TY - JOUR
T1 - Analytical solutions for the propagation of ultrashort and ultrasharp pulses in dispersive media
AU - Granot, Er'el
N1 - Publisher Copyright:
© 2019 by the authors.
PY - 2019/2/4
Y1 - 2019/2/4
N2 - Ultrashort pulses are severely distorted even by low dispersive media. While the mathematical analysis of dispersion is well known, the technical literature focuses on pulses, Gaussian and Airy pulses, which keep their shape. However, the cases where the shape of the pulse is unaffected by dispersion is the exception rather than the norm. It is the objective of this paper to present a variety of pulse profiles, which have analytical expressions but can simulate real-physical pulses with great accuracy. In particular, the dynamics of smooth rectangular pulses, physical Nyquist-Sinc pulses, and slowly rising but sharply decaying ones (and vice versa) are presented. Besides the usage of this paper as a handbook of analytical expressions for pulse propagations in a dispersive medium, there are several new findings. The main findings are the analytical expressions for the propagation of chirped rectangular pulses, which converge to extremely short pulses; an analytical approximation for the propagation of super-Gaussian pulses; the propagation of the Nyquist-Sinc Pulse with smooth spectral boundaries; and an analytical expression for a physical realization of an attenuation compensating Airy pulse.
AB - Ultrashort pulses are severely distorted even by low dispersive media. While the mathematical analysis of dispersion is well known, the technical literature focuses on pulses, Gaussian and Airy pulses, which keep their shape. However, the cases where the shape of the pulse is unaffected by dispersion is the exception rather than the norm. It is the objective of this paper to present a variety of pulse profiles, which have analytical expressions but can simulate real-physical pulses with great accuracy. In particular, the dynamics of smooth rectangular pulses, physical Nyquist-Sinc pulses, and slowly rising but sharply decaying ones (and vice versa) are presented. Besides the usage of this paper as a handbook of analytical expressions for pulse propagations in a dispersive medium, there are several new findings. The main findings are the analytical expressions for the propagation of chirped rectangular pulses, which converge to extremely short pulses; an analytical approximation for the propagation of super-Gaussian pulses; the propagation of the Nyquist-Sinc Pulse with smooth spectral boundaries; and an analytical expression for a physical realization of an attenuation compensating Airy pulse.
KW - Dispersion
KW - Optical communications
KW - Pulse distortion
KW - Ultrashort pulses
UR - http://www.scopus.com/inward/record.url?scp=85060994028&partnerID=8YFLogxK
U2 - 10.3390/app9030527
DO - 10.3390/app9030527
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AN - SCOPUS:85060994028
SN - 2076-3417
VL - 9
JO - Applied Sciences (Switzerland)
JF - Applied Sciences (Switzerland)
IS - 3
M1 - 527
ER -