Abstract

The novel concept of spatio-temporal modulation of Nyquist pulses is introduced, and the resulting wave-packets are termed Nyquist Localized Waves (LWs). Ideal Nyquist LWs belong to the generic family of LW solutions and can propagate indefinitely in unbounded media without attenuation or chromatic dispersion. The possibility of modulating Nyquist LWs for free-space optical (FSO) communication systems is demonstrated using two different modulation techniques. The first technique is on-off keying (OOK) with alternate mark inversion (AMI) coding for 1-bit per symbol transmission, and the second one is 16-ary quadrature amplitude modulation (16-QAM) for 4-bits per symbol transmission. Aspects related to the performance, detection and generation of the spatio-temporally coupled wave-packets are discussed and future research directions are outlined.

© 2012 OSA

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    [CrossRef]
  2. E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun.22, 1896–1906 (2004).
    [CrossRef]
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    [PubMed]
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  6. M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
    [CrossRef] [PubMed]
  7. E. J. Lee and V. W. Chan, “Diversity coherent and incoherent receivers for free-space optical communication in the presence and absence of interference,” J. Opt. Commun. Netw.1, 463–483 (2009).
    [CrossRef]
  8. N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol.28, 1218–1227 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. M. A. Salem and H. Bağcı, “On the propagation of truncated Localized Waves in dispersive silica,” Opt. Express18, 25482–25493 (2010).
    [CrossRef] [PubMed]
  16. J. N. Brittingham, “Focus waves modes in homogeneous Maxwell’s equations: Transverse electric mode,” J. Appl. Phys.54, 1179–1189 (1983).
    [CrossRef]
  17. R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A39, 2005–2033 (1989).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  21. S. S. Assimonis, M. Matthaiou, G. K. Karagiannidis, and J. A. Nossek, “Improved parametric families of intersymbol interference-free Nyquist pulses using inner and outer functions,” IET Signal Process.5, 157–163 (2011).
    [CrossRef]
  22. S. Haykin, Communication Systems, 4th ed. (Wiley, 2001).
  23. J.-Y. Lu and A. Liu, “An X wave transform,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control47, 1472–1481 (2000).
    [CrossRef]
  24. J. Salo, A. T. Friberg, and M. Salomaa, “Orthogonal X waves,” J. Phys. A: Math. Gen.34, 9319–9327 (2001).
    [CrossRef]
  25. R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
    [CrossRef] [PubMed]
  26. R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
    [CrossRef] [PubMed]
  27. M. Zamboni-Rached, “Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures,” J. Opt. Soc. Am. A23, 2166–2176 (2006).
    [CrossRef]

2012

M. A. Salem and H. Bağcı, “Reflection and transmission of normally incident full-vector X waves on planar interfaces,” J. Opt. Soc. Am. A29, 139–152 (2012).
[CrossRef]

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

2011

S. S. Assimonis, M. Matthaiou, G. K. Karagiannidis, and J. A. Nossek, “Improved parametric families of intersymbol interference-free Nyquist pulses using inner and outer functions,” IET Signal Process.5, 157–163 (2011).
[CrossRef]

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

A. Belmonte and J. M. Kahn, “Field conjugation adaptive arrays in free-space coherent laser communications,” J. Opt. Commun. Netw.3, 830–838 (2011).
[CrossRef]

A. M. Shaarawi, A. S. El-Halawani, and I. M. Besieris, “Diffraction of spatiotemporally localized X-wave pulses from a screen containing two rectangular slits,” J. Opt. Soc. Am. A28, 534–540 (2011).
[CrossRef]

2010

N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol.28, 1218–1227 (2010).
[CrossRef]

M. A. Salem and H. Bağcı, “On the propagation of truncated Localized Waves in dispersive silica,” Opt. Express18, 25482–25493 (2010).
[CrossRef] [PubMed]

2009

E. Recami, “Superluminal waves and objects: an overview of the relevant experiments,” J. Phys.: Conf. Ser.196, 012020 (2009).
[CrossRef]

E. J. Lee and V. W. Chan, “Diversity coherent and incoherent receivers for free-space optical communication in the presence and absence of interference,” J. Opt. Commun. Netw.1, 463–483 (2009).
[CrossRef]

2006

V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol.24, 4750–4762 (2006).
[CrossRef]

M. Zamboni-Rached, “Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures,” J. Opt. Soc. Am. A23, 2166–2176 (2006).
[CrossRef]

2004

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun.22, 1896–1906 (2004).
[CrossRef]

2003

V. W. S. Chan, “Optical satellite networks,” J. Lightwave Technol.21, 2811–2827 (2003).
[CrossRef]

2001

J. Salo, A. T. Friberg, and M. Salomaa, “Orthogonal X waves,” J. Phys. A: Math. Gen.34, 9319–9327 (2001).
[CrossRef]

2000

J.-Y. Lu and A. Liu, “An X wave transform,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control47, 1472–1481 (2000).
[CrossRef]

1992

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves – exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39, 19–31 (1992).
[CrossRef] [PubMed]

1989

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A39, 2005–2033 (1989).
[CrossRef] [PubMed]

I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, “A bidirectional traveling plane representation of exact solutions of the scalar wave equation,” J. Math. Phys.30, 1254–1269 (1989).
[CrossRef]

1987

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).
[CrossRef]

1983

J. N. Brittingham, “Focus waves modes in homogeneous Maxwell’s equations: Transverse electric mode,” J. Appl. Phys.54, 1179–1189 (1983).
[CrossRef]

Ambrosio, L. A.

L. A. Ambrosio, M. Zamboni-Rached, and H. E. Hernández-Figueroa, “Diffraction-Attenuation Resistant Beams,” in “Applications of Lasers for Sensing and Free Space Communications,” (Optical Society of America, 2011), LWD4.

Assimonis, S. S.

S. S. Assimonis, M. Matthaiou, G. K. Karagiannidis, and J. A. Nossek, “Improved parametric families of intersymbol interference-free Nyquist pulses using inner and outer functions,” IET Signal Process.5, 157–163 (2011).
[CrossRef]

Bagci, H.

M. A. Salem and H. Bağcı, “Reflection and transmission of normally incident full-vector X waves on planar interfaces,” J. Opt. Soc. Am. A29, 139–152 (2012).
[CrossRef]

M. A. Salem and H. Bağcı, “On the propagation of truncated Localized Waves in dispersive silica,” Opt. Express18, 25482–25493 (2010).
[CrossRef] [PubMed]

Bäuerle, B.

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Becker, J.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Belmonte, A.

A. Belmonte and J. M. Kahn, “Field conjugation adaptive arrays in free-space coherent laser communications,” J. Opt. Commun. Netw.3, 830–838 (2011).
[CrossRef]

Ben-Ezra, S.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Besieris, I. M.

A. M. Shaarawi, A. S. El-Halawani, and I. M. Besieris, “Diffraction of spatiotemporally localized X-wave pulses from a screen containing two rectangular slits,” J. Opt. Soc. Am. A28, 534–540 (2011).
[CrossRef]

I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, “A bidirectional traveling plane representation of exact solutions of the scalar wave equation,” J. Math. Phys.30, 1254–1269 (1989).
[CrossRef]

Brittingham, J. N.

J. N. Brittingham, “Focus waves modes in homogeneous Maxwell’s equations: Transverse electric mode,” J. Appl. Phys.54, 1179–1189 (1983).
[CrossRef]

Chan, V. W.

E. J. Lee and V. W. Chan, “Diversity coherent and incoherent receivers for free-space optical communication in the presence and absence of interference,” J. Opt. Commun. Netw.1, 463–483 (2009).
[CrossRef]

Chan, V. W. S.

V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol.24, 4750–4762 (2006).
[CrossRef]

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun.22, 1896–1906 (2004).
[CrossRef]

V. W. S. Chan, “Optical satellite networks,” J. Lightwave Technol.21, 2811–2827 (2003).
[CrossRef]

E. Shin and V. W. S. Chan, “Optical communication over the turbulent atmospheric channel using spatial diversity,” in “IEEE GLOBECOM ’02,” (2002) 3, 2055–2060.
[PubMed]

Cvijetic, N.

N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol.28, 1218–1227 (2010).
[CrossRef]

Dippon, T.

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

Dreschmann, M.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).
[CrossRef]

Eisaman, M. D.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

El-Halawani, A. S.

A. M. Shaarawi, A. S. El-Halawani, and I. M. Besieris, “Diffraction of spatiotemporally localized X-wave pulses from a screen containing two rectangular slits,” J. Opt. Soc. Am. A28, 534–540 (2011).
[CrossRef]

Fan, J.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

Freude, W.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

Friberg, A. T.

J. Salo, A. T. Friberg, and M. Salomaa, “Orthogonal X waves,” J. Phys. A: Math. Gen.34, 9319–9327 (2001).
[CrossRef]

Greenleaf, J. F.

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves – exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39, 19–31 (1992).
[CrossRef] [PubMed]

Haykin, S.

S. Haykin, Communication Systems, 4th ed. (Wiley, 2001).

Hemmati, H.

H. Hemmati, Deep Space Optical Communications (Wiley, 2006).
[CrossRef]

Hernández-Figueroa, H. E.

L. A. Ambrosio, M. Zamboni-Rached, and H. E. Hernández-Figueroa, “Diffraction-Attenuation Resistant Beams,” in “Applications of Lasers for Sensing and Free Space Communications,” (Optical Society of America, 2011), LWD4.

Hillerkuss, D.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

Huang, Y.-K.

N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol.28, 1218–1227 (2010).
[CrossRef]

Huebner, M.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Kahn, J. M.

A. Belmonte and J. M. Kahn, “Field conjugation adaptive arrays in free-space coherent laser communications,” J. Opt. Commun. Netw.3, 830–838 (2011).
[CrossRef]

Karagiannidis, G. K.

S. S. Assimonis, M. Matthaiou, G. K. Karagiannidis, and J. A. Nossek, “Improved parametric families of intersymbol interference-free Nyquist pulses using inner and outer functions,” IET Signal Process.5, 157–163 (2011).
[CrossRef]

Kleinow, P.

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

Koos, C.

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Lee, E. J.

E. J. Lee and V. W. Chan, “Diversity coherent and incoherent receivers for free-space optical communication in the presence and absence of interference,” J. Opt. Commun. Netw.1, 463–483 (2009).
[CrossRef]

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun.22, 1896–1906 (2004).
[CrossRef]

Leuthold, J.

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Liu, A.

J.-Y. Lu and A. Liu, “An X wave transform,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control47, 1472–1481 (2000).
[CrossRef]

Lu, J.-Y.

J.-Y. Lu and A. Liu, “An X wave transform,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control47, 1472–1481 (2000).
[CrossRef]

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves – exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39, 19–31 (1992).
[CrossRef] [PubMed]

Ludwig, A.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Matthaiou, M.

S. S. Assimonis, M. Matthaiou, G. K. Karagiannidis, and J. A. Nossek, “Improved parametric families of intersymbol interference-free Nyquist pulses using inner and outer functions,” IET Signal Process.5, 157–163 (2011).
[CrossRef]

Meyer, J.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Meyer, M.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Migdall, A.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

Nebendahl, B.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

Nossek, J. A.

S. S. Assimonis, M. Matthaiou, G. K. Karagiannidis, and J. A. Nossek, “Improved parametric families of intersymbol interference-free Nyquist pulses using inner and outer functions,” IET Signal Process.5, 157–163 (2011).
[CrossRef]

Polyakov, S. V.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

Qian, D.

N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol.28, 1218–1227 (2010).
[CrossRef]

Recami, E.

E. Recami, “Superluminal waves and objects: an overview of the relevant experiments,” J. Phys.: Conf. Ser.196, 012020 (2009).
[CrossRef]

Salem, M. A.

M. A. Salem and H. Bağcı, “Reflection and transmission of normally incident full-vector X waves on planar interfaces,” J. Opt. Soc. Am. A29, 139–152 (2012).
[CrossRef]

M. A. Salem and H. Bağcı, “On the propagation of truncated Localized Waves in dispersive silica,” Opt. Express18, 25482–25493 (2010).
[CrossRef] [PubMed]

Salo, J.

J. Salo, A. T. Friberg, and M. Salomaa, “Orthogonal X waves,” J. Phys. A: Math. Gen.34, 9319–9327 (2001).
[CrossRef]

Salomaa, M.

J. Salo, A. T. Friberg, and M. Salomaa, “Orthogonal X waves,” J. Phys. A: Math. Gen.34, 9319–9327 (2001).
[CrossRef]

Schindler, P. C.

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

Schmogrow, R.

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Shaarawi, A. M.

A. M. Shaarawi, A. S. El-Halawani, and I. M. Besieris, “Diffraction of spatiotemporally localized X-wave pulses from a screen containing two rectangular slits,” J. Opt. Soc. Am. A28, 534–540 (2011).
[CrossRef]

I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, “A bidirectional traveling plane representation of exact solutions of the scalar wave equation,” J. Math. Phys.30, 1254–1269 (1989).
[CrossRef]

Shin, E.

E. Shin and V. W. S. Chan, “Optical communication over the turbulent atmospheric channel using spatial diversity,” in “IEEE GLOBECOM ’02,” (2002) 3, 2055–2060.
[PubMed]

Wang, T.

N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol.28, 1218–1227 (2010).
[CrossRef]

Winter, M.

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

Wolf, S.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

Yu, J.

N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol.28, 1218–1227 (2010).
[CrossRef]

Zamboni-Rached, M.

M. Zamboni-Rached, “Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures,” J. Opt. Soc. Am. A23, 2166–2176 (2006).
[CrossRef]

L. A. Ambrosio, M. Zamboni-Rached, and H. E. Hernández-Figueroa, “Diffraction-Attenuation Resistant Beams,” in “Applications of Lasers for Sensing and Free Space Communications,” (Optical Society of America, 2011), LWD4.

Ziolkowski, R. W.

I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, “A bidirectional traveling plane representation of exact solutions of the scalar wave equation,” J. Math. Phys.30, 1254–1269 (1989).
[CrossRef]

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A39, 2005–2033 (1989).
[CrossRef] [PubMed]

IEEE J. Sel. Areas Commun.

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun.22, 1896–1906 (2004).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves – exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39, 19–31 (1992).
[CrossRef] [PubMed]

J.-Y. Lu and A. Liu, “An X wave transform,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control47, 1472–1481 (2000).
[CrossRef]

IET Signal Process.

S. S. Assimonis, M. Matthaiou, G. K. Karagiannidis, and J. A. Nossek, “Improved parametric families of intersymbol interference-free Nyquist pulses using inner and outer functions,” IET Signal Process.5, 157–163 (2011).
[CrossRef]

J. Appl. Phys.

J. N. Brittingham, “Focus waves modes in homogeneous Maxwell’s equations: Transverse electric mode,” J. Appl. Phys.54, 1179–1189 (1983).
[CrossRef]

J. Lightwave Technol.

V. W. S. Chan, “Optical satellite networks,” J. Lightwave Technol.21, 2811–2827 (2003).
[CrossRef]

V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol.24, 4750–4762 (2006).
[CrossRef]

N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol.28, 1218–1227 (2010).
[CrossRef]

J. Math. Phys.

I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, “A bidirectional traveling plane representation of exact solutions of the scalar wave equation,” J. Math. Phys.30, 1254–1269 (1989).
[CrossRef]

J. Opt. Commun. Netw.

A. Belmonte and J. M. Kahn, “Field conjugation adaptive arrays in free-space coherent laser communications,” J. Opt. Commun. Netw.3, 830–838 (2011).
[CrossRef]

E. J. Lee and V. W. Chan, “Diversity coherent and incoherent receivers for free-space optical communication in the presence and absence of interference,” J. Opt. Commun. Netw.1, 463–483 (2009).
[CrossRef]

J. Opt. Soc. Am. A

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).
[CrossRef]

A. M. Shaarawi, A. S. El-Halawani, and I. M. Besieris, “Diffraction of spatiotemporally localized X-wave pulses from a screen containing two rectangular slits,” J. Opt. Soc. Am. A28, 534–540 (2011).
[CrossRef]

M. A. Salem and H. Bağcı, “Reflection and transmission of normally incident full-vector X waves on planar interfaces,” J. Opt. Soc. Am. A29, 139–152 (2012).
[CrossRef]

M. Zamboni-Rached, “Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures,” J. Opt. Soc. Am. A23, 2166–2176 (2006).
[CrossRef]

J. Phys. A: Math. Gen.

J. Salo, A. T. Friberg, and M. Salomaa, “Orthogonal X waves,” J. Phys. A: Math. Gen.34, 9319–9327 (2001).
[CrossRef]

J. Phys.: Conf. Ser.

E. Recami, “Superluminal waves and objects: an overview of the relevant experiments,” J. Phys.: Conf. Ser.196, 012020 (2009).
[CrossRef]

Opt. Express

M. A. Salem and H. Bağcı, “On the propagation of truncated Localized Waves in dispersive silica,” Opt. Express18, 25482–25493 (2010).
[CrossRef] [PubMed]

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Bäuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express20, 317–337 (2012).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, S. Wolf, B. Bäuerle, M. Winter, P. Kleinow, B. Nebendahl, T. Dippon, P. C. Schindler, C. Koos, W. Freude, and J. Leuthold, “512QAM Nyquist sinc-pulse transmission at 54 Gbit/s in an optical bandwidth of 3 GHz,” Opt. Express20, 6439–6447 (2012).
[CrossRef] [PubMed]

Phys. Rev. A

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A39, 2005–2033 (1989).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum.82, 071101 (2011).
[CrossRef] [PubMed]

Other

E. Shin and V. W. S. Chan, “Optical communication over the turbulent atmospheric channel using spatial diversity,” in “IEEE GLOBECOM ’02,” (2002) 3, 2055–2060.
[PubMed]

H. Hemmati, Deep Space Optical Communications (Wiley, 2006).
[CrossRef]

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves (Wiley, 2008).
[CrossRef]

L. A. Ambrosio, M. Zamboni-Rached, and H. E. Hernández-Figueroa, “Diffraction-Attenuation Resistant Beams,” in “Applications of Lasers for Sensing and Free Space Communications,” (Optical Society of America, 2011), LWD4.

S. Haykin, Communication Systems, 4th ed. (Wiley, 2001).

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Figures (7)

Fig. 1
Fig. 1

Plots of three Nyquist pulses (a) in time as temporal symbols yq(t) and (b) in frequency as the real part of the corresponding spectra Re[Yq(ω)]. In (a), the pulses are centered at times tq−1, tq and tq+1 and separated by the symbol spacing Ts, while in (b) the sum of the spectra represent a single specific frequency-domain Nyquist symbol centered at ω = 0.

Fig. 2
Fig. 2

A plot of (a) the real part and (b) the intensity of a Nyquist X-Wave with ωc = 3 × 1015rad, Ws/ωc = 0.1 and V = 1.2c. Note the ‘X-shaped’ arms characteristic to LW solutions as shown in (a). This wave-packet behaves as a Nyquist pulse in the longitudinal direction and is propagation-invariant. The Nyquist X-Wave is localized in the transverse direction and is confined within a spot-size smaller than 1.5Ts/V.

Fig. 3
Fig. 3

An OOK modulated stream of 8-bits. The bit stream is encoded in NRZ in (a) and the resulting Nyquist LW stream is shown in (b). The same bit stream encoded using AMI is shown in (c) with the corresponding Nyquist LW stream shown in (d).

Fig. 4
Fig. 4

A comparison between the intensities of NRZ (red dash-dot) and AMI (blue straight) encoded Nyquist LW bit stream along the optical axis.

Fig. 5
Fig. 5

Gray-coded 16-QAM constellation, where any two adjacent constellation points differ only by one bit.

Fig. 6
Fig. 6

A plot of the (a) in-phase amplitude, (b) quadrature amplitude, and (c) intensity of the 16-QAM modulated bit stream ‘1101000111100010’ using four Nyquist LWs.

Fig. 7
Fig. 7

A schematic showing a possible configuration for modulated LW generation. A digital signal processing unit (DSP) generates an electrical Nyquist pulse. The digital pulse is converted to an analog one through a digital-to-analog converter (DAC). The clock for both units is provided by a master oscillator (CLK). The resulting electric pulse modulates an optical signal generated by an optical source (OS) via an electro-optical modulator (EOM). The resulting optical Nyquist pulse is fed to a LW generation setup (LWS) that generates a Nyquist LW.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

( 1 ρ ρ [ ρ ρ ] + 1 ρ 2 2 ϕ 2 + 2 z 2 1 c 2 2 t 2 ) Ψ ( ρ , ϕ , z , t ) = 0 ,
Ψ ( ρ , ϕ , z , t ) = n = 0 d k ρ d k z d ω k ρ Ψ ˜ n ( k ρ , k z , ω ) J n ( k ρ ρ ) e i [ k z z ω t ] e in ϕ ,
ω = V k z + α m ,
Ψ ( ρ , ϕ , z + Δ z 0 , t + Δ z 0 V ) = Ψ ( ρ , ϕ , z , t ) e i α m Δ z 0 V .
ω 2 c 2 = k ρ 2 + k z 2 .
k ρ Ψ ˜ n ( k ρ , k z , ω ) = m S n m ( ω ) δ ( k z [ ω α m V ] ) δ ( k ρ 2 [ ω 2 c 2 k z 2 ] ) ,
Ψ ( ρ , ϕ , ζ ) = n = m e i α m z V ω m ω m + d ω S n m ( ω ) J n ( ρ [ 1 c 2 1 V 2 ] ω 2 + 2 α m V 2 ω α m 2 V 2 ) e i ω V ζ e in ϕ ,
y q ( t ) = sinc ( t t q T s ) , Y q ( ω ) = T s rect ( ω W s ) e i ω t q ,
Ψ ( ρ , ζ ; q , ω c ) = A j q 0 d ω γ ω Y q ( ω ω c ) J 0 ( γ ω ρ ) e i ω V ζ ,
y ( t ) = j = 0 N 1 y ( j ) ( t ) , y ( j ) ( t ) = q = Ψ ( ρ , ζ + j V T s ; q , ω c ) .

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