Residual and absolute timing jitter in actively mode-locked semiconductor lasers

The magnitude and origin of the pulse-to-pulse timing jitter that is added to the modulating source by an active mode-locked laser is discussed. Residual and absolute RMS timing jitter measurements as low as 50 fs and 170 fs, respectively, have been measured in optimally tuned cavities.<>     

Cyclic wavelength jitter in actively mode-locked semiconductor lasers

Large spectral broadening has been observed in an actively mode-locked semiconductor laser tuned for minimum average pulsewidth. Numerical simulations show that the spectral broadening was a result of cyclic wavelength variations associated with large amplitude and timing instabilities.<>     

Quantum-limited timing jitter in actively modelocked lasers

Expressions for the quantum-limited timing jitter in an actively modelocked fiber laser are derived. We identify a set of characteristic constants that govern the timing jitter for the cases using amplitude modulation (AM) and phase modulation (PM) as the active modelocking elements. We find that when using AM, the Gordon-Haus jitter is proportional to the square of the group-velocity dispersion and reaches a minimum value for the case of low dispersion. Using PM, the Gordon-Haus jitter increases only linearly proportional to group-velocity dispersion, and there exists an optimum group-velocity dispersion that minimizes the jitter. We compare the theory to recent experiments of the timing jitter for an active harmonically modelocked fiber laser.     

Tunable monolithic mode-locked lasers on InP with low timing jitter

Pulse trains with only 2 ps in width and low root-mean-square timing jitter of 220 fs are demonstrated from fine tunable monolithic 40-GHz laser integrated circuits on GaInAsP-InP. The repetition rate is tunable within 500 MHz by changing only the gain current and the absorber voltage. Simultaneously, the small pulsewidths are kept constant and the timing jitter remains below 300 fs. The determined time-bandwidth products between 0.37 and 0.5 are close to the transform limit and the fiber coupled optical power is /spl ges/1 mW. The fact that pulsewidth and timing jitter remain small over the whole repetition-rate tuning range constitutes an important step toward economic commercial applications, especially if frequency shifts caused by fabrication tolerances have to be compensated.     

Design guidelines of actively mode-locked fiber ring lasers

This letter presents guidelines of how to design actively mode-locked fiber ring lasers to generate nearly transform-limited soliton pulses. The minimum fiber cavity length and/or dispersion, with which nearly transform-limited soliton pulses can be generated, need to satisfy an additional condition besides two previously known conditions of stability     

A rate equation analysis of actively mode-locked semiconductor lasers

A rate equation has been used to analyze the actively mode-locked diode laser which is biased with a subthreshold dc current upon which a sinusoidal signal, whose frequency is equal to the mode spacing (or its multiple) of the external cavity, is superimposed. Steady-state operation of the laser enables us to find out many important parameters of the system. Based upon the experimental observations, we have established the time evolution of the injection carrier density which suggests the existence of a subpulse following the main pulse and provides the possibility of predicting the time gap between them. Meanwhile, the average output power of the laser, the threshold condition of the mode-locked oscillator, the arrival time of the main pulse at the gain medium, the temporal difference between the main pulse, and the peak of the small-signal gain have also been derived.     

Theory of mode-locked semiconductor lasers

We present a theoretical study of semiconductor mode-locked lasers at a phenomenological level. We use the slow absorber model of New and Haus, but extend the analysis by taking into account the shift in the gain maximum due to the changing number of carriers. In our analysis of the resulting equation, we show that due to stability requirements the shortest attainable pulse duration is limited. The use of self-phase modulation due to a slow medium can at most lead to a shortening of the pulse by a factor of 2. We show that the shifting of the gain maximum due to the changing number of carriers in the laser is a crucial aspect in the operation of mode-locked semiconductor lasers. We further find that the end mirrors must be reflecting more than about half of the light intensity to prevent a self-pulsation type instability similar to the relaxation oscillation     

Harmonically mode-locked glass waveguide laser with 21-fs timing jitter

We report on experimental jitter results of a 10-GHz mode-locked laser. The laser is an actively harmonically mode-locked fiber laser using an erbium-doped glass waveguide as the gain medium. Amplitude noise and corresponding phase noise effects are greatly reduced by the inclusion of an intracavity high-finesse fiber Fabry-Pe/spl acute/rot etalon. Typical results show timing jitter of 21-fs root mean square, integrated from 10 Hz to 100 MHz.     

Polarization-maintaining fiber Bragg gratings for wavelengthselection in actively mode-locked Er-doped fiber lasers

Fiber Bragg gratings written in polarization-maintaining fiber are proposed for wavelength selection in actively mode-locked Er-doped fiber lasers. Combined with single-polarization optical circulator, they form unidirectional transmission filters that can be incorporated in polarization-maintaining laser cavities. We have fabricated such a grating in hydrogen-loaded PANDA fiber and we have incorporated it in a polarization-maintaining actively mode-locked Er-doped fiber laser designed to generate soliton-like pulses. Dependencies of pulse duration and spectral width on average intracavity power were measured. The power range over which soliton-like pulses were generated without pedestals was found to be ultimately limited by the grating's bandwidth     

Extreme timing jitter reduction of a passively mode-locked laserdiode by optical pulse injection

Reduction of the timing jitter to less than that of the master laser pulses was achieved for a passively mode-locked laser diode stabilized by subharmonic-frequency optical pulse injection. Detailed investigation revealed that this phenomenon originates from the short-term stability of the mode locking frequency under passively mode-locking operation with suitable bias conditions of the saturable absorber and the gain sections     

Universality of mode-locked jitter performance

It is shown experimentally that the jitter of actively mode-locked laser pulses is determined by two factors: first, by spontaneous noise associated with cavity loss, and second, by round-trip propagation time. As the round-trip time is increased, a characteristic frequency which defines the high-frequency limit of phase noise decreases. For a comparable round-trip time and cavity loss, the jitter of mode-locked lasers based on diverse gain media, whether semiconductor or erbium ion is universal and independent of the upper-state transition lifetime.     

Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation

A quantum theory for the noise of optical pulses in actively mode-locked lasers is presented. In the presence of phase modulation and/or group velocity dispersion, the linear operator that governs the time evolution of the pulse fluctuations inside the laser cavity is not Hermitian (or normal) and the eigenmodes of this operator are not orthogonal. As a result, the eigenmodes have excess noise and the noise in different eigenmodes is highly correlated. We construct quantum operators for the pulse photon number, phase, timing, and frequency fluctuations. The nonorthogonality of the eigenmodes results in excess noise in the pulse photon number, phase, timing, and frequency. The excess noise depends on the frequency chirp of the pulse and is present only at low frequencies in the spectral densities of the pulse noise operators.     

Effect of tunable filter characteristics on the pulse performance of actively mode-locked fiber lasers

The effect of filter characteristics on the output performance of actively mode-locked fiber ring lasers has been studied experimentally and numerically, with the same 3-dB bandwidth, the filter that has a flatter wavelength response tends to generate narrower soliton-like pulses.     

Theory of mode-locked lasers containing a reverse saturable absorber

An analytic solution is presented for mode-locking a laser using a saturable absorber and reverse saturable absorber with long relaxation times compared to the temporal pulse widths. A reverse saturable absorber is a material with an excited-state absorption cross section larger than the ground-state absorption cross section, where increasing the incident light intensity increases the absorption. The reverse saturable absorber plays an important role in mode-locking laser materials where individual pulses cannot saturate the gain. A numerical example of mode-locking a CW alexandrite laser with a reverse saturable absorber and a saturable absorber is presented.     

锁模Cr4+:YAG固体激光器脉冲的时间抖动理论性分析

固体激光器的脉冲稳定性限制了激光器在很多方面的应用.从被动锁模Cr4 :YAG激光器腔内脉冲的传播方程出发,得到了带噪声的非线性Schr(o)dinger方程,进一步分析了脉冲在激光器腔内的时间传播形式,建立了锁模Cr4 :YAG固体激光器振荡脉冲参数的线性扰动方程,推导出了脉冲参数波动的动力学方程以及时间和相位的均方根波动关系式.提出了一个减少锁模Cr4 :YAG固体激光器脉冲时间抖动的实验方案,旨为锁模Cr4 :YAG固体激光器能够用作光纤通信和量子通信中的光源提供理论上的帮助.     

Measurement of the timing jitter and pulse energy fluctuation of aPLL regeneratively mode-locked fiber laser

We measured the timing jitter and pulse energy fluctuation from the noise RF power spectra of a 10-GHz regeneratively mode-locked erbium-doped fiber laser in both free-running and phase-locked-loop (PLL) operation. The measured timing jitter was 90 and 120 fs for free-running and PLL operation, respectively. These values are to our knowledge the smallest timing jitter reported in actively mode-locked fiber lasers. The pulse energy fluctuation was 0.24% for both operation     

Effects of current modulation on timing jitter of single-modesemiconductor lasers in short external cavities

Turn-on jitter of single-mode semiconductor lasers with modulated injection current and weak optical feedback exhibits periodic oscillations as a function of the length of the external cavity, under configurations appropriate for packaged laser diodes. Numerical results for both periodic and pseudorandom word modulation show that the oscillations persist even when increasing the external cavity length to a few millimeters. It is found that under particular positions of the external reflector a large increase of jitter occurs as compared with the jitter without optical feedback     

Noise of mode-locked lasers

A theory of noise in mode-locked lasers is developed that applies to additive pulse mode-locked and Kerr lens mode-locked systems. Equations of motion are derived for pulse energy, carrier linewidth, frequency pulling, and timing jitter. The effect of gain fluctuations, mirror vibrations, and index fluctuations are determined. Measurements that can determine all four fluctuation spectra are described. Experimental data in the literature are compared with theory     

Higher order FM mode locking for pulse-repetition-rate enhancementin actively mode-locked lasers: theory and experiment

We present a novel higher order FM mode-locked technique for active mode-locked lasers which utilizes the higher order sidebands generated by an intracavity phase modulator to establish the mode locking. The resulting mode-locked output exhibits an enhancement of the pulse repetition rate over the modulation frequency by an integral multiple. The higher order FM mode locking is studied theoretically in a laser with a homogeneous gain medium, and simple analytical expressions are obtained to characterize the output pulses. It is shown that the scheme not only enhances the pulse repetition rate but also ensures chirp-free pulses and is effective in eliminating the output pulse phase-state instability, which are commonly observed in conventional FM mode-locked lasers. The effect of group velocity dispersion and cavity nonlinearity is also investigated through numerical solution of the self-consistency equation applied to a fiber ring laser. Finally, detailed experimental results on repetition rate enhancement in fiber lasers are presented and shown to be in good agreement with the theoretical results