Abstract

In optical communication, pulses have approximately a rectangular shape with smooth boundaries. In order to understand the dynamics of these pulses: (A) the generic dynamics of singular quantum mechanics’ wave functions was applied to sharp-boundaries pulses propagation in short dispersive medium and (B) an analytical expression for the propagation of a smooth rectangular pulse in dispersive medium was derived. This analytical expression consists of a couple of complex error functions and can be applied in good approximation to most rectangular pulses propagations in dispersive medium. (C) An analytical approximation was derived for the propagation of any pulse with sharp boundaries. This approximation, despite being analytical, can be applied to any sharp-boundaries pulse with any given shape. These exact expressions and approximations can be used in other systems where the Schrödinger dynamics hold, such as the paraxial approximation.

© 2012 Optical Society of America

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  1. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2002).
  2. G. Keiser, Optical Fiber Communications4th ed. (McGraw-Hill, 2010).
  3. G. Goldfarb and L. Guifang, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19, 969–971 (2007).
    [CrossRef]
  4. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lank, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. 27, 3614–3622 (2009).
    [CrossRef]
  5. P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. 21, 1862–1879 (1985).
    [CrossRef]
  6. G. P. Agrawal, P. J. Anthony, and T. M. Shen, “Dispersion penalty for 1.3 μm lightwave systems with multimode semiconductor lasers,” J. Lightwave Technol. 6, 620–625 (1988).
    [CrossRef]
  7. E. Granot and A. Marchewka, “Generic short-time propagation of sharp-boundaries wave packets,” Europhys. Lett. 72, 341–347 (2005).
    [CrossRef]
  8. A. Marchewka, E. Granot, and Z. Schuss, “Short time propagation of a singular wave function: some surprising results,” Optics Spectrosc. 103, 330–335 (2007).
    [CrossRef]
  9. E. Granot and A. Marchewka, “Universal potential-barrier penetration by initially confined wave packets,” Phys. Rev. A 76, 012708 (2007).
    [CrossRef]
  10. R. P. Feynman, “The space–time formulation of nonrelativistic quantum mechanics,” Rev. Mod. Phys. 20, 367–387 (1948).
    [CrossRef]
  11. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, 1965).
  12. M. Moshinsky, “Diffraction in time,” Phys. Rev. 88, 625–631 (1952).
    [CrossRef]
  13. M. Abramowitz and A. Stegun, Handbook of Mathematical Functions (Dover, 1965).
  14. A. del Campo, G. Garcia-Calderon, and J. G. Muga, “Quantum transients,” Phys. Rep. 476, 1–50 (2009).
    [CrossRef]
  15. E. Granot and A. Marchewka, “Emergence of currents as a transient quantum effect in nonequilibrium systems,” Phys. Rev. A 84, 032110 (2011).
    [CrossRef]

2011 (1)

E. Granot and A. Marchewka, “Emergence of currents as a transient quantum effect in nonequilibrium systems,” Phys. Rev. A 84, 032110 (2011).
[CrossRef]

2009 (2)

2007 (3)

G. Goldfarb and L. Guifang, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19, 969–971 (2007).
[CrossRef]

A. Marchewka, E. Granot, and Z. Schuss, “Short time propagation of a singular wave function: some surprising results,” Optics Spectrosc. 103, 330–335 (2007).
[CrossRef]

E. Granot and A. Marchewka, “Universal potential-barrier penetration by initially confined wave packets,” Phys. Rev. A 76, 012708 (2007).
[CrossRef]

2005 (1)

E. Granot and A. Marchewka, “Generic short-time propagation of sharp-boundaries wave packets,” Europhys. Lett. 72, 341–347 (2005).
[CrossRef]

1988 (1)

G. P. Agrawal, P. J. Anthony, and T. M. Shen, “Dispersion penalty for 1.3 μm lightwave systems with multimode semiconductor lasers,” J. Lightwave Technol. 6, 620–625 (1988).
[CrossRef]

1985 (1)

P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. 21, 1862–1879 (1985).
[CrossRef]

1952 (1)

M. Moshinsky, “Diffraction in time,” Phys. Rev. 88, 625–631 (1952).
[CrossRef]

1948 (1)

R. P. Feynman, “The space–time formulation of nonrelativistic quantum mechanics,” Rev. Mod. Phys. 20, 367–387 (1948).
[CrossRef]

Abramowitz, M.

M. Abramowitz and A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Agrawal, G. P.

G. P. Agrawal, P. J. Anthony, and T. M. Shen, “Dispersion penalty for 1.3 μm lightwave systems with multimode semiconductor lasers,” J. Lightwave Technol. 6, 620–625 (1988).
[CrossRef]

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2002).

Alfiad, M. S.

Anthony, P. J.

G. P. Agrawal, P. J. Anthony, and T. M. Shen, “Dispersion penalty for 1.3 μm lightwave systems with multimode semiconductor lasers,” J. Lightwave Technol. 6, 620–625 (1988).
[CrossRef]

del Campo, A.

A. del Campo, G. Garcia-Calderon, and J. G. Muga, “Quantum transients,” Phys. Rep. 476, 1–50 (2009).
[CrossRef]

Feynman, R. P.

R. P. Feynman, “The space–time formulation of nonrelativistic quantum mechanics,” Rev. Mod. Phys. 20, 367–387 (1948).
[CrossRef]

R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, 1965).

Garcia-Calderon, G.

A. del Campo, G. Garcia-Calderon, and J. G. Muga, “Quantum transients,” Phys. Rep. 476, 1–50 (2009).
[CrossRef]

Goldfarb, G.

G. Goldfarb and L. Guifang, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19, 969–971 (2007).
[CrossRef]

Granot, E.

E. Granot and A. Marchewka, “Emergence of currents as a transient quantum effect in nonequilibrium systems,” Phys. Rev. A 84, 032110 (2011).
[CrossRef]

E. Granot and A. Marchewka, “Universal potential-barrier penetration by initially confined wave packets,” Phys. Rev. A 76, 012708 (2007).
[CrossRef]

A. Marchewka, E. Granot, and Z. Schuss, “Short time propagation of a singular wave function: some surprising results,” Optics Spectrosc. 103, 330–335 (2007).
[CrossRef]

E. Granot and A. Marchewka, “Generic short-time propagation of sharp-boundaries wave packets,” Europhys. Lett. 72, 341–347 (2005).
[CrossRef]

Guifang, L.

G. Goldfarb and L. Guifang, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19, 969–971 (2007).
[CrossRef]

Hauske, F. N.

Henry, P. S.

P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. 21, 1862–1879 (1985).
[CrossRef]

Hibbs, A. R.

R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, 1965).

Keiser, G.

G. Keiser, Optical Fiber Communications4th ed. (McGraw-Hill, 2010).

Kuschnerov, M.

Lank, B.

Marchewka, A.

E. Granot and A. Marchewka, “Emergence of currents as a transient quantum effect in nonequilibrium systems,” Phys. Rev. A 84, 032110 (2011).
[CrossRef]

E. Granot and A. Marchewka, “Universal potential-barrier penetration by initially confined wave packets,” Phys. Rev. A 76, 012708 (2007).
[CrossRef]

A. Marchewka, E. Granot, and Z. Schuss, “Short time propagation of a singular wave function: some surprising results,” Optics Spectrosc. 103, 330–335 (2007).
[CrossRef]

E. Granot and A. Marchewka, “Generic short-time propagation of sharp-boundaries wave packets,” Europhys. Lett. 72, 341–347 (2005).
[CrossRef]

Moshinsky, M.

M. Moshinsky, “Diffraction in time,” Phys. Rev. 88, 625–631 (1952).
[CrossRef]

Muga, J. G.

A. del Campo, G. Garcia-Calderon, and J. G. Muga, “Quantum transients,” Phys. Rep. 476, 1–50 (2009).
[CrossRef]

Napoli, A.

Piyawanno, K.

Schuss, Z.

A. Marchewka, E. Granot, and Z. Schuss, “Short time propagation of a singular wave function: some surprising results,” Optics Spectrosc. 103, 330–335 (2007).
[CrossRef]

Shen, T. M.

G. P. Agrawal, P. J. Anthony, and T. M. Shen, “Dispersion penalty for 1.3 μm lightwave systems with multimode semiconductor lasers,” J. Lightwave Technol. 6, 620–625 (1988).
[CrossRef]

Spinnler, B.

Stegun, A.

M. Abramowitz and A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Europhys. Lett. (1)

E. Granot and A. Marchewka, “Generic short-time propagation of sharp-boundaries wave packets,” Europhys. Lett. 72, 341–347 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. 21, 1862–1879 (1985).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. Goldfarb and L. Guifang, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19, 969–971 (2007).
[CrossRef]

J. Lightwave Technol. (2)

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lank, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. 27, 3614–3622 (2009).
[CrossRef]

G. P. Agrawal, P. J. Anthony, and T. M. Shen, “Dispersion penalty for 1.3 μm lightwave systems with multimode semiconductor lasers,” J. Lightwave Technol. 6, 620–625 (1988).
[CrossRef]

Optics Spectrosc. (1)

A. Marchewka, E. Granot, and Z. Schuss, “Short time propagation of a singular wave function: some surprising results,” Optics Spectrosc. 103, 330–335 (2007).
[CrossRef]

Phys. Rep. (1)

A. del Campo, G. Garcia-Calderon, and J. G. Muga, “Quantum transients,” Phys. Rep. 476, 1–50 (2009).
[CrossRef]

Phys. Rev. (1)

M. Moshinsky, “Diffraction in time,” Phys. Rev. 88, 625–631 (1952).
[CrossRef]

Phys. Rev. A (2)

E. Granot and A. Marchewka, “Universal potential-barrier penetration by initially confined wave packets,” Phys. Rev. A 76, 012708 (2007).
[CrossRef]

E. Granot and A. Marchewka, “Emergence of currents as a transient quantum effect in nonequilibrium systems,” Phys. Rev. A 84, 032110 (2011).
[CrossRef]

Rev. Mod. Phys. (1)

R. P. Feynman, “The space–time formulation of nonrelativistic quantum mechanics,” Rev. Mod. Phys. 20, 367–387 (1948).
[CrossRef]

Other (4)

R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, 1965).

M. Abramowitz and A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2002).

G. Keiser, Optical Fiber Communications4th ed. (McGraw-Hill, 2010).

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