Four-wave Mixing Products Research Articles

Design of an interferometric fiber optic parametric amplifier for the rejection of unwanted four-wave mixing products.

We introduce a novel (to our knolwedge) interferometric fiber optic parametric amplifier (FOPA), allowing for the suppression of unwanted four-wave mixing products. We perform simulations of two configurations where one rejects idlers and, the other rejects nonlinear crosstalk from the signal output port. The numerical simulations presented here demonstrate the practical feasibility of suppressing idlers by >28 dB across at least 10 THz enabling the reuse of the idler frequencies for signal amplification and thus doubling the employable FOPA gain bandwidth. We demonstrate it can be achieved even when the interferometer employs real-world couplers by introducing a small attenuation in one of the interferometer arms.

Accurate Evaluation of Cascaded Four-Wave Mixing Products Generation in Fiber with Optical Feedback Based on Multilayer Perceptronaccurate Evaluation of Cascaded Four-Wave Mixing Products Generation in Fiber with Optical Feedback Based on Multilayer Perceptron

Accurate Evaluation of Cascaded Four-Wave Mixing Products Generation in Fiber with Optical Feedback Based on Multilayer Perceptronaccurate Evaluation of Cascaded Four-Wave Mixing Products Generation in Fiber with Optical Feedback Based on Multilayer Perceptron

Suppression of four wave mixing effect in DWDM system

Abstract This article discusses the nonlinear effect, four-wave mixing (FWM), which lowers the performance of optical communication systems. The concept of orthogonal polarization was introduced to reduce the effects of FWM. Here, orthogonal polarization is used with various modulation techniques such as NRZ, RZ, GAUSSIAN and RAISED COSINE. Orthogonal polarization was found to reduce the effect of FWM more than round polarization. Weaknesses of the four wavelength mixes were analyzed for various levels of input power. The capacity of a four-wave mixing product (FWM) is assessed by an optical spectrum analyzer. System performance is analyzed in terms of quality factors and BER.

Temperature Compensated High-Resolution Interrogation of FBG Strain Sensor Based on Four Wave Mixing

Realization of temperature compensation and high sensitivity is a challenging task in the field of FBG based strain sensor. A unique scheme of high sensitive temperature compensated interrogation technique for FBG strain sensors is proposed. Two chirped FBGs are designed in such a way that effect of temperature on one FBG is compensated by the other FBG. The strain sensitivity is enhanced by a factor of sixteen compared to the signal reflected from the edge of the FBG using only third order Four wave mixing (FWM) product. The third order FWM product generated in the $1^{st}$ stage FWM process is filtered and utilized in the $2^{nd}$ stage FWM process to enhance the sensitivity. The proposed scheme attains high sensitivity of 0.312 dBm/ ${\mu \varepsilon }$ with strain resolution of $0.032 {\mu \varepsilon }$ using only $3^{rd}$ order FWM product.

Highly Sensitive FBG Strain Sensor With Enhanced Measurement Range Based On Higher Order FWM

To meet the simultaneous requirement of high sensitivity and high measurement range is an uphill task in the development of fiber Bragg grating (FBG) strain sensor. A unique scheme of highly sensitive FBG strain sensor is proposed based on nonlinear four wave mixing (FWM) with a high measuring range. In this paper, both the edges of FBG reflection spectrum are used without increasing the number of sources. The FWM products generated are tuned to the reflection edges of the FBG. The signals reflected from the edges of the FBG are then utilized in the subsequent FWM process to enhance the sensitivity of the system. The proposed scheme can provide a strain measurement range of 2310 με with strain sensitivity of 91.21 dBm/nm.

Decreasing base units-unequally spaced channel allocation algorithm for dense wavelength division multiplexed transmission systems

We propose an unequally spaced channel allocation algorithm, i.e., decreasing base units-unequally spaced (DBU-US) algorithm tested for high-capacity dense wavelength division multiplexed (DWDM) transmission systems. The new scheme decides upon the number of base units (BUs) covering the entire bandwidth and the allocation of different number of channels in the BUs. Starting from BUi = 0, the number of channels in each subsequent BU(BUi = 1 , 2 , 3 ) reduces by a factor of 2, “i” being the index of the BUs. The BUi , BUi + 1 , … have even and odd slot frequency allocations, which creates a substantial degree of unequal channel spacing, which virtually proves to reduce the four wave mixing (FWM) products effectively for any number of transmitted channels. When compared with existing unequal channel allocation schemes of unequally spaced repeated unequally spaced (URUS), alternately paired URUS (APRUS), a reduction of 6.25% and 13.7% in bandwidth is observed, respectively. Similarly, a reduction of FWM products by 45.5%, 41.3%, and 31.7% is observed, when compared with URUS, paired URUS, and APRUS, respectively. The FWM intensities generated by DBU-US are reported to be 5 dBm lesser when compared to widely accepted URUS scheme. Therefore, it is concluded that DBU-US is superior and is considered suitable for DWDM transmission systems.

Four-wave mixing effect on high-power continuous-wave all-fiber lasers

A four-wave mixing effect on high-power continuous-wave fiber lasers has been demonstrated theoretically and experimentally. Detailed theoretical description of phase matching is presented and we found that the phase matching condition is satisfied at the frequency shift of 5.16 THz. While the intensity in fiber core region is more than about 394 MW/cm2, the four-wave mixing products of 1100 nm and 1060 nm were also observed in high-power all-fiber laser. The comparison shows that the experiment result is in good agreement with the simulation result. In addition, the beam quality deterioration for the laser is caused by the four-wave mixing effect and the mode instability. The [Formula: see text] factor measured at maximal intensity of 478 MW/cm2 is 2.80.

Augmentation of sensitivity of FBG strain sensor for biomedical operation.

The performance of a highly sensitive strain sensor based on nonlinear four wave mixing (FWM) using two uniform fiber Bragg gratings (FBGs) is investigated. Strain is measured by the proposed setup with high resolution and precision. It is observed that the wavelength shift induced by very small strain over the FBG is significantly magnified by the higher-order FWM process. The sensitivity is enhanced by a factor of nine based on a wavelength shift of the eighth-order FWM product. Strain sensitivity of 11.23pm/μϵ is achieved against initial strain sensitivity of 1.23pm/μϵ. The proposed scheme can provide a strain measurement range of about 3500μϵ. Application of the proposed setup in the cardiac and respiratory systems is also studied, and the results are found to be reliable and accurate, even if the applied strain on the FBG is of the order of 0.1μϵ.

Two-pump fiber optical parametric amplifiers: Beyond the 6-wave model

Abstract Two-pump (2-P) fiber optical parametric amplifiers (FOPAs) are a versatile class of FOPAs which can exhibit wide and flat gain spectra in arbitrary wavelength regions, when compared with one-pump (1-P) FOPAs. The 4-wave and the 6-wave models are commonly used to simulate 2-P FOPAs by considering four and six interacting waves, respectively. Although the 6-wave model provides more accurate results than the 4-wave model, it does not take into account higher-order four-wave mixing products (HFPs) especially when the FOPA saturates. The main goal of this paper is to accurately model the 2-P FOPA in which HFPs beyond six interacting waves are included. To this end, the nonlinear Schrodinger equation (NLSE) is solved using the split-step Fourier method and the results are compared with those of previous models such as the 4-wave and 6-wave models as well as an existing analytical solution. The results, which are compared with available experimental data, show that for high input signal levels where the FOPA operates in saturation, the 6-wave model fails to provide accurate simulation results and deviates from results obtained by the NLSE. Therefore, NLSE-based modeling, which includes arbitrary interacting waves beyond the 6-wave model is important for applications in the saturation regime such as signal processing, noise suppression and regeneration.

Temporal coherence study of four-wave mixing products with and without the laser cavity effect.

In this work, we have studied the temporal coherence property of a four-wave mixing (FWM)-assisted continuous-wave erbium-doped fiber ring laser source. To understand the temporal coherence characteristics of FWM, we have analyzed the visibility of their interference pattern with the help of a Mach-Zehnder-based fiber interferometer. The visibility of FWM sidebands is compared with respect to the input pumps, with and without the cavity effect. The stand-alone FWM without any cavity effect has a visibility comparable to its input coherent pumps, while the FWM in the presence of the cavity effect has a poorer visibility due to the intra-cavity noise arising from the amplified spontaneous emission, which is not entirely annulled in broadband lasers. The study also confirms that the visibility/temporal coherence property of FWM sidebands does not depend on the efficiency of their generation.

Crosstalk Mitigation in Multichannel Optical Parametric Sampling via Raman Amplification

We propose to use backward Raman amplification to mitigate the crosstalk in multichannel optical parametric sampling. The performances of multichannel sampling based on four-wave mixing (FWM) have been experimentally compared with different Raman pump powers. Optical crosstalk is suppressed by lowering the input signal power so that the depletion of the parametric pump and higher order FWM products are reduced. Meanwhile, Raman amplification compensates the parametric pump power and improves the conversion efficiency, thus maintaining the output idler power. A 12.2- and 13.6-dB reduction of crosstalk-induced frequency components has been achieved in two output channels. We also analyze bandwidth broadening resulting from the self-phase modulation of the pulsed parametric pump for the two cases when it is amplified by an erbium-doped fiber amplifier and by the Raman pump.

Enhancement of multiple four-wave mixing via cascaded fibers with discrete dispersion decreasing**Project supported by the National Key Scientific Instrument and Equipment Development Project, China (Grant No. 2014YQ510403) and the National Natural Science Foundation of China (Grant Nos. 61377039 and 51527901).

Cascaded fiber geometry with the dispersion of each fiber decreasing is proposed to enhance the multiple four-wave mixing (FWM) generation. The first fiber with relatively large dispersion initiates and accelerates the expansion of multiple FWM, and the second fiber with small dispersion would allow the phase-matching process (thus the spectrum broadening) to keep going. Numerical and experimental results show that with this geometry not only multiple FWM expansion can be accelerated, but also the efficiency of multiple FWM products can be effectively improved with shorter fibers.

Wavelength multicasting through four-wave mixing with an optical comb source.

Based on four-wave mixing (FWM) with an optical comb source (OCS), we experimentally demonstrate 26-way or 15-way wavelength multicasting of 10-Gb/s differential phase-shift keying (DPSK) data in a highly-nonlinear fiber (HNLF) or a silicon waveguide, respectively. The OCS provides multiple spectrally equidistant pump waves leading to a multitude of FWM products after mixing with the signal. We achieve error-free operation with power penalties less than 5.7 dB for the HNLF and 4.2 dB for the silicon waveguide, respectively.

Theoretical Analysis of the Four-Wave Mixing Effect in Virtual Carrier-Assisted DD MB-OFDM Ultradense WDM Metropolitan Networks

A theoretical method (TM) to evaluate the four-wave mixing (FWM) power in multiband orthogonal frequency division multiplexing (MB-OFDM) ultradense wavelength division multiplexing (WDM) metropolitan networks using virtual carriers (VCs) and direct detection is proposed and validated numerically. It considers a band spacing of 3.125 GHz and 10-Gb/s data rate per band. A simplified TM (STM) to obtain the FWM power for MB-OFDM systems employing high-dispersion fiber is also proposed to relax the computation complexity. Both methods consider that FWM products generated from the mixing between two VCs and an OFDM band are dominant. Analytical expressions for the maximum allowed average power of the worst band (the band most impaired by FWM) are also derived. The TM and STM enable estimating the average power level per WDM channel corresponding to the threshold error vector magnitude (EVM) (threshold average power—TAP), where the threshold EVM is the maximum allowed EVM due to FWM, which induces a 2-dB EVM penalty to the EVM at the forward error correction threshold. Results show that, when a total data bit rate of 450 Gb/s is transmitted (nine WDM channels with five bands each) along the standard single-mode fiber (SSMF), the discrepancy between the numerical simulation-estimated and TM-estimated TAPs does not exceed 0.5 dB. By defining the upper bound of the power limit (UBPL) as the TAP obtained with 17 WDM channels, the discrepancy between the TM-estimated and STM-estimated UBPLs does not exceed 1 dB for transmission along up to 10 SSMF spans and for channel gaps up to 22.81 GHz.

Photonic‐assisted microwave amplification using four‐wave mixing

This work reports the development of a high-gain and wideband photonic-assisted amplified radio over fibre (RoF) system based on the non-linear effect four-wave mixing (FWM). The microwave gain is defined as the difference between the electrical power photodetected using a FWM product and that from the conventional RoF system at the same optical power level. Numerical simulations and experimental results prove that microwave gain strongly depends on the system parameters, such as wavelength separation between pump sources, state of polarisation, radio frequency modulation frequency and DC bias voltage of optical modulator. Microwave amplification from 4 to 19 GHz, electrical signal-to-noise ratio higher than 51 dB and gain up to 26 dB at 17 GHz are demonstrated. Moreover, an optical-wireless network based on the photonic-assisted microwave application is proposed, with the purpose of illustrating its applicability.

Effective suppression of nonlinear distortion in optical phase conjugation of optical OFDM signals using backward Raman pumping

ABSTRACTThe use of backward Raman amplification to mitigate nonlinear distortion in optical phase conjugation (OPC) of orthogonal frequency-division multiplexing (OFDM) signals in a fibre communication system is investigated in this paper. A ∼29 dB reduction in the nonlinear distortion is achieved, while comparable conjugated output signal power is maintained through the Raman gain. By numerically solving the nonlinear Schrodinger equation (NLSE) along the fibre, a detailed theoretical model is developed to elaborate the mechanism in Raman-assisted OPC. Different optical network scenarios have been analysed using this model. The mechanism of Raman-assisted OPC is further explained by comparing the power profiles of both the conjugated signal and the nonlinear distortion with those in the conventional scheme. In addition to investigating the nonlinear distortion caused by spurious four-wave mixing (FWM) products, the waveform distortion resulting from pump depletion in the OPC system is also analysed. The ...

Analysis of the four-wave mixing impact on the most heavily affected channels of dense and ultra-dense wavelength division multiplexing systems using non-zero dispersion shifted fibers

In this paper, the impact of four-wave mixing (FWM) phenomenon on the system performance has been analyzed via focusing on effects of FWM products falling into the center channels, i.e. the most heavily affected ones among all, of equally spaced 9-, 11-, 13- and 15-channel DWDM systems having channel spacing values of 12.5GHz, 25GHz, 50GHz and 100GHz, and UDWDM systems having 6.25GHz channel spacing value. DWDM and UDWDM systems using four different single-span commercially available NZDSFs, i.e. TeraLight™, LEAF®, TrueWave®-Reach and TrueWave®-RS, have been considered in simulations. Results show that for all NZDSF types, input powers even as low as 1mW do not satisfy a minimum 23dB signal-to-crosstalk ratio (SXR) criterion in UDWDM and DWDM systems using 6.25GHz and 12.5GHz channel spacing values, respectively. Furthermore, for all DWDM and UDWDM systems, the lowest and the highest FWM crosstalk values belong to the TeraLight and the TrueWave-RS fibers, respectively, at all input powers, channel numbers and channel wavelengths while the minimum and the maximum SXR variations with varying channel wavelengths are obtained in the TrueWave-Reach and the LEAF fibers, respectively.

Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems.

In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error.

Broadband cascaded four-wave mixing in As2S3 chalcogenide waveguide with optical feedback and Mach–Zehnder interferometer

A scheme to enhance the efficiency and number of the cascaded four-wave mixing (FWM) products in [Formula: see text] chalcogenide planar waveguide is proposed and investigated numerically. Through introducing the optical feedback cavity and Mach–Zehnder interferometer, the modulated broadband cascaded FWM products can be obtained based on the high nonlinear [Formula: see text] chalcogenide planar waveguide. The numerical results show that the bandwidth of the modulated cascaded FWM is increased and the number of cascaded FWM products is improved compared with the single pass way of generating cascaded FWM products. Moreover, the feedback ratio plays an important role in the modulated cascaded FWM. This research can find important potential applications in nonlinear optics and integrated optics.

All-Optical DPSK Regenerative One-to-Nine Wavelength Multicasting Using Dual-Pump Degenerate Phase Sensitive Amplifier

We present theoretical investigation of all-optical differential phase-shift keying (DPSK) regenerative wavelength multicasting using dual-pump degenerate phase sensitive amplifier (PSA), based on seven-wave model rather than traditional three-wave model. We first test the accuracy of the seven-wave model in the context of 40 Gb/s DPSK all-optical regenerative multicasting. We find that the seven-wave model is more accurate than the three-wave model. Meanwhile, we successfully optimize optical signal power, frequency spacing between two pumps, and regeneration capability of all multicasting channels. All-optical DPSK regenerative one-to-nine wavelength multicasting can be successfully realized. Both eye diagrams and the calculated bit error rate curve demonstrate that the optical signal to noise ratio penalties of all multicasting channels are improved by around 3 dB. Finally, to the best of our knowledge, we investigate, for the first time, the effects of the high-order four-wave mixing (FWM) products on the evolution of pump-to-signal intensity modulation transfer (IMT) and IMT from the pump to all wavelength-multicasting channels in a dual-pump degenerate PSA. We find that high-order FWM products contribute to the suppression of pump-to-signal IMT after proper optimization of dual-pump's frequency spacing and signal optical power. Both regenerative one-to-nine wavelength multicasting and pump-to-signal IMT smaller than 1 can be simultaneously achieved under the gain saturation region.