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Title: Periodic waves in fiber Bragg gratings

Abstract

We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named ''sn'' and ''cn'' waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies ({omega}<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and, in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and {omega}>0, is identified. However, the sn waves with {omega}<0, as well as all cn solutions, are strongly unstable.

Authors:
 [1];  [2];  [3];  [4]; ;  [5]
  1. Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road (Hong Kong)
  2. Department of Electrical and Electronics Engineering, The University Center of Judea and Samaria, Ariel (Israel)
  3. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
  4. School of Engineering, King's College, University of Aberdeen, Aberdeen AB24 3UE, Scotland (United Kingdom)
  5. Photonics Research Center and Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong (China)
Publication Date:
OSTI Identifier:
21101953
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print); Journal Volume: 77; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevE.77.026602; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BRAGG REFLECTION; COMPUTERIZED SIMULATION; DIFFRACTION GRATINGS; EQUATIONS; FIBERS; INSTABILITY GROWTH RATES; KERR EFFECT; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PERIODICITY; PERTURBATION THEORY; SOLITONS

Citation Formats

Chow, K. W., Merhasin, Ilya M., Malomed, Boris A., Nakkeeran, K., Senthilnathan, K., and Wai, P. K. A. Periodic waves in fiber Bragg gratings. United States: N. p., 2008. Web. doi:10.1103/PHYSREVE.77.026602.
Chow, K. W., Merhasin, Ilya M., Malomed, Boris A., Nakkeeran, K., Senthilnathan, K., & Wai, P. K. A. Periodic waves in fiber Bragg gratings. United States. doi:10.1103/PHYSREVE.77.026602.
Chow, K. W., Merhasin, Ilya M., Malomed, Boris A., Nakkeeran, K., Senthilnathan, K., and Wai, P. K. A. 2008. "Periodic waves in fiber Bragg gratings". United States. doi:10.1103/PHYSREVE.77.026602.
@article{osti_21101953,
title = {Periodic waves in fiber Bragg gratings},
author = {Chow, K. W. and Merhasin, Ilya M. and Malomed, Boris A. and Nakkeeran, K. and Senthilnathan, K. and Wai, P. K. A.},
abstractNote = {We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named ''sn'' and ''cn'' waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies ({omega}<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and, in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and {omega}>0, is identified. However, the sn waves with {omega}<0, as well as all cn solutions, are strongly unstable.},
doi = {10.1103/PHYSREVE.77.026602},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},
number = 2,
volume = 77,
place = {United States},
year = 2008,
month = 2
}
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  • Environmentally stable high-power erbium fiber soliton lasers are constructed by Kerr or carrier-type mode locking. We obtain high-energy pulses by using relatively short fiber lengths and providing large amounts of negative dispersion with chirped fiber Bragg gratings. The pulse energies and widths generated with both types of soliton laser are found to scale with the square root of the cavity dispersion. Kerr mode locking requires pulses with an approximately three times higher nonlinear phase shift in the cavity than carrier mode locking, which leads to the generation of slightly shorter pulses with as much as seven times higher pulse energiesmore » at the mode-locking threshold. {copyright} {ital 1995} {ital Optical} {ital Society} {ital of} {ital America}.« less
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  • We report the use of distributed fiber Bragg gratings to monitor thermal conditions within a simulated nuclear reactor core located at the Early Flight Fission Test Facility of the NASA Marshall Space Flight Center. Distributed fiber-optic temperature measurements promise to add significant capability and advance the state-of-the-art in high-temperature sensing. For the work reported herein, seven probes were constructed with ten sensors each for a total of 70 sensor locations throughout the core. These discrete temperature sensors were monitored over a nine hour period while the test article was heated to over 700 deg. C and cooled to ambient throughmore » two operational cycles. The sensor density available permits a significantly elevated understanding of thermal effects within the simulated reactor. Fiber-optic sensor performance is shown to compare very favorably with co-located thermocouples where such co-location was feasible.« less