TY - JOUR

T1 - Hamiltonian approach for optimization of phase-sensitive double-pumped parametric amplifiers

AU - Medvedev, Sergey

AU - Bednyakova, Anastasia

N1 - Publisher Copyright: © 2018 Optical Society of America.

PY - 2018/6/11

Y1 - 2018/6/11

N2 - In this work we applied a Hamiltonian formalism to simplify the equations of non-degenerate nonlinear four-wave mixing to the one-degree-of-freedom Hamiltonian equations with a three-parameter Hamiltonian. Thereby, a problem of signal amplification in a phase-sensitive double-pumped parametric fiber amplifier with pump depletion was reduced to a geometrical study of the phase portraits of the one-degree-of-freedom Hamiltonian system. For a symmetric case of equal pump powers and equal signal and idler powers at the fiber input, it has been shown that the theoretical maximum gain occurs on the extremal trajectories. However, to reduce the nonlinear interaction of waves, we proposed to choose the separatrix as the optimal trajectory on the phase plane. Analytical expressions were found for the maximum amplification, as well as the length of optical fiber and the relative phase of interacting waves allowing this amplification. Using the proposed approach, we optimized of the phase-sensitive parametric amplifier. As a result, the optimal parameters of the phase-sensitive amplifier were found and the maximum possible signal amplification was realized in a broad range of signal wavelengths.

AB - In this work we applied a Hamiltonian formalism to simplify the equations of non-degenerate nonlinear four-wave mixing to the one-degree-of-freedom Hamiltonian equations with a three-parameter Hamiltonian. Thereby, a problem of signal amplification in a phase-sensitive double-pumped parametric fiber amplifier with pump depletion was reduced to a geometrical study of the phase portraits of the one-degree-of-freedom Hamiltonian system. For a symmetric case of equal pump powers and equal signal and idler powers at the fiber input, it has been shown that the theoretical maximum gain occurs on the extremal trajectories. However, to reduce the nonlinear interaction of waves, we proposed to choose the separatrix as the optimal trajectory on the phase plane. Analytical expressions were found for the maximum amplification, as well as the length of optical fiber and the relative phase of interacting waves allowing this amplification. Using the proposed approach, we optimized of the phase-sensitive parametric amplifier. As a result, the optimal parameters of the phase-sensitive amplifier were found and the maximum possible signal amplification was realized in a broad range of signal wavelengths.

KW - FIBER

KW - AMPLIFICATION

KW - INSTABILITY

KW - 3-WAVE

UR - http://www.scopus.com/inward/record.url?scp=85048357664&partnerID=8YFLogxK

U2 - 10.1364/OE.26.015503

DO - 10.1364/OE.26.015503

M3 - Article

C2 - 30114810

AN - SCOPUS:85048357664

VL - 26

SP - 15503

EP - 15518

JO - Optics Express

JF - Optics Express

SN - 1094-4087

IS - 12

ER -