Spectral phase shift and residual angular dispersion of an acousto-optic programmable dispersive filter

Spectral phase shift and both types of wavelength dependent angular deviation introduced by an acousto-optic programmable dispersive filter (AOPDF) into a femtosecond laser beam at 800 nm have been measured with high precision. With the use of spectrally and spatially resolved interferometry, we have proved experimentally that the AOPDF controls the group delay dispersion (GDD) and third-order dispersion (TOD) with an accuracy of better than 1% and 3% of the preset values within the range of 10–1000 fs² and 1000–40,000 fs³, respectively. The values of angular deviation and angular dispersion are primarily dependent on the set absolute value of GDD of the AOPDF when it is operating in continuous mode. Besides of a small offset value, there is no added angular dispersion at 0 fs², while it can increase up to 0.2 μrad/nm at 10,000 fs².     

Integrative optimization of chirped mirrors for intracavity dispersion compensation

A new integrative optimization of three chirped mirrors for precise broadband intracavity group delay dispersion compensation in ring cavity is proposed. Simulation demonstrates that the residual group delay dispersion ripples of these three chirped mirrors are less than 25 fs² for most of the wavelengths from 600 to 1200 nm. Pulse evolution simulation shows that these three matched chirped mirrors compensate the group delay dispersion in the Ti:Sapphire ring cavity laser well to obtain an octave-spanning spectrum.     

钛宝石飞秒激光器用色散补偿Gires-Tournois镜的研究

根据钛宝石飞秒激光器的色散补偿要求设计了单次反射平均补偿量为-60 fs²的GT(Gires-Tournois)镜,采用离子束辅助沉积技术结合光学监控技术制作了器件.用分光光度计对650—950 nm波段薄膜反射率进行测试,结果表明反射率测试曲线与设计曲线十分符合,同时利用白光干涉系统对群延迟色散进行了测试,测试结果与设计符合得很好,实际的色散曲线振荡基本控制在±20 fs²以内.应用该GT镜进行钛宝石飞秒激光系统的色散补偿,取得了很好的锁模效果,得到了29 fs的超短脉冲. 关键词： 色散补偿 钛宝石飞秒激光器 GT镜 离子束辅助沉积     

1.5-octave chirped mirror for pulse compression down to sub-3 fs

We demonstrate numerically and experimentally a chirped mirror with controlled reflectivity and dispersion of up to 1.5 octaves. A complementary pair of such mirrors has a reflectivity of 95% in the wavelength range 400–1200 nm with residual group delay dispersion ripples <100 fs² in all of this range. The mirror pair allows one to compensate a chirp of the corresponding spectrum (with a smooth phase), resulting in sub-3-fs pulses. PACS 42.65.Re; 42.79.Fm; 42.79.Wc     

Phase-measurement interferometry as a simulation of optimal quantum-state tomography

In this work we present an optical simulation of quantum tomography for state reconstruction based on projective measurements on mutually unbiased bases (MUBs-QT). A quantum state of dimension D = 2 is codified in the amplitude and phases of spatially separated beams in the arms of a Michelson interferometer. The quantum tomography is performed by introducing different displacements in one of the arms of the interferometer and recording the interferograms. We show that in this case the MUBs-QT is equivalent to obtain the set of measurements to extract information from the amplitude and phase of a wavefront using the four step phase shift interferometry.     

飞秒激光器中超宽带色散补偿啁啾镜对的设计

根据设计目标和制备要求, 以双啁啾作为啁啾镜膜系初始结构设计方法, 详细分析了双啁啾调制系数以及双啁啾层数对啁啾镜反射特性和色散特性的影响, 确立了两者之间的最佳取值组合. 利用分析结果设计了单个啁啾镜, 并实现了啁啾镜的配对设计, 获得了600–1050 nm范围内反射率大于99.5%, 平均群延迟色散-40 fs², 振荡小于± 20 fs²的啁啾镜对, 满足了钛宝石飞秒激光系统的色散补偿要求. 关键词： 超快激光 色散补偿薄膜 双啁啾镜 啁啾镜对     

Single-shot multiple-delay crossed-beam spectral interferometry for measuring extremely complex pulses

We demonstrate a single-shot measurement technique based on spectral interferometry (SI) for measuring the complete intensity and phase vs. time of extremely complex ultrashort laser pulses. Ordinarily, such a method would require an extremely-high-resolution spectrometer, but, by temporally interleaving many SI measurements, each using a different reference-pulse delay, our method overcomes this need. It involves introducing a transverse time delay into the reference pulse by tilting its pulse front transversely to the spectrometer dispersion plane. The tilted reference pulse then gates the unknown pulse by interfering with it at the image plane of a low-resolution imaging spectrometer, yielding an effective increase in the delay range and spectral resolution—by a factor of 30 in our proof-of-principle implementation. Our device achieved a temporal resolution of ~ 130 fs and a temporal range of 120 ps. This simple device has the potential to measure even longer and more complex pulses.     

Design and fabrication of Gires�CTournois interferometers for?Yb-doped photonic crystal fiber laser system

A Gires?CTournois interferometer (GTI) with large dispersion compensation was designed and fabricated according to the requirement of the Yb-doped photonic crystal fiber laser system. The designed GTI can provide an average group delay dispersion (GDD) of ?1500 fs² and a high reflectance (>99.7%) from 1030 to 1050 nm. The Ion-assisted Deposition (IAD) technique was utilized to manufacture the mirror. Good agreement between the measured and designed results both for reflectance and GDD was achieved. The reflectance during 1030?C1050 nm was above 99.5% and the GDD ripple was less than ±300 fs². The GTI was used both in the intracavity dispersion compensation and extracavity pulse compression for the Yb-doped photonic crystal fiber laser system. A mode-locked soliton pulse with a 506-fs duration was recorded. An extracavity pulse compression test showed that the GTI had identical pulse compression capability as the conventional grating pairs while the energy loss was obviously reduced. Our results demonstrated that the HDM, which was able to provide quite a large amount of negative dispersion (???8×10⁴ fs²), could be an ideal alternative to replace the dispersive compensating grating pairs for the dispersion compensation of the Yb-doped photonic crystal fiber laser system.     

Polarization maintaining holey fibers for residual dispersion compensation over S + C + L wavelength bands

We report on a highly birefringent holey fiber for broadband dispersion compensation covering the S, C, and L telecommunication bands i.e. wavelength ranging from 1460 to 1625 nm. The finite element method with circular perfectly matched layer boundary condition is used to investigate the guiding properties. Numerical analysis demonstrates that it is possible to obtain negative dispersion coefficient of about −470 to −850 ps/nm/km over S to L-bands and a relative dispersion slope perfectly matched with single mode fiber (SMF) of about 0.0036 nm⁻¹ at 1550 nm. At the same time birefringence of the order 2.53 × 10⁻² is realized at 1550 nm wavelength. Owing to superior optical properties of the proposed holey fiber, this can be a promising candidate for broadband dispersion compensation and sensing applications.     

Design of single polarization single mode dispersion compensating photonic crystal fiber

In this paper, we present a photonic crystal fiber based on hexagonal structure for improved negative dispersion as well as high birefringence in the telecom wavelength bands. It is demonstrated that it is possible to obtain negative dispersion coefficient of −712 ps/(nm km) and relative dispersion slope (RDS) perfectly match to that of single mode fiber (SMF) of about 0.0036 nm⁻¹ at the operating wavelength 1550 nm. The proposed fiber exhibits high birefringence of the order 2.11 × 10⁻² with nonlinear coefficient about 57.57 W⁻¹ km⁻¹ at 1550 nm. Moreover, it is confirmed that the designed fiber successfully operates as a single mode in the entire band of interest.     

Analysis of BPSK homodyne receivers based on modified balanced optical phase-locked loop in the presence of non-negligible loop propagation delay

Optical homodyne receivers based on modified balanced optical phase-locked loop is analyzed taking into account loop propagation delay. This modified loop contains all the components of a standard BOPLL in conjunction of an additional phase modulator. This modified loop offers a much improved tracking performance and also shows good improvements in the reduction performance over previously reported methods, like, relaxed line-width requirement and improved lock-in range. This study for the first time shows the imperfect-phase-recovery-induced power penalty as a function of laser line-width with the optimum phase deviations in the presence of non-negligible loop propagation delay. It is found that in order to maintain a 10⁻¹⁰ BER system performance with ξ = 1, R = 1 A/W, P_R = −53 dBm, Δυ = 1 MHz, phase modulator sensitivity K_PM = 10 rad/V and 10° phase deviation between the two transmitted bits, the loop delay must be kept below 3 ns. Further, the required line-width with the non-negligible loop delay time is evaluated and found to be (2.1 × 10⁻³)/τ, where τ (s) is the loop delay. This number corresponds to BER = 10⁻¹⁰, imperfect phase recovery power penalty of 1 dB and phase modulator sensitivity K_PM = 20 rad/V.     

Birefringence dispersion in a quartz crystal retrieved from a channeled spectrum resolved by a fiber-optic spectrometer

We present a simple method for measuring the wavelength dependence of both the phase and group birefringences in a quartz crystal of known thickness. The method utilizes interference of polarized waves resolved by a fiber-optic spectrometer as a channeled spectrum (spectral fringes). The fringe order versus the precise position of the interference maximum in the spectrum is fitted to the approximate function, from which the phase birefringence as a function of wavelength is retrieved. We also determine the group birefringence dispersion. The functions measured in a range from 500 to 900 nm are compared with those resulting from the available dispersion relation, and very good agreement is confirmed.     

Determination of the refractive index over a wide wavelength range through time-delay measurements of femtosecond pulses

We present a simple method to measure the refractive index dispersion over a broad wavelength range (0.6-1.6 μm). In a first step, the optical group indices are obtained by measuring the time-retardation of tunable 150 fs laser pulses within a sample relative to air. The refractive index dispersion is then calculated using a Sellmeier equation that describes the measured group index dispersion. We show that our experimental data agree with previously published results to within 2 × 10⁻⁴ for a 3 mm thick sample of fused silica and to within 3 × 10⁻³ for the index n₁ of a 2 mm thick crystal of the highly dispersive and anisotropic organic crystal 4-N,N-dimethylamino-4′-N′-methyl stilbazolium tosylate (DAST).     

光谱位相相干电场法的参数分析及测量

从光谱位相相干电场重构法（ＳＰＩＤＥＲ）的原理出发,实现了算法、讨论时间延迟、光谱剪切量、滤波窗口宽度、色散量等几个方面的优化选取。当展宽器色散和脉冲宽度一定时,脉冲对的时间延迟存在一个最佳取值范围。相对光谱剪切量在５％～１５％间,滤波窗口宽度为／３,重构出的位相误差最小。对干涉图取平均来减小噪声的影响。用ＳＰＩＤＥＲ算法还原了脉冲的电场和位相信息,由ＳＰＩＤＥＲ测量的脉冲宽度为１７.７ fs。同时为了比较,用自相关法测量了同一脉冲,由自相关曲线可估算出脉冲宽度为１６.８ fs,与ＳＰＩＤＥＲ 的误差比为５．１％,说明了实验的有效性。     

Group delay dispersion measurement of Yb:YAl3(BO3)4 crystal with white-light interferometry

We report the group delay dispersion of Yb³⁺:YAl₃(BO₃)₄ (Yb:YAB) crystal measured by a white-light interferometer, and compare with that calculated from the Sellmeier formulae provided by the crystal supplier, over the wavelength range from 1000 nm to 1080 nm. The data should be useful for the dispersion compensation for femtosecond pulse generation in Yb:YAB lasers.     

A detailed experimental investigation of the KMM + KMN + KNN Auger electron spectrum of Cd from the EC-decay of In

KMM, KMN and KNN Auger electron spectra of ¹¹¹Cd emitted in EC-decay of ¹¹¹In were analyzed at instrumental resolutions of 14 and 21 eV using a combined electrostatic spectrometer. Energies and relative intensities of 26 resolved components were determined and compared with theoretical predictions. For the first time, the predicted intermediate coupling structure of some KMM Auger lines was observed. A structure of the KNN Auger group for Z < 54 was resolved for the first time. Relative intensities of the KMM, KMN and KNN Auger groups were also determined.     

Maintaining single polarization and dispersion compensation with modified rectangular microstructure optical fiber

In this paper, we propose and numerically demonstrate a highly birefringent microstructure optical fiber which shows negative dispersion coefficient of about −288 to −550 ps/(nm km) covering S to L wavelength bands and −425 ps/(nm km) at the excitation wavelength 1550 nm. This proposed design successfully compensate the dispersion covering S to L communication bands ranging from 1460 to 1625 nm along with relative dispersion slope (RDS) perfectly matched to that of single mode fiber of about 0.0036 nm⁻¹. Apart from dispersion compensation, the designed MOF offers high birefringence of 2.94 × 10⁻² at 1550 nm and better compensation ratio with design simplicity due to circular air-holes in the fiber cladding.     

Design and characterization of single mode circular photonic crystal fiber for broadband dispersion compensation

In this paper, we present a single mode circular photonic crystal fiber (C-PCF) for broadband dispersion compensation covering 1400 to 1610 nm wavelength band over the telecommunication windows. Investigations of guiding properties are carried out using finite element method (FEM) with circular perfectly matched layer boundary condition. Numerical study reveals that a negative dispersion coefficient of about −386.57 to −971.44 ps/(nm km) is possible to obtain over the wavelength ranging from 1400 to 1610 nm with a relative dispersion slope (RDS) of about 0.0036 nm⁻¹ at 1550 nm wavelength. In addition, the single mode behaviour of C-PCF is demonstrated by employing V parameter. According to simulation, it is found that the proposed C-PCF acts as a single mode fiber within 1340 to 1640 nm wavelength. Moreover, effective dispersion, relative dispersion slope, birefringence and confinement loss are also presented and discussed.     

Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift

An iterative algorithm to extract the arbitrary unknown phase shift in two-frame phase-shifting interferometry and then reconstruct the complex object wave is proposed. In combination with the least square principle and some calculation formulae we developed, this algorithm allows us to find the value of unknown phase shift by using only two interferograms without additional knowledge or measurement. Computer simulations have shown that this algorithm works well for both the smooth and diffusing objects to a very high accuracy over a wide range of the phase shift from 0.4 to 2.5 rad.     

Performance comparison between digital back propagation (DBP) and pilot-aided method for fiber nonlinearity compensation in different fiber links

We numerically investigate and compare the performance of fiber nonlinearity compensation using digital back propagation (DBP) method and pilot-aided method in coherent optical transmission systems using different fiber links. Simulations for wavelength division multiplexed (WDM) 112 Gb/s polarization division multiplexed quadrature phase shift keying (PDM-QPSK) systems with dispersion unmanaged (no DM) and dispersion managed (DM) fiber links are implemented. System Q-factor and maximum transmission distance at bit error rate (BER) of 3.8 ÿ 10^?3 are calculated for performance comparison. The results show that, for system with no DM fiber link, DBP method outperforms pilot-aided method, because DBP method has better performance for intra-channel fiber nonlinearity compensation. However, for system with DM fiber link where inter-channel fiber nonlinearity plays an important role, pilot-aided method performs better than DBP method, because of its ability for inter-channel fiber nonlinearity compensation.