The propagation of intense ultra-short optical pulses in a Kerr medium such as an optical fibre still remains a critical issue for the performance of many optical systems such as beam delivery, optical communication or pulse amplification systems. This is because the self-phase modulation (SPM) of the propagating pulse usually causes a broadening of the pulse spectrum that is typically accompanied by an oscillatory structure covering the entire frequency range. Several strategies have been proposed and successfully deployed to counteract the deleterious effects of SPM in fibre-optic systems. These include spatial or temporal scaling to reduce the impact of nonlinearity via the use of very large mode area fibres or chirped pulse amplification. A different class of approaches relies on the exploitation of the peculiar properties of parabolic shaped pulses and self-similar evolution, the use of other types of pre-shaped input pulses, and the compensation of nonlinear phase shifts with third-order dispersion. However, none of these last techniques preserves the pulse temporal duration.
A simple technique to compensate the nonlinear phase due to SPM and related spectrum broadening of nanosecond or picosecond optical pulses consists in using an electro-optic phase modulator to impart the opposite phase to the pulses. This method, which emulates the use of a material with a negative nonlinear index of refraction, has proved successful in fibre-optic and free-space optical telecommunication applications using phase-shift keying systems and in the generation of high-peak-power nanosecond pulses.
We have recently experimentally demonstrated that for Gaussian shaped input pulses, the use of a simple sinusoidal drive signal for the phase modulator with appropriate amplitude and frequency is sufficient to reduce the nonlinear spectrum broadening to a large degree, and to significantly enhance the spectral quality of the pulses while their temporal duration remains unaffected. In this paper, we present a comprehensive analysis of the SPM-mitigation method involving the use of a sinusoidal phase modulation. Most of the previous works are primarily experimental in nature and have not discussed the sensitivity of the technique to the initial pulse characteristics.
First, we recall the concept of our method and overview our proof-of-principle experiment. Next, we derive an exact closed formula for the rms spectral width of an initially Gaussian pulse after undergoing SPM and with the corrective phase applied, which confirms the substantial reduction of the SPM-induced spectrum broadening attainable with the phase compensation. Then, we describe the impact of the initial pulse shape and duration on the effectiveness of the technique through numerical simulation of the governing equation. We show that for hyperbolic secant pulses, optimisation of the parameters of the modulating sinusoid through a scan of the amplitude-frequency space outperforms the parameter choice based on simple analytic guidelines. By varying the initial pulse duration across an order of magnitude, we highlight the significant differences in performance between pre- and post-propagation compensation schemes, and show that remarkable SPM mitigation is attainable even in the presence of non-negligible fibre dispersion.
A series of waveguides were inscribed in lithium niobate by tightly focused femtosecond-laser pulses of 11-MHz repetition rate and 790-nm wavelength. To establish the inscription conditions for optimal low-loss waveguides, within each sample we varied laser pulse energy, speed and direction of translation stage movement, and focus depth of the beam. We deployed two new approaches to enhance the inscription results: 1) increase of the pulse energy with increasing focus depth inside the material to compensate for the corresponding decrease of refractive-index modification, and 2) decrease of the laser energy for the modification tracks closer to the waveguide’s core region to reduce scattering losses due to high-laser-energy driven non-uniformities. All waveguides had an optical-lattice-like hexagonal packing geometry with track-spacing of 9.9 μm (optimized for effective suppression of high-order modes). Each structure comprised 84 single-scan Type-II-modification tracks, aligned with the crystalline X-axis of lithium niobate. After heat treatment at 350 °C for 3 hours, the lowest propagation loss of less than (0.4±0.1) dB/cm and (3.5±0.3) dB/cm for the ordinary and extraordinary light polarization states, respectively, were achieved at the 1550- nm wavelength. These low-attenuation waveguides were obtained with the inscription energy varying between 50.6 nJ and 53.6 nJ and the translation speed of 10 mm/s. The corresponding refractive-index contrast of individual tracks was (–1.55±0.04)×10-3 . The waveguides also showed low attenuation in the visible and near-infrared portion of the spectrum (532 nm to 1456 nm). Our results offer promising means for the development of low-loss waveguides with preserved-nonlinearity and high thermal stability.
We show both numerically and experimentally that dispersion management can be realized by manipulating the dispersion of a filter in a passively mode-locked fibre laser. A programmable filter the dispersion of which can be software configured is employed in the laser. Solitons, stretched-pulses, and dissipative solitons can be targeted reliably by controlling the filter transmission function only, while the length of fibres is fixed in the laser. This technique shows remarkable advantages in controlling operation regimes in ultrafast fibre lasers, in contrast to the traditional technique in which dispersion management is achieved by optimizing the relative length of fibres with opposite-sign dispersion. Our versatile ultrafast fibre laser will be attractive for applications requiring different pulse profiles such as in optical signal processing and optical communications.
We present a perturbation analysis that describes the effect of third-order dispersion on the similariton pulse solution
of the nonlinear Schr¨odinger equation in a fibre gain medium. The theoretical model predicts with sufficient
accuracy the pulse structural changes induced, which are observed through direct numerical simulations.
Considering a numerical example, we analyse the performance of Return-to-Zero (RZ) Differential Phase Shift Keyed (DPSK) transmission when deployed in a large scale transmission system. It is shown that at high distances, RZ-DPSK performs well whilst being limited by nonlinear effects. We also show that when nonlinear effects become dominant, we can still estimate channel statistics to reasonable accuracy.
We present a simplified model for a simple estimation of the eye-closure penalty for amplitude noise-degraded signals.
Using a typical 40-Gbit/s return-to-zero amplitude-shift-keying transmission, we demonstrate agreement between the
model predictions and the results obtained from the conventional numerical estimation method over several thousand
Applying direct error counting, we assess the performance of 20 Gbit/s wavelength-division multiplexing return-to-zero differential phase-shift keying (RZ-DPSK) transmission at 0.4 bit/(s Hz) spectral efficiency for application on installed non-zero dispersion-shifted fibre based transoceanic submarine systems. The impact of the pulse duty cycle on the system performance is investigated and the reliability of the existing theoretical approaches to the BER estimation for the RZ-DPSK format is discussed.
A novel all-optical time domain regeneration technique using nonlinear pulse broadening and flattening in normal dispersion fiber and subsequent temporal slicing by an amplitude modulator (or a device performing a similar function) is proposed. Substantial suppression of the timing jitter of jitter-degraded optical signals is demonstrated using the proposed approach.
A theoretical model is developed to describe the propagation of ultra-short optical pulses in fiber transmission systems in the quasi-linear regime, with periodically inserted in-line lumped nonlinear optical devices. Stable autosoliton solutions are obtained for a particular application of the general theory.
We describe the linear and nonlinear transfer characteristics of a multi-resonance optical device consisting of two ring resonators coupled one to another and to a waveguide. The propagation effects displayed by the device are compared with those of a sequence of a waveguide-coupled fundamental ring resonators.