Joint Estimation of Carrier Frequency and Phase Offset Based on Pilot Symbols in Quasi-Constant Envelope OFDM Satellite Systems

Spectral efficiency and energy efficiency are two important performance indicators of satellite systems. The Quasi-Constant Envelope Orthogonal Frequency Division Multiplexing(QCE-OFDM) technique can achieve both high spectral efficiency and low peak-to-average power ratio(PAPR). Therefore, the QCE-OFDM technique is considered as a promising candidate multi-carrier technique for satellite systems. However, the Doppler effect will cause the carrier frequency offset(CFO), and the non-ideal oscillator will cause the carrier phase offset(CPO) in satellite systems. The CFO and CPO will further result in the bit-error-rate(BER) performance degradation. Hence, it is important to estimate and compensate the CFO and CPO. This paper analyzes the effects of both CFO and CPO in QCE-OFDM satellite systems. Furthermore, we propose a joint CFO and CPO estimation method based on the pilot symbols in the frequency domain. In addition, the optimal pilot symbol structure with different pilot overheads is designed according to the minimum Cramer-Rao bound(CRB) criterion. Simulation results show that the estimation accuracy of the proposed method is close to the CRB.

Carrier envelope phase effect on the spatial distribution of high-order harmonic generation in asymmetric molecule

The spatial distribution in high-order harmonic generation（HHG） from the asymmetric diatomic molecule He H^（2＋） is investigated by numerically solving the non-Born–Oppenheimer time-dependent Schr？dinger equation（TDSE）. The spatial distribution of the HHG spectra shows that there is little contribution in HHG around the geometric center of two nuclei（z = 1.17 a.u.） and the equilibrium internuclear position of the H nucleus（z = 3.11 a.u.）. We demonstrate the carrier envelope phase（CEP） effect on the spatial distribution of HHG in a few-cycle laser pulse. The HHG process is investigated by the time evolution of the electronic density distribution. The time–frequency analysis of HHG from two nuclei in HeH^（2＋） is presented to further explain the underlying physical mechanism.

Relative carrier-envelope phase dependence of resonant propagation of two-colour femtosecond pulses in V-type atomic medium

Using numerical solution of the full Maxwell-Bloch equations, which is obtained by the finite-difference time-domain method and the iterative predictor-orrector method, we investigate the modulation effect of relative carrierenvelope phase （hereinafter referred to as the relative phase） on resonant propagation of two-colour femtosecond ultrashort laser pulses in a V-type three-level atomic medium. It is found that the pulse splitting occurs for a smaller value of relative phase; when the value of relative phase increases to a certain value, only the variation of pulse shape is present and the pulse splitting does not occur any more; moreover, when the value of relative phase is smaller, the pulse group velocity is larger. The relative phase also has an obvious effect on population and spectral property. Different population transfers can be realized by adjusting the value of relative phase. Generally speaking, for the pulses with smaller areas their spectral strengths and frequency ranges decrease obviously with the value of relative phase increasing; for the pulses with larger areas, with value of the relative phase increasing, their spectral strengths decrease remarkably but the relative strengths of the higher frequency components increase significantly, while the spectral frequency range is not varied evidently.

All optical method for measuring the carrier envelope phase from half-cycle cutoffs

An all optical method is demonstrated for measuring the carrier-envelope phase （CEP） of few-cycle laser pulses. It is found that, in the few-cycle regime, the high harmonic spectrum generated from asymmetric molecules shows several half-cycle cutoffs that change their positions as the CEP varies. Such half-cycle cutoffs represent the fingerprint of different quantum trajectories and the waveform of the driving pulse. In this case, the CEP can be accurately measured from the half-cycle cutoffs.

Generation of 10 fs Ti:sapphire laser at repetition rate of 525 MHz and measurement of carrier-envelope phase frequency

This paper presents a Kerr-lens mode-locked Ti：sapphire laser at the repetition rate of 525 MHz, stable laser pulse as short as 10 fs with average output power of 480 mW is obtained. By injecting the pulse into photonics crystal fibre, octave-spanning spectrum covered from 500 to 1050 nm is generated, carrier-envelope phase frequency with signal-to- noise ratio of 31dB is measured, which paves the way for the generation of a compact frequency comb.

Carrier-envelope phase measurement using plasmonic-field-enhanced high-order harmonic generation of H atom in few-cycle laser pulses

We investigate the plasmonic-field-enhanced high-order harmonic generation（HHG） of H atom driven by few-cycle laser pulses, by solving the time-dependent Schr？dinger equation（TDSE）. Compared with the homogeneous field, HHG spectra generated by inhomogeneous field exhibit two-plateau structure. We analyze the origin of the two plateaus by using the semiclassical trajectory method. Our results from both classical and TDSE simulations show that the cutoffs of the two plateaus are dramatically affected by the carrier-envelope phase（CEP） of laser pulse in the inhomogeneous field, even for a little longer pulse. Thus, we can determine the CEP of driving laser based on the cutoff position of HHG generated in the inhomogeneous field.

Carrier-envelope phase effects for a dipolar molecule interacting with ultrashort laser pulse

In this paper the phase-dependent features of ultrashort laser pulse resonant propagation in a two-level dipolar molecule are demonstrated by solving full Maxwell-Bloch equations. The electronic properties of dipolar molecule 4-trans-[p-（N, N-Di-n-butylamino）-p-stilbenylvinyl] pyridine （DBASVP） molecule, one-dimensional asymmetric organic molecule, is calculated by density functional theory at ab initio level. The numerical results show that the carrier propagation and the spectrum evolution of the pulse are sensitive to its initial phase and the phase sensitivity is more obvious for larger area pulse. The phase-dependent feature is more evident in dipolar molecule because the permanent dipole moment makes the nonlinear effects stronger.

Carrier-envelope phase effects on high-harmonic generation driven by mid-infrared laser field

The influence of the carrier-envelope phase on high-harmonic generation is investigated, both experimentally and theoretically, for three different interaction gas media, driven by mid-infrared, few-cycle and CEP-stabiUzed laser pulses. Different patterns of harmonic spectra with varying CEP for the three interaction gas media are observed. Furthermore, in comparing our experiment results to the previous works driven by near-infrared laser pulses, different phenomena are found. Through numerical simulation, we find that for the two different kinds of driving fields, i.e. mid-infrared and near-infrared laser pulses, different kinds of electron trajectories contribute to the generation of high harmonics.

Effect of Carrier Envelope Phase on High-Order Harmonic Generation from Solid

The dependence of harmonic emission from a solid on the carrier envelope phase (CEP) is discussed by numerically solving the time-dependent Schr?dinger equation. The harmonic spectra periodically exhibit three distinct oscillating structures, which indicate the different dependences of the cutoff energies on the CEP. Furthermore,with time-dependent population imaging and the populations of different energy bands, the underlying physical mechanism is explored.

Carrier Envelope Phase Description for an Isolated Attosecond Pulse by Momentum Vortices

As a crucial parameter for a few-cycle laser pulse, the carrier envelope phase(CEP) substantially determines the laser waveform. We propose a method to directly describe the CEP of an isolated attosecond pulse(IAP) by the vortex-shaped momentum pattern, which is generated from the tunneling ionization of a hydrogen atom by a pair of time-delayed, oppositely and circularly polarized IAP-IR pulses. Superior to the angular streaking method that characterizes the CEP in terms of only one streak, our method describes the CEP of an IAP by the features of multiple streaks in the vortex pattern. The proposed method may open the possibility of capturing sub-cycle extreme ultraviolet dynamics.

Carrier-envelope phase locking of 5 fs amplified Ti:sapphire laser pulse at 1 kHz repetition rate

This paper reports the carrier-envelop phase (CEP) locking for the 5 fs re-compressed laser pulse generated from a chirped pulse amplified (CPA) Ti:sapphire laser at 1 kHz repetition rate. A phase locking feedback system with two loops was designed to control the fast fluctuation arising from the seeding laser and the slow fluctuation arising from the sub-mJ amplified pulse. The principle and structure of the phase control system, including the CEP detection, servo loop design and phase locking result, are analyzed. The experiment shows that our phase locking system can be well used to establish the stable phase locking of few-cycle amplified laser pulse, and the CEP variation of below 53 mrad (rms) was demonstrated during a locking period of more than 3 h.

Monolithic CEO-stabilization scheme-based frequency comb from an octave-spanning laser

We demonstrate a carder-envelope phase-stabilized octave-spanning oscillator based on the monolithic scheme. A wide output spectrum extending from 480 nm to 1050 nm was generated directly from an all-chirped mirror Ti：sapphire laser. After several improvements, the carder-envelope offset （CEO） beat frequency accessed nearly 60 dB under a reso- lution of 100 kHz. Using a feedback system with 50-kHz bandwidth, we compressed the residual phase noise to 55 mrad （integrated from 1 Hz to 1 MHz） for the stabilized CEO, corresponding to 23-as timing jitter at the central wavelength of 790 nm. This is, to the best of our knowledge, the smallest timing jitter achieved among the existing octave-spanning laser based frequency combs.

Isolated attosecond pulse generation with few-cycle two-color counter-rotating circularly polarized laser pulses

Most of the schemes for generating isolated attosecond pulses（IAP） are sensitive to the carrier-envelope phase（CEP）of the driving lasers. We propose a scheme for generating IAP using two-color counter-rotating circularly polarized（TCCRCP） laser pulses. The results demonstrate that the dependence of the IAP generation on CEP stability is largely reduced in this scheme. IAP can be generated at most of CEPs. Therefore, the experiment requirements become lower.

Carrier-envelope phase passively stabilized near-infrared laser pulses from a dual-frequency pumped noncollinear optical parametric amplifier

By inversing the signal and idler in a two-stage noncollinear optical parametric amplifier which is,respectively,pumped by the second harmonic and fundamental wave of femtosecond Ti:sapphire laser at repetition rate of1 kHz,the carrier-envelope phase(CEP)passively stabilized pulses with a tunable wavelength from 1.1 to 1.6 lm are obtained with maximum energy of 95 lJ at 1.3 lm under the pump energy of 500 lJ.The CEP jitter of pulses is 108 mrad measured by an f-2f interferometer.This work demonstrates a new way to efficiently generate tunable near-infrared femtosecond laser pulses with self-stabilized CEP.

Time-energy properties of an attosecond extreme ultra-violet pulse

The time-energy properties of high-order harmonic generation （HHG） are calculated for a linearly polarized 7- fs laser pulse with different carrier-envelope phases （CEPs）. The quantum trajectory paths that contribute to an as （1 as=10^-18 s） pulse in HHG are identified. The laser-duration dependence and the CEP dependence of HHG energy property are investigated. The study shows that an as extreme ultra-violet （XUV） pulse can be selected from HHG spectrum near cut-off energy with a bandpass optical filter. The theoretical prediction of the pulse duration is proportional to bandwidth. Analysis suggests that a measured narrowband as XUV pulse may consist of instantaneous shorter pulses each dependent on laser pulse duration, intensity, and CEP. These information can be used as references for producing, selecting, improving and manipulating （timing） as pulses.

High-Conversion-Efficiency and Broadband Tunable Femtosecond Noncollinear Optical Parametric Amplifier

We build a compact high-conversion-efficiency and broadband tunable noncollinear optical parametric amplifier （OPA） in the infra-red （IR） pumped by a femtosecond Ti：sapphire CPA laser. The OPA consists of an internal seed of white-light continuum generator （WLG） and two noncollinear optical parametric amplifiers. The tunable wavelength range is from 1.2μm to 2.4μm for both signal and idle pulses. The total OPA efficiency in the last OPA stage reaches about 40% in a wider tunable spectral range （from 1.3μm to 1.7μm for signal pulse, from 1.5μm to 2.0 μm for idle pulse respectively）.

Control of the carrier-envelope phases of a synchronously pumped femtosecond optical parametric oscillator and its applications

The intrinsic synchronization, multi-color outputs and related carrier-envelope phases (CEP) among pulses bring advantages to synchronously pumped femtosecond optical parametric oscillators and the pumping sources for broadband frequency comb generation and ultrashort waveform coherent syn-thesis. In this paper, we discuss our latest research results in this field, which cover the following as-pects: the phase relationship and energy conservation law in an OPO and related experimental verifi-cation; control of the pumping Ti:sapphire femtosecond laser's CEP by self-referencing technology, and its repetition-rate locking by piezoelectric transducer (PZT); CEP locking of the pulses from the OPO by beating the non-phase-matched visible outputs against pump supercontinuum to obtain a driving signal for a fast PZT on the OPO end mirror; the generation of a broadband frequency comb spanning from 400 nm to 2.4 μm with 1.2 kHz bandwidth; and the realization of coherent interference between phase controlled pump pulses and signal second harmonic pulses.

A proposed approach for detecting terahertz pulses by using double few-cycle laser pulses with opposite carrier envelope phases

Previous research shows that few-cycle laser（FCL） pulses with low energy and without a bias field can be used to coherently detect terahertz（THz） pulses. As we know, it is very difficult to stabilize the carrier envelope phase（CEP） of FCL pulses, i.e., there are some random fluctuations for the CEP. Here we theoretically investigate the influence of such instability on the accuracy of THz detection. Our results show that although there is an optimum CEP for THz detection, the fluctuations of the CEP will lead to terrible thorns on the detected THz waveform. In order to solve this problem, we propose an approach using two few-cycle laser pulses with opposite CEPs, i.e., their CEPs are differed by π.

两类单阿秒脉冲产生技术的相位依赖性分析

为了分析目前国际上现有的两类高次谐波极紫外单阿秒脉冲产生技术——振幅选通技术和偏振选通技术在驱动脉冲场载波-包络相位设置方面的差异,基于这两类单脉冲产生技术基本原理并借助于高次谐波产生3步理论分析模型,半定量分析了这两类技术的驱动光场载波-包络相位依赖性及其差异。结果表明,两者的最佳驱动脉冲场载波-包络相位设置分别为0与0.5π,出现此差异的根本原因是高次谐波现象对驱动光场偏振度的高度依赖性。此分析结果对更短脉宽极紫外阿秒脉冲光源的产生和相关应用具有重要的参考价值。

激光驱动晶体发射高次谐波的特性研究

通过数值模拟激光驱动下电子在周期性势阱中的动力学行为,研究了晶体在激光场中发射高次谐波的特性.研究发现在一定的激光波长和光强驱动下,晶体发射的谐波谱会呈现出双平台结构,经分析后得知第一个平台主要来自于最低导带与价带间的电流(电子-空穴对复合),第二个平台主要来源于较高导带与价带间的电流(电子-空穴对复合),且两个平台的截止位置处的能量都与激光场的振幅呈线性关系.在少周期激光驱动下,晶体谐波第二平台的截止位置与激光的载波相位呈单调变化,由此我们提出可以利用晶体谐波第二平台的截止位置来确定少周期激光的载波相位.进一步研究发现,在啁啾激光驱动下,晶体发射谐波谱的第二平台有较大变化,第二平台的发射效率会随啁啾参数而改变,能够通过改变啁啾激光场来提高晶体谐波第二平台的发射效率.