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Updated: Jul 6, 2026
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Writing Bragg Gratings in Multicore Fibers
Published on: April 20, 2016
Periodic waves in fiber Bragg gratings
K W Chow1, Ilya M Merhasin, Boris A Malomed
1Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong.
Summary
We found new periodic solutions for fiber Bragg gratings (FBG) with Kerr nonlinearity, called sn and cn waves. A stable subfamily of sn waves was identified, offering potential for practical applications in nonlinear optics.
Area of Science:
- Nonlinear Optics
- Condensed Matter Physics
- Photonics
Background:
- Fiber Bragg gratings (FBGs) are crucial components in optical fiber communications and sensing.
- Kerr nonlinearity in FBGs leads to complex wave phenomena, including soliton formation.
- Understanding exact periodic solutions is key to controlling light propagation in nonlinear optical systems.
Purpose of the Study:
- To construct and analyze exact periodic solutions for the standard fiber Bragg grating (FBG) model with Kerr nonlinearity.
- To investigate the spectral properties and stability of these novel solutions.
- To identify potentially stable wave families for practical applications.
Main Methods:
- Analytical construction of two families of exact periodic solutions using elliptic functions (sn and cn waves).
- Direct numerical simulations to assess the stability of the derived solutions.
- Calculation of instability growth rates for small perturbations to rigorously analyze stability.
Main Results:
- Two families of exact periodic solutions, 'sn' and 'cn' waves, were derived.
- 'sn' waves exist within the FBG spectral bandgap, while 'cn' waves appear at negative frequencies.
- A subfamily of 'sn' waves with positive frequencies and large spatial periods exhibits practical stability, despite rigorous instability.
- 'cn' waves and 'sn' waves at negative frequencies are strongly unstable.
Conclusions:
- The study provides new analytical insights into nonlinear wave propagation in FBGs.
- While all periodic solutions are rigorously unstable, a practically stable regime of 'sn' waves is identified.
- These findings contribute to the understanding and potential application of nonlinear phenomena in optical fiber technologies.
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