Abstract

Optical networks are facing fundamental capacity scalability problems owing to Shannon limits in silica fiber, frequently summarized as the “optical networks capacity crunch.” We explore the possibility of scaling communication capacities through the use of significantly higher carrier frequencies, such as the extreme ultraviolet or the soft x-ray spectral region, in analogy to the 3–7 orders of magnitude increase in carrier frequencies when optical fiber replaced microwave transmission technologies in the late 1970s. We find that only very limited capacity gains on the order of 10 may be achieved relative to the 1550-nm telecommunications band without fundamentally increasing a system's received energy per bit, its relative bandwidth, or its degree of spatial parallelism. Conversely, we predict the required reduction of waveguide losses that would be needed to make higher carrier frequencies a viable proposition from an energy efficiency point of view. Our analyses include the use of as of yet unexplored quantum communication techniques, whose required energy per bit we find to be lower-bounded by $\boldsymbol{kT}/\log _2\boldsymbol{e}$ at any carrier frequency, which may have implications beyond the communications applications discussed in this paper.

© 2018 IEEE

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2018 (4)

2017 (1)

P. J. Winzer and D. T. Neilson, “From scaling disparities to integrated parallelism: A decathlon for a decade,” J. Lightw. Technol. vol. 35, no. 5, pp. 1099–1115, 2017.

2016 (3)

P. J. Winzer, “From first fibers to mode-division multiplexing,” Chin. Opt. Lett., vol. 14, no. 12, 2016, Art. no. .

K. Kikuchi, “Fundamentals of coherent optical fiber communications,” J. Lightw. Technol., vol. 34, no. 1, pp. 157–179, 2016.

B. R. Bardhan and J. H. Shapiro, “Ultimate capacity of a linear time-invariant bosonic channel,” Phys. Rev. A, vol. 93, 2016, Art. no. .

2015 (2)

A. Ludwiget al., “Stacked modulation formats enabling highest-sensitivity optical free-space links,” Opt. Express, vol. 23, pp. 21942–21957, 2015.

V. Giovannetti, A. S. Holevo, and R. Garcia-Patron, “A solution of the Gaussian optimizer conjecture,” Commun. Math. Phys., vol. 334, pp. 1553–1571, 2015.

2014 (4)

R. Dar, M. Shtaif, and M. Feder, “New bounds on the capacity of the nonlinear fiber-optic channel,” Opt. Lett., vol. 39, pp. 398–401, 2014.

V. Giovannetti, R. Garcia-Patron, N. J. Cerf, and A. S. Holevo, “Ultimate classical communication rates of quantum optical channels,” Nature Photon., vol. 8, pp. 796–800, 2014.

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Quantum limits on the energy consumption of optical transmission systems,” J. Lightw. Technol., vol. 32, no. 10, pp. 1853–18602014.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN model of fiber non-linear propagation and its applications,” J. Lightw. Technol., vol. 32, no. 4, pp. 694–721, 2014.

2013 (1)

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Electromagnetic channel capacity for practical purposes,” Nature Photon., vol. 7, pp. 834–838, 2013.

2011 (1)

R. S. Tucker, “Green optical communications—Part I: Energy limitations in transport,” IEEE J. Sel. Topics Quantum Electron., vol. 17, no. 2, pp. 245–260, 2011.

2010 (2)

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J., vol. 14, no. 4, pp. 3–9, 2010.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

2008 (1)

2006 (3)

B. S. Robinsonet al., “781 Mbit/s photon-counting optical communications using a superconducting nanowire detector,” Opt. Lett., vol. 31, pp. 444–446, 2006.

E. B. Desurvire, “Capacity demand and technology challenges for lightwave systems in the next two decades,” J. Lightw. Technol., vol. 24, no. 12, pp. 4697–4710, 2006.

P. I. Hopman, P. W. Boettcher, L. M. Candell, J. B. Glettler, R. Shoup, and G. Zogbi, “An end-to-end demonstration of a receiver array based free-space photon counting communications link,” Proc. SPIE, vol. 6304, 2006, Art. no. .

2004 (1)

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett., vol. 92, no. 2, 2004, Art. no. .

2001 (1)

A. Mori, H. Masuda, K. Shikano, K. Oikawa, K. Kato, and M. Shimizu, “Ultra-wideband tellurite-based Raman fibre amplifier,” Electron. Lett., vol. 37, no. 24, pp. 1442–1443, 2001.

1999 (1)

P. J. Winzer, A. Kalmar, and W. R. Leeb, “The role of amplified spontaneous emission in optical free-space communication links with optical amplification - impact on isolation and data transmission; utilization for pointing, acquisition, and tracking,” Proc. SPIE, vol. 3615, pp. 104–114, 1999.

1998 (1)

S. Holevo, “The capacity of the quantum channel with general signal states,” IEEE Trans. Inf. Theory, vol. 44, no. 1, pp. 269–273, 1998.

1997 (1)

B. Schumacher and M. D. Westmoreland, “Sending classical information via noisy quantum channels,” Phys. Rev. A, vol. 56, no. 1, pp. 131–138, 1997.

1993 (1)

H. P. Yuen and M. Ozawa, “Ultimate information carrying limit of quantum systems,” Phys. Rev. Lett., vol. 70, no. 4, pp. 363–366, 1993.

1990 (1)

A. R. Chraplyvy, “Limitations on lightwave communications imposed by optical-fiber nonlinearities,” J. Lightw. Technol., vol. 8, no. 10, pp. 1548–1557, 1990.

1989 (1)

1973 (1)

S. Holevo, “Bounds for the quantity of information transmitted by a quantum communication channel,” Probl. Peredachi Inf., vol. 9, no. 3, pp. 3–11, 1973.

1968 (1)

G. F. Engen, “A method of calibrating coaxial noise sources in terms of a waveguide standard,” IEEE Trans. Microw. Theory Techn., vol. MTT-16, no. 9, pp. 636–639, 1968.

1962 (1)

J. P. Gordon, “Quantum effects in communications systems,” Proc. IRE, vol. 50, no. 8, pp. 1898–1908, 1962.

1949 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE, vol. 37, no. 1, pp. 10–21, 1949.

1948 (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423, 623–656, 1948.

Albota, M. A.

M. A. Albota, B. S. Robinson, D. O. Caplan, S. A. Hamilton, and D. M. Boroson, “Photon-counting 1.55 μm optical communications with pulse-position modulation and a multimode upconversion single-photon receiver,” in Proc. Annu. Meeting IEEE Lasers Electro Opt. Soc., 2008, Paper TuC4.

Antonelli, C.

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Quantum limits on the energy consumption of optical transmission systems,” J. Lightw. Technol., vol. 32, no. 10, pp. 1853–18602014.

Bardhan, B. R.

B. R. Bardhan and J. H. Shapiro, “Ultimate capacity of a linear time-invariant bosonic channel,” Phys. Rev. A, vol. 93, 2016, Art. no. .

Boettcher, P. W.

P. I. Hopman, P. W. Boettcher, L. M. Candell, J. B. Glettler, R. Shoup, and G. Zogbi, “An end-to-end demonstration of a receiver array based free-space photon counting communications link,” Proc. SPIE, vol. 6304, 2006, Art. no. .

Boroson, D. M.

M. L. Stevens, D. O. Caplan, B. S Robinson, D. M. Boroson, and A. L. Kachelmyer, “Optical homodyne PSK demonstration of 1.5 photons per bit at 156 Mbps with rate-½ turbo coding,” Opt. Express, vol. 16, pp. 10412–10420, 2008.

M. A. Albota, B. S. Robinson, D. O. Caplan, S. A. Hamilton, and D. M. Boroson, “Photon-counting 1.55 μm optical communications with pulse-position modulation and a multimode upconversion single-photon receiver,” in Proc. Annu. Meeting IEEE Lasers Electro Opt. Soc., 2008, Paper TuC4.

Bosco, G.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN model of fiber non-linear propagation and its applications,” J. Lightw. Technol., vol. 32, no. 4, pp. 694–721, 2014.

Burrows, E. C.

X. Liu, S. Chandrasekhar, T. H. Wood, R. W. Tkach, E. C. Burrows, and P. J. Winzer, “Demonstration of 2.7-PPB receiver sensitivity using PDM-QPSK with 4-PPM and unrepeatered transmission over a single 370-km unamplified ultra-large-area fiber span,” in Proc. Eur. Conf. Opt. Commun., 2011, Paper Tu.3.B.4.

Candell, L. M.

P. I. Hopman, P. W. Boettcher, L. M. Candell, J. B. Glettler, R. Shoup, and G. Zogbi, “An end-to-end demonstration of a receiver array based free-space photon counting communications link,” Proc. SPIE, vol. 6304, 2006, Art. no. .

Caplan, D. O.

M. L. Stevens, D. O. Caplan, B. S Robinson, D. M. Boroson, and A. L. Kachelmyer, “Optical homodyne PSK demonstration of 1.5 photons per bit at 156 Mbps with rate-½ turbo coding,” Opt. Express, vol. 16, pp. 10412–10420, 2008.

M. A. Albota, B. S. Robinson, D. O. Caplan, S. A. Hamilton, and D. M. Boroson, “Photon-counting 1.55 μm optical communications with pulse-position modulation and a multimode upconversion single-photon receiver,” in Proc. Annu. Meeting IEEE Lasers Electro Opt. Soc., 2008, Paper TuC4.

Caplan, O.

O. Caplan, “Laser communication transmitter and receiver design,” in Free Space Laser Communications, A. K. Majumdar and J. C. Ricklineds.Berlin, Germany: Springer, 2008, pp. 109–246.

Carena, A.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN model of fiber non-linear propagation and its applications,” J. Lightw. Technol., vol. 32, no. 4, pp. 694–721, 2014.

Cerf, N. J.

V. Giovannetti, R. Garcia-Patron, N. J. Cerf, and A. S. Holevo, “Ultimate classical communication rates of quantum optical channels,” Nature Photon., vol. 8, pp. 796–800, 2014.

Chandrasekhar, S.

S. L. I. Olsson, J. Cho, S. Chandrasekhar, X. Chen, P. J. Winzer, and S. Makovejs, “Probabilistically shaped PDM 4096-QAM transmission over up to 200 km of fiber using standard intradyne detection,” Opt. Express, vol. 26, no. 4, pp. 4522–4530, 2018.

X. Liu, S. Chandrasekhar, T. H. Wood, R. W. Tkach, E. C. Burrows, and P. J. Winzer, “Demonstration of 2.7-PPB receiver sensitivity using PDM-QPSK with 4-PPM and unrepeatered transmission over a single 370-km unamplified ultra-large-area fiber span,” in Proc. Eur. Conf. Opt. Commun., 2011, Paper Tu.3.B.4.

Chen, X.

Cheng, M. K.

M. K. Cheng, B. E. Moision, J. Hamkins, and M. A. Nakashima, “Implementation of a coded modulation for deep space optical communications,” in Proc. IEEE Globecom, SAT05-4, 2006.

Cho, J.

Chraplyvy, A. R.

P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, “Fiber-optic transmission and networking: The previous 20 and the next 20 years,” Opt. Express, vol. 26, pp. 24190–24239, 2018.

A. R. Chraplyvy, “Limitations on lightwave communications imposed by optical-fiber nonlinearities,” J. Lightw. Technol., vol. 8, no. 10, pp. 1548–1557, 1990.

A. R. Chraplyvy, “The coming capacity crunch,” in Proc. Eur. Conf. Opt. Commun., Vienna, Austria, 2009, plenary talk.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. Hoboken, NJ, USA: Wiley, 2006.

Curri, V.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN model of fiber non-linear propagation and its applications,” J. Lightw. Technol., vol. 32, no. 4, pp. 694–721, 2014.

Dar, R.

R. Daret al., “Cost-optimized submarine cables using massive spatial parallelism,” J. Lightw. Technol., vol. 36, no. 18, pp. 3855–3865, 2018.

R. Dar, M. Shtaif, and M. Feder, “New bounds on the capacity of the nonlinear fiber-optic channel,” Opt. Lett., vol. 39, pp. 398–401, 2014.

Desurvire, E. B.

E. B. Desurvire, “Capacity demand and technology challenges for lightwave systems in the next two decades,” J. Lightw. Technol., vol. 24, no. 12, pp. 4697–4710, 2006.

Engen, G. F.

G. F. Engen, “A method of calibrating coaxial noise sources in terms of a waveguide standard,” IEEE Trans. Microw. Theory Techn., vol. MTT-16, no. 9, pp. 636–639, 1968.

Essiambre, R.-J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Feder, M.

Forghieri, F.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN model of fiber non-linear propagation and its applications,” J. Lightw. Technol., vol. 32, no. 4, pp. 694–721, 2014.

Foschini, G. J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Garcia-Patron, R.

V. Giovannetti, A. S. Holevo, and R. Garcia-Patron, “A solution of the Gaussian optimizer conjecture,” Commun. Math. Phys., vol. 334, pp. 1553–1571, 2015.

V. Giovannetti, R. Garcia-Patron, N. J. Cerf, and A. S. Holevo, “Ultimate classical communication rates of quantum optical channels,” Nature Photon., vol. 8, pp. 796–800, 2014.

Geisler, D. J.

D. J. Geisleret al., “Demonstration of 2.1 photon-per-bit sensitivity for BPSK at 9.94-Gb/s with rate-½ FEC,” in Proc. Fiber Opt. Eng. Conf., 2013, Paper OM2C.6.

Giovannetti, V.

V. Giovannetti, A. S. Holevo, and R. Garcia-Patron, “A solution of the Gaussian optimizer conjecture,” Commun. Math. Phys., vol. 334, pp. 1553–1571, 2015.

V. Giovannetti, R. Garcia-Patron, N. J. Cerf, and A. S. Holevo, “Ultimate classical communication rates of quantum optical channels,” Nature Photon., vol. 8, pp. 796–800, 2014.

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Electromagnetic channel capacity for practical purposes,” Nature Photon., vol. 7, pp. 834–838, 2013.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett., vol. 92, no. 2, 2004, Art. no. .

Glettler, J. B.

P. I. Hopman, P. W. Boettcher, L. M. Candell, J. B. Glettler, R. Shoup, and G. Zogbi, “An end-to-end demonstration of a receiver array based free-space photon counting communications link,” Proc. SPIE, vol. 6304, 2006, Art. no. .

Goebel, B.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Gordon, J. P.

J. P. Gordon, “Quantum effects in communications systems,” Proc. IRE, vol. 50, no. 8, pp. 1898–1908, 1962.

Guha, S.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett., vol. 92, no. 2, 2004, Art. no. .

Hamaoka, F.

F. Hamaokaet al., “150.3-Tb/s ultra-wideband (S, C, and L bands) single-mode fibre transmission over 40-km using >519 Gb/s/λ PDM-128QAM signals,” in Proc. Eur. Conf. Opt. Commun., 2018, Paper Mo4G.1.

Hamilton, S. A.

M. A. Albota, B. S. Robinson, D. O. Caplan, S. A. Hamilton, and D. M. Boroson, “Photon-counting 1.55 μm optical communications with pulse-position modulation and a multimode upconversion single-photon receiver,” in Proc. Annu. Meeting IEEE Lasers Electro Opt. Soc., 2008, Paper TuC4.

Hamkins, J.

M. K. Cheng, B. E. Moision, J. Hamkins, and M. A. Nakashima, “Implementation of a coded modulation for deep space optical communications,” in Proc. IEEE Globecom, SAT05-4, 2006.

Holevo, A. S.

V. Giovannetti, A. S. Holevo, and R. Garcia-Patron, “A solution of the Gaussian optimizer conjecture,” Commun. Math. Phys., vol. 334, pp. 1553–1571, 2015.

V. Giovannetti, R. Garcia-Patron, N. J. Cerf, and A. S. Holevo, “Ultimate classical communication rates of quantum optical channels,” Nature Photon., vol. 8, pp. 796–800, 2014.

Holevo, S.

S. Holevo, “The capacity of the quantum channel with general signal states,” IEEE Trans. Inf. Theory, vol. 44, no. 1, pp. 269–273, 1998.

S. Holevo, “Bounds for the quantity of information transmitted by a quantum communication channel,” Probl. Peredachi Inf., vol. 9, no. 3, pp. 3–11, 1973.

Hopman, P. I.

P. I. Hopman, P. W. Boettcher, L. M. Candell, J. B. Glettler, R. Shoup, and G. Zogbi, “An end-to-end demonstration of a receiver array based free-space photon counting communications link,” Proc. SPIE, vol. 6304, 2006, Art. no. .

Jiang, Y.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN model of fiber non-linear propagation and its applications,” J. Lightw. Technol., vol. 32, no. 4, pp. 694–721, 2014.

Kachelmyer, A. L.

Kalmar, A.

P. J. Winzer, A. Kalmar, and W. R. Leeb, “The role of amplified spontaneous emission in optical free-space communication links with optical amplification - impact on isolation and data transmission; utilization for pointing, acquisition, and tracking,” Proc. SPIE, vol. 3615, pp. 104–114, 1999.

Kato, K.

A. Mori, H. Masuda, K. Shikano, K. Oikawa, K. Kato, and M. Shimizu, “Ultra-wideband tellurite-based Raman fibre amplifier,” Electron. Lett., vol. 37, no. 24, pp. 1442–1443, 2001.

Kikuchi, K.

K. Kikuchi, “Fundamentals of coherent optical fiber communications,” J. Lightw. Technol., vol. 34, no. 1, pp. 157–179, 2016.

Kramer, G.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Kurzke, C.

A. Splett, C. Kurzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, Paper MoC2.4.

Leeb, W. R.

P. J. Winzer, A. Kalmar, and W. R. Leeb, “The role of amplified spontaneous emission in optical free-space communication links with optical amplification - impact on isolation and data transmission; utilization for pointing, acquisition, and tracking,” Proc. SPIE, vol. 3615, pp. 104–114, 1999.

W. R. Leeb, “Degradation of signal to noise ratio in optical free space data links due to background illumination,” Appl. Opt., vol. 28, pp. 3443–3449, 1989.

Liu, X.

X. Liu, S. Chandrasekhar, T. H. Wood, R. W. Tkach, E. C. Burrows, and P. J. Winzer, “Demonstration of 2.7-PPB receiver sensitivity using PDM-QPSK with 4-PPM and unrepeatered transmission over a single 370-km unamplified ultra-large-area fiber span,” in Proc. Eur. Conf. Opt. Commun., 2011, Paper Tu.3.B.4.

Lloyd, S.

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Electromagnetic channel capacity for practical purposes,” Nature Photon., vol. 7, pp. 834–838, 2013.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett., vol. 92, no. 2, 2004, Art. no. .

Ludwig, A.

Maccone, L.

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Electromagnetic channel capacity for practical purposes,” Nature Photon., vol. 7, pp. 834–838, 2013.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett., vol. 92, no. 2, 2004, Art. no. .

Makovejs, S.

Masuda, H.

A. Mori, H. Masuda, K. Shikano, K. Oikawa, K. Kato, and M. Shimizu, “Ultra-wideband tellurite-based Raman fibre amplifier,” Electron. Lett., vol. 37, no. 24, pp. 1442–1443, 2001.

Mecozzi, A.

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Quantum limits on the energy consumption of optical transmission systems,” J. Lightw. Technol., vol. 32, no. 10, pp. 1853–18602014.

Moision, B. E.

M. K. Cheng, B. E. Moision, J. Hamkins, and M. A. Nakashima, “Implementation of a coded modulation for deep space optical communications,” in Proc. IEEE Globecom, SAT05-4, 2006.

Mori, A.

A. Mori, H. Masuda, K. Shikano, K. Oikawa, K. Kato, and M. Shimizu, “Ultra-wideband tellurite-based Raman fibre amplifier,” Electron. Lett., vol. 37, no. 24, pp. 1442–1443, 2001.

Nakashima, M. A.

M. K. Cheng, B. E. Moision, J. Hamkins, and M. A. Nakashima, “Implementation of a coded modulation for deep space optical communications,” in Proc. IEEE Globecom, SAT05-4, 2006.

Neilson, D. T.

P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, “Fiber-optic transmission and networking: The previous 20 and the next 20 years,” Opt. Express, vol. 26, pp. 24190–24239, 2018.

P. J. Winzer and D. T. Neilson, “From scaling disparities to integrated parallelism: A decathlon for a decade,” J. Lightw. Technol. vol. 35, no. 5, pp. 1099–1115, 2017.

Oikawa, K.

A. Mori, H. Masuda, K. Shikano, K. Oikawa, K. Kato, and M. Shimizu, “Ultra-wideband tellurite-based Raman fibre amplifier,” Electron. Lett., vol. 37, no. 24, pp. 1442–1443, 2001.

Olsson, S. L. I.

Ozawa, M.

H. P. Yuen and M. Ozawa, “Ultimate information carrying limit of quantum systems,” Phys. Rev. Lett., vol. 70, no. 4, pp. 363–366, 1993.

Petermann, K.

A. Splett, C. Kurzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, Paper MoC2.4.

Pilipetskii, A. N.

A. N. Pilipetskii, “High capacity submarine transmission systems,” in Proc. Opt. Fiber Commun. Conf., 2015, Paper W3G.5.

Poggiolini, P.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN model of fiber non-linear propagation and its applications,” J. Lightw. Technol., vol. 32, no. 4, pp. 694–721, 2014.

Proakis, J. G.

J. G. Proakis, Digital Communications, 4th ed.New York, NY, USA: McGraw-Hill, 2001.

Renaudier, J.

J. Renaudieret al., “First 100-nm continuous-band WDM transmission system with 115Tb/s transport over 100km using novel ultra-wideband semiconductor optical amplifiers,” in Proc. Eur. Conf. Opt. Commun., 2017, Paper Th.PDP.A.3.

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D. J. Richardson, “Hollow core fibres and their applications,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Tu3H.1.

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B. S. Robinsonet al., “781 Mbit/s photon-counting optical communications using a superconducting nanowire detector,” Opt. Lett., vol. 31, pp. 444–446, 2006.

M. A. Albota, B. S. Robinson, D. O. Caplan, S. A. Hamilton, and D. M. Boroson, “Photon-counting 1.55 μm optical communications with pulse-position modulation and a multimode upconversion single-photon receiver,” in Proc. Annu. Meeting IEEE Lasers Electro Opt. Soc., 2008, Paper TuC4.

Schumacher, B.

B. Schumacher and M. D. Westmoreland, “Sending classical information via noisy quantum channels,” Phys. Rev. A, vol. 56, no. 1, pp. 131–138, 1997.

Shannon, C. E.

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE, vol. 37, no. 1, pp. 10–21, 1949.

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423, 623–656, 1948.

Shapiro, J. H.

B. R. Bardhan and J. H. Shapiro, “Ultimate capacity of a linear time-invariant bosonic channel,” Phys. Rev. A, vol. 93, 2016, Art. no. .

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Electromagnetic channel capacity for practical purposes,” Nature Photon., vol. 7, pp. 834–838, 2013.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett., vol. 92, no. 2, 2004, Art. no. .

Shikano, K.

A. Mori, H. Masuda, K. Shikano, K. Oikawa, K. Kato, and M. Shimizu, “Ultra-wideband tellurite-based Raman fibre amplifier,” Electron. Lett., vol. 37, no. 24, pp. 1442–1443, 2001.

Shimizu, M.

A. Mori, H. Masuda, K. Shikano, K. Oikawa, K. Kato, and M. Shimizu, “Ultra-wideband tellurite-based Raman fibre amplifier,” Electron. Lett., vol. 37, no. 24, pp. 1442–1443, 2001.

Shoup, R.

P. I. Hopman, P. W. Boettcher, L. M. Candell, J. B. Glettler, R. Shoup, and G. Zogbi, “An end-to-end demonstration of a receiver array based free-space photon counting communications link,” Proc. SPIE, vol. 6304, 2006, Art. no. .

Shtaif, M.

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Quantum limits on the energy consumption of optical transmission systems,” J. Lightw. Technol., vol. 32, no. 10, pp. 1853–18602014.

R. Dar, M. Shtaif, and M. Feder, “New bounds on the capacity of the nonlinear fiber-optic channel,” Opt. Lett., vol. 39, pp. 398–401, 2014.

Sinkin, O. V.

O. V. Sinkinet al., “SDM for power-efficient undersea transmission,” J. Lightw. Technol., vol. 36, no. 2, pp. 361–371, 2018.

Splett, A.

A. Splett, C. Kurzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, Paper MoC2.4.

Stevens, M. L.

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. Hoboken, NJ, USA: Wiley, 2006.

Tkach, R. W.

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J., vol. 14, no. 4, pp. 3–9, 2010.

X. Liu, S. Chandrasekhar, T. H. Wood, R. W. Tkach, E. C. Burrows, and P. J. Winzer, “Demonstration of 2.7-PPB receiver sensitivity using PDM-QPSK with 4-PPM and unrepeatered transmission over a single 370-km unamplified ultra-large-area fiber span,” in Proc. Eur. Conf. Opt. Commun., 2011, Paper Tu.3.B.4.

Tucker, R. S.

R. S. Tucker, “Green optical communications—Part I: Energy limitations in transport,” IEEE J. Sel. Topics Quantum Electron., vol. 17, no. 2, pp. 245–260, 2011.

Westmoreland, M. D.

B. Schumacher and M. D. Westmoreland, “Sending classical information via noisy quantum channels,” Phys. Rev. A, vol. 56, no. 1, pp. 131–138, 1997.

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M. M. Wilde, Quantum Information Theory, 2nd ed.Cambridge, U.K.: Cambridge Univ. Press, 2017.

Winzer, P. J.

S. L. I. Olsson, J. Cho, S. Chandrasekhar, X. Chen, P. J. Winzer, and S. Makovejs, “Probabilistically shaped PDM 4096-QAM transmission over up to 200 km of fiber using standard intradyne detection,” Opt. Express, vol. 26, no. 4, pp. 4522–4530, 2018.

P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, “Fiber-optic transmission and networking: The previous 20 and the next 20 years,” Opt. Express, vol. 26, pp. 24190–24239, 2018.

P. J. Winzer and D. T. Neilson, “From scaling disparities to integrated parallelism: A decathlon for a decade,” J. Lightw. Technol. vol. 35, no. 5, pp. 1099–1115, 2017.

P. J. Winzer, “From first fibers to mode-division multiplexing,” Chin. Opt. Lett., vol. 14, no. 12, 2016, Art. no. .

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Quantum limits on the energy consumption of optical transmission systems,” J. Lightw. Technol., vol. 32, no. 10, pp. 1853–18602014.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

P. J. Winzer, A. Kalmar, and W. R. Leeb, “The role of amplified spontaneous emission in optical free-space communication links with optical amplification - impact on isolation and data transmission; utilization for pointing, acquisition, and tracking,” Proc. SPIE, vol. 3615, pp. 104–114, 1999.

X. Liu, S. Chandrasekhar, T. H. Wood, R. W. Tkach, E. C. Burrows, and P. J. Winzer, “Demonstration of 2.7-PPB receiver sensitivity using PDM-QPSK with 4-PPM and unrepeatered transmission over a single 370-km unamplified ultra-large-area fiber span,” in Proc. Eur. Conf. Opt. Commun., 2011, Paper Tu.3.B.4.

Wood, T. H.

X. Liu, S. Chandrasekhar, T. H. Wood, R. W. Tkach, E. C. Burrows, and P. J. Winzer, “Demonstration of 2.7-PPB receiver sensitivity using PDM-QPSK with 4-PPM and unrepeatered transmission over a single 370-km unamplified ultra-large-area fiber span,” in Proc. Eur. Conf. Opt. Commun., 2011, Paper Tu.3.B.4.

Yuen, H. P.

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett., vol. 92, no. 2, 2004, Art. no. .

H. P. Yuen and M. Ozawa, “Ultimate information carrying limit of quantum systems,” Phys. Rev. Lett., vol. 70, no. 4, pp. 363–366, 1993.

Zogbi, G.

P. I. Hopman, P. W. Boettcher, L. M. Candell, J. B. Glettler, R. Shoup, and G. Zogbi, “An end-to-end demonstration of a receiver array based free-space photon counting communications link,” Proc. SPIE, vol. 6304, 2006, Art. no. .

Appl. Opt. (1)

Bell Labs Tech. J. (1)

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J., vol. 14, no. 4, pp. 3–9, 2010.

Bell Syst. Tech. J. (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423, 623–656, 1948.

Chin. Opt. Lett. (1)

P. J. Winzer, “From first fibers to mode-division multiplexing,” Chin. Opt. Lett., vol. 14, no. 12, 2016, Art. no. .

Commun. Math. Phys. (1)

V. Giovannetti, A. S. Holevo, and R. Garcia-Patron, “A solution of the Gaussian optimizer conjecture,” Commun. Math. Phys., vol. 334, pp. 1553–1571, 2015.

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A. Mori, H. Masuda, K. Shikano, K. Oikawa, K. Kato, and M. Shimizu, “Ultra-wideband tellurite-based Raman fibre amplifier,” Electron. Lett., vol. 37, no. 24, pp. 1442–1443, 2001.

IEEE J. Sel. Topics Quantum Electron. (1)

R. S. Tucker, “Green optical communications—Part I: Energy limitations in transport,” IEEE J. Sel. Topics Quantum Electron., vol. 17, no. 2, pp. 245–260, 2011.

IEEE Trans. Inf. Theory (1)

S. Holevo, “The capacity of the quantum channel with general signal states,” IEEE Trans. Inf. Theory, vol. 44, no. 1, pp. 269–273, 1998.

IEEE Trans. Microw. Theory Techn. (1)

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P. J. Winzer and D. T. Neilson, “From scaling disparities to integrated parallelism: A decathlon for a decade,” J. Lightw. Technol. vol. 35, no. 5, pp. 1099–1115, 2017.

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K. Kikuchi, “Fundamentals of coherent optical fiber communications,” J. Lightw. Technol., vol. 34, no. 1, pp. 157–179, 2016.

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Quantum limits on the energy consumption of optical transmission systems,” J. Lightw. Technol., vol. 32, no. 10, pp. 1853–18602014.

O. V. Sinkinet al., “SDM for power-efficient undersea transmission,” J. Lightw. Technol., vol. 36, no. 2, pp. 361–371, 2018.

R. Daret al., “Cost-optimized submarine cables using massive spatial parallelism,” J. Lightw. Technol., vol. 36, no. 18, pp. 3855–3865, 2018.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

E. B. Desurvire, “Capacity demand and technology challenges for lightwave systems in the next two decades,” J. Lightw. Technol., vol. 24, no. 12, pp. 4697–4710, 2006.

P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN model of fiber non-linear propagation and its applications,” J. Lightw. Technol., vol. 32, no. 4, pp. 694–721, 2014.

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V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Electromagnetic channel capacity for practical purposes,” Nature Photon., vol. 7, pp. 834–838, 2013.

V. Giovannetti, R. Garcia-Patron, N. J. Cerf, and A. S. Holevo, “Ultimate classical communication rates of quantum optical channels,” Nature Photon., vol. 8, pp. 796–800, 2014.

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (2)

B. R. Bardhan and J. H. Shapiro, “Ultimate capacity of a linear time-invariant bosonic channel,” Phys. Rev. A, vol. 93, 2016, Art. no. .

B. Schumacher and M. D. Westmoreland, “Sending classical information via noisy quantum channels,” Phys. Rev. A, vol. 56, no. 1, pp. 131–138, 1997.

Phys. Rev. Lett. (2)

V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: The exact solution,” Phys. Rev. Lett., vol. 92, no. 2, 2004, Art. no. .

H. P. Yuen and M. Ozawa, “Ultimate information carrying limit of quantum systems,” Phys. Rev. Lett., vol. 70, no. 4, pp. 363–366, 1993.

Probl. Peredachi Inf. (1)

S. Holevo, “Bounds for the quantity of information transmitted by a quantum communication channel,” Probl. Peredachi Inf., vol. 9, no. 3, pp. 3–11, 1973.

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P. J. Winzer, A. Kalmar, and W. R. Leeb, “The role of amplified spontaneous emission in optical free-space communication links with optical amplification - impact on isolation and data transmission; utilization for pointing, acquisition, and tracking,” Proc. SPIE, vol. 3615, pp. 104–114, 1999.

P. I. Hopman, P. W. Boettcher, L. M. Candell, J. B. Glettler, R. Shoup, and G. Zogbi, “An end-to-end demonstration of a receiver array based free-space photon counting communications link,” Proc. SPIE, vol. 6304, 2006, Art. no. .

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M. A. Albota, B. S. Robinson, D. O. Caplan, S. A. Hamilton, and D. M. Boroson, “Photon-counting 1.55 μm optical communications with pulse-position modulation and a multimode upconversion single-photon receiver,” in Proc. Annu. Meeting IEEE Lasers Electro Opt. Soc., 2008, Paper TuC4.

X. Liu, S. Chandrasekhar, T. H. Wood, R. W. Tkach, E. C. Burrows, and P. J. Winzer, “Demonstration of 2.7-PPB receiver sensitivity using PDM-QPSK with 4-PPM and unrepeatered transmission over a single 370-km unamplified ultra-large-area fiber span,” in Proc. Eur. Conf. Opt. Commun., 2011, Paper Tu.3.B.4.

J. Cho and S. L. I. Olsson, Laboratory notes related to Ref. [50].

D. J. Geisleret al., “Demonstration of 2.1 photon-per-bit sensitivity for BPSK at 9.94-Gb/s with rate-½ FEC,” in Proc. Fiber Opt. Eng. Conf., 2013, Paper OM2C.6.

M. K. Cheng, B. E. Moision, J. Hamkins, and M. A. Nakashima, “Implementation of a coded modulation for deep space optical communications,” in Proc. IEEE Globecom, SAT05-4, 2006.

O. Caplan, “Laser communication transmitter and receiver design,” in Free Space Laser Communications, A. K. Majumdar and J. C. Ricklineds.Berlin, Germany: Springer, 2008, pp. 109–246.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. Hoboken, NJ, USA: Wiley, 2006.

J. G. Proakis, Digital Communications, 4th ed.New York, NY, USA: McGraw-Hill, 2001.

A. N. Pilipetskii, “High capacity submarine transmission systems,” in Proc. Opt. Fiber Commun. Conf., 2015, Paper W3G.5.

A. R. Chraplyvy, “The coming capacity crunch,” in Proc. Eur. Conf. Opt. Commun., Vienna, Austria, 2009, plenary talk.

D. J. Richardson, “Hollow core fibres and their applications,” in Proc. Opt. Fiber Commun. Conf., 2017, Paper Tu3H.1.

J. Renaudieret al., “First 100-nm continuous-band WDM transmission system with 115Tb/s transport over 100km using novel ultra-wideband semiconductor optical amplifiers,” in Proc. Eur. Conf. Opt. Commun., 2017, Paper Th.PDP.A.3.

F. Hamaokaet al., “150.3-Tb/s ultra-wideband (S, C, and L bands) single-mode fibre transmission over 40-km using >519 Gb/s/λ PDM-128QAM signals,” in Proc. Eur. Conf. Opt. Commun., 2018, Paper Mo4G.1.

A. Splett, C. Kurzke, and K. Petermann, “Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities,” in Proc. Eur. Conf. Opt. Commun., 1993, Paper MoC2.4.

M. M. Wilde, Quantum Information Theory, 2nd ed.Cambridge, U.K.: Cambridge Univ. Press, 2017.

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