Chromatic Dispersion Research Articles

Revisitation of “Implicit Quiescent Optical Solitons with Complex Ginzburg-Landau Equation Having Nonlinear Chromatic Dispersion“: Linear Temporal Evolution

Revisitation of “Implicit Quiescent Optical Solitons with Complex Ginzburg-Landau Equation Having Nonlinear Chromatic Dispersion“: Linear Temporal Evolution

Extending the coverage of user-diversified IM-DD PON by FDM: a mathematical model with experimental verification.

Future passive optical networks (PONs) call for more flexibility to support diversified users with various rate demands and link qualities. Using traditional time-division multiplexing (TDM), the concept of a flexible rate PON was proposed to accommodate more users with link diversity by rate adaptation. In this Letter, we reveal the PON coverage can be further extended through frequency-division multiplexing (FDM) in the presence of multiuser diversity, namely, (i) there exist users with frequency-dependent link conditions and (ii) the link conditions exhibit disparity among users. We build a mathematical model and propose an optimization algorithm based on the binary tree search to optimize diversity gain. We experimentally verify its feasibility by studying the diversity gain concerning chromatic dispersion, optical path loss, and signal-to-noise ratio (SNR) variation in a 200G-class intensity-modulation direct-detection (IM-DD) system.

Symbol error rate minimization using deep learning approaches for short-reach optical communication networks

Short-reach optical communication networks have various applications in areas where high-speed connectivity is needed, for example, inter- and intra-data center links, optical access networks, and indoor and in-building communication systems. Machine learning (ML) approaches provide a key solution for numerous challenging situations due to their robust decision-making, problem-solving, and pattern-recognition abilities. In this work, our focus is on utilizing deep learning models to minimize symbol error rates in short-reach optical communication setups. Various channel impairments, such as nonlinearity, chromatic dispersion (CD), and attenuation, are accurately modeled. Initially, we address the challenge of modeling a nonlinear channel. Consequently, we harness a deep learning model called autoencoders (AEs) to facilitate communication over nonlinear channels. Furthermore, we investigate how the inclusion of a nonlinear channel within an autoencoder influences the received constellation as the optical fiber length increases. Another facet of our work involves the deployment of a deep neural network-based receiver utilizing a channel influenced by chromatic dispersion. By gradually extending the optical length, we explore its impact on the received constellation and, consequently, the symbol error rate. Finally, we incorporate the split-step Fourier method (SSFM) to emulate the combined effects of nonlinearities, chromatic dispersion, and attenuation in the optical channel. This is accomplished through a neural network-based receiver. The outcome of this work is an evaluation and reduction of the symbol error rate as the length of the optical fiber is varied.

Parallel wavelength-division-multiplexed signal transmission and dispersion compensation enabled by soliton microcombs and microrings

The proliferation of computation-intensive technologies has led to a significant rise in the number of datacenters, posing challenges for high-speed and power-efficient datacenter interconnects (DCIs). Although inter-DCIs based on intensity modulation and direct detection (IM-DD) along with wavelength-division multiplexing technologies exhibit power-efficient and large-capacity properties, the requirement of multiple laser sources leads to high costs and limited scalability, and the chromatic dispersion (CD) restricts the transmission length of optical signals. Here we propose a scalable on-chip parallel IM-DD data transmission system enabled by a single-soliton Kerr microcomb and a reconfigurable microring resonator-based CD compensator. We experimentally demonstrate an aggregate line rate of 1.68 Tbit/s over a 20-km-long SMF. The extrapolated energy consumption for CD compensation of 40-km-SMFs is ~0.3 pJ/bit, which is calculated as being around 6 times less than that of the commercial 400G-ZR coherent transceivers. Our approach holds significant promise for achieving data rates exceeding 10 terabits.

Time-frequency dual-dimension deep neural network (TF-DD-DNN)-based OSNR and XT monitoring in mode-division multiplexing systems

We propose a time-frequency dual-dimension deep neural network (TF-DD-DNN)-based optical performance monitoring (OPM) scheme to jointly monitor the optical signal-to-noise ratio (OSNR) and the mode-coupling induced crosstalk strength (XT) in mode-division multiplexing (MDM) systems, by revealing the diversity of the amplified spontaneous emission (ASE) and XT distortions on optical signals in the time- and frequency-domains. We numerically quantify the predictions of OSNR and XT for a coherent MDM transmission link, achieving the OSNR prediction accuracy of more than 0.99 and the XT prediction accuracy of up to 1 with the root mean square error (RMSE) of 0.11 dB at OSNR = 30 dB @0.1 nm for the case of quadrature-phase-shift keying (QPSK) signals. We evaluate the impacts of the chromatic dispersion (CD) of fibers and the low-pass filter bandwidth on the prediction procedures. The dependency of the modulation formats is also discussed, confirming the robust operation of the proposed scheme. Finally, the TF-DD-DNN scheme is experimental verified. High consistency is obtained between the simulation and experimental results.

A Novel Inserting Pilot Radio over Fiber System without the Bit Walk-Off Effect for the Generation and Distribution of Frequency 16-Tupling Millimeter Waves by Mach–Zehnder Modulators

A novel inserting pilot scheme to generate and distribute a frequency 16-tupling millimeter wave (MMW) radio over fiber (ROF) system without the bit walk-off effect via Mach–Zehnder modulators (MZMs) is proposed. The operation principle is analyzed and the feasibility of our proposed scheme is verified by simulation test. The main part of our scheme is a ±8th-order sidebands generator (SG), which is constructed by four MZMs connected in parallel. In the back-to-back (BTB) transmission case, by properly adjusting the voltage and initial phase of the radio frequency (RF) drive signals of the MZMs, ±8th-order sidebands are generated by the SG. In the data transmission case, the data signal is first split into two beams, one of which modulates the RF drive signal with an electrical phase modulator (PM) while the other is amplified by an electrical gainer (EG), and then the two beams are combined into one and used as the composite RF drive signal of the MZMs. By adjusting the modulation index of the PM and the gain of the EG, the data signal can only be modulated to the +8th-order sideband of the output of the SG. The optical carrier from the continuous wave (CW) laser is split into two paths: one is sent into the SG, and the other is used as a pilot signal. The output signal of SG is combined with the pilot signal and is transmitted to the base station (BS) via optical fiber. At the BS, the pilot signal is filtered out by a fiber Bragg grating (FBG) and used as the carrier for the uplink for carrier reuse. After filtering out the pilot, the signal from the FBG, which is composed of ±8th-order sidebands, is injected into a photodetector, and a frequency 16-tupling MMW with downlink data is generated. The key parameters’ influence on the bit error rate (BER) and Q factor in the system is also analyzed. Our scheme can not only effectively overcome the bit walk-off effect caused by optical fiber chromatic dispersion and greatly increase the fiber transmission distance but can also effectively improve the performance and the tunability of system. Therefore, it has important application prospects in ROF systems.

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.

Large optoelectronic chromatic dispersion in PN-type silicon photodiodes and photovoltaic cells.

Optoelectronic chromatic dispersion (OED) is a significant source of effective chromatic dispersion in photodiodes. We present an experimental and theoretical study of OED in PN-type Si photodiodes and photovoltaic cells and report on a very large effective chromatic dispersion in these devices. As measured with the modulation phase-shift technique at a frequency of 4 kHz for these slow devices, the OED spectral sensitivity for a commercial Si photodiode is approx. 0.02 deg/nm in the 720-850 nm wavelength band and increases to 0.25 deg/nm at λ = 1µm. For a Si photovoltaic cell, the OED is approx. 0.09 deg/nm in this spectral region. These values translate into an effective chromatic dispersion parameter of approx. 1012ps/(n m ×k m) for these sub-millimeter device lengths, which is over eight orders of magnitude larger than high-dispersion materials such as chalcogenide glass. The enormous dispersion in these sub-millimeter sized silicon-based devices can be utilized for on-chip optoelectronic sensors such as wavelength monitoring and spectroscopy. The substantial OED of photovoltaic cells can be utilized for the characterization and optimization and new applications for optical sensing with these self-powered devices.

Advanced linear axial wavelength spreading through cascaded double hyperchromats

This study explores the design and optimization of cascaded double-hyperchromatic optical systems (i.e., 2×2 lenses), focusing on achieving an extremely linear axial spectral decomposition characterized by an exceptionally low equivalent Abbe number. The investigation involves two double hyperchromats, considering both purely refractive systems and hybrid configurations that combine refractive and diffractive elements. For purely refractive systems, alternating focal length signs of divergent and collective lenses are crucial to achieve significant axial chromatic dispersion. In hybrid systems, the position of the diffractive optical element (DOE) and the selection of focal lengths play key roles in obtaining extremely low equivalent Abbe numbers. The optimized systems demonstrate absolute equivalent Abbe numbers of 0.983 for purely refractive and 0.65 for hybrid systems—more than four times lower than the absolute Abbe number of a single diffractive element. Notably, even systems using standard materials exhibit significantly low equivalent Abbe numbers of 2.5 and 1.4 for pure refractive and hybrid configurations, respectively. These results offer promising opportunities for improving optical applications based on axial spectral decomposition, overcoming previous limitations of axial chromatic spreading.

Extraction of optical wave structures to the coupled fractional system in magneto-optic waveguides

In this article, truncated M-fractional coupled nonlinear Schrodinger equation (NLSE) with quadratic–cubic nonlinearity is under observation. The studied model is composed of chromatic dispersion, magneto-optic parameter and inter-modal dispersion. The NLSE is the most significant physical model to explain the fluctuations of optical soliton proliferation. The NLSEs have become more popular because of the clarity with which they explain a wide range of complex physical phenomena and the depth with which they display dynamical patterns via localized wave solutions. Optical soliton propagation in magneto-optic is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. The optical solitons are secured in the forms of bright, dark, singular and combo solitons. In addition, hyperbolic, periodic and exponential function solutions have been recovered. The modified Sardar subequation and enhanced modified extended tanh-expansion approaches recently developed integration tools are adopted in this study for securing the solutions. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. The effect of parameters have been observed by allotting suitable values and sketching the different shapes of the graphs.

Large and tunable optoelectronic chromatic dispersion in PIN-type photodiodes.

It is known that PN-type photodiodes possess high optoelectronic chromatic dispersion (OED). Here we present a theoretical and experimental study of OED in PIN-type photodiodes. Applying the modulation phase-shift technique, a Ge PIN photodiode exhibits ∼0.5 deg/nm phase-shift sensitivity at 10 MHz modulation, corresponding to a dispersion of 1.4 ×109ps/(n m ×k m), many orders of magnitude larger than high-dispersion optical materials such as chalcogenide glass. A striking feature of the PIN device is the ability to tune the amount and sign of the OED through the bias voltage. Electronic tuning between -0.8 deg/nm and +0.5 deg/nm is shown. The PIN photodiode is an on-chip device possessing significant tunable dispersion for applications in optical sensing and spectroscopy.

Collisions of Light Bullets with Different Circular Polarizations

Collisions of left- and right-polarized spatiotemporal optical solitons have been numerically simulated for a locally isotropic focusing Kerr medium with anomalous chromatic dispersion. The stable propagation of such “light bullets” in a moderate nonlinear regime is ensured by a transverse parabolic profile of the refraction index in a multimode waveguide. The transverse motion of centers of mass of wave packets in such systems occurs on classical trajectories of a harmonic oscillator, whereas the motion in the longitudinal direction is uniform. Therefore, collisions of two solitons can be not only head-on but also tangential. An inelastic collision of two solitons with opposite circular polarizations can result either in two binary light bullets combining the left and right polarization or in more complex bound systems.

Broadband high-efficiency plasmonic metalens with negative dispersion characteristic

Controlling the dispersion characteristic of metasurfaces (or metalenses) along a broad bandwidth is of great importance to develop high-performance broadband metadevices. Different from traditional lenses that rely on the material refractive index along the light trajectory, metasurfaces or metalenses provide a new regime of dispersion control via a sub-wavelength metastructure, which is known as negative chromatic dispersion. However, broadband metalenses design with high-performance focusing especially with a reduced device dimension is a significant challenge in society. Here, we design, fabricate, and demonstrate a broadband high-performance diffractive-type plasmonic metalens based on a circular split-ring resonator metasurface with a relative working bandwidth of 28.6%. The metalens thickness is only 0.09λ0 ( λ0 is at the central wavelength), which is much thinner than previous broadband all-dielectric metalenses. The full-wave simulation results show that both high transmissive efficiency above 80% (the maximum is even above 90%) and high average focusing efficiency above 45% (the maximum is 56%) are achieved within the entire working bandwidth of 9–12 GHz. Moreover, an average high numerical aperture of 0.7 ( NA=0.7 ) of high-efficiency microwave metalens is obtained in the simulations. The broadband high-performance metalens is also fabricated and experimental measurements verify its much higher average focusing efficiency of 55% (the maximum is above 65% within the broad bandwidth) and a moderate high NA of 0.6. The proposed plasmonic metalens can facilitate the development of wavelength-dependent broadband diffractive devices and is also meaningful to further studies on arbitrary dispersion control in diffractive optics based on plasmonic metasurfaces.

Revisitation of “implicit quiescent optical solitons with complex Ginzburg–Landau equation having nonlinear chromatic dispersion": generalized temporal evolution

AbstractThis paper is a revisitation to the study on the retrieval of quiescent optical solitons to the complex Ginzburg–Landau equation that is considered with generalized temporal evolution and nonlinear chromatic dispersion. The results are recovered with the application of Lie symmetry. Apart from a couple of self-phase modulation structures where the results are in quadratures, the integrals are with a range of special functions. Two new forms of self-phase modulation structures are addressed in the paper.

Bright soliton of the third-order nonlinear Schrödinger equation with power law of self-phase modulation in the absence of chromatic dispersion

In this article, we are interested in two principal topics. First, the bright optical soliton solutions of the third-order (1+1)-nonlinear Schrödinger equation including power law nonlinearity with inter-modal and spatio-temporal dispersions are perused by taking advantage of the new Kudryashov method. Second, the impacts of power law nonlinearity parameters on soliton attitude are investigated for acquired bright soliton form. With the proposed technique, the bright optical soliton solution is acquired, and 3D, contour, and 2D plots are depicted. Then, the impact of power law nonlinearity parameters on the soliton attitude has been successfully demonstrated. As is clear from this perusal power law parameters have an important impact on the soliton attitude, and this impact alters based on the soliton form. As regards our investigation, this form of the equation has not been studied with the power law nonlinearity in the absence of the chromatic dispersion for nonlinear models and the proposed method has not been applied the introduced equation before. It is expected that the consequences which are acquired in this study will shed light on the studies in this field.

Chromatic dispersion-tolerant mode-locking of directly synthesized graphene for the control of laser pulse energy

Transfer-free direct synthesis of graphene (Gf) has been anticipated to develop small-footprint ultrafast optical devices that rely on the excellent nonlinearity of defect-suppressed Gf. Atomic carbon spraying (ACS) technique enables a direct and conformal growth of 3-dimensional (3D) Gf on the 3D surface of substrates by introducing a new ceramic catalyst. However, with the high density of grain boundaries retained in the resultant Gf nanocrystals, their unimpaired optical nonlinearity should be verified. We demonstrate a fiber ring femtosecond laser based on passive mode-locking of the ACS Gf synthesized on the side-polished surface of an optical fiber for the asymmetric nonlinear interaction of laser evanescent field and Gf. Widely operable chromatic dispersion range for the ACS Gf-based mode-locking is shown experimentally to tune the individual pulse energy. The ACS Gf manages a reliable interplay between the anomalous dispersion and optical nonlinearity of the laser cavity at high-intracavity power, resulting in dispersion-tolerant short pulse generation. Output pulse energy up to 9.05 nJ of the hyperbolic secant pulses is achieved with the extra-length of single mode fibers ranging from 30 to 250 m, ensuring the robust nonlinear operation of the ACS Gf.

High-speed data transmission over a microresonator frequency comb with dispersion compensation for augmented data rates and reach

Abstract Microresonator frequency comb-based high-speed data transmission provides a pathway towards augmented data capacity without increasing the number of laser sources. Their use with intensity-modulated direct detection modulation (IMDD) formats is especially pertinent in data center communications where minimizing cost, latency and complexity is paramount. This however implies that the same extent of digital signal processing techniques commonly used in coherent detection for the management of fiber impairments including chromatic dispersion are not available. With the proliferation of silicon photonics technologies in data center transceivers integrated dispersion compensation which can overcome fiber impairments would be of great merit. We demonstrate low power generation of the primary comb state in a silicon nitride microresonator and transmission of 25 Gb/s NRZ and 50 Gb/s PAM4 data over 20 km of single mode fiber. This represents the longest fiber reach demonstrated to date for the transmission of IMDD data using an integrated, microresonator frequency comb. An integrated, tunable grating device for dispersion compensation that reduces dispersion impairments after several fiber lengths generates significant improvements in the eye diagram, six orders of magnitude improvement in the bit-error rate and 14 dB improvement in the transmitter and dispersion eye closure quaternary values. Concurrently, doubling data transmission is demonstrated via polarization multiplexing a comb line and successful dispersion compensation of up to 20 km.

Optical solitons and stability analysis for NLSE with nonlocal nonlinearity, nonlinear chromatic dispersion and Kudryashov’s generalized quintuple-power nonlinearity

In this paper, we consider the nonlinear Schrödinger equation (NLSE) with nonlocal nonlinearity having nonlinear chromatic dispersion and Kudryashov’s generalized quintuple-power. For the suggested model, dark solitons, and singular solitons are investigated using the modified extended mapping approach. Furthermore, rational solutions, exponential solutions, hyperbolic wave solutions, singular periodic solutions, and Jacobi elliptic function solutions are shown. We impose certain limits on the parameters in order to guarantee the existence of the obtained soliton solutions. Furthermore, a few chosen solutions are also displayed graphically to illustrate the physical characteristics of the precise solutions. Furthermore, we use the idea of modulation instability analysis to discuss the stability of the derived wave solutions.

Investigation of hybrid chalcogenide photonic crystal fiber for MIR supercontinuum generation and optical communication

Abstract This study describes a wideband supercontinuum generation (SCG) in the mid-infrared range using a chalcogenide multi-material microstructured fiber design with significant non-linearity under optical communication. The fiber has a single core of As2Se3 and three rings of As2S5 rods arranged in hexagonal pattern in the AsSe2 cladding region. The reported PCF design has effective area and nonlinear coefficients as 59.4174 μm2 and 219.36 W−1 km−1 respectively at 5.3 μm pump wavelength. Additionally, it has a chromatic dispersion profile that is nearly zero and flattened over a large wavelength range of 5–15 µm, which is advantageous for broadband supercontinuum spectrum in the mid-infrared region. Specifically, with pulse width and pulse peak power of 200 fs and 10 kW, respectively, for a 100 mm fibre length, this research work illustrates the SCG that expands from 1000 nm to over 15,000 nm. These extremely nonlinear PCFs are robust contenders for applications that are nonlinear in nature, such as the generation of slow-light and supercontinuum.

Soliton solutions of the improved perturbed nonlinear Schrödinger equation having parabolic law with non-local nonlinearity in the presence of chromatic and spatio-temporal dispersion terms

This paper was organized to examine the analytical solutions of the improved perturbed parabolic-law nonlinear Schrodinger equation including non-local nonlinearity in the presence of chromatic and spatio-temporal dispersion. This model mostly makes use of studying the propagation of optical pulses in fiber optic communication systems. We performed the Sinh-Gordon equation expansion method so that we produce the analytical solutions of the model under consideration. It was confirmed that the acquired solutions satisfy the main model. Therefore, bright and dark soliton solutions were retrieved; besides, various 3D and 2D graphical illustrations of the solitons were demonstrated via appropriate values of the parameters. Furthermore, this manuscript focused on the parameters’ effect on the acquired solitons behavior.