Physics of nonlinear fiber couplers

A. W. Snyder; D. J. Mitchell; L. Poladian; D. R. Rowland; Y. Chen

doi:10.1364/JOSAB.8.002102

Journal of the Optical Society of America B
Vol. 8,
Issue 10,
pp. 2102-2118
(1991)
•https://doi.org/10.1364/JOSAB.8.002102

Physics of nonlinear fiber couplers

A. W. Snyder, D. J. Mitchell, L. Poladian, D. R. Rowland, and Y. Chen

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A. W. Snyder, D. J. Mitchell, L. Poladian, D. R. Rowland, and Y. Chen, "Physics of nonlinear fiber couplers," J. Opt. Soc. Am. B 8, 2102-2118 (1991)

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Abstract

A simple qualitative description of nonlinear couplers is presented whereby the maximum and minimum values of core power are immediately apparent from a graphical representation, here called the power flow portrait. Each coupler has a characteristic portrait, revealing its unique physics. We believe that this approach is novel to all branches of nonlinear theory. Full details are given for nonlinear couplers with cores composed of different materials, Kerr law being a special case only. The study is motivated from the familiar perspective of linear couplers and is augmented by a comprehensive quantitative description leading to new analytical results.

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P₁, P₂	Powers in cores 1 and 2.
P	Total power P = P₁ + P₂ in both cores.
ϕ	Phase difference between core excitations.
β₁, β₂	Propagation constants of modes in cores 1 and 2 in isolation.
${\bar{β}}_{1}, {\bar{β}}_{2}$	Linear (P → 0) limit of propagation constants β₁ and β₂.
β₊, β₋	Propagation constants of the even and odd modes of a matched (linear) coupler.
M	Mismatch parameter defined in Eq. (1).
$\bar{M}$	Linear (P → 0) limit of mismatch parameter M.
K₁, K₂	Kerr coefficients for cores 1 and 2.
K	Kerr coefficient for identical core Kerr law coupler.
P_B	Bifurcation power for the identical core Kerr law coupler. In general, points where the stable and unstable modes meet or separate are called bifurcations, and the corresponding total power is a bifurcation power.
P_C	Critical power for the identical core Kerr law coupler. In general, points where the separatrix crosses the edge of the graph are called critical, and the corresponding power is a critical power.

P₁, P₂	Powers in cores 1 and 2.
P	Total power P = P₁ + P₂ in both cores.
ϕ	Phase difference between core excitations.
β₁, β₂	Propagation constants of modes in cores 1 and 2 in isolation.
${\bar{β}}_{1}, {\bar{β}}_{2}$	Linear (P → 0) limit of propagation constants β₁ and β₂.
β₊, β₋	Propagation constants of the even and odd modes of a matched (linear) coupler.
M	Mismatch parameter defined in Eq. (1).
$\bar{M}$	Linear (P → 0) limit of mismatch parameter M.
K₁, K₂	Kerr coefficients for cores 1 and 2.
K	Kerr coefficient for identical core Kerr law coupler.
P_B	Bifurcation power for the identical core Kerr law coupler. In general, points where the stable and unstable modes meet or separate are called bifurcations, and the corresponding total power is a bifurcation power.
P_C	Critical power for the identical core Kerr law coupler. In general, points where the separatrix crosses the edge of the graph are called critical, and the corresponding power is a critical power.

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Journal of the Optical Society of America B