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Physica Scripta

Effect of four-wave mixing spatial dependence on idler residual modulation

Zoran Vujičić, Natasa B. Pavlović, Giorgia Parca, Antonio Teixeira

Published Apr 27, 2012• 2 citations
Publisher

Abstract

We investigate the possibilities of controlling and exploiting the spatial evolution of the four-wave mixing (FWM) idler in a fiber optical parametric amplifier, considering standard single-mode fibers. We found that the use of high pump powers, for a given requirement on the signal extinction ratio and frequency separation between pump and signal, can considerably affect the optical signal-to-noise ratio on the idler frequency due to the residual modulation. We observe that by choosing an opportune length of the fiber, the residual idler modulation can be suppressed or counteracted by an increase of optical average power. Thus, a proper choice of the transmission fiber length can considerably improve the remodulated idler characteristics.

DOI
10.1088/0031-8949/2012/t149/014045

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We investigate the possibilities of controlling and exploiting the spatial evolution of the four-wave mixing (FWM) idler in a fiber optical parametric amplifier, considering standard single-mode fibers. We found that the use of high pump powers, for a given requirement on the signal extinction ratio and frequency separation between pump and signal, can considerably affect the optical signal-to-noise ratio on the idler frequency due to the residual modulation. We observe that by choosing an opportune length of the fiber, the residual idler modulation can be suppressed or counteracted by an increase of optical average power. Thus, a proper choice of the transmission fiber length can considerably improve the remodulated idler characteristics.
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.
The stagnating increase in data transmission capacity in optical communication systems combined with the ever growing demand of transmission bandwidth is leading to an impending capacity crunch, referring to the point in time after which the available bandwidth of the individual user starts to decrease. To postpone this point in time, existing technologies in terms of data transmission through optical fibers must be optimized and new degrees of freedom must be introduced to continue the exponential increase in available bandwidth; space-division multiplexing is believed to be the strongest candidate for another degree of freedom in transmission fibers. This thesis is two-fold: firstly, starting at Maxwell’s equations and basic principles of quantum mechanics, a semi-classical model of the noise properties of fiber optical parametric amplifiers and frequency converters is presented. The model accounts for multiple effects present in nonlinear fibers such as four-wave mixing, Raman scattering, distributed loss, and dispersion, and it is valid in the depleted pump regime. After validating the model against well-known results of quantum models, the model is used to predict the impacts of Raman noise, loss, and pump depletion on the noise properties of parametric frequency conversion and phase-insensitive and phase-sensitive parametric amplification. An important part of realizing space-division multiplexing is the ability of optical signal processing so the second part of this thesis addresses few-mode Raman fiber amplifiers and parametric amplifiers and frequency converters. A model of weak random linear mode coupling in the pump of a two-mode distributed Raman fiber amplifier is presented and it is shown that an amplification noise figure induced by mode coupling increases with the degree of mode coupling and that this tendency increases as the pump depletes. Also, a very low mode-dependent gain of 0.25 dB per 10 dB gain is experimentally demonstrated in a two-mode distributed Raman fiber amplifier by exciting the pump in a combination of two modes. A comprehensive model of four-wave mixing in two-mode fibers acvi counting for six simultaneous processes is derived, and the conversion efficiency from signal to idler in the four-wave mixing processes of phase conjugation and Bragg scattering in two two-mode fibers with different phase matching properties are experimentally investigated. A conversion efficiency of > −2.70 dB is demonstrated for Bragg scattering in the conversion of a signal in the LP01-mode to the idler in the LP11-mode; the signal-to-idler separation is ∼ 25 nm. Good qualitative agreement between experiments and theory is found for both processes in both fibers.
In this paper we propose and demonstrate a novel technique to suppress pump in four-wave mixing experiments. The residual pump powers at the fiber output are reflected by fiber-Bragg gratings (FBGs), amplified by an EDFA to compensate for pump losses in feedback path, and fed back to the fiber. With the increase in total input power to the fiber, the ratio of signal and idler to pump increases. Additional optical filters can then be used for further pump suppression. In our experiments, two pump waves of wavelengths 1549.70nm and 1549.85nm are combined using a 3dB coupler and fed to a highly-nonlinear fiber (HNLF) of length 1km, nonlinear coefficient of 12.4/W-km, and zero dispersion wavelength (ZDW) of 1513nm. Without feedback, we obtained the signal and idler to pump ratios of -21dB and -20.6dB respectively. After filtering by FBGs of 95% reflectivity and unity gain feedback, the ratio becomes - 14.1dB and -12.2dB respectively. When the residual pumps are amplified and fed back to the HNLF, the ratio improves to -7.5dB and -8.6dB indicating the potential of our method.
We derive an analytical theory for the noise figure of an undepleted and lossless fiber optical parametric amplifier (FOPA). Both the signal and the wavelength converted idler are investigated. Our theory is applicable for both an ideal pump power source, as well as a noisy one. We find that a noisy pump source can severely degrade the performance at high gain due to the stochastic gain-variations the signal and idler will experience. The theory is compared with Monte Carlo simulations of the FOPA and an excellent agreement is obtained. Simulations in the gain-depleted region show the possibility to reach below quantum-limited, phase-insensitive amplification for single channel transmission.
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 fibers have unwanted residual birefringence due to imperfections in fabrication processes and environmental conditions. This birefringence will randomize the state of polarization of propagating signals and may harm the performance of four-wave mixing based processing devices. Here, we present a quantitative study of the effects of birefringence in orthogonal-pump four-wave mixing systems, and identify different regions of operation of the optical fiber, mainly determined by the relative magnitude between the physical length L and beat length L b . This finding clarifies the characteristics of the complex interplay between birefringence and four-wave mixing and advises appropriate fiber length selection for minimized polarization dependent gain.