Four-wave Mixing In Optical Fibers Research Articles

Intra-envelope four-wave mixing in optical fibers.

We report experimentally on the phenomenon of intra-envelope four-wave mixing (FWM) in optical fibers. We demonstrate that the non-linear interaction between two pulse trains operating at the same repetition rate, but with slightly different carrier frequencies, leads by FWM to the generation of new components within their spectral envelops. The frequency differences between the FWM components and the pump lines are in the RF domain, making it almost impossible to observe the process using a standard optical spectrum analyzer. We show that using a third light source as a multi-line local oscillator makes the analysis of these new spectral components accessible. It enables to extract these FWM components from the spectra of the initial light sources by converting optical frequencies into radio frequencies. The experimental results are in excellent agreement with the numerical simulations.

Phase space topology of four-wave mixing reconstructed by a neural network.

The dynamics of ideal four-wave mixing in optical fiber is reconstructed by taking advantage of the combination of experimental measurements together with supervised machine learning strategies. The training data consist of power-dependent spectral phase and amplitude recorded at the output of a short fiber segment. The neural network is shown to be able to accurately predict the nonlinear dynamics over tens of kilometers, and to retrieve the main features of the phase space topology including multiple Fermi-Pasta-Ulam recurrence cycles and the system separatrix boundary.

Effects of Self-Phase and Cross-Phase Modulations at Four-Wave Mixing in Optical Fibers

Effects of Self-Phase and Cross-Phase Modulations at Four-Wave Mixing in Optical Fibers

Palliation of Four-Wave Mixing in Optical Fibers Using Improved DSP Receiver

A long haul optical communication system (LHOCS) is one of the key resources to fulfill the higher capacity requirements in future communication networks. To launch LHOCS, the system mainly faces high order nonlinear effects. The four-wave mixing (FWM) is one of the major nonlinear effects, which limits the transmission distance. Therefore, in this paper, an advanced duo-binary (DB) modulation scheme-based system is evaluated by employing an improved digital signal processing (IDSP) approach at the receiver side to suppress the FWM effect. In addition, an analytical analysis is also performed for the proposed system. To observe the difference between the IDSP and conventional digital signal processing (DSP), the various performance metrics such as bit error rate (BER), Q-factor, and optical signal-to-noise ratio (OSNR) parameters are evaluated. Variable channel spacing along with polarization mode dispersion (PMD) are analyzed at several ranges of input powers and fiber lengths. The analytical and simulation-based calculations exhibit the effectiveness of the proposed model and hence, FWM effect are compensated to achieve 500 km optical fiber propagation range with a BER below 10−6.

Photon-Pair Sources Based on Intermodal Four-Wave Mixing in Few-Mode Fibers

Four-wave mixing in optical fibers has been proven to have many applications within processing of classical optical signals. In addition, recent developments in multimode fibers have made it possible to achieve the necessary phase-matching for efficient four-wave mixing over a very wide bandwidth. Thus, the combination of multimode fiber optics and four-wave mixing is very attractive for various applications. This is especially the case for applications in quantum communication, for example in photon-pair generation. This is the subject of this work, where we discuss the impact of fluctuations in core radius on the quality of the heralded single-photon states and demonstrate experimental results of intermodal spontaneous four-wave mixing for photon-pair generation.

Tunable triple-wavelength mode-locked ytterbium fiber laser with birefringence filter

A mode-locked ytterbium fiber laser based on all normal dispersion (ANDi) technique and nonlinear polarization rotation (NPR) is investigated with birefringent plate as a spectral filter in this paper. Tunable triple-wavelength simultaneous operation is realized at central wavelengths of 1031.4, 1046.8 and 1066.5 nm, respectively. A maximum output power up to 161.4 mW is obtained at 1031.4 nm wavelength. By only changing the direction of the optical axis of the uniaxial birefringent filter, tunable range as wide as 19 nm is demonstrated. To the best of our knowledge, this is the widest tuning range and highest power reported so far for ANDi mode-locked ytterbium fiber lasers with triple-wavelength operation. Our analysis shows that the mechanism of the triple-wavelength mode-locked operation results mainly from the four-wave mixing in optical fibers; in addition, the wide gain bandwidth of Yb also plays a critical role for the stable oscillation of the third mode-locked wavelength. The energy conversion process governed by a set of four coupled equations is realized experimentally through the adjustment of the polarization controller, which is related to the phase matching.

Converting one photon into two via four-wave mixing in optical fibers

Observing nonlinear optical quantum effects or implementing quantum information protocols using nonlinear optics requires moving to ever-smaller input light intensities. However, low light intensities generally mean weak optical nonlinearities, which are inadequate for many applications. Here we calculate the performance of four-wave mixing in various optical fibers for the case where one of the input beams is a single photon. We show that in tapered chalcogenide glass fibers (microwires) a single photon plus strong pump beam can produce a pair of photons with a probability of 0.1%, much higher than in previous work on bulk and wave-guided crystal sources. Such a photon converter could be useful for creating large entangled photon states, for performing a loophole-free test of Bell's inequalities, and for quantum communication.

Comprehensive characterization of a heralded single photon source based on four-wave mixing in optical fibers

A detailed statistical characterization of an optical signal obtained from a heralded single photon source is performed. The source is based on the spontaneous four-wave mixing process, and a dispersion shifted fiber is used to achieve phase matching. At source output, the derivation of the second-order coherence function shows the importance of choosing carefully the frequency detuning between the optical fields in order to avoid the uncorrelated photons generated through Raman scattering. Results indicate that with an accurate adjustment of the source parameters, it is possible to obtain an almost perfect conditional single photon source using spontaneous four-wave mixing. When a transmission fiber is considered, the losses change the source statistics due to the coupling with the noise absorption reservoir. Nevertheless, even at room temperature the impact of the absorption reservoir tends to be quite small, and the change is only observable for very long transmission lengths.

Role of Absorption on the Generation of Quantum-Correlated Photon Pairs Through FWM

The impact of fiber absorption on the generation rate of quantum-correlated photon pairs through spontaneous four-wave mixing in optical fibers is studied theoretically. We quantify the impact of the loss through the analysis of the Cauchy-Schwarz correlation parameter and the Clauser, Horne, Shimony, and Holt inequality. Results show that fiber loss can improve the quantum-correlation between the photon pairs. This is a consequence of the decrease of the individual signal and idler photon-fluxes, which reduces the rate of uncorrelated photons generated through Raman scattering inside the optical fiber. Findings show that a high degree of polarization entanglement is obtained when the ratio of signal to idler photon-fluxes lies between 0.5 and 0.8, in a regime with high losses on the signal wave.

Erasing quantum distinguishability via single-mode filtering

Erasing quantum-mechanical distinguishability is of fundamental interest and also of practical importance, particularly in subject areas related to quantum information processing. We demonstrate a method applicable to optical systems in which single-mode filtering is used with only linear optical instruments to achieve quantum indistinguishability. Through ``heralded'' Hong-Ou-Mandel interference experiments we measure and quantify the improvement of indistinguishability between single photons generated via spontaneous four-wave mixing in optical fibers. The experimental results are in excellent agreement with predictions of a quantum-multimode theory we develop for such systems, without the need for any fitting parameter.

Interference in a Quantum Channel Due to Classical Four-Wave Mixing in Optical Fibers

The second-order coherence function for idler photons generated through stimulated four-wave mixing (FWM) is theoretically derived, considering both spontaneous and stimulated Raman contributions. Two distinct cases and two different power regimes are analyzed. First, we consider that the idler wave is fully generated inside the fiber. In a second scenario, we admit that at the fiber input there exist a quantum channel and idler photons will be created at that frequency through the combined processes of FWM and Raman scattering. Results show that for the first case, in a low power regime, the idler photons follow a thermal statistics. In a moderate power regime, the statistics of the generated idler wave presents a Poissonian distribution. Results also show that in the second case, in a low power regime, the statistics of the input quantum channel goes from a Poissonian statistics at the fiber input to a thermal statistics at the fiber output. Findings show that in a moderate power regime, the quantum channel maintains its Poissonian distribution through fiber propagation.

Coherent anti-Stokes Raman scattering microscopy imaging with suppression of four-wave mixing in optical fibers

We demonstrated an optical fiber delivered coherent anti-Stokes Raman scattering (CARS) microscopy imaging system with a polarization-based mechanism for suppression of four-wave mixing (FWM) signals in delivery fiber. Polarization maintaining fibers (PMF) were used as the delivery fiber to ensure stability of the state of polarization (SOP) of lasers. The pump and Stokes waves were coupled into PMFs at orthogonal SOPs along the slow and fast axes of PMFs, respectively, resulting in a significant reduction of FWM signals generated in the fiber. At the output end of PMFs, a dual-wavelength waveplate was used to realign the SOPs of the two waves into identical SOPs prior to their entrance into the CARS microscope. Therefore, it allows the pump and Stokes waves with identical SOPs to excite samples at highest excitation efficiency. Our experimental results showed that this polarization-based FWM-suppressing mechanism can dramatically reduce FWM signals generated in PMFs up to approximately 99%. Meanwhile, the PMF-delivered CARS microscopy system with this mechanism can still produce high-quality CARS images. Consequently, our PMF-delivered CARS microscopy imaging system with the polarization-based FWM-suppressing mechanism potentially offers a new strategy for building fiber-based CARS endoscopes with effective suppression of FWM background noises.

Terahertz-wave generation by surface-emitted four-wave mixing in optical fiber

We propose a novel terahertz-wave source through the four-wave mixing effect in a conventional single-mode optical fiber pumped by a dual-wavelength laser whose difference frequency lies in the terahertz range. Surface-emitted geometry is employed to decrease absorption loss. A detailed derivation of the terahertz-wave power expression is presented using the coupled-wave theory. This is a promising way for realizing a reasonable narrow-band terahertz-wave source.

All-Optical Regeneration Based on Phase-Sensitive Nondegenerate Four-Wave Mixing in Optical Fibers

An optical regeneration scheme based on nondegenerate phase-sensitive amplification in highly nonlinear fibers is numerically investigated. The proposed regenerator exhibits significant amplitude and phase noise suppression properties and eliminates the need for precise phase and frequency locking with the input return-to-zero differential phase-shift keying signal.

Autoresonant four-wave mixing in optical fibers

A theory of autoresonant four-wave mixing in tapered fibers is developed in application to optical parametric amplification (OPA). In autoresonance, the interacting waves (two pump waves, a signal, and an idler) stay phase-locked continuously despite variation of system parameters (spatial tapering). This spatially extended phase-locking allows complete pump depletion in the system and uniform amplification spectrum in a wide frequency band. Different aspects of autoresonant OPA are described including the automatic initial phase-locking, conditions for autoresonant transition, stability, and spatial range of the autoresonant interaction.

Analysis of Heralded Single-Photon Source Using Four-Wave Mixing in Optical Fibers via Wigner Function and its Use in Quantum Key Distribution

In this paper, we use the Wigner function in order to determine the photon number statistics of a heralded single-photon source constructed from a photon-pair source using four-wave mixing in optical fibers. Having this result, we discuss the performance of a quantum key distribution system when this kind of single-photon source is employed.

Noise Properties of Degenerate Dual Pump Phase Sensitive Amplifiers

The noise properties of phase sensitive amplifiers based on degenerate four-wave mixing in optical fibers are studied taking into account the quantum noise amplification, the amplitude and phase noise properties of the pump sources. An analytical tool is presented for the direct calculation of the amplifier noise figure also verified by extensive numerical simulations. The signal power dependence of noise figure is both analytically and numerically accented. The need for high speed and precise phase locking is also revealed in order to diminish the effect of phase noise on the noise properties of the amplifier.

Effective Nonlinear Parameter Measurement Using FWM in Optical Fibers in a Low Power Regime

The four-wave mixing (FWM) process in a low power regime is studied both theoretically and experimentally. The coupled-equations for the complex amplitudes are derived and solved. The proposed model is compared with experimental data. Results shows the need of considering both nonlinear and polarization dependent effects in order to obtain an accurate description of the four-wave mixing process in a low power regime. The effective nonlinear parameter is experimentally measured in a dispersion-shifted fiber, and the transition region between an almost co-polarized situation to a decorrelated state of polarization is observed.

Multiple four-wave mixing in optical fibers: 1.5–3.4-THz femtosecond pulse sources and real-time monitoring of a 20-GHz picosecond source

In this work, we report recent progress on the design of all-fibered ultra-high repetition-rate pulse sources for telecommunication applications around 1550 nm. The sources are based on the non-linear compression of an initial beat-signal through a multiple four-wave mixing process taking place into an optical fiber. We experimentally demonstrate real-time monitoring of a 20 GHz pulse source having an integrated phase noise 0.01 radian by phase locking the initial beat note against a reference RF oscillator. Based on this technique, we also experimentally demonstrate a well-separated high-quality 110 fs pulse source having a repetition rate of 2 THz. Finally, we show that with only 1.4 m of standard single mode fiber, we can achieve a twofold increase of the repetition rate, up to 3.4 THz, through the self-imaging Talbot effect. Experimental results are supported by numerical simulations based on the generalized non-linear Schrödinger equation.

Optimal design of tunable parametric wavelength converters based on degenerate four-wave mixing in optical fibers

We prove that the tuning range of a one-pump fiber parametric wavelength converter based on degenerate four-wave mixing can be maximized by selecting fibers with appropriate zero dispersion wavelength and high-order dispersion coefficients. The maximal tuning range is proportional to the cube root of the product of the pump power and fiber nonlinear coefficient. If the effects of fourth-order dispersion are utilized, the tuning range can increase dramatically.