Polarization Mode Dispersion In Fibers Research Articles

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 $\sqrt{km}$ .

Temperature dependence of polarization mode dispersion in tight-buffered optical fibers

—Experiments and theoretical analysis of influence of temperature on polarization mode dispersion (PMD) in single mode optical fibers and cables are presented. Forces generated by contracting buffer create optical birefringence and increase fiber PMD at low temperatures. Single mode fiber (SMF) in 0.9 mm polymeric tight-buffer can exhibit an extra component of PMD exceeding 0.3 ps/√km in such conditions. On the other hand, tight-buffered spun nonzero dispersion-shifted fibers (NZDSF) and optical units with stranded single mode fibers have showed good stability of PMD over wide range of temperatures. This is due to presence of circular strain in the core, blocking accumulation of mechanically induced birefringence.

Disentanglement induced by combined effects of polarization mode dispersion and polarization-dependent loss in optical fibers

Disentanglement induced by combined effects of polarization mode dispersion and polarization-dependent loss in optical fibers

Blind SOP recovery of eigenvalue communication system based on a nonlinear Fourier transform.

Owing to the random birefringence of optical fibers, the recovery of the state of polarization (SOP) is urgently needed, especially in the nonlinear spectrum division multiplexing transmissions. Based on the variance of the polarization power ratio among symbols as the cost function, we propose a novel algorithm for the blind SOP recovery of eigenvalue communications. In the single eigenvalue transmissions with phase-shift keying or 16-ary amplitude and phase-shift keying constellations, at least 25.3 dB polarization extinction ratio can be achieved by using a block length of 30, even under 7 dB OSNR condition. It also shows that the proposed algorithm can be employed in multi-eigenvalue NFDM transmissions and full-spectrum modulated NFDM system. In the experiment, our proposed algorithm performs the same as the training symbol based method in back-to-back and less than 3000 km fiber link conditions; a maximum performance gain of 1.6 dB was obtained in ultra-long-haul condition (4300 km). It also shows that the impact of the polarization mode dispersion of a single-mode fiber on the algorithm is negligible.

Open-loop polarization mode dispersion mitigation for fibre-optic time and frequency transfer.

The non-reciprocal and dynamic nature of polarization mode dispersion (PMD) in optical fibers can be a problem for accurate time and frequency transfer. Here, a simple, passive solution is put forward that is based on transmitting optical pulses with alternating orthogonal polarization. The fast and deterministic polarization modulation means that the PMD noise is pushed far away from the frequencies of interest. Furthermore, upon reflection from a Faraday mirror at the receiver, the pulses have a well-defined polarization when they return to the transmitter, which facilitates stable optical phase detection and fibre phase compensation. In an open-loop test setup that uses a mode-locked laser and a simple pulse interleaver, the polarization mode dispersion is shown to be reduced by more than two orders of magnitude.

Optical Performance Monitoring for Intra-LP-Mode Dispersion in Weakly-Coupled Mode-Division Multiplexed Systems

Weakly-coupled mode-division multiplexing (MDM) technique based on linearly-polarized (LP) modes in ultralow-modal-crosstalk few-mode fiber (FMF) has been considered as a promising candidate for capacity enhancement of next-generation optical transmission systems. Similar to polarization mode dispersion in single-mode fibers (SMFs), signals in weakly-coupled FMFs suffer from the impacts of intra-LP-mode dispersion (ILMD) for both degenerate and non-degenerate LP modes.In this paper, we propose an effective method for ILMD monitoring in weakly-coupled MDM systems. The ILMD evaluation method for degenerate LP modes is designed by the analysis of channel transfer matrix in a digital coherent receiver. Then the ILMD monitoring scheme is experimentally validated for all the 6 LP mods in a weakly-coupled FMF. The influences of chromatic dispersion, optical signal to noise ratio and inter-LP-mode crosstalk to the method are also investigated.

Comments about dispersion of light waves

Dispersion of light waves is well known, but the subject deserves some comments. Certain classical equations do not fully respect causality; as an example, group velocity vg is usually given as the first derivative of the angular frequency ω with respect to the angular spatial frequency km (or wavenumber) in the medium, whereas it is km that depends on ω. This paper also emphasizes the use of phase index n and group index ng, as inverse of their respective velocities, normalized to 1/c, the inverse of free-space light velocity. This clarifies the understanding of dispersion equations: group dispersion parameter D is related to the first derivative of ng with respect to wavelength λ, whilst group velocity dispersion GVD is also related to the first derivative of ng, but now with respect to angular frequency ω. One notices that the term second order dispersion does not have the same meaning with λ, or with ω. In addition, two original and amusing geometrical constructions are proposed; they simply derive group index ng from phase index n with a tangent, which helps to visualize their relationship. This applies to bulk materials, as well as to optical fibers and waveguides, and this can be extended to birefringence and polarization mode dispersion in polarization-maintaining fibers or birefringent waveguides.

Analysis and Measurement of Intra-LP-Mode Dispersion for Weakly-Coupled FMF

Weakly-coupled mode division multiplexing (MDM) technique based on linearly-polarized (LP) modes in ultralow-modal-crosstalk few-mode fibers (FMF) has been considered as a promising candidate for capacity enhancement of short-reach transmission applications. Similar to the polarization mode dispersion (PMD) in single-mode fibers (SMF), signals in weakly-coupled FMFs suffer from the influence of intra-LP-mode dispersion (ILMD). In this paper, the generation mechanism of ILMD is firstly analyzed and the mean ILMDs in a typical step-index circular-core FMF are calculated. Then numerical simulations are carried out to investigate its impact and the severe performance degradation indicates that it may be one of the major transmission impairments for intensity-modulation/direct-detection (IM/DD) MDM systems. Moreover, an Improved Fixed Analyzer Method (IFAM) is proposed for ILMD measurement, based on which a weakly-coupled FMF supporting 6 LP modes is measured. Experimental results show that the ILMD for each circularly-symmetric LP mode behaviors like PMD in a SMF, while it may be up to tens of times larger for the non-circularly-symmetric LP modes. This work evaluates for the first time the ILMD impact and is beneficial for the design of weakly-coupled FMFs and IM/DD MDM systems.

COOMET Supplementary comparison on polarization mode dispersion in optical fiber

Main textINMETRO, KRISS, METAS and VNIIOFI carried out the supplementary comparison on Polarization mode dispersion in optical fiber (PMD). The aim of this comparison is to examine the equivalence of the PMD values for fiber optics among participating laboratories.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/.The final report has been peer-reviewed and approved for publication by the CCPR, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Impact of Wind Gust on High-Speed Characteristics of Polarization Mode Dispersion in Optical Power Ground Wire Cables.

Polarization mode dispersion is recognized as a key factor limiting optical transmission systems, particularly those fiber links that run at bit rates beyond 10 Gbps. In-line test and characterization of polarization mode dispersion are thus of critical importance to evaluate the quality of installed optical fibers that are in use for high-speed signal traffics. However, polarization-based effects in optical fibers are stochastic and quite sensitive to a range of environmental changes, including optical cable movements. This, in turn, gives rise to undesired variations in light polarization that adversely impair the quality of the signal transmission in the link. In this work, we elaborate on experimental testing and theoretical analysis to asses changes of polarization mode dispersion in optical fibers that are caused by environmental variations, here wind gusts in particular. The study was performed on commercially harnessed optical fibers installed within optical power ground wire cables, taking into account different weather conditions. More specifically, we showed that changes caused by wind gusts significantly influence the differential group delay and the principal state of polarization in those optical fibers. For this, we experimentally measured a number of parameters to characterize light polarization properties. Measurements were carried out on C-band operated fiber-optic link formed by 111-km-long power ground wire cables and 88 spectral channels, with a test time step of 1 min during 12 consecutive days. Variations in differential group delay allowed for sensitive testing of environmental changes with measured maxims up to 10 ps under the worst wind conditions. Moreover, measured parameters were used in a numerical model to assess the quality of transmitted high-bit-rate optical signals as a function of wind conditions. The analysis revealed a negligible impact of wind on a 10 Gbps transmission, while substantial influence was noticed for higher bit rates up to 100 Gbps. These results show promises for efficient sensing of environmental changes and subsequent monitoring of the quality of recently used fiber-optic link infrastructures.

Polarization Multiplexed Optical OFDM System With a Beat Interference Cancellation Receiver

A novel beat interference cancellation receiver (BICR) is proposed to cancel the signal-signal beat interference (SSBI) for polarization division multiplexed (PDM) optical orthogonal frequency division multiplexing (OOFDM) system, where two single sideband (SSB) OOFDM signals are polarization multiplexed along with their offset optical carriers (OCs) located at opposite sides. At receiver, the PDM SSB-OOFDM signal is equally power split into four beams with one or two OCs filtered out, and then fed into two balanced photodiode pairs for recovering the RF-OFDM signals with SSBI cancellation. The PDM SSB-OOFDM system is insensitive to fiber polarization mode dispersion since the proposed BICR is implemented without polarization-sensitive devices. Moreover, the spectral efficiency is greatly improved because of PDM and the small guard band since the SSBIs are eliminated. The proposed BICR scheme is validated with a simulation link of 112 Gbps 16-QAM PDM SSB-OOFDM signals. After 120km SSMF transmission, the EVM keeps below forward error correction limit of 16.3%.

POLARIZATION MODE DISPERSION COMPENSATOR BASED ON ANISOTROPIC OPTICAL FIBER

Abstract. In this paper, a new method of polarization mode dispersion (PMD), which can significantly limit the speed and range of transmission of fiber optic transmission systems (FOTS), compensation was developed and analyzed. In contrast to the existing types of PMD compensators, in which the optical fiber is subjected to mechanical stresses to create a photoelastic anisotropy, in this work the use of alternative method of creating photoelasticity in optical fiber (OF) by creating a helical ordered rotation of the glass microstructure (ORMG) is proposed. The helical orientation of the microstructure of the OF glass is achieved by acting on the fiber in the process of manufacture (drawing), when it is in a hot state, electromagnetic field, the power lines of which are directed in a circle. I am not sure what this sentence is trying to say. The result is an asymmetry of the dielectric constant of the fiber glass material and therefore the anisotropy of the optical properties. When the optical signal propagates in such OF, there is a double refraction, which is the cause of artificial PMD in the compensator fiber. Compensation is achieved by performing the equality of the modulus and the sign-opposite between the linear path PMD and the PMD of the anisotropic OF with the ORMG. The expression of the calculation of the PMD of the compensator, which depends on the rotation step of the microstructure of the glass, the chemical composition of the OF, the length of the line, the width of the radiation spectrum and the wavelength of the optical signal, and the optical characteristics of the OF, is analyzed, as well as the spectral dependence of polarization mode dispersion for different chemical compositions of the OF. The expression of determining the length of the OF with the ORMG is presented to compensate for the set value of the PMD in the line. The results of the studies made it possible to determine the lengths of the segments of OF with ORMG, which will provide partial or complete compensation of PMD over a wide range of wavelengths and create passive compensators for dispersion.

Digital nonlinearity compensation in the presence of polarization mode dispersion

The impact of polarization mode dispersion (PMD) on the performance of coherent transmission systems employing different digital nonlinearity compensation (NLC) schemes is numerically investigated for a seven-channel PM-16QAM Nyquist-wavelength division multiplexing system at 256 Gbit / s. In these nonlinearity compensation schemes, the digital signal processing is divided between the transmitter (Tx) and receiver (Rx) with different splitting ratios. We demonstrate that by splitting the NLC equally between the Tx and Rx, one can always obtain the best performance improvement regardless of whether PMD is present or not. Results of 1000-km dispersion-unmanaged transmission show that when fiber PMD is equal to 0.05 ps / km, splitting the NLC can give a signal-to-noise ratio improvement of 1.1-dB over receiver-side NLC, while it is 0.9 dB for 0.1 ps / km of the fiber PMD coefficient.

Microwave frequency transfer over a 112-km urban fiber link based on electronic phase compensation**Project supported by the National Natural Science Foundation of China (Grant Nos. 61825505, 91536217, and 61127901).

We demonstrate the transmission of a microwave frequency signal at 10 GHz over a 112-km urban fiber link based on a novel simple-architecture electronic phase compensation system. The key element of the system is the low noise frequency divider by 4 to differentiate the frequency of the forward signal from that of the backward one, thus suppressing the effect of Brillouin backscattering and parasitic reflection along the link. In terms of overlapping Allan deviation, the frequency transfer instability of 4.2 × 10−15 at 1-s integration time and 1.6 × 10−18 at one-day integration time was achieved. In addition, its sensitivity to the polarization mode dispersion in fiber is analyzed by comparing the results with and without laser polarization scrambling. Generally, with simplicity and robustness, the system can offer great potentials in constructing cascaded frequency transfer system and facilitate the building of fiber-based microwave transfer network.

Polarization-dependent pulse dynamics of mode-locked fiber laser with near-zero net dispersion

We demonstrate novel polarization-dependent pulse dynamics in a fiber laser cavity mode-locked by single-wall carbon nanotubes. By managing the net dispersion and polarization state, we obtain two noise-like pulsing procedures with distinctive polarization characteristics. Ultrafast polarization measurements reveal double pulses are produced by the combined effects of double-scroll chaotic polarization attractors and the polarization mode dispersion of single-mode fiber. The corresponding single-shot spectra provide evidence of coherent energy coupling between pulses during the switching process, due to the polarization hole burning of the active medium. The relative results provide new information for the polarization control of ultrafast lasers.

Clock Recovery Challenges in DSP-Based Coherent Single-Mode and Multi-Mode Optical Systems

We present an analysis of clock recovery algorithms in both polarization division multiplexing systems and mode division multiplexing systems. The impact of inter-polarization time skew and polarization mode dispersion in single-mode fibers, as well as the combined impact of mode mixing and mode group delay spread in multi-mode fibers under different coupling regimes are investigated. Results show that although the clock tone vanishing has a known solution for single-mode systems, in multi-mode systems even for low group delay spread, strong coupling will cause clock tone extinction, making it harder to implement an effective clock recovery scheme.

Reference Optical Spectrum Based In-Band OSNR Monitoring Method for EDFA Amplified Multispan Optical Fiber Transmission System With Cascaded Filtering Effect

The reference optical spectrum (ROS) based in-band optical signal-to-noise-ratio (OSNR) monitoring methods are accurate and inherently robust to fiber chromatic dispersion and polarization mode dispersion. They are also very simple and suitable to be deployed ubiquitously in the transmission system. In this paper, a ROS-based in-band OSNR monitoring method is proposed for erbium doped fiber amplifier (EDFA) amplified multispan dense wavelength division multiplexing systems with cascaded filtering effect (CFE) caused by cascaded add-drop filters or wavelength selective switches. In such systems, the optical signal as well as the optical noise may experience significant CFE making the ROS-based methods proposed before ineffective. The new method solves this problem and performs very well for OSNR in the range of 10–30 dB when the fiber nonlinear effect and nonideal filtering effect are present. The OSNR monitor based on the new method is also more convenient to use as only one-time calibration is required when used at different monitoring locations along the optical link.

BER Performance of PDM 4-QAM Optical Transmission System Considering the Effects of PMD and GVD Using Exact Probability Density Function

A noble theoretical approach is presented to evaluate the bit error rate (BER) performance of an optical polarization division multiplexed (PDM) 4-multilevel quadrature amplitude modulation (4-QAM) transmission system under the combined influence of polarization mode dispersion (PMD) and group velocity dispersion (GVD) in a single mode fiber (SMF). The analysis is carried out considering a coherent homodyne receiver. The exact probability density function (pdf) fluctuation due to PMD and GVD is evaluated from its moments using a Monte-Carlo simulation technique. Average BER is evaluated by averaging the conditional BER over the pdf of the random phase fluctuation. BER performance results are evaluated for different system parameters. It is found that PDM 4-QAM coherent homodyne system doubles the data rate but suffers more power penalty than the 4-QAM system. Results show that for a BER of 10^-9 at DGD of 0.5T and GVD value of 1700 ps/nm the PDM 4-QAM system needs 2.21 dB more power than 4-QAM systems giving the leverage of doubling the data rate.

Suppression of amplitude modulation induced by polarization mode dispersion using a multi-degree-of-freedom fiber filter

Polarization mode dispersion (PMD) in fibers for high-power lasers can induce significant frequency modulation to amplitude modulation (FM-to-AM) conversion. However, existing techniques are not sufficiently flexible to achieve efficient compensation for such FM-to-AM conversion. By analyzing the nonuniform transmission spectrum caused by PMD, we found that the large-scale envelope of the transmission spectrum has more serious impacts on the amount of AM. In order to suppress the PMD-induced FM-to-AM conversion, we propose a novel tunable spectral filter with multiple degrees of freedom based on a half-wave plate, a nematic liquid crystal, and an axis-rotated polarization-maintaining fiber. Peak wavelength, free spectral range (FSR), and modulation depth of the filter are decoupled and can be controlled independently, which is verified through both simulations and experiments. The filter is utilized to compensate for the PMD-induced FM-to-AM conversion in the front end of a high-power laser facility. The results indicate that, for a pulse with phase-modulation frequency of 22.82 GHz, the FM-to-AM conversion could be reduced from 18% to 3.2% within a short time and maintained below 6.5% for 3 h. The proposed filter is also promising for other applications that require flexible spectral control such as high-speed channel selection in optical communication networks.

Analytical evaluation of the combined influence of polarization mode dispersion and group velocity dispersion on the bit error rate performance of optical homodyne quadrature phase-shift keying systems

A theoretical approach is presented to evaluate the bit error rate (BER) performance of an optical fiber transmission system with quadrature phase-shift keying (QPSK) modulation under the combined influence of polarization mode dispersion (PMD) and group velocity dispersion (GVD) in a single-mode fiber (SMF). The analysis is carried out without and with polarization division multiplexed (PDM) transmission considering a coherent homodyne receiver. The probability density function (pdf) of the random phase fluctuations due to PMD and GVD at the output of the receiver is determined analytically, considering the pdf of differential group delay (DGD) to be Maxwellian distribution and that of GVD to be Gaussian approximation. The exact pdf of the phase fluctuation due to PMD and GVD is also evaluated from its moments using a Monte Carlo simulation technique. Average BER is evaluated by averaging the conditional BER over the pdf of the random phase fluctuation. The BER performance results are evaluated for different system parameters. It is found that PDM-QPSK coherent homodyne system suffers more power penalty than the homodyne QPSK system without PDM. A PDM-QPSK system suffers a penalty of 4.3 dB whereas power penalty of QPSK system is 3.0 dB at a BER of 10−9 for DGD of 0.8 Tb and GVD of 1700 ps/nm. Analytical results are compared with the experimental results reported earlier and found to have good conformity.