Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Express

Phase quadrature discrimination based on three-pump four-wave mixing in nonlinear optical fibers

Maxime Baillot, Mathilde Gay, Christophe Peucheret, Michel Joindot, Thierry Chartier

Published Nov 11, 2016• 19 citations
Publisher

Abstract

We theoretically and experimentally study the principle of phase-sensitive frequency conversion in a highly-nonlinear fiber using three pump waves. This mechanism, originally demonstrated with four continuous-wave pumps and a signal wave, is based on four-wave mixing and enables to convert the two quadrature components of the signal to different frequencies. In this work, we derive a set of two simple equations to describe this mechanism and find analytic solutions. We show that only three pumps are required, instead of four as originally proposed. We give simple relations to determine the initial conditions for the power levels and the phases of the pumps. To validate this approach, we perform an experimental demonstration of the three-pump scheme and find excellent agreement with the theory.

DOI
10.1364/oe.24.026930

Related papers

Orthogonal Phase Quadratures Conversion to Different Wavelengths Through Phase-Sensitive Four Wave Mixing in an Highly Nonlinear Fiber

Francesco Da Ros, Pachito Marco Calabrese, Ning Kang +2 more

Phase-sensitive processes exploiting FWM in an HNLF allow simultaneously converting two orthogonal quadratures of an optical signal to different wavelengths. Conversion efficiencies to two 90°-phase-shifted idlers exceeding 10 dB of phase-sensitive extinction ratio are obtained experimentally.

Optical Fiber Communication Conference•Jan 1, 2013•2 citations

Optimization of the conversion efficiency and evaluation of the noise figure of an optical frequency converter based on a dual-pump fiber phase sensitive amplifier

Debanuj Chatterjee, Yousra Bouasria, Fabienne Goldfarb +2 more

We propose a new architecture of phase sensitive optical frequency converter based on dual-pump phase sensitive amplification in a highly nonlinear fiber. This frequency converter allows generation of extra tones through nonlinear four-wave mixing between two strong pumps and an input tone. The frequency channel to which the input tone is converted can be chosen by adjusting the phase of the input signal. The conversion efficiency and extinction ratio of this frequency converter are predicted and optimized and its noise figure is calculated using a numerical approach based on the nonlinear Schrödinger equation. A semi-classical noise figure calculation for this approach was used and validated using an analytical fully quantum calculation based on the multi-wave model.

Optics Express•Oct 19, 2022•6 citations

Phase detection through four-wave mixing in an optical fiber

Amira S. Ahsan, Aneesh Sobhanan, Deepa Venkitesh +1 more

A scheme for detecting the phase of an incoming optical signal is systematically optimized and demonstrated experimentally. It makes use of four-wave mixing in a highly nonlinear fiber but differs from a phase-sensitive amplifier by its focus on phase detection, rather than on phase-dependent noise reduction. This experimental setup combines the signal with its phase-conjugated idler at the same frequency, before sending the combination to a photodetector. Experimental results show that the ratio of maximum and minimum currents can exceed 1000 even at a relatively low pump power of 10 mW. The proposed scheme may be useful for detecting the signal phase in coherent communication systems without the need of heterodyne detection.

Optical Engineering•Nov 26, 2020•2 citations

Fiber-based phase-sensitive optical amplifiers and their applications

Peter A. Andrekson, Magnus Karlsson

Optical parametric amplifiers rely on second-order susceptibility (three-wave mixing) or third-order susceptibility (four-wave mixing) in a nonlinear process where the energy of incoming photons is not changed (elastic scattering). In the latter case, two pump photons are converted to a signal and to an idler photon. Under certain conditions, related to the phase evolution of the waves involved, this conversion can be very efficient, resulting in large amplification of an input signal. As the nonlinear process can be very fast, all-optical applications aside from pure amplification are also possible. If the amplifier is implemented in an optical input-phase-sensitive manner, it is possible to amplify a signal wave without excess noise, i.e., with a noise figure of 0 dB. In this paper, we will provide the fundamental concepts and theory of such amplifiers, with a focus on their implementation in highly nonlinear optical fibers relying on four-wave mixing. We will discuss the distinctions between phase-insensitive and phase-sensitive operation and include several experimental results to illustrate their capability. Different applications of parametric amplifiers are also discussed, including their use in optical communication links.

Advances in Optics and Photonics•Feb 20, 2020•102 citations

Phase matching for spontaneous frequency conversion via four-wave mixing in graded-index multimode optical fibers

Elham S. Nazemosadat, Hamed Pourbeyram, Arash Mafi

A detailed analysis of four-wave mixing (FWM) and its required phase-matching conditions in graded-index multimode optical fibers is presented. The analysis is relevant mainly for spontaneous frequency conversion and photon pair generation via FWM, when the fiber length is of the order of a meter or shorter, and the signal and idler are generated at large frequency separations from the pump. An analytic expression for calculating the phase mismatch occurring as a result of the waveguide dispersion among the pump, signal, and idler beams is derived, and it agrees well with independent numerical analysis. This expression simplifies calculations considerably, as it allows the prediction of the wavelengths of the signal and idler by using only the mode group number of the spatial modes involved in the FWM process and the refractive index profile of the fiber. The scaling of the signal–pump–idler frequency separations with the mode group numbers is explored. The abundance of the configuration degeneracies of the FWM process in graded-index multimode fibers indicates that nearly identical signal and idler frequencies can be obtained for many different pump, signal, and idler spatial mode profile combinations.

Journal of the Optical Society of America B•Jan 6, 2016•90 citations

Optical Amplification in a Nonlinear Fiber Interferometer

M.E. Marhic, S.-H. Hsia, J.-M. Jeong

Optical amplification in optical fibers by means of degenerate four-wave mixing (DFWM) is studied by classical equations. A balanced interferometer is used to mix and separate the signal and the pump. Exact solutions are obtained even with pump depletion. If the cross-phase modulation is small, the signal power gain varies as the square of the pump self-phase shift. This gain can be sizable for moderate fiber lengths and laser powers, before the onset of stimulated Raman scattering. We have experimentally verified these calculations with a Sagnac interferometer, comprising a 300 m long polarization-preserving fiber, emitting pulses with 100-200 W peak power and 100-200 nsec duration. We have measured a signal power gain of 22 (13.3 dB); this value correlated well with a pump self-phase shift of 3π/2 measured in a separate two-wavelength experiment. This system can be used for squeezing fluctuations of the signal quadrature which is not amplified. We have performed a classical derivation of squeezing, based upon a geometrical study of the transformation of the signal phasor. The results are in agreement with those of more elaborate quantum-mechanical derivations.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations
We theoretically and experimentally study the principle of phase-sensitive frequency conversion in a highly-nonlinear fiber using three pump waves. This mechanism, originally demonstrated with four continuous-wave pumps and a signal wave, is based on four-wave mixing and enables to convert the two quadrature components of the signal to different frequencies. In this work, we derive a set of two simple equations to describe this mechanism and find analytic solutions. We show that only three pumps are required, instead of four as originally proposed. We give simple relations to determine the initial conditions for the power levels and the phases of the pumps. To validate this approach, we perform an experimental demonstration of the three-pump scheme and find excellent agreement with the theory.
We propose a new architecture of phase sensitive optical frequency converter based on dual-pump phase sensitive amplification in a highly nonlinear fiber. This frequency converter allows generation of extra tones through nonlinear four-wave mixing between two strong pumps and an input tone. The frequency channel to which the input tone is converted can be chosen by adjusting the phase of the input signal. The conversion efficiency and extinction ratio of this frequency converter are predicted and optimized and its noise figure is calculated using a numerical approach based on the nonlinear Schrödinger equation. A semi-classical noise figure calculation for this approach was used and validated using an analytical fully quantum calculation based on the multi-wave model.
A scheme for detecting the phase of an incoming optical signal is systematically optimized and demonstrated experimentally. It makes use of four-wave mixing in a highly nonlinear fiber but differs from a phase-sensitive amplifier by its focus on phase detection, rather than on phase-dependent noise reduction. This experimental setup combines the signal with its phase-conjugated idler at the same frequency, before sending the combination to a photodetector. Experimental results show that the ratio of maximum and minimum currents can exceed 1000 even at a relatively low pump power of 10 mW. The proposed scheme may be useful for detecting the signal phase in coherent communication systems without the need of heterodyne detection.
Optical parametric amplifiers rely on second-order susceptibility (three-wave mixing) or third-order susceptibility (four-wave mixing) in a nonlinear process where the energy of incoming photons is not changed (elastic scattering). In the latter case, two pump photons are converted to a signal and to an idler photon. Under certain conditions, related to the phase evolution of the waves involved, this conversion can be very efficient, resulting in large amplification of an input signal. As the nonlinear process can be very fast, all-optical applications aside from pure amplification are also possible. If the amplifier is implemented in an optical input-phase-sensitive manner, it is possible to amplify a signal wave without excess noise, i.e., with a noise figure of 0 dB. In this paper, we will provide the fundamental concepts and theory of such amplifiers, with a focus on their implementation in highly nonlinear optical fibers relying on four-wave mixing. We will discuss the distinctions between phase-insensitive and phase-sensitive operation and include several experimental results to illustrate their capability. Different applications of parametric amplifiers are also discussed, including their use in optical communication links.
A detailed analysis of four-wave mixing (FWM) and its required phase-matching conditions in graded-index multimode optical fibers is presented. The analysis is relevant mainly for spontaneous frequency conversion and photon pair generation via FWM, when the fiber length is of the order of a meter or shorter, and the signal and idler are generated at large frequency separations from the pump. An analytic expression for calculating the phase mismatch occurring as a result of the waveguide dispersion among the pump, signal, and idler beams is derived, and it agrees well with independent numerical analysis. This expression simplifies calculations considerably, as it allows the prediction of the wavelengths of the signal and idler by using only the mode group number of the spatial modes involved in the FWM process and the refractive index profile of the fiber. The scaling of the signal–pump–idler frequency separations with the mode group numbers is explored. The abundance of the configuration degeneracies of the FWM process in graded-index multimode fibers indicates that nearly identical signal and idler frequencies can be obtained for many different pump, signal, and idler spatial mode profile combinations.
Optical amplification in optical fibers by means of degenerate four-wave mixing (DFWM) is studied by classical equations. A balanced interferometer is used to mix and separate the signal and the pump. Exact solutions are obtained even with pump depletion. If the cross-phase modulation is small, the signal power gain varies as the square of the pump self-phase shift. This gain can be sizable for moderate fiber lengths and laser powers, before the onset of stimulated Raman scattering. We have experimentally verified these calculations with a Sagnac interferometer, comprising a 300 m long polarization-preserving fiber, emitting pulses with 100-200 W peak power and 100-200 nsec duration. We have measured a signal power gain of 22 (13.3 dB); this value correlated well with a pump self-phase shift of 3π/2 measured in a separate two-wavelength experiment. This system can be used for squeezing fluctuations of the signal quadrature which is not amplified. We have performed a classical derivation of squeezing, based upon a geometrical study of the transformation of the signal phasor. The results are in agreement with those of more elaborate quantum-mechanical derivations.