Review:Chromatic Dispersion Manipulation Based on Optical Metasurfaces

Metasurfaces are densely arrayed two⁃dimensional(2D)artificial planar metamaterials,which can manipulate the polarization,distribution,and amplitude of light by accurately controlling the phase of the scattering light.The flat metasurface has the potential to substantially reduce the thickness and complexity of the structures and allows ease of fabrication and integration into devices.However,the inherent chromatic aberration of the metasurface originating from the resonant dispersion of the antennas and the intrinsic chromatic dispersion limit their quality.How to effectively suppress or manipulate the chromatic aberration of metalenses has attracted worldwide attention in the last few years,leading to a variety of excellent achievements.Furthermore,utilizing the chromatic dispersion of metasurface to realize special functionalities is also of significant importance.In this review,the most promising recent examples of chromatic dispersion manipulation based on optical metasurface materials are highlighted and put into perspective.

Joint nonlinearity and chromatic dispersion pre-compensation for coherent optical orthogonal frequency-division multiplexing systems

This paper introduces a joint nonlinearity and chromatic dispersion pre-compensation method for coherent optical orthogonal frequency-division multiplexing systems. The research results show that this method can reduce the walk- off effect and can therefore equalize the nonlinear impairments effectively. Compared with the only other existing nonlinearity pre-compensation method, the joint nonlinearity and chromatic dispersion pre-compensation method is not only suitable for low-dispersion optical orthogonal frequency-division multiplexing system, but also effective for high- dispersion optical orthogonal frequency-division multiplexing transmission system with higher input power but without optical dispersion compensation. The suggested solution does not increase computation complexity compared with only nonlinearity pre-compensation method. For 40 Gbit/s coherent optical orthogonal frequency-division multiplexing 20 × 80 km standard single-mode fibre system, the suggested method can improve the nonlinear threshold （for Q 〉 10 dB） about 2.7, 1.2 and 1.0 dB, and the maximum Q factor about 1.2, 0.4 and 0.3 dB, for 2, 8 and 16 ps/（nm.km） dispersion coefficients.

Chirped optical solitons and stability analysis of the nonlinear Schrödinger equation with nonlinear chromatic dispersion

The present paper aims to investigate the chirped optical soliton solutions of the nonlinear Schrödinger equation with nonlinear chromatic dispersion and quadratic-cubic law of refractive index.The exquisite balance between the chromatic dispersion and the nonlinearity associated with the refractive index of a fiber gives rise to optical solitons,which can travel down the fiber for intercontinental distances.The effective technique,namely,the new extended auxiliary equation method is implemented as a solution method.Different types of chirped soliton solutions including dark,bright,singular and periodic soliton solutions are extracted from the Jacobi elliptic function solutions when the modulus of the Jacobi elliptic function approaches to one or zero.These obtained chirped optical soliton solutions might play an important role in optical communication links and optical signal processing systems.The stability of the system is examined in the framework of modulational instability analysis.

Chromatic dispersion manipulation based on metasurface devices in the mid-infrared region

The chromatic aberration of metasurfaces limits their application. How to cancel or utilize the large chromatic dispersion of metasurfaces becomes an important issue. Here, we design Si-based metasurfaces to realize flexible chromatic dispersion manipulation in mid-infrared region. We demonstrate the broadband achromatic metalens and achromatic gradient metasurface to cancel the chromatic aberration over a continuous bandwidth(8–12 μm). In contrast, the metalens and gradient metasurface with enhanced chromatic dispersion have also been realized, where the focal length and deflection angle with different wavelengths vary more significantly than the conventional devices designed with geometric phase. These demonstrations indicate promising potential applications.

Design procedure for photonic crystal fibers with ultra-flattened chromatic dispersion

A simple design procedure is used to generate photonic crystal fibers （PCFs） with ultra-flattened chromatic dispersion. Only four parameters are required, which not only considerably saves the computing time, but also distinctly reduces the air-hole quantity. The influence of the air-hole diameters of each ring of hexagonal PCFs （H-PCF, including 1-hole-missing and 7-hole-missing H-PCFs）, circular PCFs （C-PCF）, square PCFs （S-PCF）, and octagonal PCFs （O-PCF） is investigated through simulations. Results show that regardless of the cross section structures of the PCFs, the 1st ring air-hole diameter has the greatest influence on the dispersion curve followed by that of the 2nd ring. The 3rd ring diameter only affects the dispersion curve within longer wavelengths, whereas the 4th and 5th rings have almost no influence on the dispersion curve. The hole-to-hole pitch between rings changes the dispersion curve as a whole. Based on the simulation results, a procedure is proposed to design PCFs with ultra-flattened dispersion. Through the adjustment of air-hole diameters of the inner three rings and hole-to-hole pitch, a flattened dispersion of 0±0.5 ps/（nm·km） within a wavelength range of 1.239 – 2.083 μm for 5-ring 1-hole-missing H-PCF, 1.248 – 1.992 μm for 5-ring C-PCF, 1.237 – 2.21 μm for 5-ring S-PCF, 1.149 – 1.926 μm for 5-ring O-PCF, and 1.294 – 1.663 μm for 7-hole-missing H-PCF is achieved.

Compensation of chromatic dispersion for full-duplex ROF link with vector signal transmission using an optical phase shifter

We demonstrate the theory of chromatic dispersion （CD）-induced constellation rotation （CR） in a radio-over-fiber （ROF） link and a method for compensation. We also propose a 60 GHz full-duplex ROF system with vector signal transmission including no CD effect. The evaluation of 5 Gb/s 16 quadrature amplitude modulation signal transmission shows that the CD-induced CR can be entirely overcome due to the proposed method which is simply implemented through an optical phase shifter. The proposed ROF schedule is not only applicable for V-band （57-64 GHz） but also fits for W-band （75-110 GHz）, or any other bandwidth.

A novel chromatic dispersion monitoring method in terms of SO A spectral shift

In this paper a novel low power online chromatic dispersion (CD) monitoring method is presented, which employs spectral shift in the semiconductor optical amplifier (SOA). The advantage of this method lies in that the required input power can be much reduced, and the filter output can be used in the dynamic CD compensation system. The simulation indicates that the filtered power decreases with CD increases, and that the monitoring range increases as the filter bandwidth increases.

Application of Automatic Chromatic Dispersion Compensation for Realization of All-Optical Network

We have studied the algorithm for the automatic chromatic dispersion compensation using bit error rate (BER) and Q-factor optimization for realization of dynamically reconfigurable all-optical .network. We have made sure good performance using the compensation system by laboratory experiments.

Joint estimation of frequency offset and chromatic dispersion based on the training sequences in M-ary QAM coherent optical transmission system

A data-aided method of joint frequency offset and chromatic dispersion estimation based on the Chu training sequences is shown in 112 Gb/s polarization-multiplexed （PM） quadrature phase-shift keying and 224 Gb/s PM-16-quadrature amplitude modulation with different pulse-shaping filters, respectively. The proposed method achieves a good accuracy and is verified to be robust to polarization mode dispersion.

Simultaneous optical signal to noise ratio and symbol rate estimation with blind chromatic dispersion compensation for auxiliary amplitude modulation optical signals

Based on the peak to valley ratio（PTVR） of the average magnitude difference function（AMDF）, we present a novel optical signal to noise ratio（OSNR） and symbol rate（SR） estimation method for commonly used auxiliary amplitude modulations（AAMs）. Moreover, it is demonstrated that the influence of chromatic dispersion（CD）on the method can be mitigated by maximizing the PTVR of the AMDF with additional tunable dispersion compensators. The results of simulations show that the OSNR estimation error can be kept within 0.8 dB in the wide OSNR range of（12, 32） dB, while the SR estimation error is below 0.079% for four widely used10 Gsymbol/s AAM signals.

160 km all-optical OFDM transmission system with inline chromatic dispersion compensation

An experimental demonstration of an all-optical sampling orthogonal frequency division multiplexing （AOS-OFDM） transmission system with inline chromatic dispersion （CD） compensation is carried out to test the nonlinear influence. With five subcarriers non-return-to-zero （NRZ） modulated, the total bit rate is 50 Gb/s without polarization multiplexing. The receiver end is highly simplified with direct de- tection using optical Fourier transform filter. After transmission in 160-km standard single-mode fiber （SSMF） link with 130-ps/nm residual CD, an optimum input optical power for the system performance is achieved.

Chromatic dispersion monitoring using semiconductor optical amplifier

An all-optical real-time chromatic dispersion （CD） monitoring technique is proposed and demonstrated for 40Gbit/s differential phase-shifts keying （DPSK） signal, utilizing the cross modulation effects of semicon- ductor optical amplifier （SOA）. The optical power of the output spectral components, which is from the probe＇s frequency up to the signal bandwidth, is used for CD monitoring. This technique provides a wide monitoring range with large variation scale. The impacts of the polarization mode dispersion （PMD） and the optical signal-to-noise ratio （OSNR） on the CD monitoring results are theoretically analyzed and then experimentally investigated, showing that they have slight influence on the monitoring results within a certain range. Furthermore, simulated results for quadrature phase shift keying （QPSK） signal at 80 Gbit/s are also demonstrated, indicating that this technique is suitable for advanced modulated format as well.

Impact of Fiber Dispersion on Performance of Entanglement-Based Dispersive Optics Quantum Key Distribution

Dispersive optics quantum key distribution(DO-QKD)based on energy-time entangled photon pairs is an important QKD scheme.In DO-QKD,the arrival time of photons is used in key generation and security analysis,which would be greatly affected by fiber dispersion.In this work,we establish a theoretical model of the entanglement-based DO-QKD system,considering the protocol,physical processes(such as fiber transmission and single-photon detection),and the analysis of security tests.Based on this theoretical model,we investigate the influence of chromatic dispersion introduced by transmission fibers on the performance of DO-QKD.By analyzing the benefits and costs of dispersion compensation,the system performance under G.652 and G.655 optical fibers are shown,respectively.The results show that dispersion compensation is unnecessary for DO-QKD systems in campus networks and even metro networks.Whereas,it is still required in DO-QKD systems with longer fiber transmission distances.

Determination of Zero-Dispersion Wavelength by Four-Wave Mixing

We present an improved approach to determine the zero-dispersion wavelength by measurement of the four-wave mixing （FWM） effect employing the two-tunable-laser scanning method. The FWM behaviour of combined fibres with two different zero-dispersion wavelengths is investigated theoretically and experimentally. The results are compared with those by regular zero-dispersion wavelength test instrument using phase shift technique. The theoretical and experimental results confirm the feasibility of determination of zero-dispersion wavelength by FWM.

Effect of Third-order Dispersion of Birefringent Fiber on Pulse Transmission

The effect of third order dispersion on pulse transmission is discussed. The coupled nonlinear Schrdinger equations characterizing the birefringent single mode fibers is solved numerically with combined consideration on chromatic dispersion, including second and third order dispersions, polarization mode dispersion (PMD) and nonlinearity. Various simulation results are presented.

High Power Highly Nonlinear Holey Fiber with Low Confinement Loss for Supercontinuum Light Sources

The high power holey fiber is an efficient supercontinuum light source by using picosecond pulse,which is a less expensive laser source compared with low power and expensive femtosecond laser sources. In this paper, a high power highly nonlinear holey fiber(HN-HF) with a low confinement loss is proposed for supercontinuum light sources. The finite difference method is used to calculate the different properties of the proposed HN-HF. High nonlinear coefficients are obtained at 1.06 μm, 1.31μm, and 1.55μm wavelengths with flattened chromatic dispersion and low confinement losses simultaneously. Moreover, numerical simulation results show that high power broad supercontinuum spectra with very short length of the proposed photonic crystal fiber are achieved.

Broadband dispersion compensating fiber using index-guiding photonic crystal fiber with defected core

We present a novel broadband dispersion compensating photonic crystal fiber with defected core in this paper. The small central defect of air hole can flexibly control the chromatic dispersion properties of this kind of photonic crystal fiber. This kind of fiber has broadband large negative chromatic dispersion, and the chromatic dispersion coefficient varies from -440 to -480 ps/（nm.km） in the measured wavelength range of 1500 - 1625 nm. The calculated chromatic dispersion curve is well matched to the measured chromatic dispersion coefficient in the range of 1500 - 1625 nm. The proposed photonic crystal fiber can be used to design the dispersion compensating fiber in the desired wavelength range by adjusting its structural parameters.

Power efficiency of time-stretch imaging system by using parallel interleaving detection

A 38.88 MHz time-stretch line-scan imaging system with parallel interleaving detection is experimentally dem- onstrated. Since only half-chromatic dispersion is used to stretch optical pulses for wavelength-to-time mapping, the power efficiency is significantly improved by 6.5 dB. Furthermore, the theoretical analysis indicates that the power loss can be efficiently reduced for scan rates less than 100 MHz. In addition, a mathematical model for signal-to-noise evaluation is derived, including amplified spontaneous emission noise in the power compensation. Thanks to the improvement of the power efficiency by using parallel interleaving detection, the signal quality is enhanced.

Enhanced fourth-power algorithm for phase estimation with frequency separation in direct-detection optical OFDM systems

The optical orthogonal frequency division multiplexing （OFDM） signal is affected by impairments intro- duced by electrical filters and optical chromatic dispersion. An enhanced fourth-power algorithm for phase estimation with frequency separation is used to estimate and compensate the phase rotation of OFDM subcarriers. The performance of the proposed phase estimation algorithm is evaluated on a 4-Gb/s OFDM signal at different frequencies. Experimental results using the proposed algorithm show a 1.8-dB received power sensitivity improvement at a bit error rate of 1 × 10^-4 after a 100-kin standard single-mode fiber transmission, compared with the conventional technique.

An IIR adaptive electronic equalizer for polarization multiplexed fiber optic communication systems

An electronic digital equalizer for polarization multiplex coherent fiber optic communication systems is designed to compensate polarization mode dispersion (PMD) and residual chromatic dispersion (CD) of transmission channel. The proposed equalizer is realized with fraction spaced infinite impulse response (IIR) butterfly structure with 21 feedforward taps and 2 feedback taps. Compared with finite impulse response (FIR) structure, this structure can reduce implementation complexity of hardware under the same condition. To keep track of the random variation of channel characteristics, the filter weights are updated by least mean square (LMS) algorithm. The simulation results show that the proposed equalizer can compensate residual chromatic dispersion (CD) of 1600 ps/nm and differential group delay (DGD) of 90 ps simultaneously, and also can increase the PMD and residual CD tolerance of the whole communication system.