Effect Of Chirp Research Articles

Multi-GeV electron acceleration by a periodic frequency chirped radially polarized laser pulse in vacuum

Linear and periodic effects of frequency chirp on electron acceleration by radially polarized (RP) laser pulse in vacuum have been investigated. A frequency chirp influences the electron dynamics, betatron resonance, and energy gain by electron during interaction with the RP laser pulse and ensures effective electron acceleration with high energy gain (~GeV). The electron energy gain with a periodic frequency chirped laser pulse is about twice as high as with a linear chirp. Our observations reveal electron energy gain of about 10.5 GeV with a periodic chirped RP petawatt laser pulse in vacuum.

Towards high-order modulation using complex modulation of semiconductor lasers.

Optical communication using high-speed on-off-keying signal by directly modulated semiconductor lasers (DML) was one of the most significant breakthroughs for telecommunication in 1960s. The wide deployment of 2.5-Gb/s per-channel transoceanic optical fiber links in 1990s drove the internet as a global phenomenon. However, the detrimental frequency chirp of DML prevents its application to the subsequent internet capacity evolution. Today, the state-of-the-art long-haul optical transponder uses external modulators to support high-order complex modulation. In contrast, this paper shows that the "detrimental" chirp effect can be exploited to generate complex modulation with a single DML, which achieves dramatic sensitivity gain of signal-to-noise-ratio compared to the conventional intensity modulation of DML. By using large chirp parameters, complex-modulated DML paves an attractive pathway towards high-order pulse-amplitude modulation with an ultra-low transmitter cost, which has great potential in future medium reach optical communications.

(2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect**Project supported by the National Natural Science Foundation of China (Grant No. 41406018).

In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.

Simulation and Measurements of Chirp Penalties for Silicon Ring Resonator Modulators

Due to its compact size and its ability for wavelength dense multiplexing (WDM) implementation with low-insertion-loss, silicon ring resonator modulator (Si-RRM) is acknowledged to be a good candidate for off-board escape with demand for increased bandwidth densities (>1000 Gb/s/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) up to 2 km (intradata centers). Passive optical network with transmission reach up to ~50 km is another application where Si-RRMs could be of great interest (WDM and NGPON2 PONs). Nevertheless, one known characteristic of the Si-RRM is its inherent phase modulation when achieving intensity modulation, which leads to a modification of the transmission properties after propagation over a few kilometers of single-mode fiber (SMF). In this letter, we propose a model for simulating chirp effects of modulated Si-RRMs, and measure the associated transmission penalties over several SMF lengths. Simulations and measurements show to be in good agreement.

DUAL-CHIRP ARBITRARY MICROWAVE WAVEFORM GENERATION BY USING A DUAL PARALLEL MACH-ZEHNDER MODULATOR FEEDING WITH RF CHIRP SIGNAL

In this paper, dual-chirped arbitrary microwave waveform has been generated through photonics, incorporated with single dual parallel mach-zehnder modulator (DPMZM) inbuilt mach zehnder interferometer (MZI) structure. We have taken two cases of chirping, i.e., linear and nonlinear chirps. A case of linear chirping has been explored previously. However, to the best of the authors' knowledge effect of nonlinear chirping in this paper is evaluated for the first time. Other photonics approaches are also available, such as spectra shaping and wavelength to time mapping. But due to fixed spectral response of spectral shaper, center frequency of linear chirp generated waveform is fixed. To get large center frequency again we have to use large number of spectral shapers which will increase the system complexity. DPMZM avoids such difficulties. These MZMs are biased at the minimum transmission point to get carrier suppressed modulation. Product modulator (PM) is cascaded to the lower arm of DPMZM. Here by using DPMZM we get two advantages. First we have two complimentarily chirped microwave waveforms and second up conversion of the frequency of microwave carrier. A dual-chirped microwave waveform with centre frequency 6 GHz with bandwidth 200 MHz and 2 GHz is generated. The paper gives specific details about various performance parameters such as input signal frequency and power, output signal parameters viz output frequency, chirp rate, chirp bandwidth, time bandwidth product (TBW), etc. The overall model and its performance parameters are computed through MATLAB simulation.

级联单模光纤中初始啁啾对高阶孤子脉冲压缩的影响

级联单模光纤中初始啁啾对高阶孤子脉冲压缩的影响

Complex modulation and detection with directly modulated lasers.

Due to the chirp effect, the modulation information is carried by both intensity and phase of the optical signal generated by a directly modulated laser (DML). Compared to the signal recovery based on intensity alone, the receiver sensitivity is significantly improved when phase is also involved for signal recovery. In this paper, we provide thorough analysis of two schemes to recover the directed modulated signal based on the combined information of intensity and phase. The intensity and phase combined recovery for polarization-division-multiplexed (PDM) directly modulated signal is demonstrated for the first time, achieving a data rate of 40 Gb/s over a transmission distance of 160 km. Compared with the conventional intensity-only recovery, the receiver sensitivity is improved by 5.5 dB and 10 dB respectively by using two intensity and phase combined recovery schemes.

Trichromatic π-Pulse for Ultrafast Total Inversion of a Four-Level Ladder System

We present a numerical solution for complete population inversion in a four-level ladder system obtained by using a full π-pulse illumination scheme with resonant ultrashort phase-locked Gaussian laser pulses. We find that a set of pulse areas such as √3π , √2π , and √3π completely inverts the four-level system considering identical effective dipole coupling coefficients. The solution is consistent provided the involved electric fields are not too strong and it is amply accurate also in the case of diverse transition dipole moments. We study the effect of detuning and chirp of the laser pulses on the complete population inversion using the level structure of atomic sodium interacting with ps and fs pulses as an example. Our result opens the door for multiple applications such as efficient ultrashort pulse lasing in the UV or the engineering of quantum states for quantum computing.

Effect of initial chirp on supercontinuum generation in dispersion decreasing fibers

Numerical simulations based on generalized nonlinear Schrödinger equation are used to study the effect of initial chirp on supercontinuum generation in dispersion decreasing fibers. The simulation results show that the effect of initial chirp on SC generation is highly related to the choices of pumping conditions and fiber parameters. When the pumping condition and the fiber parameters are different, the effect of initial chirp on SC generation may follow different patterns. To better discuss the effects of pulse parameters and fiber parameters on SC generation, the three normalized parameters: input soliton order, normalized dispersion slope and normalized effective fiber length are introduced. For a given input soliton order and a given normalized dispersion slope, there exists an optimal normalized effective fiber length for generating a flattest SC spectrum. On the condition of normalized effective fiber length in the vicinity of its optimal value, when DDF has small normalized dispersion slope, proper positive chirps can significantly enhance the SC bandwidth, while negative chirps or too large positive chirps suppresses the SC bandwidth. There is a wide range of positive chirps that can enhance the SC bandwidth, but the range of proper positive chirps become narrower as input soliton order decreases; When DDF has a large normalized dispersion slope and the pump pulse is a lower-order soliton, the enhancement of SC bandwidth by initial chirp is insignificant, and the widest SC spectrum is generated when the initial chirp is close to zero.

Comparison of cost- and energy-efficient signal modulations for next generation passive optical networks.

Extensive numerical investigations are undertaken to analyze and compare, for the first time, the performance, techno-economy, and power consumption of three-level electrical Duobinary, optical Duobinary, and PAM-4 modulation formats as candidates for high-speed next-generation PONs supporting downstream 40 Gb/s per wavelength signal transmission over standard SMFs in C-band. Optimization of transceiver bandwidths are undertaken to show the feasibility of utilizing low-cost and band-limited components to support next-generation PON transmissions. The effect of electro-absorption modulator chirp is examined for electrical Duobinary and PAM-4. Electrical Duobinary and optical Duobinary are power-efficient schemes for smaller transmission distances of 10 km SMFs and optical Duobinary offers the best receiver sensitivity albeit with a relatively high transceiver cost. PAM-4 shows the best power budget and cost-efficiency for larger distances of around 20 km, although it consumes more power. Electrical Duobinary shows the best trade-off between performance, cost and power dissipation.

Modulation Schemes for Single-Laser 100 Gb/s Links: Multicarrier

We evaluate multicarrier modulation methods for 100 Gb/s single-wavelength data center interconnects. We consider two different orthogonal frequency-division multiplexing (OFDM) techniques: DC-biased OFDM (DC-OFDM) and asymmetrically clipped optical OFDM (ACO-OFDM). We also consider two different techniques for bit loading and power allocation: fixed bit loading with preemphasis and optimized bit loading and power allocation. We first present a semianalytical performance and complexity evaluation of these OFDM methods including the effects of linear filtering, clipping, and quantization. We then include the effects of chromatic dispersion and chirp, as well as intensity and shot noises. Performance is quantified in terms of the required average optical power to achieve a target bit-error probability for a given modulator bandwidth. Complexity is quantified in terms of the resolution and sampling rate required of digital-to-analog (DAC) and analog-to-digital (ADC) converters, as well as the number of signal processing operations required. For each OFDM technique, we adjust the clipping ratio to minimize the optical power requirement. For DC-OFDM, taking into account the DAC frequency response reduces the optical power requirement up to 2 dB. ACO-OFDM is more power efficient and requires lower DAC/ADC resolution than DC-OFDM, but ACO-OFDM requires prohibitively high sampling rates owing to its poor spectral efficiency.

Effect of initial chirp on the broadband amplitude noise of supercontinuum generated in fiber normal dispersion region

Based on the generalized stochastic nonlinear Schrödinger equation, the effect of initial chirp on the broadband amplitude noise of supercontinuum generated in fiber normal dispersion regime is investigated numerically. The results show that, in the normal dispersion region, where the bandwidths of the obtained spectra are less sensitive to the initial chirp parameters of the input pulses, the nonlinear process is significantly affected by the initial chirp. An optimal input positive chirp will shorten the action time of intrapulse Raman scattering, and decrease the spectral broadband amplitude noise without bandwidth and flatness loss.

Analysis of radial and longitudinal force of plasma wakefield generated by a chirped pulse laser

In present paper, the chirp effect of an electromagnetic pulse via an analytical model of wakefield generation is studied. Different types of chirps are employed in this study. Our results show that by the use of nonlinear chirped pulse the longitudinal wakefield and focusing force is stronger than that of linear chirped pulse. It is indicated that quadratic nonlinear chirped pulses are globally much efficient than periodic nonlinear chirped pulses. Our calculations also predict that in nonlinear chirped pulse case, the overlap of focusing and accelerating regions is broader than that achieved in linear chirped pulse.

Photoionization Yields in Intense fs-Laser Fields – A Systematic Investigation of Chirp Effects

Abstract The femtosecond laser ionization of several small hydrocarbon molecules (methane, ethane, propane) has been investigated as a function of the second order spectral phase (linear chirp) of laser pulses centered at λ = 807 nm. Ion yields are demonstrated to depend markedly on the linear chirp parameter. At laser intensities exceeding 5 · 1014 W/cm2 the ionization characteristics resemble an intensity-driven process, i.e. the largest ion yield is observed for a close to transform-limited laser pulse. For smaller laser intensities a pronounced sign effect in the chirp dependence appears, i.e. the maximum ion yield is observed for a negative linear chirp parameter of several hundred to thousand fs2. We suggest that this sign effect is connected to the anharmonicity of the electronic potentials involved. This suggestion is supported by the fact that basically no sign effect in the chirp dependence is observed for the noble gases argon, krypton and xenon. We further suggest that the electronic polarizability and structure plays some role as methanol does not show a marked sign-dependent chirp effect.

Electron acceleration by a chirped laser pulse in vacuum under the influence of magnetic field

A linearly polarized (LP) chirped laser pulse is employed for electron acceleration to GeV energy under the influence of azimuthal magnetic field in vacuum. LP laser pulse supports the trapping of pre-accelerated electron during laser–electron interaction in vacuum. The electron gains energy from LP laser pulse and gets accelerated in the direction of propagation of laser pulse. Additionally, the chirping increases the electron laser interaction for longer duration while the azimuthal magnetic field having pinching effect keeps the motion of electron parallel to the direction of propagation of laser pulse leads to enhance the electron acceleration. The combined effect of chirping of laser pulse and pinching of azimuthal magnetic field not only enhances the electron energy gain but also supports in retaining of gained energy by the electron for longer distances. The accelerating distance is observed to be of three times the Rayleigh length where the Rayleigh length is about 6.78 μm. We observe electron energy gain of about 1.47 GeV in the presence of azimuthal magnetic field of about 438 kG with an intense LP laser pulse of peak intensity of about 3.4 × 1021 W/cm2. Higher electron energy gain may be obtained with highly intense laser pulse.

Effect of initial frequency chirp on Airy pulse propagation in an optical fiber

We study both analytically and numerically the propagation dynamics of an initially chirped Airy pulse in an optical fiber. It is found that the linear propagation of an initially chirped Airy pulse depends considerably on whether the second-order dispersion parameter β(2) and chirp C have the same or opposite signs. For β(2)C<0, the chirped Airy pulse first undergoes an initial compression phase, then reaches a breakup area as depending on the values of C, and then experiences a lossy inversion transformation such that it continues to propagate with an opposite acceleration. The chirped Airy pulse is always dispersed during propagation in the case of β(2)C>0. The impact of truncation coefficient and Kerr nonlinearity on the chirped Airy pulse propagation is also disclosed separately.

Influence of Chirp of High-Speed Laser Diodes and Fiber Dispersion on Performance of Non-Amplified 40-Gbps Optical Fiber Links

Abstract — We model and simulate the combined effect of fiberdispersion and frequency chirp of a directly modulated high-speedlaser diode on the figures of merit of a non-amplified 40-Gbps opticalfiber link. We consider both the return to zero (RZ) and non-return tozero (NRZ) patterns of the pseudorandom modulation bits. Theperformance of the fiber communication system is assessed by thefiber-length limitation due to the fiber dispersion. We study theinfluence of replacing standard single-mode fibers by non-zerodispersion-shifted fibers on the maximum fiber length and evaluatethe associated power penalty. We introduce new dispersiontolerances for 1-dB power penalty of the RZ and NRZ 40-Gbpsoptical fiber links. Keywords — Bit error rate, dispersion, frequency chirp, fibercommunications, semiconductor laser. I. I NTRODUCTION N the current information age, there is a steady need toincrease the capacity of information transmitted to orexchanged among users, especially over optical fibers.Modern cost-effective and broadband fiber networks, such asthe fiber-to-the-home (FTTH) and radio over fiber (RoF),require directly modulated laser diodes with bandwidthexceeding 25 GHz for operating the fiber links withtransmission speeds exceeding 40 Gbps [1]. Due to theinferior characteristics in the transient regime of thesemiconductor laser, its resonance and modulation bandwidthare limited to values more or less than 10 GHz. One typicalsolution to increase the modulation bandwidth is to increasethe differential gain of the laser diode [2], [3]. This property isa typical advantage of the MQW laser diodes [4]. Sato et al.[3] demonstrated a MQW-DFB laser emitting at thewavelength of 1.55 m to meet the requirement of 40 Gbpsfiber transmission systems for use in very-short-reach fiberlinks and metro area networks [5].The intensity modulation of high-speed semiconductorlasers, however, is coupled to the phase variation through thelinewidth enhancement factor [6], [7] which then induces atime variation in the lasing frequency, referred to as“frequency chirp” [8]. This frequency chirp is proportional tothe differential gain and, therefore, attains large in high-speed

(2+1)-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves

By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new (2+1)-dimensional mKdV hierarchy is derived which popularizes the results of (1+1)-dimensional integrable system. Furthermore, the (2+1)-dimensional mKdV equation can be applied to describe the propagation of the Rossby solitary waves in the plane of ocean and atmosphere, which is different from the (1+1)-dimensional mKdV equation. By virtue of Riccati equation, some solutions of (2+1)-dimensional mKdV equation are obtained. With the help of solitary wave solutions, similar to the fiber soliton communication, the chirp effect of Rossby solitary waves is discussed and some conclusions are given.

Self-compression of intense short laser pulses in relativistic magnetized plasma

The compression of a relativistic Gaussian laser pulse in a magnetized plasma is investigated. By considering relativistic nonlinearity and using non-linear Schrödinger equation with paraxial approximation, a second-order differential equation is obtained for the pulse width parameter (in time) to demonstrate the longitudinal pulse compression. The compression of laser pulse in a magnetized plasma can be observed by the numerical solution of the equation for the pulse width parameter. The effects of magnetic field and chirping are investigated. It is shown that in the presence of magnetic field and negative initial chirp, compression of pulse is significantly enhanced.

Effect of input pulse chirp on nonlinear energy deposition and plasma excitation in water

We analyze numerically and experimentally the effect of the input pulse chirp on the nonlinear energy deposition from $5\ \mu$J fs-pulses at $800$ nm to water. Numerical results are also shown for pulses at $400$ nm, where linear losses are minimized, and for different focusing geometries. Input chirp is found to have a big impact on the deposited energy and on the plasma distribution around focus, thus providing a simple and effective mechanism to tune the electron density and energy deposition. We identify three relevant ways in which plasma features may be tuned.