. J. Collins, L. Tranchant, D. Petiteau, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Characteristics of correlated photon pairs generated in ultra-compact silicon slow-light photonic crystal waveguides,” IEEE J. Sel. Top. Quantum Electron.18(6), 1676–1683 (2012). [CrossRef]
  23. J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express16(9), 6227–6232 (2008). [CrossRef] [PubMed]

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