Nonlinear Fiber Optics Research Papers (original) (raw)

Purposeto introduce the Innovative Electronics Manufacturing Research Centre (IeMRC) Flagship Project: Integrated Optical and Electronic Interconnect PCB Manufacturing (OPCB), its objectives, its consortium of 3 Universities and 10 companies and to describe the university research being carried out. This paper briefly reviews the motivation for developing novel polymer formulations, fabrication techniques, layout design rules and characterisation techniques for hybrid electronic and optical printed circuit boards using multimode polymer optical waveguide interconnects.

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- Nonlinear Fiber Optics, Laser, Computer Aided Design, Optical Waveguides

We demonstrate that the inherent nonlinearity of a microstructured optical fiber (MOF) may be used to achieve label-free selective biosensing, thereby eliminating the need for post-processing of the fiber. This first nonlinear biosensor utilizes a change in the modulational instability (MI) gain spectrum (a shift of the Stokes-or anti-Stokes wavelength) caused by the selective capture of biomolecules by a sensor layer immobilised on the walls of the holes in the fiber. We find that such changes in the MI gain spectrum can be made detectable, and that engineering of the dispersion is important for optimizing the sensitivity. The nonlinear sensor shows a sensitivity of around 10.4nm/nm, defined as the shift in resonance wavelength per nm biolayer, which is a factor of 7.5 higher than the hitherto only demonstrated label-free MOF biosensor.

- by Per Rasmussen
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- Optics, Nonlinear Fiber Optics, Nonlinear dynamics, Computer Aided Design
- by Peter Horak
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- Nonlinear Fiber Optics, Nonlinear Optics, Supercontinuum Generation

ABSTRACT: The guided, single-mode propagation of ultrashort optical pulses is commonly described by a well studied and understood generalized nonlinear Schrödinger equation. Here we present and discuss an extended version for multimode optical fibers and waveguides including polarization effects, high-order dispersion, Kerr and Raman nonlinearities, self-steepening effects, as well as wavelength-dependent mode coupling and nonlinear coefficients. We then investigate the symmetry properties of the nonlinear coupling coefficients for the cases of step-index and circularly symmetric conventional fibers and for microstructured fibers with hexagonal symmetry. Finally, we study the computational complexity of the proposed algorithm.

- by Francesco Poletti
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- Nonlinear Fiber Optics

We solve a system of generalized nonlinear Schr¨ odinger equations to study the nonlinear dynamics of ultrashort pulse propagation in multimode fibers. Due to pulse walk-off, permanent intermodal power transfer between modes is observed even in absence of phase matching. The strength of intermodal effects is found to depend strongly on modal symmetries, which results in preferential coupling between the LP_0n modes. The scaling of nonlinear multimode effects in large-core fibers for the generation of ultra-high power ...

We investigate dark-bright vector solitary wave solutions to the coupled non-linear Schrödinger equations which describe an inhomogeneous two-species Bose-Einstein condensate. While these structures are well known in non-linear fiber optics, we show that spatial inhomogeneity strongly affects their motion, stability, and interaction, and that current technology suffices for their creation and control in ultracold trapped gases. The effects of controllably different interparticle scattering lengths, and stability against three-dimensional deformations, are also examined.

- by James Anglin
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- Nonlinear Fiber Optics, Physical sciences, Three Dimensional, Fiber Optic
- by Mohammed Abdullah
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- Nonlinear Fiber Optics

We solve a system of generalized nonlinear Schr¨odinger equations to study the nonlinear dynamics of ultrashort pulse propagation in multimode fibers. Due to pulse walk-off, permanent intermodal power transfer between modes is observed even in absence of phase matching. The strength of intermodal effects is found to depend strongly on modal symmetries, which results in preferential coupling between the LP0n modes. The scaling of nonlinear multimode effects in large-core fibers for the generation of ultra-high power spectral density supercontinua is finally discussed.

ABSTRACT: We study various fiber designs which incorporate a highly nonlinear liquid, carbon disulfide, with the aim of designing a structure with the highest possible nonlinearity and at the same time a low and flattened dispersion at telecom wavelengths, as required for many all-optical processing devices. We observe that soft glass-based fibers cannot fully exploit the high nonlinearity of carbon disulfide, whereas a silica microstructured fiber with a selectively filled core allows excellent dispersion control and a nonlinear coefficient in excess of 6500 W-1middotkm-1 at telecoms wavelengths.

- by Francesco Poletti
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- Nonlinear Fiber Optics
- by F. Anibal Fernandez
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- Nonlinear Fiber Optics, Laser, Computer Aided Design, Integrated Optics

A 40-Gb/s wavelength converter based on cross-phase modulation in a dispersion-shifted fiber has been investigated through pulse measurements and simulation. The most important parameter is the dispersive walkoff, which makes the required input power wavelength dependent and determines the optical bandwidth. Simulations show the feasability of the 160-Gb/s operation by using 2-ps pulses and a highly nonlinear dispersion-shifted fiber.

- by Daniel Blumenthal
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- Nonlinear Fiber Optics, Nonlinear Optics, Simulation, Optical network

An integrated configuration is proposed to convert tunable slow light from signal to another frequency in a wide bandwidth by using a 70 m-long highly nonlinear photonic crystal fiber (HN-PCF). A 10 GHz RZ signal is delayed by a 10 Gbit/s 2 31 1 pseudo random bit sequence (PRBS) stimulated Brillouin scattering (SBS) pump, and the slow light is converted to another frequency in a broadband by four-wave mixing (FWM). By this way, not only the slow light is converted, but the idler power is enhanced greatly. In our experiment, all-optical controlled 37.5 ps delay time is converted in a 40 nm bandwidth flatly, and 4.7 dB idler power is enhanced simultaneously. The experimental results are in good agreement with those of the theory.

- by Gaoxi Xiao
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- Optics, Medical Imaging, Nonlinear Fiber Optics, Fiber Optics

ABSTRACT: We design a number of index-guiding holey fibers with relatively simple structure which possess suitable dispersive properties for the observation of soliton spectral tunneling. Although the fabrication tolerances for these fibers are demanding, numerical simulations show that tunneling across a normal dispersion region of 150 nm width when pumped in the near infrared is in principle possible using just a few meters of these fibers

- by Francesco Poletti
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- Nonlinear Fiber Optics, Optical Soliton

We have simulated the behaviors of nonlinear fiber Bragg gratings (FBGs). The generalized nonlinear equations governing these structures are solved by a method which uses a Fourier series procedure and a simple iterative method. All of the nonlinear effects are considered. Bragg soliton generation in intrinsic media and birefringence effects in FBGs are studied. We found that the first order dispersion can causes time shifting in the input pulse peak. It is shown that FBGs are proper for optical switching too. They can use in filters, nonlinear fiber optical applications, soliton propagations etc.

- by amir hosein jafari
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- Nonlinear Fiber Optics, Optical Switch, Fiber Bragg grating, First-Order Logic

A simple reconfigurable all-optical logic gate based on cross-phase modulation in highly nonlinear fibers is numerically demonstrated. Fine performance at 160 Gb/s is obtained for five logic functions (XOR, OR, NAND, NOR and NOT). The implementation simplicity and the high-bit-rate operation make the proposed device suitable for ultrafast applications in the emerging all-optical networks.

In this paper cross-phase modulation (XPM) and its impact on multispan NRZ-modulated wavelength division multiplexing (WDM) systems is examined. An analytical model is presented to assess the signal degradation. The impairments due to XPM are related to a Q-factor. The presented formulas are examined for different dispersion compensation schemes and also mixed-fiber systems. The analytical models are verified by system

Development of All-Optical Logic functions for All-Optical Signal Processing, have attracted considerable interest in recent years. Efforts have been made to realize All-Optical Logic devices utilizing several non-linear effects and Interferometric configurations such as Mach-Zehnder Interferometer (MZI), Ultrafast Non-Linear Interferometer (UNI) & Sagnac Interferometers. Out of all Interferometric configurations, All-Optical logic devices based on Sagnac Interferometer are attractive, due to their ability to operate at high bit rates & low latency. This paper is an overview of Sagnac Interferometer fundamentals & its variants. All-Optical Binary as well as Multi-Valued (MV) Logic devices based on Sagnac Interferometers are also illustrated.

We investigate numerically the compression of femtosecond solitons at 1.55-m wavelength propagating in holey fibers which exhibit simultaneously decreasing dispersion and effective mode area. We determine optimal values of holey fiber parameters and fiber lengths for soliton compression in the adiabatic and nonadiabatic regimes. Compression factors in excess of ten are found for fibers as short as a few meters.

- by Peter Horak
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- Nonlinear Fiber Optics, Pulse Compression, Optical physics, Optical Soliton

We report on a theoretical and experimental characterization of polarization-dependent four-wave mixing processes in highly nonlinear optical fibers. Two or three idler waves at different polarizations are experimentally generated in an optical fiber from the propagation of two wavelength-detuned, orthogonally-polarized pumps and a signal. Each idler wave results from a different four-wave mixing process involving the signal and one or both pumps. Orthogonally-polarized idler waves are demultiplexed in a polarization beam splitter with a cross-polarization suppression of over 17 dB. The parametric process equations for this system are analytically solved and the efficiencies of the competing processes analyzed for the small pump detunings and identical pump powers. This experimental setup can be used in telecommunication systems for producing and selectively rerouting various copies of a data signal.

- by Anderson Gomes
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- Nonlinear Fiber Optics, Nonlinear Optics, Optical physics, Four Wave Mixing

Fiber optic systems area unit vital telecommunication infrastructure for worldwide broadband networks. Wide information measure signal transmission with low delay could be a key demand in gift day applications. Optical fibers give huge and unexceeded transmission information measure with negligible latency, and area unit currently the transmission medium of alternative for long distance and high rate transmission in telecommunication networks. This paper offers an outline of fiber optic communication systems together with their key technologies, and conjointly discusses their technological trend towards future generation.

- by Francis Idachaba
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- Engineering, Computer Science, Nonlinear Fiber Optics, Fiber Optics

A finite-band noise model for degenerate four-wave mixing (FWM) including channel walk-off in return-to-zero ON-OFF-keying (RZ-OOK) transmission is extended to include nondegenerate FWM (ND-FWM). The model is verified by comparing the results for the noise variance for each type of FWM to split-step-Fourier (SSF) simulations for a 10-Gb/s single span link, and excellent agreement is obtained. A physical interpretation of the walk-off effect on the FWM noise is formulated in terms of intracollision and intercollision interference of the corresponding generated FWM waves. The author shows that the walk-off effect modifies the FWM noise power spectral density only at high frequencies by producing distinct peaks at locations determined by the channel spacing. In principle, the walk-off effect significantly increases the noise variance for both types of FWM before any filtering at the end of fiber. Upon demultiplexing, it is found that the walk-off effect is significant and observable for the degenerate FWM case but is no longer significant for the ND-FWM case. When a sub-bit-rate electrical filter is used in the receiver, the walk-off effect becomes insignificant for all types of FWM. They systematically conclude that the walk-off effect is unimportant for FWM in typical RZ-OOK systems when tight electrical filtering is used. They also illustrate the accuracy of the model for the more general case where more than one FWM tone is coincident on a probe channel by comparing the analytic model to SSF simulations for a five-channel example.

- by shiva kumar
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- Medical Imaging, Nonlinear Fiber Optics, Fiber Optics, Modeling

The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.

- by Robert Rice
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- Thermodynamics, Nonlinear Fiber Optics, Crystal Growth, Kinetics

Recently we proposed using periodically spaced, phase-sensitive optical parametric amplifiers to balance linear loss in a nonlinear fiber-optic communication line [Opt. Lett. 18, 803 (1993)]. We present a detailed analysis of pulse propagation in such a fiber line. Our analysis and numerical simulations show that the length scale over which the pulse evolution occurs is significantly increased beyond a soliton period. This is because of the attenuation of phase variations across the pulse's profile by the amplifiers. Analytical evidence is presented that indicates that stable pulse evolution occurs on length scales much longer than the soliton period. This is confirmed through extensive numerical simulation, and the region of stable pulse propagation is found. The average evolution of such pulses is governed by a fourth-order nonlinear diffusion equation, which describes the exponential decay of arbitrary initial pulses into stable, steady-state, solitonlike pulses.

- by Prem Kumar
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- Applied Mathematics, Nonlinear Fiber Optics, Nonlinear Optics, Optical Communication

We report an original noise-like pulse dynamics observed in a figure-eight fiber laser, in which fragments are continually released from a main waveform that circulates in the cavity. Particularly, we report two representative cases of the dynamics: in the first case the released fragments drift away from the main bunch and decay over a fraction of the round-trip time, and then vanish suddenly; in the second case, the sub-packets drift without decaying over the complete cavity round-trip time, until they eventually merge again with the main waveform. The most intriguing result is that these fragments, as well as the main waveform, are formed of units with sub-ns duration and roughly the same energy.

- by Olivier Pottiez
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- Nonlinear Fiber Optics

We show theoretically that nonlinear optical media characterized by a finite response time may support the existence of discrete spectral incoherent solitons. The structure of the soliton consists of three incoherent spectral bands that propagate in frequency space toward the low-frequency components in a discrete fashion and with a constant velocity. Discrete spectral incoherent solitons do not exhibit a confinement in the space-time domain, but exclusively in the frequency domain. The kinetic theory describes in detail all the essential properties of discrete spectral incoherent solitons: A quantitative agreement has been obtained between simulations of the kinetic equation and the nonlinear Schrödinger equation. Discrete spectral incoherent solitons may be supported in both the normal dispersion regime or the anomalous dispersion regime. These incoherent structures find their origin in the causality condition inherent to the nonlinear response function of the material. Considering the concrete example of the Raman effect, we show that discrete incoherent solitons may be spontaneously generated through the process of supercontinuum generation in photonic crystal fibers.

- by antonio picozzi
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- Nonlinear Fiber Optics, Wave Energy, Nonlinear Optics, Wave turbulence

The understanding and development of 160-Gb/s transmission systems requires the study of the impact of different dispersion compensation schemes on pulse propagation in nonlinear fiber. In this paper, we present an investigation of 160-Gb/s optical transmission systems, focusing on optimal propagation regimes, and in particular, we analyze different transmission limitations and dominant nonlinear effects by comparing quasi-linear and dispersion managed soliton systems. Two quasi-linear systems, one using nonzero dispersion-shifted fiber (NZDSF) and the other single-mode fiber (SMF), and one short-period (1 km) dispersion managed soliton (DMS) system are studied, both for single-channel and wavelength-division-multiplexed (WDM) transmission. First, the performance of the two quasi-linear systems in single-channel transmission are compared and it is shown that the NZDSF and SMF systems allow similar error-free transmission distances with only small differences in the intrachannel four-wave mixing (IFWM) induced amplitude jitter. The effect of pulsewidth on transmission performance in this regime was investigated and the use of shorter pulses was found to result in lower amplitude jitter. We analyzed the behavior of the DMS system and showed that the reduced pulse broadening during transmission allowed a significantly longer single-channel transmission distance with a smaller impact of nonlinearities compared to quasi-linear propagation. The sensitivity of the DMS system performance to statistical fluctuations in the fiber dispersion was studied and the results show the level of accuracy in the dispersion management map which must be ensured in these systems. Finally, the performance of the DMS in WDM transmission was investigated and it was found that it was subject to very large penalties increasing the minimum channel spacing possible because of the strong impact of interchannel cross-phase modulation (XPM).

In this paper, we report the design of a highly nonlinear dispersion flattened high-index-core square photonic crystal fiber (PCF) for applications in optical coherence tomography (OCT). The finite-difference method with an anisotropic perfectly matched boundary layer is used as a numerical simulation tool. A set of optimized design parameters numerically resulted in a nonlinear coefficient of 79.9 W À1 km À1 and a dispersion of À0:186 ps/(nmÁkm) at a wavelength of approximately 1.06 mm. Owing to its high nonlinear coefficient and flattened dispersion, the PCF is expected to be suitable for broadband supercontinuum generation, which is considered very important in OCT medical applications. #

- by Abdur Razzak
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- Nonlinear Fiber Optics, Nonlinear Optics, Numerical Simulation, Optical

A method for fabrication of a new type of optical fiber with dispersion varying along the fiber length is described. The main optical parameters of a drawn fiber are theoretically studied and experimentally measured. These fibers are of great interest for nonlinear fiber optics. Such applications of the fibers, such as high-quality soliton pulse compression, soliton pulsewidth stabilization through compensation of losses, and generation of a high-repetition-rate train of practically uninteracting solitons, are considered.

- by Sergey Semenov
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- Nonlinear Fiber Optics, Pulse Compression, Optical physics, Optical fiber

- by Dimitris Syvridis
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- Nonlinear Fiber Optics, Nonlinear Optics, Optical physics, Logic Gates

- by prem kumar
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- Applied Mathematics, Nonlinear Fiber Optics, Nonlinear Optics, Optical Communication

In this paper we propose a method which provides a full description of solitary wave solutions of the Schrödinger equation with periodically varying dispersion. This method is based on analysis and polynomial deformation of the spectrum of an iterative map. Using this method we discover a new family of antisymmetric bisoliton solutions. In addition to the fact that these solutions are of interest for nonlinear fiber optics and the theory of nonlinear Schrödinger equations with periodic coefficients, they have potential applications for increasing of bit-rate in high speed optical fiber communications.

- by Misha Stepanov
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- Applied Mathematics, Nonlinear Fiber Optics, High Speed, Spectrum

We propose and demonstrate a simple scheme of a highly efficient polarization-independent wavelength converter utilizing the two-pump fiber optical parametric amplification. First, binary phase-shift-keying modulation is applied to two pump waves, which allows us to suppress stimulated Brillouin scattering without broadening the idler spectrum. Then, polarization states of the two pumps are aligned orthogonally to realize the wavelength conversion which is insensitive to the signal polarization. Using this method, we achieve polarization-independent wavelength conversion with an efficiency larger than 0 dB over a 30-nm signal bandwidth.

We study the Brillouin scattering behavior in several single-mode fibers with different waveguide characteristics in terms of their longitudinal mode structures in the gain spectrum, linewidth narrowing, and stimulated Brillouin scattering (SBS) threshold levels. Evolution from spontaneous to SBS is investigated by monitoring the Brillouin line-shape and the behavior of the longitudinal acoustooptic resonance modes that exist in the core. We compare our results with the current theory of Brillouin scattering generated from noise in the undepleted pump approximation. We also present experimentally Brillouin gain spectra in the highly depleted pump regime, where there is no analytical solution, by showing the evolution of the gain spectrum as a function of the injected laser intensity.

This work focuses on a secondary pumping scheme for remote L-band erbium-doped fiber amplifier (R-EDFA) generated by integrating Rayleigh-based ultralong Raman fiber laser (ULRFL) with a section of passive erbium-doped fiber (EDF). A selective wavelength reflector combined with Rayleigh feedback in the transmission span forms the ULRFL cavity while the passive EDF deployed at the end of the span converts the ULRFL into a secondary C-band pump. Optimum ULRFL wavelength is determined by tuning the selective wavelength reflector across the C-band region. Combination of R-EDFA gain, Raman amplification, and passive EDF provides gain improvement as high as 15.5 dB over conventionally pumped R-EDFA with minimal optical signal-to-noise ratio penalty.

Recent adaptive holographic equalization experiments in multimode fiber demonstrate the advantage of the rapid reconfiguration speed of the spatial light modulator in mitigating modal dispersion, the principal source of bandwidth limitation in MMF. Despite the suppression of a large number of modes, power modal coupling still manifests within the channel. In this paper, a noninterferometric modal decomposition technique was adapted for quantifying the amount of power modal coupling between the modes, for a holographic equalization experiment with a priori modal electric field input. The derivation of the objective function, simulation of binarized holograms and experimental work on intensity measurements at the MMF output are presented.

- by Ruo Ding Li
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- Applied Mathematics, Nonlinear Fiber Optics, Nonlinear Optics, Optical Communication

We consider the long-term evolution of a random nonlinear wave that propagates in a multimode optical waveguide. The optical wave exhibits a thermalization process characterized by an irreversible evolution toward an equilibrium state. The tails of the equilibrium distribution satisfy the property of energy equipartition among the modes of the waveguide. As a consequence of this thermalization, the optical field undergoes a process of classical wave condensation, which is characterized by a macroscopic occupation of the fundamental mode of the waveguide. Considering the nonlinear Schrödinger equation with a confining potential, we formulate a wave turbulence description of the random wave into the basis of the eigenmodes of the waveguide. The condensate amplitude is calculated analytically as a function of the wave energy, and it is found in quantitative agreement with the numerical simulations. The analysis reveals that the waveguide configuration introduces an effective physical frequency cutoff, which regularizes the ultraviolet catastrophe inherent to the ensemble of classical nonlinear waves. The numerical simulations have been performed in the framework of a readily accessible nonlinear fiber optics experiment.

- by Valérie Doya
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- Physics, Nonlinear Fiber Optics, Wave Energy, Nonlinear Optics

All-optical data processing is expected to play a major role in future optical communications. The fiber nonlinear optical loop mirror (NOLM) is a valuable tool in optical signal processing applications. This paper presents an overview of our recent advances in developing NOLM-based all-optical processing techniques for application in fiber-optic communications. The use of in-line NOLMs as a general technique for all-optical passive 2R (reamplification, reshaping) regeneration of return-to-zero (RZ) on-off keyed signals in both high-speed, ultralong-distance transmission systems and terrestrial photonic networks is reviewed. In this context, a theoretical model enabling the description of the stable propagation of carrier pulses with periodic all-optical self-regeneration in fiber systems with in-line deployment of nonlinear optical devices is presented. A novel, simple pulse processing scheme using nonlinear broadening in normal dispersion fiber and loop mirror intensity filtering is described, and its employment is demonstrated as an optical decision element at a RZ receiver as well as an in-line device to realize a transmission technique of periodic all-optical RZ-nonreturn-to-zero-like format conversion. The important issue of phase-preserving regeneration of phase-encoded signals is also addressed by presenting a new design of NOLM based on distributed Raman amplification in the loop fiber.

We analyze the performance of a recently proposed multichip differential phase-shift-keying (DPSK) format over the nonlinear fiber-optic channel. For a single wavelength nonlinear phase-noise-limited channel, a multichip DPSK receiver based on a three-chip observation can attain more than two orders of magnitude bit-error-rate reduction relative to a standard DPSK receiver, or equivalently 1-dB improvement in -factor, significantly exceeding the 0.2-dB improvement achieved by the same format over a linear optical channel.

- by Moshe Nazarathy
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- Nonlinear Fiber Optics, Nonlinear Optics, Q factor, Bit Error Rate

- by Stanislav Chernikov
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- Nonlinear Fiber Optics, Pulse Compression, Optical physics, Optical fiber

Photonic crystal fibers (PCFs) have had a substantial impact on nonlinear fiber optics and shortpulsed fiber laser systems due to their novel dispersion properties. The large normal or anomalous waveguide dispersion available in such fibers opens up a number of new opportunities not accessible with standard fiber technology. In this contribution, the fundamentals of PCF dispersion are briefly reviewed along with earlier results. In addition, some of our recent work on dispersion tailoring to facilitate nonlinear processes, and dispersion control in lasers will be presented.

- by Morten Bache
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- Nonlinear Fiber Optics, Topology Optimization, Finite Element, Fiber Laser

There have been numerous attempts to determine the channel capacity of a nonlinear fiber-optic communication channel. The main approach was to consider amplified spontaneous emission (ASE) noise as a predominant effect and to observe the fiber nonlinearities as the perturbation of a linear case or as the multiplicative noise. In this paper, the achievable information rates for high-speed optical transmission (40 Gb/s and above) are calculated using the finite-state-machine approach. In calcu-

- by M. Ivkovic and +1
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- Optics, Technology, Medical Imaging, Nonlinear Fiber Optics

In order to overcome the bit-rate limitations caused by Electronic Signal Processing, All-Optical
Signal Processing is required. All-Optical Half-Adder and Half-Subtracter can serve as building
blocks for All-Optical Arithmetic Logic Unit (ALU). In this paper, a demonstration of All-Optical
Half-Adder and Half-Subtracter is done operating at 1 Gbps bit rate using Continuous Wave
(CW) Lasers as carrier sources and two Semiconductor Optical Amplifiers (SOA) as basic active
elements. One of the arithmetic functions realized by this scheme i.e. Borrow Signal (A¯B)
exhibited Max Q-factor of 21.2046 to achieve error free operation at bit rate of 1Gbps.

The Helmholtz equation for the propagation of an e.m. wave in a self-focusing fiber is reduced to a Pauli-type two-component equation in the paraxial approximation. The fiber spinor components are then shown to be related to the ray height and reduced slope. Finally, comments on the meaning of the paraxial approximation are presented.
In questo lavoro si dimostra come sia possibile ridurre l’equazione di Helmholtz in approssimazione parassiale e per una fibra autofocheggiante, ad un’equazione a due componenti di tipo Pauli. Si dimostra inoltre che le componenti dello spinore di fibra sono l’altezza parassiale e la cosiddettapendenza ridotta. Infine si discute una possibile estensione relativistica della teoria sviluppata.
Уравхение Гельмгольца для распространения электромагнитной волны в самофокусирующей нити сводится к двух-компонентному уравнению типа Паули в параксиальном проиближении. Эатем показывается, что волоконно-спинорные компоненты связаны с амплитудой луча и приведенным наклоном. Обсуждается Физический смысл парсиального приближения.

This paper demonstrates a method to remove the gain ripple profile specifically for a two-segment fiber optical parametric amplifier arising from the dispersion differences between the fiber gain medium and the standard single mode fiber attached to the optical components. This is achieved by using a simple design that incorporates a gain smoothening filter at the mid-stage of the amplifier. This simple yet practical method is useful when isolators are adopted for stimulated Brillouin scattering suppression but it comes with the expense of parametric gain.