Polarization Mode Dispersion Research Articles

Highly dispersive optical solitons with polarization-mode dispersion for polynomial law of self-phase modulation

Highly dispersive optical solitons with polarization-mode dispersion for polynomial law of self-phase modulation

Optical Solitons for the Dispersive Concatenation Model with Polarization Mode Dispersion by Sardar's Sub-Equation Approach

This paper recovers the spectrum of optical solitons for the dispersive concatenation model with the application of the Sardar sub-equation approach. The single soliton solutions that emerge from this scheme are bright, dark, and of singular type. The parameter constraints for the existence of such solitons are also included.

Optical dromions with polarization–mode dispersion having parabolic law of self–phase modulation with multiplicative white noise

Optical dromions with polarization–mode dispersion having parabolic law of self–phase modulation with multiplicative white noise

Highly dispersive optical solitons with differential group delay and multiplicative white noise for Fokas–Lenells equation

AbstractThe current article addresses highly dispersive optical solitons with polarization mode dispersion, modeled by the Fokas–Lenells equation in presence of white noise. The corresponding soliton solutions are retrieved with the usage of two integration algorithms. They are the enhanced Kudryashov’s method and the enhanced direct algebraic method. The intermediary solutions are in terms of Jacobi’s elliptic functions and Weierstrass’ elliptic functions. The existence criteria of soliton solutions, by virtue of parameter constraints, are also presented.

Broadband dispersion compensation and high birefringence photonic crystal fiber for CWDM/DWDM networks

In this study, we propose a new design based on photonic crystal fibers (PCFs) for broadband dispersion compensation in telecommunication networks. The proposed design has a hexagonal structure arrangement of air-holes rings of different diameters between the silica core and the cladding. The PCF properties like effective area, nonlinearity, dispersion slope, confinement loss, and birefringence are reported and discussed. For the best performance we present three designs A, B and C. Simulation results show that the three designs cover the six-telecommunication optical bands O-, E-, S-, C-, L- and U- bands (wavelengths ranging from 1260 to 1675 nm). Design A achieves a large negative dispersion value of about − 1716 ps/(nm.km) with relative dispersion slope equals to that of conventional single-mode optical fibers (SMFs) of about 0.0036 nm−1, which makes it very suitable for long-haul DWDM transmission systems. With a little modification in the core, designs B and C achieve much higher confinement ability and achieve a very large birefringence value for polarization mode dispersion and sensing applications. Design C is engineered to have exact opposite dispersion of SMF with zero dispersion at the wavelength 1310 nm, which makes it a promising design in CWDM transmission system. The numerical values have been investigated using the full vector finite element method.

Polarization‐directed nanophotonic routers based on two‐dimensional inorganic molecular crystals

AbstractPhotonic and plasmonic hybrid nanostructures are the key solution for integrated nanophotonic circuits with ultracompact size but relative low loss. However, the poor tunability and modulability of conventional waveguides makes them cumbersome for optical multiplexing. Here we make use of two‐dimensional molecular crystal, α‐Sb2O3 as a dielectric waveguide via total internal reflection, which shows polarization‐sensitive modulation of the propagating beams due to its large polarization mode dispersion. Both experiments and simulations are performed to verify such concept. These Sb2O3 nanoflakes can be coupled with plasmonic nanowires to form nanophotonic beam splitters and routers which can be easily modulated by changing the polarization of the incidence. It thus provides a robust, exploitable and tunable platform for on‐chip nanophotonics.image

Digital calibration method to enable depth-resolved all-fiber polarization sensitive optical coherence tomography with an arbitrary input polarization state

We present a fully integrated depth-resolved all fiber-based polarization sensitive optical coherence tomography (PSOCT). In contrast to conventional fiber-based PSOCT systems, which require additional modules to generate two or more input polarization states, or a pre-adjustment procedure to generate a circularly polarized light, the proposed all-fiber PSOCT system can provide depth-resolved birefringent imaging using an arbitrary single input polarization state. Utilizing the discrete differential geometry (DDG)-based polarization state tracing (PST) method, combined with several geometric rotations and transformations in the Stokes space, two problems induced by the optical fibers can be mitigated: 1) The change in the polarization state introduced by the optical fibers can be effectively compensated using a calibration target at the distal end of the probe, and the computations of the local axis orientation and local phase retardation can be achieved with a single arbitrary input polarization state, eliminating the need for a pre-defined input polarization state, allowing a flexible system design and user-friendly experimental procedure; 2) The polarization mode dispersion (PMD) induced by the optical fibers can be compensated digitally without the requirement of additional input polarization states, providing an accurate PSOCT imaging result. To demonstrate the performance of the proposed method, the depth resolved PSOCT results of a plastic phantom and in vivo skin imaging are obtained using the proposed all-fiber PSOCT system.

Modulation Format Identification Based on Multi-Dimensional Amplitude Features for Elastic Optical Networks

A modulation format identification (MFI) scheme based on multi-dimensional amplitude features is proposed for elastic optical networks. According to the multi-dimensional amplitude features, incoming polarization division multiplexed (PDM) signals can be identified as QPSK, 8QAM, 16QAM, 32QAM, 64QAM and 128QAM signals using the k-nearest neighbors (KNNs) algorithm in the digital coherent receivers. The proposed scheme does not require any prior training or optical signal-to-noise ratio (OSNR) information. The performance of the proposed MFI scheme is verified based on numerical simulations with 28GBaud PDM-QPSK/-8QAM/-16QAM/-32QAM/-64QAM/-128QAM signals. The results show that the proposed scheme can achieve 100% of the correct MFI rate for all six modulation formats when the OSNR values are greater than their thresholds corresponding to the 20% forward error correction (FEC) related to a BER of 2.4 × 10−2. Meanwhile, the effects of residual chromatic dispersion, polarization mode dispersion and fiber nonlinearities on the proposed scheme are also explored. Finally, the computational complexity of the proposed scheme is analyzed, which is compared with relevant MFI schemes. The work indicates that the proposed technique could be regarded as a good candidate for identifying modulation formats up to 128QAM.

Joint equalization of RSOP and PMD fused probability-aware with square-root cubature Kalman filter for the PDM PCS-64QAM system under extreme scenarios.

Extreme scenario of lightning strikes would generate ultra-fast rotation of state-of-polarization (RSOP) up to 5.1 Mrad/s and large polarization mode dispersion (PMD) in optical ground wire (OPGW). Unfortunately, the conventional multiple modulus algorithm (MMA) cannot equalize these polarization impairments in polarization division multiplexing (PDM) probabilistic constellation shaping (PCS)-64QAM system. Moreover, due to unavoidable linearization errors and higher modulation order, the extended Kalman filter based on measurement equations of concatenated multiplication (EKF-CM) is highly unstable and fails under such scenarios. To address the above issues, we have proposed a joint equalization scheme of PMD and RSOP, which fuses probability-aware with square-root cubature Kalman filter (PA-SCKF). Firstly, according to the characteristic that the amplitude of PCS signals obeys mixed Rician distribution, the scheme combines maximum a posteriori criterion to obtain the optimal radius of constellation ring which the received symbol belongs to, for the sake of calculating the innovations of SCKF. Secondly, it performs joint equalization of PMD and RSOP impairments based on SCKF and time-frequency conversion architecture. 28GBaud PDM PCS-64QAM simulation results demonstrate that our scheme can jointly equalize maximum impairments of 8.34 Mrad/s RSOP and 90ps DGD under entropy of 4.5bits/symbol. Additionally, only 0.9 dB OSNR penalty is obtained after joint equalization of 6 Mrad/s RSOP with 70ps DGD impairments. Even under entropy of 5.5bit/symbol, it can still jointly equalize impairments of 6.05 Mrad/s RSOP with 60ps DGD. Furthermore, 16GBaud PCS-64QAM experimental results indicate that the maximum joint equalization performances of PA-SCKF scheme under entropy of 4.5bit/symbol and 5bit/symbol are 17 Mrad/s RSOP with 52ps DGD, and 9 Mrad/s RSOP with 52ps DGD, respectively. These results manifest that our PA-SCKF scheme outperforms both MMA and EKF-CM schemes. Importantly, its complexity is on an order of O(Llog2 L), which is comparable to that of EKF-CM scheme.

Nonlinear fiber effects in ultra-high power 10 × 10 Gbit/s WDM-IM free-space systems for satellite links.

We investigate an unexplored type of nonlinear impairments that will take place in a very short fiber after the booster amplifier in a Free Space Optical (FSO) system for space communications. In Earth-satellite links, optical power levels up to 100 W could be required at the transmitter side to achieve the foreseen 100 Gbit/s capacity, because of the extremely high losses. These systems thus need an optical booster amplifier having very high optical power and it should be connected to the transmitting telescope by means of a short fiber (few meters). Here, we discuss and investigate the impact of the nonlinear fiber effects by means of numerical simulations, and estimate the impairments in a Wavelength Division Multiplexing (WDM) 10 × 10 Gbit/s system with intensity modulation. The obtained results clearly indicate that, in this system, the most relevant effect is Four Wave Mixing. We proved that this can be observed as soon as the total power exceeds 20 W. Due to the short fiber length, the system impairments are not affected by chromatic dispersion or channel spacing. We demonstrate that an effective means to reduce the impact is by adopting Polarization Interleaving, i.e., odd and even channels with orthogonal state of polarization. This solution could not work in long terrestrial links because of polarization mode dispersion, yet it can be effectively exploited in short fiber patch cords. These results can be used as a guideline to control this type of impairment in high-power FSO systems for satellite links.

Photonic MMW Generation Using PM-DPMZM for Full Duplex 32×10 Gbps RoF-WDM System

Abstract This paper presents a study of a 32×10 Gbps Radio over Fiber and Wavelength Division Multiplexing (RoF-WDM) full-duplex system that uses Phase Modulators and a Dual-Port Mach-Zehnder Modulator (PMs-DPMZM) for bidirectional data transfer. The system employs Millimeter-Wave (MMW) signaling over optical fiber and focuses on selecting a technology that provides high transmission capacity per wavelength, improved spectral efficiency, and resistance against optical transmission impairments. The proposed method was validated using simulation results to confirm the efficiency of the proposed system in generating a 40 GHz signal and efficiently detecting and modulating the RF signals. The results demonstrate that the system exhibits strong resistance against dispersion, non-linear effects, and noise, delivering satisfactory performance for distances of up to 220 km. By analyzing the input power, the paper establishes a relationship between input power and signal quality, revealing that an optimal power of 0 dBm leads to an improved Quality Factor (QF) and reduced transmission errors. Furthermore, the evaluation of received optical power indicates the power level required to maintain an acceptable error rate, approximately -20.9690 dBm for downstream data transfer and -20.7245 dBm for upstream data transfer at the BER limit. The simulation performance also demonstrates the transmission efficiency achieved through a high Polarization Mode Dispersion (PMD) coefficient of up to 0.8. The analytical calculations conducted in this work provide valuable insights for optimizing and enhancing the performance of RoF-WDM networks.

Polarization dependent gain in Raman fiber amplifiers with multiple pumps.

In this paper, the polarization dependent gain (PDG) in Raman fiber amplifiers (RFAs) with multiple pumps is studied thoroughly. A comprehensive model, which takes the random polarization mode dispersion, the nonlinear coupling between the pumps, and the degree of polarization (DOP) of the pumps into account, is proposed. The complex nonlinear and random coupling inside the optical fiber is described by a set of nonlinear stochastic differential equations (SDEs), which enable co-simulation of the polarized part and the depolarized part of the multiple pumps. It is revealed that the average PDG and the PDG standard deviation are linearly proportional to the DOP of the pumps, which agrees with the single mode case. More importantly, when the pump wavelength is far away from the signal amplification range (pump-signal wavelength difference larger than 100 nm), its DOP still affects the PDG of the signal. Such a phenomenon is caused by the fact that the pumps interact with each other and the pump DOP could transfer among the pumps, which could enhance the PDG of the RFA. The findings in the work will have important implications for the design of the optical transmission systems with the multi-pump RFAs.

Blind Polarization Demultiplexing of Shaped QAM Signals Assisted by Temporal Correlations.

While probabilistic constellation shaping (PCS) enables rate and reach adaption with finer granularity [1], it imposes signal processing challenges at the receiver. Since the distribution of PCS-quadrature amplitude modulation (QAM) signals tends to be Gaussian, conventional blind polarization demultiplexing algorithms are not suitable for them [2]. It is known that independently and identically distributed (iid) Gaussian signals, when mixed, cannot be recovered/separated from their mixture. For PCS-QAM signals, there are algorithms such as [3], [4] which are designed by extending conventional blind algorithms used for uniform QAM signals. In these algorithms, an initialization point is obtained by processing only a part of the mixed signal, which have non-Gaussian statistics. In this paper, we propose an alternative method wherein we add temporal correlations at the transmitter, which are subsequently exploited at the receiver in order to separate the polarizations. We will refer to the proposed method as frequency domain (FD) joint diagonalization (JD) probability aware-multi modulus algorithm (pr-MMA), and it is suited to channels with moderate polarization mode dispersion (PMD) effects. Furthermore, we extend our previously proposed JD-MMA [5] by replacing the standard MMA with a pr-MMA, improving its performance. Both FDJD-pr-MMA and JD-pr-MMA are evaluated for a diverse range of PCS (entropy ) over a first-order PMD channel that is simulated in a proof-of-concept setup. A MMA initialized with a memoryless constant modulus algorithm (CMA) is used as a benchmark. We show that at a differential group delay (DGD) of 10% of symbol period and 18 dB SNR/pol., JD-pr-MMA successfully demultiplexes the PCS signals, while CMA-MMA fails drastically. Furthermore, we demonstrate that the newly proposed FDJD-pr-MMA is robust against moderate PMD effects by evaluating it over a DGD of up to 40% of . Our results show that the proposed FDJD-pr-MMA successfully equalizes PMD channels with a DGD up to 20% of .

Joint Polarization Dependent Loss and Polarization Mode Dispersion Tolerance for Single-carrier Coherent System Using Block Reversal Alamouti Coding

Joint Polarization Dependent Loss and Polarization Mode Dispersion Tolerance for Single-carrier Coherent System Using Block Reversal Alamouti Coding

OPTIMISATION OF OPTICAL INFOCOMMUNICATION NETWORKS

The article reviews existing approaches to network analysis, taking into account the topological properties of networks. A sequential analysis from a network link to the properties of a set of network links is carried out. The network link is analysed as a set of optical channels, and an analytical description of the transmission quality in such a channel is carried out. A model for calculating crosstalk in the paths of information and communication optical networks is proposed. As can be seen from the results, for an optical fibre of a given length, there is a number of steps for selecting the input polarisation ellipse for which the efficiency of the method is maximised. Also, with an increase in the number of steps, we observe a decrease in the efficiency of this compensation method. So, for an optical fibre of a given length at constant dynamics, there is a number of input signal polarisation ellipses for which the polarisation-mode dispersion will be minimal. For a particular fibre, this parameter (the number of input signals) must be selected, because this value is different for different fibres (within the range of 15-30 points).

Density-matrix-formalism based scheme for polarization mode dispersion monitoring and compensation in optical fiber communication systems

Density-matrix-formalism based scheme for polarization mode dispersion monitoring and compensation in optical fiber communication systems

Combined intra symbol frequency domain averaging channel estimation for polarization division multiplexed coherent optical OFDM/OQAM systems

Intrinsic imaginary interference (IMI) induced by chromatic dispersion (CD) and polarization mode dispersion (PMD) seriously degrades the performance of optical orthogonal frequency division multiplexing offset-quadrature amplitude modulation (O-OFDM/OQAM) systems. Therefore, effective channel estimations are required for such systems to maintain good transmission performance. In the previous publications, both the full loaded (FL) and the half loaded (HL) frequency-domain channel estimation methods for polarization-division-multiplexed (PDM) coherent optical OFDM/OQAM (CO-OFDM/OQAM) systems have been proposed. However, for these frequency-domain methods, the channel frequency-domain responses caused by the correlation of the amplified spontaneous emission (ASE) noise are not considered. In this paper, we systematically discuss the frequency-domain channel transmission model for PDM CO-OFDM/OQAM systems. With the analysis of the correlation of the ASE noise, we propose a combined intra symbol frequency-domain averaging (CISFDA) channel estimation method for PDM OFDM/OQAM systems. Compared with the full-loaded frequency-domain channel estimation (FL-FD) method, the CISFDA method promotes the system robustness against the ASE noise and fiber nonlinear effect significantly. The proposed method is validated by numerical Monte Carlo simulations of the PDM CO-OFDM/OQAM system. Our new algorithm outperforms the FL-FD method in the 36 Gb/s PDM OFDM CO-OFDM/OQAM system, and the transmission distance is improved by 500 km with the bit-error-rate (BER) target at 3.8×10-3.

PMD tolerant transmission using multiple optical phase conjugators in the discretely amplified systems

Abstract In this paper, the impact of polarization mode dispersion (PMD) on system performance in coherent optical transmission assisted by optical phase conjugation (OPC) technique is numerically investigated for a 9-channel PM-4QAM system at 128Gbit/s. The OPC-aided transmission, amplified with lumped erbium doped fiber amplifier (EDFA), is a variation of the conventional dispersion-managed link, which is also called dispersion-inverted link. We demonstrate that introducing more OPCs along the link can partly suppress the PMD-induced impairments and thus improve the system performance significantly. Results of 960-km dispersion-managed transmission show that PMD effect will cause a performance penalty of 1.8 dB when using mid-link OPC (i.e., only 1-OPC), while this penalty will decrease to about 0.4 dB when employing 6-OPCs along the link. Comparing with conventional digital back-propagation (DBP) technique, a performance improvement of about 3.1 dB is observed with multi-OPCs when fiber PMD is equal to 0.1ps/ k m $\sqrt{km}$ .

Qualitative analysis of PMD-induced long-haul optical fiber link

Abstract This paper studies the detrimental effect of polarization mode dispersion on long-haul optical fiber communication in terms of the quality factor and bit error rate. The dispersion value is varied for different fiber lengths, specifically for long-haul communication, and the results obtained are analyzed in terms of the quality factor. The polarization mode dispersion causes pulse broadening, leading to interchannel interference. There is a need to check the occurrence and the associated effects of this dispersion. The communication range for conducting the analysis varies from 150 km to 350 km. The analysis is first conducted on varied communication fiber link length for different dispersion values, and it is observed that a fiber length of 200 km gives comparatively favorable results, as seen from the BER analysis.

Solitons in birefringent optical fibers and polarization mode dispersion

The early work on solitons in optical fibers was all done using single-mode fibers, and these fibers remain important for many applications. The modes in single-mode fibers are for all practical purposes weakly confined plane waves and have two polarizations. The basic equation that describes light evolution in these fibers is the coupled nonlinear Schrödinger equation. The soliton robustness hypothesis and its origins, which were the original motivation for studying these equations, is first described. Limits on robustness due to birefringent walkoff and the impact of random birefringence variations in stabilizing solitons is then described. Questions and controversies that arose shortly after the publication of these equations are addressed. These include their relationship to the Maker and Terhune coefficients, the requirements for the validity of the nonlinear Schrödinger equation and the impact of polarization mode dispersion, and the conditions under which the birefringence can be considered linear. It is a consequence of the fluctuation-dissipation theorem that the birefringence must be linear in any homogeneous, low-loss optical medium with a local dielectric response. Any ellipticity is associated with non-locality, as would occur for example in a twisted optical fiber. This important result, which is not well-known in the optics community, is reviewed.