Fiber Nonlinearities: A Tutorial

Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications, the Raman amplification being only one of the recent examples. In this tutorial I review the various nonlinear effects occurring in optical fibers from both standpoints..

New High Nonlinear and Dispersion Flattened Photonic Crystal Fiber

A new high nonlinear dispersion flattened photonic crystal fiber is proposed. This fiber has three-fold symmetry core. The doped region in the core and the big air-holes in the 1-st ring can make high nonlinearity in the PCF. And the small air-holes in the 1-st ring and the radial increasing diameters air-holes rings in cladding can be used to turn the dispersion properties of the PCF. We can achieve the optimized optical properties by carefully selecting the PCF's structure parameters. A PCF with flattened dispersion is obtained. The dispersion is within ±0.8 ps·nm-1·km-1 from 1.50 μm to 1.62 μm. The nonlinear coefficient is about 12.645 6 W-1·km-1, the fundamental mode area is about 10.257 9 μm2 and the birefringence is about 3.086 96×10-5 at 1.55 μm. This work may be useful for effective design and fabrication of dispersion flattened photonic crystal with high nonlinearities.

Application of ABCD Formalism in Theoretical and Experimental Analysis of Actively Modelocked Fiber Laser

Time domain ABCD matrix formalism is a useful model for analyzing the characteristics of actively modelocked fiber laser. Based on this model and given more consideration on the influences of optical fiber dispersion and optical fiber nonlinearity, the laser characteristic of actively modelocked fiber laser is analyzed, and the comparision of the theoretical analysis results with experimental ones is given.

Evolution of modes in double-clad Raman fiber amplifier

Stimulated Raman scattering in a double cladding optical fiber is studied with a continuous wave laser used as a pump source. Under various launch conditions, pump modes are differently excited. Considering the mode coupling effect among the pump modes, the evolution of the power in the Stokes modes is studied. The results show that the scattered waves （the Stokes waves） in the fiber core with 9%tm diameter and 0.14 NA could propagate predominantly in the fundamental mode of the fiber by carefully adjusting the pump light launching conditions.

Impairments Approximations in Assembled mmWave and Radio Over Fiber Network

The fiber nonlinearity and phase noise(PN)are the focused impairments in the optical communication system,induced by high-capacity transmission and high laser input power.The channels include high-capacity transmissions that cannot be achieved at the end side without aliasing because of fiber nonlinearity and PN impairments.Thus,addressing of these distortions is the basic objective for the 5G mobile network.In this paper,the fiber nonlinearity and PN are investigated using the assembled methodology of millimeter-wave and radio over fiber(mmWave-RoF).The analytical model is designed in terms of outage probability for the proposed mmWave-RoF system.The performance of mmWave-RoF against fiber nonlinearity and PN is studied for input power,output power and length using peak to average power ratio(PAPR)and bit error rate(BER)measuring parameters.The simulation outcomes present that the impacts of fiber nonlinearity and PNcan be balanced for a huge capacity mmWave-RoF model applying input power carefully.

A Nonlinear Mirror Structure to Improve the Performance of the Distributed Fiber Temperature Sensor Based on Raman Backscattering

A novel nonlinear mirror structure which can increase the optical signal-to-noise ratio of a distributed fiber Raman temperature sensor is proposed, and 6 dB improvement of the optical signal-to-noise ratio is obtained. With the assistance of the nonlinear mirror, we demonstrate that the spatial resolution of the sensor is improved from 3 m to 1 m, and the temperature accuracy is improved from ±0.6℃ to ±0.2℃. The theoretical analysis and the experimental data are in good agreement.

Wideband All-Polarization-Maintaining Yb-Doped Mode-Locked Fiber Laser Using a Nonlinear Optical Loop Mirror

We report on a wide-band and stable mode-locked all-polarization-maintaining fiber laser configuration using a nonlinear optical loop mirror. The central wavelength of the laser is 1080.14nm and the 3dB bandwidth is 20.29nm. The repetition rate of the pulse is 3.28 MHz and the pulse width is 848ps. By tuning the pump power, which is centered at 980nrn, from 300mW to 380mW, we obtain a linearly changed output power from 6row to 7.12roW. The all-polarization-mMntaining fiber configuration is fundamental to the stability of the output power.

Different supercontinuum generation processes in photonic crystal fibers pumped with a 1064-nm picosecond pulse

Picosecond pulse pumped supercontinuum generation in photonic crystal fiber is investigated by performing a series of comparative experiments. The main purpose is to investigate the supercontinuum generation processes excited by a given pump source through the experimental study of some specific fibers. A 20-W all-fiber picosecond master oscillator-power amplifier （MOPA） laser is used to pump three different kinds of photonic crystal fibers for supercontinuum generation. Three diverse supercontinuum formation processes are observed to correspond to photonie crystal fibers with distinct dis- persion properties. The experimental results are consistent with the relevant theoretical results. Based on the above analyses, a watt-level broadband white light supercontinuum source spanning from 500 nm to beyond 1700 nm is demonstrated by using a picosecond fiber laser in combination with the matched photonic crystal fiber. The limitation of the group velocity matching curve of the photonic crystal fiber is also discussed in the paper.

Pulse Propagation with Self-Phase Modulation in Nonlinear Chiral Fiber and Its Applications

From Maxwell＇s equations and Post＇s formalism, a generalized chiral nonlinear Schr6dinger equation （CNLSE） is obtained for the nonlinear chiral fiber. This equation governs light transmission through a dispersive nonlinear chiral fiber with joint action of chirality in linear and nonlinear ways. The generalized CNLSE shows a modu- lation of chirality to the effect of attenuation and nonlinearity compared with the case for a conventional fiber. Simulations based on the split-step beam propagation method reveal the role of nonlinearity with cooperation to chirality playing in the pulse evolution. By adjusting its strength the role of chirality in forming solitons is demonstrated for a given circularly polarized component. The application of nonlinear optical rotation is also discussed in an all-optical switch.

Cascaded four-wave mixing all-optical wavelength converter based on highly nonlinear fiber deposited graphene oxide

The all-optical wavelength conversion using cascaded four-wave mixing(FWM)phenomena with graphene oxide(GO)and a highly nonlinear fiber(HNLF)device is demonstrated experimentally.GO has a strong third-order nonlinear effect and is an excellent nonlinear optical material for nonlinear optical wavelength conversion.The group velocity matching of pump and signal,HNLF,and GO amplification promote the cascaded nonlinear frequency mixing process.From the experimental and analytical results,the maximum spacing between signal and pump is 21 nm,and specifically,the order of cascaded FWM light increases from order 1 to order 2 with increasing GO,and the first-order FWM conversion effi-ciency increases to a maximum of−14.5 dB.To the best of our knowledge,this is the first time that cascaded FWM-based all-optical wavelength conversion in HNLF-GO with wide wavelength selectivity is investigated with combined pump and signal light.Our findings not only provide an effective method for achieving all-optical wavelength conversion in cascaded FWM but also offer the possibility of fabricating high-performance nonlinear optical devices.

Single-mode output by controlling the spatiotemporal nonlinearities in mode-locked femtosecond multimode fiber lasers

The performance of fiber mode-locked lasers is limited due to the high nonlinearity induced by the spatial confinement of the single-mode fiber core.To massively increase the pulse energy of the femtosecond pulses,amplification is performed outside the oscillator.Recently,spatiotemporal mode-locking has been proposed as a new path to fiber lasers.However,the beam quality was highly multimode,and the calculated threshold pulse energy(>100 nJ)for nonlinear beam self-cleaning was challenging to realize.We present an approach to reach high energy per pulse directly in the mode-locked multimode fiber oscillator with a near single-mode output beam.Our approach relies on spatial beam self-cleaning via the nonlinear Kerr effect,and we demonstrate a multimode fiber oscillator with M^2<1.13 beam profile,up to 24 nJ energy,and sub-100 fs compressed duration.Nonlinear beam self-cleaning is verified both numerically and experimentally for the first time in a mode-locked multimode laser cavity.The reported approach is further power scalable with larger core sized fibers up to a certain level of modal dispersion and could benefit applications that require high-power ultrashort lasers with commercially available optical fibers.

Progressive collapse resisting capacity of reinforced concrete load bearing wall structures

Reinforced concrete(RC) load bearing wall is widely used in high-rise and mid-rise buildings. Due to the number of walls in plan and reduction in lateral force portion, this system is not only stronger against earthquakes, but also more economical. The effect of progressive collapse caused by removal of load bearing elements, in various positions in plan and stories of the RC load bearing wall system was evaluated by nonlinear dynamic and static analyses. For this purpose, three-dimensional model of 10-story structure was selected. The analysis results indicated stability, strength and stiffness of the RC load-bearing wall system against progressive collapse. It was observed that the most critical condition for removal of load bearing walls was the instantaneous removal of the surrounding walls located at the corners of the building where the sections of the load bearing elements were changed. In this case, the maximum vertical displacement was limited to 6.3 mm and the structure failed after applying the load of 10 times the axial load bored by removed elements. Comparison between the results of the nonlinear dynamic and static analyses demonstrated that the "load factor" parameter was a reasonable criterion to evaluate the progressive collapse potential of the structure.

Blind Nonlinearity Equalization by Machine-Learning-Based Clustering for QAM-Based Quantum Noise Stream Cipher Transmission

In quantum noise stream cipher(QNSC)systems,it is difficult to compensate fiber nonlinearity by digital signal processing(DSP)due to interactions between chromatic dispersion(CD),amplified spontaneous emission(ASE)noise from erbiumdoped fiber amplifier(EDFA)and Kerr nonlinearity.Nonlinearity equalizer(NLE)based on machine learning(ML)algorithms have been extensively studied.However,most NLE based on supervised ML algorithms have high training overhead and computation complexity.In addition,the performance of these algorithms have a lot of randomness.This paper proposes two clustering algorithms based on Fuzzylogic C-Means Clustering(FLC)to compensate the fiber nonlinearity in quadrature amplitude modulation(QAM)-based QNSC system,including FLC based on subtractive clustering(SC)and annealing evolution(AE)algorithm.The performance of FLC-SC and FLC-AE are evaluated through simulation and experiment.The proposed algorithms can promptly obtain suitable initial centroids and choose optimal initial centroids of the clusters to achieve the global optimal initial centroids especially for high order modulation scheme.In the simulation,different parameter configurations are considered,including fiber length,optical signal-to-noise ratio(OSNR),clipping ratio and resolution of digital to analog converter(DAC).Further-more,we measure the Q-factor of transmission signal with different launched powers,DAC resolution and laser linewidth in the optical back-to-back(BTB)experiment with 80-km single mode fiber.Both simulation and experimental results show that the proposed techniques can greatly mitigate the signal impairments.

Channel Capacity of DWDM Networks with Cross-phase Modulation Effect

In dense wavelength division multiplexing(DWDM) optical transmission systems, cross phase modulation(XPM) due to Kerr effect causes phase shift and intensity modulation in each channel, which will lead the channel capacity to be a random variable. An expression of the channel capacity dealing with XPM effect is presented, and the correctness and accuracy of this method are demonstrated by numerical simulation.

Compensating for Nonlinear Effects in Coherent-Detection Optical Transmission Systems

Fiber nonlinearity is one of the most important limiters of capacity in coherent optical communications. In this paper, we review two nonlinear compensation methods： digital backward propagation （BP） and nonlinear electrical equalizer （NLEE） based on the timedomain Volterra series. These compensation algorithms are implemented in a singlechannel 50 Gb/s coherent optical singlecarrier frequency division multiplexed （CO-SCFDM） system transmitting over 10 × 80 km of standard singlemode fiber （SSMF）.

Recent Progress in Distributed Optical Fiber Raman Photon Sensors at China Jiliang University

A brief review of recent progress in researches, productions and applications of full distributed fiber Raman photon sensors at China Jiliang University （CJLU） is presented. In order to improve the measurement distance, the accuracy, the space resolution, the ability of multi-parameter measurements, and the intelligence of full distributed fiber sensor systems, a new generation fiber sensor technology based on the optical fiber nonlinear scattering fusion principle is proposed. A series of new generation full distributed fiber sensors are investigated and designed, which consist of new generation ultra-long distance full distributed fiber Raman and Rayleigh scattering photon sensors integrated with a fiber Raman amplifier, auto-correction full distributed fiber Raman photon temperature sensors based on Raman correlation dual sources, full distributed fiber Raman photon temperature sensors based on a pulse coding source, full distributed fiber Raman photon temperature sensors using a fiber Raman wavelength shifter, a new type of Brillouin optical time domain analyzers （BOTDAs） integrated with a fiber Raman amplifier for replacing a fiber Brillouin amplifier, full distributed fiber Raman and Brillouin photon sensors integrated with a fiber Raman amplifier, and full distributed fiber Brillouin photon sensors integrated with a fiber Brillouin frequency shifter. The Internet of things is believed as one of candidates of the next technological revolution, which has driven hundreds of millions of class markets. Sensor networks are important components of the Internet of things. The full distributed optical fiber sensor network （Rayleigh, Raman, and Brillouin scattering） is a 3S （smart materials, smart structure, and smart skill） system, which is easy to construct smart fiber sensor networks. The distributed optical fiber sensor can be embedded in the power grids, railways, bridges, tunnels, roads, constructions, water supply systems, dams, oil and gas pipelines and other facilities, and can be integrated with wireless networks.

Amplification and Compression of Ultrashort Fundamental Solitons in An Erbium-Doped Nonlinear Amplifying Fiber Loop Mirror

A nonlinear amplifying loop mirror constructed from erbium-doped fiber is proposed for simultaneous amplification and compression of ultrashort fundamental solitons. Numerical simulations show that, the proposed device performs efficient high-quality amplification and compression of solitons.

Noise-like pulse generation from a thulium-doped fiber laser using nonlinear polarization rotation with different net anomalous dispersion

A mode-locked thulium-doped fiber laser(TDFL) based on nonlinear polarization rotation(NPR) with different net anomalous dispersion is demonstrated. When the cavity dispersion is-1.425 ps^2, the noise-like(NL) pulse with coherence spike width of 406 fs and pulse energy of 12.342 nJ is generated at a center wavelength of 2003.2 nm with 3 dB spectral bandwidth of 23.20 nm. In the experimental period of 400 min, the 3 dB spectral bandwidth variation, the output power fluctuation, and the central wavelength shift are less than 0.06 nm, 0.04 d B, and0.4 nm, respectively, indicating that the NPR-based TDFL operating in the NL regime holds good long-term stability.

Recent progress on optical rogue waves in fiber lasers:status,challenges,and perspectives

Rogue waves(RWs)are rare,extreme amplitude,localized wave packets,which have received much interest recently in different areas of physics.Fiber lasers with their abundant nonlinear dynamics provide an ideal platform to observe optical RW formation.We review recent research progress on rogue waves in fiber lasers.Basic concepts of RWs and the mechanisms of RW generation in fiber lasers are discussed,along with representative experimental and theoretical results.The measurement methods for RW identification in fiber lasers are presented and analyzed.Finally,prospects for future RW research in fiber lasers are summarized.

Fiber soliton-form 3R regenerator and its performance analysis

A novel fiber optical 3R regenerator based on optical soliton-effect using highly nonlinear fiber is constructed and investigated for the needs of the high rate and long-haul optical communications. The propagation equation of the pulses in the proposed optical 3R regenerator with the control of optical modulator and filter is established. By the use of the variational approach, the evolution of the distorted optical pulses in the regenerator and the functions of reamplification, reshaping, and reUming are investigated. The relation between the construction parameters and the output performance of the regenerator is discussed. The stable operation condition of the regenerator is revealed.