XPM Effect Research Articles

High-precision passive stabilization of a dissipative soliton resonance laser repetition rate based on optical pulse injection.

I present what is believed to be the first demonstration of using the cross-phase modulation (XPM) effect to achieve high-precision, all-optical synchronization and stabilization of the pulse repetition rate of a dissipative soliton resonance (DSR) mode-locked (ML) fiber laser working in the 1.06 µm wavelength range. Nanosecond 1.55 µm Master oscillator pulses were injected into the Slave cavity of the DSR laser to induce the XPM effect and subsequently synchronize both repetition rates. When referencing the Master laser to a rubidium frequency standard, the fractional instability of the DSR ML laser pulse repetition rate reached 1.26 × 10-12 for 1000 s integration time. The locking range and stability of the XPM synchronization are experimentally verified under varying conditions and discussed in the paper.

Analysis of performance limits in optical communications due to fiber nonlinearity and third order dispersion

In this study, an analysis is conducted to treasure the expressions of the pulsation expansion factor, in addition to the standardized output, and solve the nonlinear Schrödinger equation (NLSE), reflecting the impact of XPM on third order dispersion. Using large effective area fiber (LEAF) and standard single-mode fiber (SSMF), the effects of transmission distances and varying input powers are assessed at various transmission speeds. The first and second order GVD XPM effects are the only factors influencing the pulse’s propagation. The second-order effects of GVD are not noticeable at short distances and low bit rates, but they become noticeable and impact system performance as the bit rate increases. The study discovered that input dominance has less of an impact on pulse width than data rate and fiber length. Methodical derivation and numerical simulation using the split-phase Fourier method at the same data rate and input power yield the SSMF and LEAF consequences. In comparison to LEAF fibers, XPM has a greater beneficial impact on second and third order dispersion in SSMF fibers.

Harnessing XPM effects in non-linear directional couplers for 4-bit gray code conversion and even parity verification

Abstract The all-optical switching phenomena in the non-linear directional coupler using cross-phase modulation (XPM) effect have been proposed. It is designed to generate an all-optical XOR functionality, considering the XOR logic gates as a basic module the design and analysis of an efficient all-optical 4-bit binary to gray code converter and 4-bit even parity checker circuit is proposed. The design methodology includes the switching of a weak continuous-wave (CW) signal, which is controlled by the combination of two controlled pump signals. In this paper, mathematical analysis of the coupled mode theory associated with optical directional couplers has been discussed. The switching characteristics of XPM effect based All-optical directional couplers have been examined for appropriate values of the controlled pump signals. Appropriate values of extinction ratio and corresponding controlled pump signal levels are investigated for an efficient generation of XOR logic gates. Further, the detailed analysis of layout generation and design aspects of All-optical 4-bit binary to gray code converter and 4-bit even parity checker circuits have been carried out. The proposed methodology is verified by the appropriate simulation results, which include the transmittivity, extinction ratio (Xratio) curve variation and dynamic time domain plot associated with proposed units.

Design and analysis of all-optical half and full adder/subtractor using nonlinear asymmetric directional couplers

The utilization of nonlinear asymmetric directional couplers has emerged as a viable alternative to conventional systems for the execution of arithmetic operations using optical signals. The present study explores the utilization of a coupler-based framework for the development of an all-optical half- and full-adder/subtractor circuit designed with the basic logic gates (AND, OR, XOR) and a soliton pulse as input signals. Nonlinear asymmetric directional couplers have been analysed theoretically and numerically, including the detailed mathematics of coupled wave theory. The switching characteristics of XPM effect based All-optical directional couplers have been examined for appropriate values of the phase shift (∆φ). Appropriate values of ∆φ, extinction ratio (dB), and corresponding controlled pump signal levels and other parameters are investigated for an efficient generation of fundamental logic gates. Further, the detailed analysis of layout generation and design aspects of an all-optical half- and full-adder/subtractor circuit along with the basic logic gates circuits has been carried out. Simulation results are validated with the standard result. The research findings demonstrate that soliton pulses might potentially be useful for optical computing applications when used as the input signal to nonlinear asymmetrical directional couplers.

Hyperbolic resonant radiation of concomitant microcombs induced by cross-phase modulation

A high-quality optical microcavity can enhance optical nonlinear effects by resonant recirculation, which provides a reliable platform for nonlinear optics research. When a soliton microcomb and a probe optical field are coexisting in a micro-resonator, a concomitant microcomb (CMC) induced by cross-phase modulation (XPM) will be formed synchronously. Here, we characterize the CMC comprehensively in a micro-resonator through theory, numerical simulation, and experimental verification. It is found that the CMCs spectra are modulated due to resonant radiation (RR) resulting from the interaction of dispersion and XPM effects. The group velocity dispersion induces symmetric RRs on the CMC, which leads to a symmetric spectral envelope and a dual-peak pulse in frequency and temporal domains, respectively, while the group velocity mismatch breaks the symmetry of RRs and leads to asymmetric spectral and temporal profiles. When the group velocity is linearly varying with frequency, two RR frequencies are hyperbolically distributed about the pump, and the probe light acts as one of the asymptotic lines. Our results enrich the CMC dynamics and guide microcomb design and applications such as spectral extension and dark pulse generation.

All-optical aggregation and de-aggregation between OOK, QPSK and 8QAM signals based on nonlinear effects

An all-optical aggregation and de-aggregation scheme between on–off keying (OOK) signals, quadrature phase shift keying (QPSK) signals and 8-ary quadrature amplitude modulation (8QAM) signals is proposed and numerically simulated based on nonlinear effects in the high nonlinear fiber (HNLF). In the de-aggregation processing, the input 30 Gbit/s 8QAM signal is firstly de-aggregated into one 20 Gbit/s QPSK signal and one 10 Gbit/s binary phase shift keying (BPSK) signal by deploying self-phase modulation (SPM), cross-phase modulation (XPM), four-wave mixing (FWM) and parameter amplification (PA) effects. One continuous optical carrier can be extracted from the converted BPSK signal by designing a feed-forward based modulation stripping configuration. The converted OOK signal can be obtained through vector superposition between the extracted optical carrier and the converted BPSK signal. In the aggregation processing, the converted 20 Gbit/s QPSK signal and the 10 Gbit/s OOK signal are fed to another HNLF and aggregated into one 30 Gbit/s 8QAM signal again by utilizing XPM and PA effects. Moreover, the aggregated 8QAM signal keeps the same wavelength and information integrity as the input 8QAM signal. the Error vector magnitude (EVM) and the bit error ratio (BER) for the 8QAM signal before and after aggregation and de-aggregation are measured to evaluate the scheme performance. The proposed all-optical aggregation and de-aggregation scheme for the advanced and simple modulation formats can be applied at the intermediate network node (INN) to solve the network traffic aggregation and de-aggregation with different modulation formats.

All-Optical Format Conversion for Star-8QAM Signals Based on Nonlinear Effects in Elastic Optical Networks

An all-optical format conversion (AOFC) scheme for star-octal quadrature amplitude modulation (star-8QAM) signals is proposed and numerically simulated based on nonlinear effects in the high nonlinear fiber (HNLF). In the first stage AOFC processing, the input 30 Gbit/s star-8QAM signal is firstly de-aggregated into one 20 Gbit/s quadrature phase shift keying (QPSK) signal and one 10 Gbit/s typical on-off keying (OOK) signal by deploying the self-phase modulation (SPM), cross-phase modulation (XPM) and parametric amplification (PA) effects. In the second stage AOFC processing, the 20 Gbit/s QPSK signal and the 10 Gbit/s typical OOK signal are aggregated into one 30 Gbit/s star-8QAM signal again by utilizing the XPM and PA effects. Moreover, the amplitude ratio (AR) between the outer ring and inner rings of the aggregated star-8QAM signal can be adjusted flexibly by changing the QPSK and OOK signals power. Other octal modulation formats can also be generated through changing the QPSK and OOK signals power, including the rectangular 8QAM signals, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pi$</tex-math></inline-formula> /4-8QAM signals and 8-ary phase shift keying (8PSK) signals. Error vector magnitude (EVM) and bit error ratio (BER) for star-8QAM signals before and after AOFC are measured to analyse the scheme performance. The AOFC scheme provides the flexibility to adopt the appreciate modulation formats at the optical nodes to connect different optical networks.

Research of fiber nonlinear effects in WDM-PON based 5G fronthaul networks

In fifth-generation (5G) fronthaul networks, the wavelength division multiplexing passive optical network (WDM-PON) is considered as an important tool to address the advanced transmission requirements. The nonlinear effects occur when multiple wavelengths are transmitted simultaneously in the same optical fiber. In this paper, we investigate the four-wave mixing (FWM) and the cross-phase modulation (XPM) effects by using non-return-to-zero (NRZ), 4-level pulse amplitude modulation (PAM4), and optical duobinary (ODB) modulation formats in WDM-PON-based 5G fronthaul networks. The results show that ODB performs better when it comes to limiting the FWM and XPM effects because of its precoded attribute. Compared to the unpredictable sensitivity penalty based on NRZ and PAM4, the FWM-induced sensitivity penalty using ODB is reduced to 2[Formula: see text]dB. Moreover, the XPM-induced sensitivity penalty is measured as 1[Formula: see text]dB by adopting ODB, which is almost 5[Formula: see text]dB better than NRZ and PAM4 modulation formats.

XPM Efficiency Versus Symbol Rate

Cross-Phase Modulation (XPM) limits the information capacity of optical fibers, due to the power fluctuations in one channel affecting the phases of the other channels. A decade ago, we showed that splitting a channel into multiple subcarriers could reduce the effect of XPM on multi-channel systems, due to a reduction in the intensity fluctuations at frequencies where walk-off is low. As commercial systems now take advantage of this effect, it is appropriate to give a more detailed and quantitative explanation of it; in particular to show that the optimal subcarrier rate scales with the square-root of the chirp rate of the symbols, which depends only on the accumulated dispersion in the fiber. Simulations show that the optimal symbol rate is when the time-spread of the symbols due to dispersion is between 2.5× to 6.5× of their transmitted (central pulse) widths. This paper presents simple arguments backed by simulations to identify the key parameters that determine the optimal subcarrier rate. In particular, we show that there is an optimal balance between the intrinsic intensity fluctuations of transmitted symbols (which are lower-frequency for lower symbol rates) and the intensity fluctuations due to chirp (which are lower-frequency for higher symbol rates). We also discuss why the traditional XPM-efficiency equation is not appropriate when data is transmitted, because it assumes the XPM contributions of all spans in an amplified link are equal, rather than increasing with distance.

High relative-intensity blue light of supercontinuum generation in photonic crystal fibers

A distinct blue peak at 430 nm of the supercontinuum spectrum is generated in 4.6 m photonic crystal fiber with a high air-filling ratio, which is pumped by a 200 ps pulse laser at 1 µm. The amplitude of the blue peak is higher than that of the remaining pump pulse, and the relative intensity blue light of supercontinuum generation is 114%. We have systematically analyzed the formation mechanism and influence factors of the distinct blue peak with different fiber lengths and input pulses. The experimental results show that the wavelength position of the blue peak in the supercontinuum spectrum is almost unchanged, and both the fiber length and pulse width have a great influence on the intensity of the blue peak. In addition, we have discussed the fact that the dynamic changes of the blue peak may be affected by the ∼ 2200 n m peak through cross-phase modulation (XPM). It is possible that the high relative intensity of the blue peak in high-order modes may be originated from the XPM effect and the third-harmonic wave of the fundamental mode.

Simulation investigation of XPM and SRS effect on upgraded Super-PON systems

Considering the increasing demands of bandwidth and the limited spectrum resources, it is necessary to organize several plans for the upgradation of the Super-PON system. Generally, two schemes have been proposed as the improvement involving the increment of the line-rate per channel up to 25 Gbit/s and using bidirectional transmission on one wavelength. Here, the influence of Cross-Phase Modulation (XPM) in the case of line-rate/channel increment and Stimulated Raman Scattering (SRS) in the case of bidirectional transmission on one wavelength has been investigated, respectively. For the former, XPM obviously causes degradation impact on 25 Gbit/s non-return-to-zero (NRZ)/4-level pulse amplitude modulation (PAM4) signal transmission, resulting in an unpredictable sensitivity penalty (cannot reach the bit error rate (BER) of 1 × 10−2), which can be counteracted in use of optical duobinary (ODB) modulation format demonstrating a sensitivity penalty of 1-dB under the same condition. For the later, the SRS effect causes a power depletion of 1 dB/0.6 dB for pump frequencies of downstream/upstream during the 10 Gbit/s bidirectional transmission on the same wavelength.

Characteristics of Attention Bias in Patients With Depression Disorder, and the Influence of High Frequency Transcranial Magnetic Stimulation Therapy on the Attention Bias

We propose a general model to entirely describe XPM effects induced by 16QAM channels in hybrid QPSK/16QAM wavelength division multiplexed (WDM) systems. A power spectral density (PSD) formula is presented to predict the statistical properties of XPM effects at the end of dispersion management (DM) fiber links. We derive the analytical expression of phase error variance for optimizing block length of QPSK channel coherent receiver with decision-aided (DA) maximum-likelihood (ML) phase estimation (PE). With our theoretical analysis, the optimum block length can be employed to improve the performance of coherent receiver. Bit error rate (BER) performance in QPSK channel is evaluated and compared through both theoretical derivation and Monte Carlo simulation. The results show that by using the DA-ML with optimum block length, bit signal-to-noise ratio (SNR) improvement over DA-ML with fixed block length of 10, 20 and 40 at BER of 10−3 is 0.18 dB, 0.46 dB and 0.65 dB, respectively, when in-line residual dispersion is 0 ps/nm.

All-Optical Aggregation and De-Aggregation Between 8QAM and BPSK Signal Based on Nonlinear Effects in HNLF

An all-optical aggregation and de-aggregation scheme between one 8-ary quadrature amplitude modulation (8QAM) signal and three binary phase shift keying (BPSK) signals is proposed and theory simulated based on nonlinear effects in high nonlinear fiber (HNLF). In this scheme, the input 8QAM signal is de-aggregated into three BPSK signals by deploying self-phase modulation (SPM), cross-phase modulation (XPM), four wave mixing (FWM) and parameter amplification (PA) effect. Firstly, an improved amplitude compression loop (ACL) is designed based on SPM effect to convert 8QAM signal into quadrature phase shift keying (QPSK) signal. A degenerate phase sensitive amplifier (PSA) based on FWM effect is used to decompose QPSK signal into the first two BPSK signals (BPSK-1 and BPSK-2). The third BPSK signal (BPSK-3) can be extracted from the probe light modulated in its phase by the input 8QAM signal thanks to XPM and PA effect. Secondly, BPSK-3 is converted into an atypical on-off keying (OOK) signal through a 1-bit delay interference (DI). BPSK-1 and BPSK-2 are recombined into one QPSK signal through a coupler. Finally, the recombined QPSK signal and the atypical OOK signal are aggregated into one 8QAM signal by using XPM and PA effect. The error vector magnitude (EVM) and bit error ratio (BER) of the 8QAM and BPSK signal before and after de-aggregation and aggregation are calculated to analyse the performance of the scheme. The scheme can be applied in the network node to connect different networks which explore to use 8QAM and BPSK signal respectively.

Simulation and experimental investigation of cross-phase modulation effect on 5G fronthaul wavelengths

Dense wavelength-division multiplexing is conceived as an appropriate solution for the 5G fronthaul system to cope with the rapidly increasing demand for bandwidth. While the cross-phase modulation (XPM) would appear when the signals are transmitted simultaneously in the single-mode fiber. The XPM effect on the 5G fronthaul wavelengths is investigated through both simulation and experimental campaigns. Simulation results show that the electrical spectrum crosstalk will occur with the wavelengths transmitting synchronously, when the channel spacing is 100 GHz and the speed is 25 Gbit / s per channel in the 10-km link. Also, the intensity of the electrical spectrum crosstalk becomes stronger when the launch power increases from 10 until 14 dBm. While comparing with the results obtained from the positive-intrinsic-negative (PIN) detector, the XPM-induced sensitivity penalty can be alleviated by 0.3 dB in use of avalanche photodiode (APD), which can provide higher signal-to-noise ratio. Consistent with the simulation results, the electrical spectrum crosstalk also appears in the experimental campaign under the same conditions. Furthermore, a sensitivity improvement of 0.5 dB is obtained using 25-GHz APD receiver, compared with the adoption of 35-GHz PIN receiver case.

Mitigation of the XPM in 5G fronthaul wavelengths by using orthogonal polarization method

In the dense wavelength-division multiplexing (DWDM)-based 5G fronthaul network, cross-phase modulation (XPM) would become more obvious to degrade the signal when the interval between the channels becomes narrower. Meanwhile, theoretically, the relative polarization angle between the adjacent channels tends to be more consistent in the same case, that it appears effective on the suppression of XPM by using the orthogonal polarization method In this paper, the orthogonal polarization method has been analyzed and applied on multi-channel transmission for suppressing the XPM effect at a 5G fronthaul system which is illustrated on both simulation and experimental results. By the simulation in the case of 25 Gbit/s per channel, ∼0.6/∼0.8 dB sensitivity improvement can be achieved in orthogonal-polarization-state after 10 km/15 km transmission, comparing with the same-polarization-state. In the real experiment, ∼0.7 dB/∼0.9 dB sensitivity improvement has been realized under the same condition as the simulation. This is relatively-more effective comparing with the published results in using one single method to suppress XPM in the WDM systems.

Performance Evaluation of SD-WDM System to Mitigate the Effect of XPM using HOA

This paper has dealt with the mitigation effect of cross-phase modulation (XPM) which is a nonlinear effect of fiber losses. To control the losses, we have used a quantum dot vertical cavity semiconductor optical amplifier with vertical cavity semiconductor optical amplifier as hybrid optical amplifier (HOA). Further, an analysis of 560 channels with a data rate of 40 Gbps has been done to achieve the acceptable rating of gain, quality factor and noise figure. The final suggestion has recommended that the proposed HOA is most suitable to control the XPM with a received quality factor from 40 to 16 dB.

Theoretical analysis of ultra-fast multi-wavelength switch containing Kerr nonlinear material and its application as simultaneous AND and NOR logic gates.

In this paper, an all-optical plasmonic multi-wavelength switch based on Kerr nonlinear material is proposed. It consists of circular waveguides wrapped around three side-coupled nano-ring resonators. Fundamentally, introducing the circular waveguide increases the coupling coefficient and switching modulation depth. The transmission response of the proposed multi-switching structure is studied theoretically based on coupled mode and transfer matrix theories. The validity of the derived transmission formula is confirmed by the numerical result obtained by the finite element method. Also, based on the self-phase modulation and cross-phase modulation (XPM) nonlinear effects, the resonance wavelengths are effortlessly tuned by changing the intensity of the incident lightwave without changing the dimensions of the structure. As a result, by utilizing the XPM effect, the required input signal intensity is significantly decreased to 6.5MW/cm2. The obtained modulation depths are 18.08, 31.83, and 28.40 dB at wavelengths of 850, 1310, and 1550 nm, respectively. Finally, to show the application of the proposed switch, the simultaneous AND and NOR logic gates are designed with intensity contrast ratios of 78.81 and 85.49 dB, respectively. The proposed plasmonic switch has many advantages such as being multi-wavelength and having low required switching intensity, ultra-fast switching time of 23 fs, and optical bistability. These features are promising for future integrated plasmonic devices for applications such as communications, signal processing, and sensing.

XPM mitigation in WDM systems enabled by split NLC and modified DD-RLS based NLPN tracking

We propose a cross-phase modulation (XPM) mitigation method in wavelength division multiplexing (WDM) systems, which is enabled by the split nonlinearity compensation (NLC) and the modified decision directed recursive least square (DD-RLS) based nonlinear phase noise (NLPN) tracking algorithm. In the proposed method, the split NLC reduces the interaction between the dispersion and the XPM and makes the impact of the XPM on the signal more tend to the NLPN. Combined with the proposed modified DD-RLS algorithm, which can effectively track the fast-changing NLPN, the XPM effect in WDM systems can be mitigated. The proposed method is demonstrated by a WDM transmission simulation with 11 channels. The simulation results show that the proposed modified DD-RLS algorithm has better NLPN tracking ability and noise tolerance than the normal DD-RLS algorithm, and together with the split NLC, 0.8 dB Q2-factor improvement can be seen in the 1000-km transmission.

Performance Analysis of Full-Duplex NG-PON2-RoF System with Non-linear Impairments

The motivation of this study springs from the need of exploiting the advantages of high data rate and increased mobility of the transmitted signal in the Next Generation Passive Optical Network stage 2 (NG-PON2) incorporated into Radio over Fiber (RoF) system. Nonetheless, such system is prone to degradation due to the nonlinear effects, namely, the non-linear impairments. Accordingly, this study suggests a design for a full-duplex NG-PON2-RoF system and it investigates the impact of the nonlinear effects on the performance of system, such as; Self-Phased Modulation (SPM), Cross-Phase Modulation (XPM), and Four-Wave Mixing (FWM). However, these effects would result in a significant data loss in Time and Wavelength Division Multiplexing-Passive Optical Network (TWDM-PON). To achieve the intended purpose of this investigation, both the performance of the suggested system and the nonlinear effects of SPM, XPM, and FWM are measured with reference to the qualitative parameters, such as; Bit Error Rate (BER), Q-Factor, Power link Budget, and the Eye-diagram. The results show that the system performs efficiently; however, in the presence of the nonlinear effects, the performance of the systems degrades significantly affecting the signal quality. It is worth noting that the FWM effect yields the most negative impact followed by the XPM, and the SPM effect yields the least significant impact on the system. Also, the system yields the capacity of transmitting range of 20-100 Km, and it results in data rate of 40-80 Gbps. The proposed system is simulated using the software Optisystem 15.

Mid-infrared dual-comb generation via the cross-phase modulation effect in a normal-dispersion microcavity.

We numerically demonstrate orthogonally polarized dual-comb generation in a single microcavity with normal dispersion assisted by the cross-phase modulation (XPM) effect. It is found that the XPM effect facilitates the emission of a secondary polarized comb with different temporal properties in a wide existence range covering the blue- to red-detuned regime and thus releases the requirements for delicate control on the detuned region of pump frequency. Also, the energy transfer between two polarization components together with the normal-dispersion property contributes to a more balanced intensity difference and significantly increased conversion efficiency from the pump light into the comb operation. This work could provide a route to a low-cost and compact mid-infrared dual-comb system with a lower power requirement as well as an effective approach to higher comb teeth power with improved efficiency for practical applications.