On-line simultaneous monitoring of polarization mode dispersion and chromatic dispersion

We have developed new expressions for power fading and average power fading owing to polarization mode dispersion (PMD) and chromatic dispersion in terms of the angle of precession of the output state of polarization about the PMD vector. Based on these expressions, a simple and novel pilot-tone-based technique for simultaneous monitoring of chromatic dispersion and PMD is proposed. Experimental results demonstrate the effectiveness of the proposed technique; these results agree well with the theoretical analysis.     

New approach to determine the effects of polarization mode dispersion and chromatic dispersion on pulse and RF signals

We present a novel analytical expression relating the output state of polarization (SOP) and the polarization mode dispersion (PMD) vector, including polarization-dependent chromatic dispersion (PCD), in terms of the angle of precession of the output SOP around the PMD vector. We derive a number of new expressions incorporating for the first time this angle of precession. First, a general relation to study the effect of differential group delay, PCD, and chromatic dispersion on pulses of arbitrary shapes is given. From this general relation, we derive expressions for pulse broadening and power penalty for Gaussian pulses. Moreover, a new expression for PMD-induced power fading for single-sideband modulated radio frequency signals is also derived. Measured experimental results are presented to support the derived expressions.     

Compensation of chromatic dispersion-induced power fading using optimised chirped fibre Bragg grating for millimetre-wave radio-over-fibre system

Compensation of fibre dispersion-induced power fading in an externally modulated sub- carrier multiplexed radio-over-fibre transmission link using the chirped fibre Bragg grating (CFBG) has been investigated. The results show that periodic power fading caused by fibre chromatic dispersion is significantly reduced and the optimum transmission distance can be increased by proper design of grating parameters and optimum selection of apodisation profile. The investigation also reveals that carrier-to-noise ratio and bit-error rate of 156 Mbps DPSK signal are also significantly improved using the CFBG with asymmetric apodisation profile as the dispersion compensator.     

10Gbit/s色散补偿系统中自相位调制效应的研究

首先讨论了单模光纤中自相位调制对系统色散的影响。数值计算和实验结果表明。增加入纤功率能在一定程度上抑制色散效应 ,当入纤功率为 1 5dBm时 ,对于 4 0 .0km的单模光纤 ,自相位调制效应和色散恰好抵消 ,功率代价接近为零。然后比较了前、后置色散补偿系统的性能。理论分析和实验表明 ,在入纤光功率较大的情况下 ,采取前置、完全色散补偿系统具有较低的误码率。前置补偿最佳入纤功率比后置补偿最佳入纤功率高约 1 0 .0dB。这表明 ,采取前置、完全色散补偿 ,系统具有较长的中继距离和较高的接收端光信噪比 ,对 (1 6 0× 1 0Gbit/s)DWDM系统 30 0 0km超长距离传输中光放大和色散补偿问题的整体优化具有重要现实意义。     

Chromatic dispersion effects in analog polarization-modulated links

The effect of chromatic dispersion on a photonic link employing polarization modulation is studied analytically and experimentally. For analog polarization modulation, dispersion introduces a frequency-dependent rotation to the orientation of modulation about the center of modulation. As a result, the dispersion-limited bandwidth of the link will depend on receiver design.     

Effects of chromatic dispersion on microwave and millimetre wave carrier transmission in optical fibres

Abstract

A new formalism for the analysis of optical (phase) noise in fibre-optic communication links is presented. The formalism is applied to an amplitude modulated millimetre-wave (or microwave) link with chromatic dispersion. A realistic link model is described and rigorously solved. In general, the power spectrum of the output signal consists of a ‘comb’ of spectral components with centre separation equal to the modulation frequency. Each spectral component contains a smooth ‘noise’ curve and a narrow spike which represents a modulated field component (carrier). With the new method it is possible to compute each spectral component and, consequently, the full power spectrum. From the power spectrum one can compute quantities relevant to the link design, in particular the carrier-to-noise ratio. Several graphs are presented, showing the power spectrum and the carrier-to-noise ratio for different values of the modulation frequency, link dispersion and modulation index. Several conclusions regarding the millimetre-wave fibre-optic link are dis-cussed.     

Analog domain adaptive equalizer for low power 40 Gbps DP-QPSK receivers

Electrical domain equalization of chromatic and polarization mode dispersion is attractive in coherent optical communication links. Digital coherent receivers used for this purpose are based on high speed ADCs followed by DSP, which dissipate excessive amount of power and are very costly to implement. We propose analog coherent receiver to drastically reduce the power consumption, size and cost. An adaptive feed forward equalizer for 40 Gbps dual polarization quadrature phase shift keying (DP-QPSK) systems, which processes signals in analog domain itself, is demonstrated using circuit and system simulations. The equalizer, designed in 90 nm CMOS technology, consumes 450 mW of power and occupies 1.8 mm × 1.1 mm chip area. System simulations are used to show that blind equalization is also possible when this approach is used in decision directed mode.     

A new experimental approach to second-order polarization mode dispersion analysis for optical communications systems

This article analyzes the polarization mode dispersion (PMD) in optical fibers and presents a new approach for its measurement. This approach permits the combined analysis of the first-order PMD and the second-order polarization mode dispersion (SOPMD) in optical systems for different values of temperature. The relation between SOPMD and the differential group delay (DGD) in a single-mode fiber is discussed. The analysis is based on time/wavelength and temperature variations changing/impacting PMD and DGD measured values. We present long-term statistical characteristics of SOPMD acquired by a PMD emulator constructed with some pieces of high birefringence fiber, and the correlation between the SOPMD, depolarization (Depol) and polarization-dependent chromatic dispersion (PCD) was investigated. A new interpretation of SOPMD is presented to analyze the problem of the temperature spectral stability. The actual techniques for SOPMD determination, consequently Depol and PCD, use the variation with time and/or wavelength. In some studies, the results obtained for SOPMD are correlated to first-order PMD. We demonstrate experimentally that the temperature is an important factor for the correlation between SOPMD and PMD and cannot be neglected in the optimization of high-speed optical communications links.     

High-rate-long-distance fiber-optic communication based on advanced modulation techniques.

The presence of fiber attenuation and chromatic dispersion is one of the major design aspects of fiber-optic communication systems when one addresses high-rate and long-distance digital data transmission. Conventional digital communication systems implement a modulation technique that generates light pulses at the fiber input end and tries to detect them at the fiber output end. Here an advanced modulation transmission system is developed based on knowledge of the exact dispersion parameters of the fiber and the principles of space-time mathematical analogy. The information encodes the phase of the input light beam (a continuous laser beam). This phase is designed such that, when the signal is transmitted through a fiber with a given chromatic dispersion, high peak pulses emerge at the output, which follows a desired bit pattern. Thus the continuous input energy is concentrated into short time intervals in which the information needs to be represented at the output. The proposed method provides a high rate-distance product even for fibers with high dispersion parameters, high power at the output, and also unique protection properties. Theoretical analysis of the proposed method, computer simulations, and some design aspects are given.     

Comments on,Xuan Li,Shanghong Zhao,Zihang Zhu,Bing Gong,Xingchun Chu,Yongjun Li,Jing Zhao and Yun Liu ‘an optical millimeter-wave generation scheme based on two parallel dual-parallel Mach–Zehnder modulators and polarization multiplexing’, Journal of Modern Optics, 2015

Abstract

In the title paper, Li et al. have presented a scheme for filter-less photonic millimetre-wave (mm-wave) generation based on two polarization multiplexed parallel dual-parallel Mach–Zehnder modulators (DP-MZMs). For frequency octo-tupling, all the harmonics are suppressed except those of order 4l, where l is the integer. The carrier is then suppressed by the polarization multiplexing technique, which is the principal innovative step in their design. Frequency 12-tupling and 16-tupling is also described following a similar method. The two DP-MZM are similarly driven and provide identical outputs for the same RF modulation indices. Consequently, a demerit of their design is the requirement to apply two different RF signal modulation indexes in a particular range and set the polarizer to a precise angle which depends on the pair of modulation indices used in order to suppress the unwanted harmonics (e.g. the carrier) without simultaneously suppressing the wanted harmonics. The aim of this comment is to show that, an adjustment of the RF drive phases with a fixed polarizer angle with the design presented by Li, all harmonics can be suppressed except those of order4l, where l is an odd integer. Hence, a filter-less frequency octo-tupling can be generated whose performance is not limited by the careful adjustment of the RF drive signal, rather it can be operated for a wide range of modulation indexes (m ~ 2.5 → 7.5). If the modulation index is adjusted to suppress 4th harmonics, then the design can be used to perform frequency 24-tupling. Since, the carrier is suppressed by design in the modified architecture, the strict requirement to adjust the RF drive (and polarizer angle) can be avoided without any significant change to the circuit complexity.     

Plasmonic waves of graphene on a conducting substrate

The properties of plasmonic waves of graphene on a conducting substrate are discussed based on the classical electrodynamics and linearized hydrodynamic model. General expressions are given and illustrated graphically for the dispersion relation, power flow, energy density and energy transport velocity of the plasmonic waves. The numerical results show that acoustic plasmon mode of the system has a group velocity that can be made arbitrarily close to the graphene Fermi velocity by tuning the graphene–metal distance or graphene sheet carrier density.     

Frequency Offset Due to Spectral Impurities in Cesium-Beam Frequency Standards

Theoretical expressions for the frequency offset due to spectral impurities in beam-tube frequency standards are given for the case of small sideband to carrier power ratios. They are valid for any value of the separation between the extraneous sideband and the carrier which interrogates the atomic transition, as well as for any value of the power in the carrier. Useful approximations are given in special cases of interest. The effects of the velocity distribution of the detected atoms and of the frequency modulation technique (sine or square wave) are considered.     

Optical post-equalization based on self-imaging

Optical fibre transmission systems operate in the presence of inter-symbol interference (ISI) caused by chromatic dispersion (CD), polarization-mode dispersion (PMD), and other impairments. As the transmission rate increases, ISI mitigation becomes mandatory. Many schemes for dispersion compensation have been proposed. We present and discuss a new optical method for post-compensating the chromatic dispersion in a particular dispersive medium, namely the single mode fibre. This method is based on the self-imaging phenomenon known as the temporal Talbot effect. The main advantage of our method results in using standard optical fibres instead of special fibres. We also have all freedom in subdividing and processing sequences of the dispersed optical signal.     

Coded-orthogonal frequency division multiplexing in hybrid optical networks

Future Internet should be able to support a wide range of services containing large amount of multimedia over different network types at a high speed. The future optical networks will therefore be hybrid, composed of different single-mode fibre (SMF), multi-mode fibre (MMF) and free-space optical (FSO) links. In these networks, novel modulation and coding techniques are needed that are capable of dealing with different channel impairments, be it in SMF, MMF or FSO links. The authors propose a coded-modulation scheme suitable for use in hybrid FSO - fibre-optics networks. The proposed scheme is based on polarization-multiplexing and coded - orthogonal frequency division multiplexing (OFDM) with large girth quasi-cyclic low-density parity-check (LDPC) codes as channel codes. The proposed scheme is able to simultaneously deal with atmospheric turbulence, chromatic dispersion and polarisation mode dispersion (PMD). With a proper design for 16-quadrature amplitude modulation (QAM)-based polarisation-multiplexed coded-OFDM, the aggregate data rate of 100 Gb/s can be achieved for OFDM signal bandwidth of only 12.5 GHz, which represents a scheme compatible with 100 Gb/s per wavelength channel transmission and 100 Gb/s Ethernet.     

Chromatic Dispersion Manipulation Based on Metalenses

Metasurfaces are 2D metamaterials composed of subwavelength nanoantennas according to specific design. They have been utilized to precisely manipulate various parameters of light fields, such as phase, polarization, amplitude, etc., showing promising functionalities. Among all meta-devices, the metalens can be considered as the most basic and important application, given its significant advantage in integration and miniaturization compared with traditional lenses. However, the resonant dispersion of each nanoantenna in a metalens and the intrinsic chromatic dispersion of planar devices and optical materials result in a large chromatic aberration in metalenses that severely reduces the quality of their focusing and imaging. Consequently, how to effectively suppress or manipulate the chromatic aberration of metalenses has attracted worldwide attention in the last few years, leading to variety of excellent achievements promoting the development of this field. Herein, recent progress in chromatic dispersion control based on metalenses is reviewed.     

Performance analysis of rectangular quadrature amplitude modulation with combined arbitrary transmit antenna selection and receive maximal ratio combining in nakagami-m fading

The average symbol error probability (SEP) performance of arbitrary rectangular quadrature amplitude modulation in the context of arbitrarily ordered transmit antenna selection and receive maximal ratio combining diversity system is analysed. The channel gains are assumed to follow Nakagami-m fading distribution with in general arbitrary fading parameters. Exact expressions for the average SEP performance are derived for the general case of unequal in-phase and quadrature decision distances as well as distinct in-phase and quadrature modulation orders. The results generalise many previous case studies, and can be used to investigate the impact of various diversity-combining schemes and different modulation and channel parameters on the system average SEP performance.     

Dispersion control with use of long-period fiber gratings

Chirped long-period fiber gratings are analyzed for management of dispersion in optical fiber communications systems. A ray model is used to derive simple analytic expressions that describe the transmission, chromatic delay, and dispersion properties of chirped long-period fiber gratings. A numerical model based on coupled-mode theory is used to verify the accuracy of the analytic expressions and explore design issues of the chirped long-period grating. With certain reasonable restrictions, chirped long-period gratings are found to be a viable and desirable alternative to existing dispersion compensation techniques.     

Spectral-domain measurement of chromatic dispersion difference of polarization modes in polarization-maintaining fibers

A spectral white-light interferometric (WLI) technique for measuring the chromatic dispersion difference of the two polarization eigenmodes in polarization-maintaining fibers (PMFs) is presented. The approach is based on the application of a transverse point-like force on the fiber that causes coupling between the two modes and utilizes their spectral interferogram. A Fourier-transform spectral interferogram (FTSI) and a polynomial curve fitting are applied to obtain the phase function. The chromatic dispersion difference of the long PMFs can be obtained by taking the second derivative of the phase function. The experimental results for two kinds of PMFs of 110 and 750?m length are presented, respectively.     

Investigation of polarization-induced fading in fiber-optic interferometers with polarizer-based polarization diversity receivers

A technique is described to eliminate polarization-induced fading in fiber-optic interferometers with two or three polarizers. Modeling and simulation show that two polarizers should be angularly spaced by 90 degrees to alleviate polarization-induced fading. A test system is set up with two 6.5 km fiber coils to link the data. A bistate polarization diversity receiver is tested for reducing polarization-induced fading. The signal is demodulated using a digital phase-generated carrier and the system demonstrates self-noise up to 7.7 microrad/square root Hz (at 1 kHz).     

Closed-form expressions for symbol error probability of orthogonal space?time block codes over Rician?Nakagami channels

The performances of orthogonal space-time block codes (OSTBCs) over Rician- Nakagami channels are investigated. In particular, we derive closed-form symbol error probability (SEP) expressions for OSTBC systems in which M-ary phase-shift-keying modulation and M-ary quadrature-amplitude modulation are used. These SEP results are expressed in terms of Lauricella's multivariate hypergeometric functions, which can be easily evaluated numerically. When the Rician-Nakagami channel degenerates to the Rician-Rayleigh channel, or equivalently the Rayleigh fading channel, the closed-form SEP expressions are rewritten in terms of higher transcendental functions, that is, Gauss hypergeometric function and Appell hypergeometric function.