Oscillator Laser Model

A laser model is formulated in terms of quantum harmonic oscillators. Emitters in the low lasing states are usual harmonic oscillators, and emitters in the upper states are inverted harmonic oscillators. Diffusion coefficients, consistent with the model and necessary for solving quantum nonlinear laser equations analytically, are found. Photon number fluctuations of the lasing mode and fluctuations of the population of the lasing states are calculated. Collective Rabi splitting peaks are predicted in the intensity fluctuation spectra of the superradiant lasers. Population fluctuation mechanisms in superradiant lasers and lasers without superradiance are discussed and compared with each other.     

Characterization of the noise in continuously operating mode-locked lasers

An experimental and theoretical investigation of the fluctuations of the pulses from continuous-wave mode-locked lasers is presented. It is shown that these fluctuations can be detected and quantitatively characterized from measurements of the power spectrum of the light intensity. Such power spectra can be measured with great accuracy by shining the laser output on a suitable photodetector and by processing the detector signal with the use of an electronic spectrum analyzer. Different types of noise such as fluctuations of the pulse energy, pulse repetition time, and pulse duration, can be readily recognized from their characteristic spectral signature. Experimental results of noise measurements are presented for a synchronously mode-locked dye laser pumped by an acousto-optically mode-locked argon ion laser, and also for a colliding pulse passively mode-locked dye laser.     

Low-frequency fluctuations in two-state quantum dot lasers

We study the feedback-induced instabilities in a quantum dot semiconductor laser emitting in both ground and excited states. Without optical feedback the device exhibits dynamics corresponding to antiphase fluctuations between ground and excited states, while the total output power remains constant. The introduction of feedback leads to power dropouts in the ground state and intensity bursts in the excited state, resulting in a practically constant total output power.     

Stabilization of intracavity frequency-doubled lasers with type I phase matching

We report a new method for stabilizing the power of intracavity frequency-doubled multimode lasers with type I phase matching. Such lasers usually show strong fluctuations of the output power caused by coupling of longitudinal laser modes in the nonlinear crystal. We eliminate these fluctuations by placing the gain medium and nonlinear crystal in specific locations in the laser cavity where the nonlinear coupling of different longitudinal modes is strongly reduced.     

Theory of intensity noise in semiconductor laser emission

The intensity fluctuations expected in the output of cw semiconductor lasers are studied analytically using linearized multimode rate equations. Spontaneous emission causes intrinsic fluctuations of the laser wave. A power-independent contribution to the intensity fluctuations may occur due to inversion-induced modulation noise. The correlation of the low-frequency noise of different laser modes is investigated. The results are in agreement with experimental data reported in the literature.     

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.     

Fluctuations in synchronously mode-locked dye lasers

We present detailed experimental data on random fluctuations of the pulse properties of a cw rhodamine 6G dye laser synchronously pumped by an acousto-optically mode-locked argon ion laser. It is shown that quantitative information about the fluctuations of the energy, the pulse repetition time and the duration of the pulses can be obtained from the power spectrum of the laser intensity which is measured with the use of an electronic spectrum analyser. This method is capable of revealing small, subpicosecond temporal pulse jitter. We show that the dye laser pulses exhibit an absolute r.m.s. jitter of 20 ps which is induced by the pump laser. The relative jitter in a dual system can be less than 1 ps because well defined correlations of the output fluctuations exist when two lasers are pumped by a common source.     

双模环型激光增益噪声模型的非线性效应

讨论了一个双模环型激光增益噪声模型，其中考虑了完全饱和效应且乘法噪声由增益系数涨落引起。在共振及两模具有相同泵参数时，获得了光强联合定态分布的精确解析表达式。通过与现有的双模激光摸型（其中乘法噪声由损失系数涨落引起）的比较，发现乘法噪声系数的非线性效应减弱了乘法噪声给激光光强统计性质带来的反常特性，并且这种减弱随着乘法噪声增强或损失系数减小而愈加明显。     

非线性激光场中量子噪声之间的耦合效应

用二维气体激光模型对量子噪声的实部和虚部存在耦合的激光场进行了理论分析，通过福克－普朗克方程导出了定态激光光场强度和位相的分布函数，算出了定态激光强度和位相的平均值，方差和偏斜度，与量子噪声的两个分量为独立随机变量的激光场相比，噪声间的耦合极大地改变了激光场强度和位相的涨落，并引起了激光场强度与位相之间的耦合。     

Generation of 740 mW of blue light by intracavity frequency doubling with a first-order quasi-phase-matched KTiOPO(4) crystal

We report on efficient intracavity frequency doubling of a cw diode-pumped Nd:YAG laser on the (4)F(3/2)?(4)I(9/2) laser transition at 946 nm. The nonlinear crystal used in the experiments was a first-order quasi-phase-matched flux-grown KTiOPO(4) crystal (period, 6.09mum ; thickness, 1 mm; length, 9 mm). The fluctuations in the generated second-harmonic wave were lower than 3% at output powers of as much as 500 mW. The overall optical-to-optical efficiency was 5.7%. A maximum output power of 740 mW of blue light was generated, which was stable for only 0.5 min. The decrease the output power at this power level was attributed to heating and thermal lensing in the periodically poled KTiOPO(4) crystal. The short-term behavior of the second-harmonic wave exhibited switching between a cw mode and chaotic intensity fluctuations.     

行波管放大器中辐射场的极限环振荡和混沌

以行波管放大器中辐射场的非线性不稳定阈值分析为基础，对辐射场从频率分叉到混沌的演化过程和不同区域这些非线性不稳定态的时间特性和频率特性进行了研究.在“软”非线性区域，辐射场表现为极限环振荡和频率分岔，频谱是离散的且相对于载波频率是不对称的.这种不稳定是阵发性的，适当的调节控制参量，可使器件工作在所需的定态或极限环振荡态上；在“硬”非线性区域，辐射场表现为非周期的随机振荡和频率混沌，频谱连续且频带很宽，场幅值较大的成分集中在接近于零频的低频范围里.这种不稳定是连续性的，不能通过调节参量来消除. 关键词： 行波管 辐射场 分岔 极限环 混沌     

Tunable and switchable multi-wavelength Erbium-doped photonic crystal fiber ring laser incorporating a length of highly nonlinear photonic crystal fiber

A tunable and switchable multi-wavelength Erbium-doped photonic crystal fiber ring laser incorporating a length of single-mode highly nonlinear photonic crystal fiber is proposed and demonstrated experimentally. Stable dual-wavelength and triple-wavelength operations at room temperature are achieved by employing the highly nonlinear photonic crystal fiber to induce four-wave mixing effect and a polarization controller to vary the polarization states of propagation lights in the laser cavity. The laser cavity is free from any wavelength selection components. The laser obtains maximal 30 dB signal-to-noise ratio and the peak power fluctuations of lasing lines are less than 1.39 dB.     

TEMPORAL CHARACTERIZATION OF LASER PULSES FROM JIGUANG-I LASER FACILITY WITH A COMPACT DUAL FUNCTION AUTOCORRELATOR

An optical pulse autocorrelator for rapid and slow scanning is described in this paper. Using an audio loudspeaker on one arm, an interferometric rapid-scanning signal of the output from a high-repetition laser oscillator is obtained. However, by adjusting the positions of the mirrors and using a step-motor on another arm, the intensity autocorrelation function of the output from a low-repetition laser amplifier can be easily measured. Using all-reflecting optics and an adequate nonlinear crystal, the whole instrument is very compact and has been used to measure sub-20 fs light pulses in both configurations with excellent agreement. In the slow-scanning configuration, a pulse train as long as 500ps has been determined. Using this autocorrelator, the home-made JIGUANG-I CPA laser facility was characterized for its pulse duration evolution.     

Intra-cavity second-harmonic and sum-frequency generation in a diode-pumped broadband Yb-doped fibre laser

Intra-cavity nonlinear frequency mixing in a diode-pumped, broadband Yb-doped fibre laser has been investigated. Second-harmonic generation of the fibre output, second-harmonic generation of the residual pump beam and sum frequency mixing between the two was achieved simultaneously, resulting in three colour operation in the blue-green region. Including the nonlinear crystal inside the cavity is also shown to be effective in reducing fluctuations in the output power.     

Radiative corrections in laser-dressed atoms: formalism and applications

The dressing of atomic states in a strong laser field modifies the structure of the incoherently scattered fraction of the laser intensity, which is described to a good approximation by the Mollow spectrum. The incoherent spectrum is generated by the fluctuations of the atomic dipole moment about its expectation value, and the positions of the peaks are approximately given by the energy differences between the dressed atomic energy levels. In this paper, we investigate radiative corrections received by the dressed states. Our calculations are motivated by the quest to understand in detail the interplay of a bound electron dressed by the highly populated laser mode and its interaction with the vacuum modes. Alternatively, this may be seen as an electron experiencing modified stimulated and spontaneous radiative corrections in a vacuum tailored by the laser field. We obtain dressed self-energy shifts that depend on the Rabi flopping frequency (and in turn on the laser intensity) and on the detuning of the laser field relative to the atomic resonance frequency. We find that the dressed radiative corrections differ in a nontrivial manner from the radiative shifts of the ‘bare’ atomic states.     

Theory of intensity and phase fluctuations of a homogeneously broadened laser

We extend our previous quantum mechanical nonlinear treatment of laser noise to the following problem: We consider a set of atoms each with three levels, which support laser action of one or several modes. The laser action can take place either between the upper or the lower two levels. The atomic line is assumed to be homogeneously broadened. The broadening can be caused by the decay into the nonlasing modes, by the pumping process, lattice vibrations and other, non specified sources. The fluctuations of the atomic variables (or operators) are taken into account in a quantum mechanically consistent way using results of previous papers byHaken andWeidlich as well asSchmid andRisken. The laser modes are coupled to the thermal resonator noise usingSenitzky's method. In the first part of the present paper, we treat quite generally multimode laser action. It is shown, that each light mode chooses a specificcollective atomic “mode” to interact with. We introduce a set of suitable collective atomic “modes”, which leads to a simplification of the equations of motion for theHeisenberg operators of the light field and the atomic operators. From the new equations we can eliminate all atomic operators. We are then left with a set of coupled nonlinear, integro-differential equations for the light field operators alone. These equations, which are completely exact and valid both for running and standing waves, represent a considerable simplification of the original problem. In the second part of this paper, these equations are specialized to single mode operation, which is studied above laser threshold. In the vicinity of the threshold the laser equation can be simplified to an operator-equation, whose classical analogue is vander-Pol's equation with a noisy driving force. With increasing inversion, the full equation must be treated, however. Using the method of our previous paper, we decompose the light amplitude into a phase-factor and a real amplitude, which is expanded around its stable value. We determine the Fourier-transform of the intensity correlation function and the total intensity of the fluctuating part of the amplitude. Somewhat above threshold this intensity drops down with the inverse of the photon output power,P, while the inherent relaxation frequency increases withP. The noise intensity stems in this region from the off-diagonal elements of the noise operators and not from the diagonal elements, which are responsible for the shot noise. This result is insofar remarkable, as a rate equation treatment would include only the latter ones. Under certain conditions the intensity fluctuations can show resonances with increasing output power,P. At high inversion the vacuum fluctuations of the light field are dominant, while the other noise sources give rise to contributions which vanish with the inverse of the output power. As a by-product our treatment yields the following formula for the linewidth (half width at half power) which is caused by phase fluctuations:

$$\Delta \nu = \frac{{\gamma _{3 2}^2 \kappa ^2 }}{{(\kappa + \gamma _{3 2} )^2 }}\frac{{\hbar \omega }}{P}\left( {\frac{1}{2}\frac{{(N_3 + N_2 )}}{{N_3 - N_2 }} + n_{Th} + \frac{1}{2}} \right)$$     

Periodic intensity variations on the pulse-train of a passively mode-locked fiber ring laser

We investigate the evolvement of the periodic intensity variations of the pulse-train in a fiber ring laser mode-locked by the nonlinear polarization rotation technique. It is found that the phenomenon of such intensity fluctuations is related to the orientation of the polarization controllers when the pump power is fixed. The numerical results show that the mechanism of the periodic intensity variations is caused by the interaction of the nonlinear polarization rotation and the passive polarizer in the cavity.     

Effect of nonlinear gain on the phase noise of Y-branch lasers

Effect of nonlinear gain on the phase noise of modulated grating Y-branch (MGY) lasers is investigated by experiments and simulations. The phase noise is first characterized by measuring the frequency modulation noise spectrum of the MGY laser, and some interesting phenomena are observed. In order to understand the underlying physic mechanism of those phenomena, simulations are performed with taking Langevin noise sources and nonlinear gain terms into account. Simulated results show that, in the presence of the nonlinear gain, fluctuations of side-modes can bring excess phase noise to the lasing mode, especially when the side-modes are on the long-wavelength side of the main mode. Furthermore, it has been found that the phase noise hopping phenomenon can be induced by a bi-stable state of the laser, which is also closely related to the nonlinear gain. The investigation is helpful for explaining the complicated phase noise characteristics of the MGY laser.     

一种控制掺铒光纤激光器超混沌的方法——非线性延时反馈参数调制法

提出一种非线性延时反馈参数调制法来控制混沌/超混沌，给出了利用这种方法控制处于超混沌状态的双环掺铒光纤激光器的方案.数值模拟表明，只要延时时间和反馈强度合适就可以把双环掺铒光纤激光器从超混沌状态成功地控制到不同的周期状态. 关键词： 掺铒光纤激光器 超混沌 非线性延时反馈参数调制 混沌控制     

Influence of Nonlinear Gain and Nonradiative Recombination on the Quantum Noise in InGaAsP Semiconductor Lasers

Effects of nonlinear gain and nonradiative recombination on characteristics of intensity and phase noises of InGaAsP lasers emitting in a wavelength of 1.55 Μm are investigated. The investigations are performed based on a self consistent numerical approach that takes into account the cross correlation of fluctuations among the injected electron number, photon number and the optical phase. Time variations of the fluctuations of the intensity and the shift of the lasing frequency are statistically analyzed. The corresponding frequency dependencies of intensity and frequency noises are characterized. The results show that both intensity and frequency noises around the relaxation frequency are suppressed when counting the nonlinear gain in the rate equations. The intensity noise is enhanced in the low frequency regime by increasing the nonradiative recombination. The results fit well with those predicted by the small-signal analysis.