Nonlinear interaction between a two-level atom and a weak polychromatic field

The interaction between two-level media and a polychromatic field is considered in the limit of small field amplitudes. The obtained third-order corrections allow us to describe a nonlinear response to the field and intermodal interaction. The obtained polarization spectra are compared to numerical solutions to the density matrix equation in the rotating wave approximation. The results can be used in nonlinear comb spectroscopy.     

Investigation of passively mode-locked erbium doped fiber ring laser due to nonlinear polarization rotation

Passively mode-locked erbium doped fiber ring laser was investigated. We present optimization of laser configuration where nonlinear polarization rotation was used for modes synchronization. Simulations of pulse propagation inside a laser cavity were applied in order to confirm the optimisation technique. Experimental results are presented and more than 32-nm spectral width of the output frequency comb was obtained.     

块状介质超连续谱相位的相干特性

 块状介质超连续谱由一系列复杂的非线性过程产生。用两路飞秒泵浦光聚焦到熔石英玻璃上得到两束独立的超连续谱,实验上观察到它们形成的稳定干涉条纹;改变两路泵浦光的时间延迟,得到共线超连续谱形成的频率梳。实验证明,块状介质超连续谱的产生保持了泵浦光的相位锁定关系,泵浦光能量抖动和介质的缺陷都不会对超连续谱的相位带来明显的扰动。     

Polarization effects in nanoaggregates of silver caused by local and nonlocal nonlinear-optical responses

A theoretical and experimental study is made into the combined manifestation of local and nonlocal optical responses in a cubic nonlinear isotropic medium such as an aggregated colloidal silver solution. The phenomenological treatment of polarization effects is performed for the general case with due regard for the frequency dispersion of both local and nonlocal nonlinearities and for the noncollinear propagation of pump and probe light waves. The inverse Faraday effect, the optical Kerr effect, and the self-rotation of the polarization ellipse in a fractal-disordered nonlinear medium are observed for the first time. The tensor components of the local and nonlocal cubic nonlinearities of colloidal silver solutions are measured for different degrees of aggregation. It is demonstrated that, as the size of silver aggregate increases, the nonlocal nonlinear response increases much more strongly than the local one. An inference is made that the mechanical motion of metal nanoparticles because of their dynamic interaction with the light wave field can contribute to the nonlinear polarization effects.     

Optical generation of a precise microwave frequency comb by harmonic frequency locking

A semiconductor laser under negative optoelectronic feedback is applied to the generation of a microwave frequency comb through the nonlinear dynamics. The laser system is operated in a harmonic frequency-locked pulsing state, where its power spectrum is a microwave frequency comb that consists of multiples of a locking frequency. Every frequency component of the comb can be simultaneously stabilized by simply injecting an external microwave modulation at any component of the comb. This phenomenon can be viewed as a kind of microwave injection locking of the laser dynamics.     

Coherence and saturation properties of second-harmonic generation with a nonlinear crystal inside the laser cavity

The basic equations for second-harmonic generation including noise are derived for the case that the nonlinear crystal is put inside the laser cavity. A realistic model of a (detuned) laser with two-level atoms in single-mode operation is taken using the nonlinear theory of laser noise which describes the laser saturation effects, the phase diffusion and the intensity fluctuations. The reaction of the second-harmonic field on the fundamental field is taken into account as well as the reaction of the fundamental field on the laser. The nonlinear crystal is described by microscopic anharmonic oscillator equations (without introducing nonlinear susceptibilities by perturbation theory). The saturation of the polarization of the nonlinear medium is taken into account exactly with the only assumption that the influence of third and higher harmonics should be small. The electromagnetic field is described semiclassically by stochastic equations. In all equations, the damping is introduced simultaneously with Markoffian fluctuating forces by coupling to heatbaths. The equations are solved exactly in the stationary state without noise (the time dependent solution including noise will be presented in a subsequent paper). The most important saturation effect is a frequency shift which depends on the laser intensity.     

Absolute-frequency measurements with a stabilized near-infrared optical frequency comb from a Cr:forsterite laser

A frequency comb is generated with a chromium-doped forsterite femtosecond laser, spectrally broadened in a dispersion-shifted highly nonlinear fiber, and stabilized. The resultant evenly spaced comb of frequencies ranges from 1.1 to beyond 1.8 microm. The frequency comb was referenced simultaneously to the National Institute of Standards and Technology's optical frequency standard based on neutral calcium and to a hydrogen maser that is calibrated by a cesium atomic fountain clock. With this comb we measured two frequency references in the telecommunications band: one half of the frequency of the d/f crossover transition in 87Rb at 780 nm, and the methane v2 + 2v3 R(8) line at 1315 nm.     

Optical clockwork with an offset-free difference-frequency comb: accuracy of sum- and difference-frequency generation

We demonstrate a simple optical clockwork mechanism based on the broadened frequency comb of a femtosecond laser and on difference-frequency generation (DFG) in a nonlinear crystal. The DFG comb possesses a vanishing carrier envelope offset frequency that permits the construction of a simple and thus potentially more stable optical clockwork. In addition it offers the possibility of extending the frequency comb into the infrared spectral region. The overall accuracy and stability of the DFG comb relative to the initial frequency comb were measured to be 6.6 x 10(-21) and 10(-18) tau(-1), respectively, where tau is the averaging time in seconds. Assuming that sum- and difference-frequency generation are independent processes, our measurements suggest a <10(-20) accuracy for them.     

Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared

A phase-locked frequency comb in the near infrared is demonstrated with a mode-locked, erbium-doped, fiber laser whose output is amplified and spectrally broadened in dispersion-flattened, highly nonlinear optical fiber to span from 1100 to >2200 nm. The supercontinuum output comprises a frequency comb with a spacing set by the laser repetition rate and an offset by the carrier-envelope offset frequency, which is detected with the standard f-to-2f heterodyne technique. The comb spacing and offset frequency are phase locked to a stable rf signal with a fiber stretcher in the laser cavity and by control of the pump laser power, respectively. This infrared comb permits frequency metrology experiments in the near infrared in a compact, fiber-laser-based system.     

Nonlinear asymptotic impedance model for a Helmholtz resonator liner

The usual nonlinear corrections for a Helmholtz resonator type impedance do not seem to be based on a systematic asymptotic solution of the pertaining equations. We aim to present a systematic derivation of a solution of the nonlinear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including nonlinear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the nonlinear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the nonlinear terms). Close to the resonance frequency, the nonlinear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding nonlinear impedance. Sample results are presented including a few comparisons with measurements available in the literature. The validity of the model is understood in the near resonance and non-resonance regimes.     

偏振模色散及非线性效应对40 Gbit/s密集波分复用系统的影响

高速率、大容量的密集波分复用系统是光纤通信系统的最终发展方向 ,单信道速率达到 4 0Gbit/s时 ,光纤的非线性效应、偏振模色散现象对系统的影响更加突出。在综合考虑群速度色散、自相位调制、交叉相位调制、四波混合、偏振模色散等因素的基础上 ,推导了密集波分复用系统中任意信道的耦合非线性薛定谔方程组。利用扩展的分步傅里叶方法对该方程进行了数值计算 ,通过对 8× 4 0Gbit/s密集波分复用系统的仿真 ,分别研究了非线性效应和偏振模色散对密集波分复用系统的影响。发现由于交叉相位调制和四波混合作用 ,多波长的密集波分复用系统比单波系统受非线性效应影响严重 ;系统受偏振模色散与非线性效应的影响程度与输入信号功率有关 ,在入射光单信道平均功率较低 0 .1mW时 ,偏振模色散是影响系统性能的主要因素 ;当入射光单信道平均功率较高1mW时 ,系统受非线性效应影响严重。而偏振模色散在使信号脉冲展宽的同时 ,类似于非零色散位移光纤中的微小色散 ,对非线性效应又有一定的抑制作用。     

基于飞秒光频梳的压电陶瓷闭环位移控制系统

利用飞秒光频梳、外腔可调谐半导体激光器和法布里-珀罗干涉仪建立了一套压电陶瓷亚纳米级闭环位移控制系统. 将可调谐半导体激光器锁定至光频梳, 通过精确调谐光频梳的重复频率, 实现了半导体激光器在其工作频率范围内的精密调谐. 利用Pound-Drever-Hall锁定技术将带有压电陶瓷的法布里-珀罗腔锁定至半导体激光器, 进而通过频率发生系统控制压电陶瓷产生亚纳米级分辨率的位移. 实验研究发现锁定至光频梳后可调谐半导体激光器1 s的Allan标准偏差为1.68×10^-12, 将其在30.9496 GHz范围内进行连续闭环调谐, 可获得压电陶瓷的位移行程约为4.8 μm; 以3.75 Hz的步长扫描光频梳的重复频率, 实现了压电陶瓷的450 pm闭环位移分辨率并测定了压电陶瓷的磁滞特性曲线. 该系统不存在非线性测量误差, 且激光频率及压电陶瓷位移均溯源至铷钟频率源. 关键词： 光频梳 压电陶瓷 法布里-珀罗腔 可调谐半导体激光器     

Polarization dependent dispersion and its impact on optical parametric process in high nonlinear microstructure fibre

High nonlinear microstructure fibre （HNMF） is preferred in nonlinear fibre optics, especially in the applications of optical parametric effects, due to its high optical nonlinear coefficient. However, polarization dependent dispersion will impact the nonlinear optical parametric process in HNMFs. In this paper, modulation instability （MI） method is used to measure the polarization dependent dispersion of a piece of commercial HNMF, including the group velocity dispersion, the dispersion slope, the fourth-order dispersion and group birefringence. It also experimentally demonstrates the impact of the polarization dependent dispersion on the continuous wave supercontinuum （SC） generation. On one axis MI sidebands with symmetric frequency detunings are generated, while on the other axis with larger MI frequency detuning, SC is generated by soliton self-frequency shift.     

Widely-tunable mid-infrared frequency comb source based on difference frequency generation

We report on a mid-IR frequency comb source of unprecedented tunability covering the entire 3-10 μm molecular fingerprint region. The system is based on difference frequency generation in a GaSe crystal pumped by a 151 MHz Yb:fiber frequency comb. The process was seeded with Raman-shifted solitons generated in a highly nonlinear suspended-core fiber with the same source. Average powers up to 1.5 mW were achieved at the 4.7 μm wavelength.     

Precise determination of characteristic laser frequencies by an Er-doped fiber optical frequency comb

Femtosecond optical frequency combs correlate the microwave and optical frequencies accurately and coherently. Therefore, any optical frequency in visible to near-infrared region can be directly traced to a microwave frequency. As a result, the length unit "meter" is directly related to the time unit "second". This paper validates the capability of the national wavelength standards based on a home-made Er-doped fiber femtosecond optical frequency comb to measure the laser frequencies ranging from visible to near-infrared region. Optical frequency conversion in the femtosecond optical frequency comb is achieved by combining spectral broadening in a highly nonlinear fiber with a single-point frequency-doubling scheme. The signal-to-noise ratio of the beat notes between the femtosecond optical frequency comb and the lasers at 633, 698, 729, 780, 1064, and 1542 nm is better than 30 dB. The frequency instability of the above lasers is evaluated by using a hydrogen clock signal with a instability of better than 1×10^-13 at 1-s averaging time. The measurement is further validated by measuring the absolute optical frequency of an iodine-stabilized 532-nm laser and an acetylene-stabilized 1542-nm laser. The results are within the uncertainty range of the international recommended values. Our results demonstrate the accurate optical frequency measurement of lasers at different frequencies using the femtosecond optical frequency comb, which is not only important for the precise and accurate traceability and calibration of the laser frequencies, but also provides technical support for establishing the national wavelength standards based on the femtosecond optical frequency comb.     

Broad multiwavelength source with 50 GHz channel spacing for wavelength division multiplexing applications in the telecom C band

We present a multiwavelength source with a spectral width of 42 nm at -20 dB. The frequency comb is generated by spectrally broadening the output of an amplified 50 GHz Er:Yb:glass laser with a highly nonlinear photonic crystal fiber. After spectral flattening the comb covers 37 channels with 5.4 mW average power per channel, and locking only one central wavelength channel to the International Telecommunication Union grid results in a maximum frequency error of 0.24% for all channels.     

Generation of difference frequencies on the basis of nonlinear effects

The production of a difference frequency (subharmonic) by nonlinear polarization in a dielectric or semiconductor receiving two strong light fluxes has some differences from other nonlinear effects. Here the question is discussed theoretically.     

Polarization characteristics of the “forbidden” second optical harmonic of femtosecond laser pulses in a bacteriorhodopsin solution

The generation of the second harmonic of femtosecond laser pulses in a bacteriorhodopsin solution has been experimentally studied for various wavelengths and polarization states of radiation at the fundamental frequency. The polarization properties of the effect are analyzed under various experimental conditions. The nature and properties of the signal are treated as the manifestation of a superposition of nonlinear optical effects of various orders (the second and the fourth). The second-order effects can have both an electric-dipole and a magnetic-dipole or electric-quadrupole character. In analyzing fourth-order processes, besides the direct electric-dipole contribution, the possibility of the participation of cascade processes at second-and third-order nonlinearities is also allowed. Zh. éksp. Teor. Fiz. 112, 97–114 (July 1997)     

Intrinsic optical bistability in Kerr ferroelectric materials

In this paper we investigate the intrinsic optical bistability (IOB) in a ferroelectric (FE) single layer using an alternative analysis. The FE material is considered to have an intensity-dependent refractive index where the third order nonlinear susceptibility χ⁽³⁾ acts like Kerr coefficient. The nonlinear response of the FE medium is modeled using the Landau-Khalatnikov (LK) dynamical equation with the nonlinear anharmonic potential obtained from the Landau-Devonshire free energy expressed in terms of polarization. Within a single frequency approximation, the electromagnetic wave equation is written in terms of the polarization P rather than the electric field E as the dependent variable. With the application of the nonlinear boundary conditions we have derived expressions for both reflectance and transmittance as a function of the electric field incident amplitude, polarization and other material parameters. The formalism proves to be more suitable for FE materials since most of these materials have highly linear and nonlinear coefficients especially when the operating frequency is in the resonance region. The effects of thickness, operating frequency and temperature on BaTiO₃ single film are investigated theoretically. The results presented here agree in principle with the recent experimental observations of intrinsic OB in BaTiO₃ monocrystal and other FE photorefractive materials.     

一种基于电光调制光频梳光谱干涉的绝对测距方法

提出了一种基于电光调制光学频率梳的光谱干涉测距方法.理论分析了电光调制光学频率梳的数学模型和光谱扩展原理,并分析得出了光谱干涉测距方法的非模糊范围和分辨力的影响因素.在实验中,使用三只级联的电光相位调制器调制单频连续波激光生成了40多阶高功率梳齿状边带,并通过单模光纤和高非线性光纤对电光调制器输出的激光进行光谱扩展,得到重复频率为10 GHz,光谱宽度达30 nm的光学频率梳.将该光频梳作为光谱干涉测距装置的光源,可以实现无"死区"的绝对距离测量.另外,使用等频率间隔重采样和二次方程脉冲峰值拟合算法对测量结果进行数据处理,可以修正系统误差,提升测距精度.实验结果表明,在1 m的测量范围内,使用该装置可以在任意位置达到±15μm以内的绝对测距精度.