Jan Litvik

Influence of nonlinear effects in WDM system with non-equidistant channel spacing using different types of high-order PSK and QAM modulation formats

The objective of this paper is to investigate nonlinear effects in Wavelength-Division Multiplex (WDM) systems in the case when different types of high-order M-PSK and M-QAM modulation formats for various structures of channel spacing are used optical signals. In general, the degradation mechanisms are caused by transmitted optical signals and their impact on each optical channel in WDM can be very different. Therefore, it is suitable to investigate possibilities for channel arrangement from the point of view of equidistant and non-equidistant channel spacing, respectively, what would lead to the suppression of nonlinear effects. In this article we investigate new types of high-order modulation formats that have ability for increasing of spectral efficiency and total improvement of performance of the transmission WDM system. The attention is put on two classes of channel spacing in WDM system, equidistant channel spacing (Δf = 100, 50, 25 and 12.5 GHz) and non-equidistant channel spacing (Δf ≠ const.), respectively. For investigation of signal propagation the numerical model is created. The model is based on mathematical method Symmetrical-Split Step Fourier Method (S-SSFM), which is utilized for solving the coupled nonlinear Schrödingers equations (CNLSE) describing the transmission of signals in multichannel systems. The results of the created numerical model are analyzed, compared to each other and interpreted in a way that leads to the determination of suitable high-order modulation formats and we try to propose the optimal arrangement of optical channels in WDM system. The key issue is to suppress the impact of nonlinearities on modulated signals for each channel with respect to the employed types of digital modulation formats, various system parameters, different types of optical fibers and localization of reference channel in the wavelength area.

Design of narrowband Bragg spectral filters in subwavelength grating metamaterial waveguides

Properties of reflection and transmission spectral filters based on Bragg gratings in subwavelength grating (SWG) metamaterial waveguides on silicon-on-insulator platform have been analyzed using proprietary 2D and 3D simulation tools based on Fourier modal method and the coupled-mode theory. We also demonstrate that the coupled Bloch mode theory can be advantageously applied to design of Bragg gratings in SWG waveguides. By combining different techniques, including judiciously positioning silicon loading segments within the evanescent field of the SWG waveguide and making use of its dispersion properties, it is possible to attain sub-nanometer spectral bandwidths for both reflection and transmission filters in the wavelength range of 1550 nm while keeping minimum structural features of the filters as large as 100 nm. Numerical simulations have also shown that a few nanometer jitter in the size and position of Si segments is well tolerated in our filter designs.

Numerical representation of optical sources for coherent lightwave systems

The numerical model of CW-DFB optical source for fiber-optic transmission systems employing coherent detection technique is presented. The developed model is based on numerical solution of quantum-mechanical coupled rate equations. The numerical model is suitable for optical transmission systems for purpose of generation of optical carrier wave on the transmitter side as well as it can be used as local laser for coherent detection on the receiver side. The main attention of proposed optical source model is focused on signal, time-dependent characteristics to determine spectral properties of presented laser, which fully satisfies current requirements on coherent optical transmission systems. The efficiency of numerical model is also discussed. We have showed that by employing the re-sampling technique, both computational effort and accuracy of presented laser model are markedly enhanced.

Numerical model for DGD estimation in optical transmission system

In this paper we investigate the nonlinear and polarization effects in optical transmission systems and its influence on transmitted pulses. The main attention is focused on fundamental description of refractive index in nonlinear birefringent environment. In general, optical fiber is nonlinear transmission medium. The mutual interaction between transmission medium and optical intensity induces changes in the refractive index resulting to nonlinear effects that can be polarization-dependent in presence of birefringence. The global effect has a significant impact on pulse propagation. The aim of this paper is to present a numerical model, which will be suitable for estimation of DGD (Differential Group Delay) parameter in nonlinear birefringence medium. The DGD is crucial for evaluation of the impact of PMD (Polarization Mode Dispersion) in high-bit-rates fiber-optic system. Our approach opens the novel opportunity for DGD estimation based on numerical model of optical pulse propagation in nonlinear birefringence medium. Numerical model is based on solving NLSE (Nonlinear Schrodinger Equation) through the SSFM (Split-Step Fourier Method). The model is compatible for various input parameters, different kinds of optical fibers and also for different types of modulation formats. The obtained results show the DGD for different system parameters (such as input power and wavelength) and for different fiber polarization characteristics (birefringence and mode coupling). The total pulse broadening is also calculated and illustrates how all degradation effects influence the performance of fiber-optic transmission system.

Modeling of WDM transmission system with high-order phase modulation formats

The objective of this paper is focused on numerical modeling of WDM (Wavelength-Division Multiplex) transmission systems that employ new classes of high-order PSK (Phase-Shift Keying) modulation formats. This paper provides investigation of signals propagation with corresponding degradation mechanisms in physical layer, when high-order phase modulation formats are used for their transmission. The impacts of linear and nonlinear effects on modulated signal in multichannel system are studied. For this purpose, it was created numerical model by solving CNLSE (Coupled Nonlinear Schrödingers Equations) through SSFM (Split-Step Fourier Method). The fundamental characteristics of optical fibers, employed modulation format and WDM system parameters are significant for our investigation, because they play important role for behavior of modulated signals. Our results are analyzed and interpreted by the way of finding out the suitable and optimal system settings for transmission of phase modulated signals.

Numerical investigation of noise chracteristics of telecommunication laser sources for various modulation formats

We present numerical investigation of noise properties of lasers for telecommunication purposes with emphasis on widely used distributed feedback (DFB) lasers and its influence on multi-level modulation formats. DFB lasers can be used in optical transmitters with internal and external modulation, as well as in optical receivers employing coherent detection, where they act as local oscillator. The main noise factors influencing signal characteristics of semiconductor-based lasers are intensity and phase noise. These random impairments cause degradation of fundamental output laser characteristics such as power and phase fluctuation, which are directly related to the optical signal-to-noise ratio and the laser linewidth. In case of implementation of new modulation formats into the transmission system, these stochastic processes are of main importance and significantly impact the transmission properties of modulated signals and total performance of fiber-optic transmission systems. Throughout this paper, the noise influence on the multi-level modulation formats is evaluated by effective signal-to-noise ratio (SNR) algorithms in combination with bit-error ratio (BER) formulas for appropriate type of modulation format. The obtained results have shown that the noise of DFB laser is serious restriction for multi-level modulation formats and can be improved by higher power levels, yielding to higher SNR, as required for better values of BER.

Modeling of single-channel optical transmission systems with high-order ASK and PSK modulation formats

This paper is focused on numerical investigation of optical signal propagation in the single-channel transmission systems, which employ novel types of high-order modulation formats. In the paper we present comparison of two types of high-order modulation formats, namely Amplitude Shift Keying (M-ASK) and Phase Shift Keying (M-PSK). The investigation is based on solving the nonlinear Schrodinger equation (NLSE) through Split-Step Fourier Method (SSFM). The using of high-order modulation format is one of the key solutions for future optical networks and systems. Our aim is to describe the behavior of modulated pulses and show the suitability of using the investigated modulation formats, when their transmission is influenced by various kinds of optical channel impairments.

Simulation of FWM effects in WDM systems with various modulation formats

One of the most dominant degradation effect in the optical communication systems with wavelength division multiplexing is four-wave mixing. The development of optical networks in recent years has caused increasing demands on the transmission capacity. The transmission capacity can be increased by using advanced modulation formats. In this paper, the effect of four-wave mixing in multi-channel optical communication system with different modulation formats was simulated. As simulation tool the VPIphotonic software was used. The simulation results show, that impact of the four-wave mixing is suppressed under certain conditions and performance of optical communication systems can be improved. Advanced modulation formats increase the transmission capacity and allow better adaptation of transmission signal to transmission channel.

Impact of impulse response of avalanche photodiode to eye-closure penalty

Active elements are one of the key components of fiber-optic communication systems. In this paper, we discuss the influence of avalanche photodiode (APD) on the resulting eye-closure penalty as a parameter quantifying the degradation of transmission quality. Quality degradation due to the signal distortion and noise leads to the decreasing of the bit-error rate. The attention is focused on the numerical investigation of transient response of APD, which characteristics are comparable to the experiments. The behavior of APD response directly affect the inter-symbol interference of transmitted pulses and its impact is related to the eye-diagram closure.

Numerical investigation of four-wave mixing in DWDM systems with high-order QAM modulation formats

The wavelength-division multiplex (WDM) systems represent the key technology for future optical networks. Next step for achieving the improvement of transmission system and growth of capacity is employment of high-order modulation formats. This paper provides an insight into the numerical investigation on one of the most detrimental degradation effect in multichannel systems – four-wave mixing (FWM) and its impact on transmitted signals which used novel types of high-order square and star quadrature amplitude modulation (QAM) formats, respectively. This type of nonlinear effect causes inter- and intra-channel crosstalk interference, what are the worst cases of all possible channel impairments, because all spectral properties of transmitted signal are mixed together resulting to the decreasing system performance. Our investigation is based on finding the precise solution of coupled nonlinear Schrödinger’s equations (CNLSE) for DWDM system with channel spacing according to the ITU-T standardization. For solving CNLSE, it was created numerical model through mathematical method referred as split-step Fourier method (SSFM). The investigation is oriented especially on QAM formats, different kinds of optical fibers which are typically used in today’s networks and various types of system parameters such as value of channel spacing, input power and number of channels. The obtained results are discussed and analyzed with the aim of finding the most optimal and suitable properties of DWDM transmission system.