Adaptive control of femtosecond pulse propagation in optical fibers

Nonlinear effects present fundamental obstacles to the propagation of femtosecond pulses of detectable energy in single-mode optical fibers, inducing severe distortion even after a very short (a few meters) propagation distance. We show here that adaptive pulse shaping can overcome these limitations by synthesizing pulses that are self-correcting for higher-order nonlinear effects when they are launched in the fiber. This approach would not only affect optical communications but also yield benefits in various disciplines requiring optimized fiber-based femtosecond pulse delivery, for example, nonlinear imaging techniques such as multiphoton microscopy, material processing, and medical diagnostics.     

One-photon wavepacket interacting with a two-level atom in a waveguide: Constraint on the pulse shape

We study theoretically the temporal shaping effects experienced by a one-photon wavepacket propagating in a one-dimensional waveguide containing a two-level atom. We show that the transmitted field distorts such that its pulse area (time integral of electric field amplitude) vanishes. As a consequence, specific pulses with initial zero pulse area are shown to be robust with respect to propagation whereas pulses with initial non-vanishing pulse area are shown to be more sensitive, leading to significant distortion after propagation.     

Nonlinear propagation acoustics of dual-frequency wide-band excitation pulses in a focused ultrasound system

In this article, acoustic propagation effects of dual-frequency wide-band excitation pulses in a focused ultrasound system are demonstrated in vitro. A designed and manufactured dual-frequency band annular array capable of transmitting 0.9/7.5 MHz center frequency wide-band pulses was used for this purpose. The dual-frequency band annular array, has been designed using a bi-layer piezo-electric stack. Water tank measurements demonstrate the function of the array by activating the low- and high-frequency layers individually and simultaneously. The results show that the array works as intended. Activating the low- and high-frequency layers individually, results in less than -50 dB signal level from the high- and low-frequency layers respectively. Activating both layers simultaneously, produce a well defined dual-frequency pulse. The presence of the low-frequency pulse leads to compression, expansion, and a time delay of the high-frequency pulse. There is a phase shift between the low- and high-frequency pulse as it propagates from the array to the focus. This makes the latter described effects also dependent on the array configuration. By varying the low-frequency pressure, a shift of up to 0.5 MHz in center frequency of a 8.0 MHz transmitted high-frequency pulse is observed at the array focus. The results demonstrate the high propagation complexity of dual-frequency pulses.     

Ultrashort pulse propagation and nonlinear frequency conversion in superconducting and magnetic photonic crystal

We study the propagation and second harmonic generation of ultrashort pulse in nonlinear photonic crystal using a combination of Fourier transform and transfer matrix method. The focus is on the reflected and transmitted output of fundamental pump pulse and second harmonic pulse in frequency and time domains, the temperature dependence of the reflection and transmission spectra where the superconducting transition frequency is close to the magnetic resonance. Interesting features include output pump and second harmonic pulses that can be strongly modulated with the transmitted pulses being delayed by slow light effect.     

Intraband effects on ultrafast pulse propagation in semiconductor optical amplifier

High bit-rate (>10 Gb/s) signals are composed of very short pulses and propagation of such pulses through a semiconductor optical amplifier (SOA) requires consideration of intraband phenomena. Due to the intraband effects, the propagating pulse sees a fast recovering nonlinear gain which introduces less distortion in the pulse shape and spectrum of the output pulse but introduces a positive chirping at the trailing edge of the pulse.     

Nonlinear pulse propagation in periodic media with and without defects

The influence of single defects within a periodic structure on the nonlinear transmission of optical pulses through the structure is investigated numerically. A stack of alternating linear and cubically nonlinear layers of submicron thicknesses is considered. The simulations are based on a modified equation for the pulse envelope. Diffraction of the pulse has been taken into account, too. The results of simulations have been demonstrated as an essential influence of defects within the periodic structure on the nonlinear propagation of optical pulses, when the carrier frequency is chosen within the stop band of the structure with the defect.     

Ultra-short pulse propagation in 3D GaAs photonic crystals

We have investigated ultra-short pulse propagation through 3D GaAs photonic crystals with a complete photonic band gap in the optical wavelength region. The pulse propagation was calculated by using the finite-differential time-domain (FDTD) method. This is the first time pulse shape measurements have been made using femtosecond pulses. From the experimental results, the shapes of the ultra-short pulses were found to change when the frequency was above the photonic band-gap after the propagation through the photonic crystal, corresponding to the simulation results.     

Effects of initial frequency chirp on the linear propagation characteristics of the exponential optical pulse

In this paper, the linear propagation characteristics of the exponential optical pulse with initial linear and nonlinear frequency chirp are numerically studied in a single mode fibre for \be₂<0. It can be found that the temporal full width at half maximum and time-bandwidth product of exponential pulse monotonically increase with the increase of propagation distance and decrease with the increase of linear chirp C for C<0.5, go through an initial decreasing stage near \zeta=1, then increase with the increase of propagation distance and linear chirp C for C\geq0.5. The broadening of pulses with negative chirp is faster than that with positive chirp. The exponential pulse with linear chirp gradually evolves into a near-Gaussian pulse. The effect of nonlinear chirp on waveform of the pulse is much greater than that of linear chirp. The temporal waveform breaking of exponential pulse with nonlinear chirp is first observed in linear propagation. Furthermore, the expressions of the spectral width and time-bandwidth product of the exponential optical pulse with the frequency chirp are given by use of the numerical analysis method.     

An improved nonlinear optical pulse propagation equation

A new equation for self-focusing of extremely focused short-duration intense pulses is derived using a method that treats diffraction and dispersion to all orders with nonlinearity present, and self-consistently determines the nonlinear derivative terms present in the propagation equation. It generalizes both the previous formulation of linear optical pulse propagation to the nonlinear regime, and the cw nonlinear regime propagation to the pulsed regime by including temporal characteristics of the pulse. We apply the new equation and propagate a tightly focused picosecond pulse in silica and explicitly show the effects of spatial-derivative nonlinear coupling terms.     

Observation of negative velocity pulse propagation

The propagation of suitably shaped millimetre wave pulses through a linear resonant molecular absorber is studied in order to give an experimental support to the concept of negative group velocity. Significant pulse advances with negligible distortion are actually observed with a true shape detection.     

光脉冲在一维负折射材料光子晶体中的传播

讨论了一维负折射光子晶体对光脉冲传播的影响.通过对光脉冲的透射场强的数值计算发现,频谱处于一维负折射率材料光子晶体禁带中的短脉冲通过光子晶体后基本保持形状不变,而对同样的短脉冲通过传统的一维光子晶体的透射脉冲则出现严重畸变.当考虑负折射率材料的色散时,讨论了位相时间随光脉冲载波频率的变化情况.     

The Distortion Characteristics of a Pulse Wave Propagating through Fog Medium at Millimeter Wave Band

When a pulse wave propagates through fog, the effects of distortion, being severer at millimeter wave band, is caused by fog because of its dispersive property. The transfer function of a pulse signal is obtained by the theory of radio wave propagation; the complex envelope is deduced by the solution of Fourier integral. The broadening and compressing effects of a pulse wave are discussed. The variations of distortion effects with pulse-width, propagation distance and visibility of fog are found. As an example, the simulating and calculating results of distortion effects for Gaussian pulse at millimeter wave band are given.     

高阶效应对超短艾里-高斯脉冲相互作用的影响

本文运用分步傅里叶变换,对满足高阶耦合非线性薛定谔方程的超短艾里脉冲与超短高斯脉冲,利用MATLAB数值模拟了在高阶效应下两脉冲相互作用后的演化过程以及时域上的强度变化。结果表明：负三阶色散效应使超短脉冲相互作用能传输更远距离;正三阶色散效应会减慢超短脉冲相互作用的传输。自陡峭效应通过孤子分裂现象的形式使超短脉冲相互作用产生时域位移,内拉曼效应可以将超短脉冲相互作用的能量由前沿处转移到后沿处。     

高阶效应对超短艾里-高斯脉冲相互作用的影响

本文运用分步傅里叶变换,对满足高阶耦合非线性薛定谔方程的超短艾里脉冲与超短高斯脉冲,利用MATLAB数值模拟了在高阶效应下两脉冲相互作用后的演化过程以及时域上的强度变化.获得了负三阶色散效应使超短脉冲相互作用能传输更远距离;正三阶色散效应会减慢超短脉冲相互作用的传输.自陡峭效应通过孤子分裂现象的形式使超短脉冲相互作用产生时域位移.内拉曼效应可以将超短脉冲相互作用的能量由前沿处转移到后沿处.     

高阶效应对超短艾里-高斯脉冲相互作用的影响

本文运用分步傅里叶变换,对满足高阶耦合非线性薛定谔方程的超短艾里脉冲与超短高斯脉冲,利用MATLAB数值模拟了在高阶效应下两脉冲相互作用后的演化过程以及时域上的强度变化。结果表明：负三阶色散效应使超短脉冲相互作用能传输更远距离;正三阶色散效应会减慢超短脉冲相互作用的传输。自陡峭效应通过孤子分裂现象的形式使超短脉冲相互作用产生时域位移,内拉曼效应可以将超短脉冲相互作用的能量由前沿处转移到后沿处。     

Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers

A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed in the combined frequency-time domain algorithm. The diffraction is described using the implicit backward finite-difference scheme and the alternate direction implicit method. An analytic solution in the time domain is employed for the nonlinearity operator. The absorption and dispersion of the sound speed are also described using an analytic solution but in the frequency domain. Numerical solutions are obtained for the nonlinear acoustic field in a homogeneous tissue-like medium obeying a linear frequency law of absorption and in a thermoviscous fluid with a quadratic frequency law of absorption. The model is applied to study the spatial distributions of the fundamental and second harmonics for a typical diagnostic ultrasound source. The nonlinear distortion of pulses and their spectra due to the propagation in tissues are presented. A better understanding of nonlinear propagation in tissue may lead to improvements in nonlinear imaging and in specific tissue harmonic imaging. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 560–570. This article was translated by the authors.     

Ultrafast pulse sources based on multi-mode optical fibers

Ultrafast pulse sources based on multi-mode optical fibers are discussed. High-power passively mode-locked fiber lasers based on multi-mode rare-earth-doped optical fibers greatly exceed the power limitations of single-mode oscillators. Ultrafast multi-mode fiber amplifiers operating in conjunction with multi-mode oscillators provide even higher power levels, where nonlinear propagation effects enable pulse compression to below 100 fs. Multi-mode fiber oscillators can be combined with single-mode Raman-shifting fibers to produce widely wavelength-tunable sources of femtosecond pulses. Further amplification in Yb fibers allows for the generation of sub-100-fs pulses with W-level average powers.     

Contact phase modulation method for acoustic nonlinear parameter measurement in solid

In this work, a new method to measure in contact the nonlinearity parameter beta of solid plates is presented. A high frequency (HF) tone-burst signal of 20 MHz is inserted in the material by a contact-transducer (with a suitable coupling). A low frequency (LF) pulse (2.5 MHz) is applied to the other face, in the opposite direction, so that the nonlinear interaction of the two waves takes place during the back propagation toward the HF transducer. This collinear interaction creates a phase modulation of the HF tone-burst which is proportional to the beta coefficient and the particle velocity of the LF wave. To determine this particle velocity, in time domain, an extended self-reciprocity calibration of the contact LF transducer is used. A numeric phase demodulation is then performed, giving the beta coefficient of the sample. The proposed method is validated by nonlinearity parameter measurements in Fused Silica. The nonlinear parameter of Fused Silica measured is found to be in good agreement with the literature, and specially the negative sign of this parameter.     

Research on the nonlinear pulse propagation by numerical analysis

Based on the computation approaches of numerical analysis in electromagnetic, the nonlinear pulse propagation in optical fiber is investigated in this paper. The transforming rule of the shape and spectrum of Gauss pulse are also researched in chirped and non-chirped scenarios from the nonlinear Schrödinger equation (NLSE). Analyzing the transient wave behavior in time domain and frequency domain respectively, the compression effect of chirp is also presented at different propagation distance. Then by the nonlinear Schrödinger equation, we discuss a specific solution in the quasi soliton without distortion, which has the stable propagation properly, and do the numerical simulation in soliton wave. Finally, by selecting proper fiber structure parameters and adjusting the width in soliton pulse, the soliton communication system can be optimized.     

Propagation dynamics of nonlinear chirped optical laser pulses in a two-level medium

We investigate the propagation dynamics of nonlinear chirped optical laser pulses in a two-level medium. For certain chirp strength and chirp width, an incident 2π nonlinear chirped pulse will split into optical precursors and a stable self-induced transparency soliton. This is caused by the particular Fourier spectrum that includes not only central resonant frequency components but also high-frequency and low-frequency sidebands. Moreover, the effects of chirp parameters on the evolution of nonlinear chirped pulses are also discussed.