Locking and Noise Properties of Multisection Semiconductor Lasers With Optical Injection. Application to Fabry–PÉrot and DFB Cavities

An analytical theory is presented for the study of injection locking in multisection semiconductor lasers. The Helmoltz equation for the electric field is solved using the Green's function method and the injected fields are included via the boundary conditions. Two cases are distinguished, injection through the front facet of the laser and injection through the rear facet. In both cases, an equation of evolution for the envelope of the electric field is established, taking into account the longitudinal distribution of the carrier and photon densities and the nonlinear gain. The expressions of the intensity, phase and carrier density noise spectra are derived using a matrix formulation. Comparison to classical equations used for Fabry-Perot lasers is discussed. The locking properties of a distributed feedback laser with an antireflection coated front facet are studied in detail. Results demonstrate the strong sensitivity of the locking properties on the phase grating and rear facet reflectivity.     

外注入锁定对FP激光器强度噪声的抑制

采用较强的外注入光锁定FP激光器,获得了理想的强度噪声抑制效果. 在自由运转的FP激光器的弛豫振荡峰处,最大噪声抑制强度可达9dB. 研究了注入光功率和频率失谐对于强度噪声抑制效果的影响. 此外,通过实验研究了理想噪声抑制范围与激光器稳定锁定范围之间的关系：它们都随着注入光功率的增加而增大;但在相同的注入光功率下,稳定锁定范围允许更大的频率失谐.     

外注入锁定对FP激光器强度噪声的抑制

采用较强的外注入光锁定FP激光器,获得了理想的强度噪声抑制效果.在自由运转的FP激光器的弛豫振荡峰处,最大噪声抑制强度可达9dB.研究了注入光功率和频率失谐对于强度噪声抑制效果的影响.此外,通过实验研究了理想噪声抑制范围与激光器稳定锁定范围之间的关系:它们都随着注入光功率的增加而增大;但在相同的注入光功率下,稳定锁定范围允许更大的频率失谐.     

Effects of noise on transients of injection locked semiconductorlasers

Semiconductor laser injection locking transients are analyzed. By adiabatically eliminating the carrier dynamics, a single nonlinear stochastic differential equation is obtained for the relative phase between the master and slave lasors. The corresponding Fokker-Planck equation is used to study the steady-state locked conditions as well as phase transients of the locking process. Noise causes the steady-state relative phase between the master and the slave lasers to be a random variable with a standard deviation of approximately a few degrees for typical injection levels. The standard deviation can be reduced by using a phase detector with a limited bandwidth. The mean locking time in the presence of noise is slightly less than the deterministic prediction. Noise also causes the locked lasers to have a finite probability to momentarily unlock     

Fabry-Perot semiconductor laser injection locking

Injection locking of a semiconductor laser is studied using a Fabry-Perot (FP) model. For low injection powers the FP model gives the same results as the rate equation model. At higher injection powers, the FP laser has an unlimited injection locking bandwidth; however, regions of the bandwidth are dynamically unstable. The influence of the linewidth enhancement factor on injection locking and its stability are also studied using the FP model. Finite values of the linewidth enhancement factor lead to increased locking bandwidth, asymmetry in the locking range and a saddle-node bifurcation in the injection locked solutions, of which only lower carrier density arm has linearly stable solutions.     

Locking range and stability of injection locked 1.54 µm InGaAsp semiconductor lasers

Measurements of the intensity of an injection locked 1.54 μm InGaAsP laser are reported. The change in intensity of the locked laser across the locking range is quite asymmetric, with a shape that agrees well with the theory of Lang. A linewidth parameter ofalpha = 6 pm 1was determined from the magnitude of the locking range. The injection locked laser was found to be unstable on the high frequency end of the locking range. The physical origin of this instability is explained in terms of a laser intensity change altering the phase of the laser field relative to that of the injected field.     

光注入MQW半导体激光器分岔及其动力学稳定性

研究外部光注入多量子阱激光器四维系统动力学行为及其分岔,数值模拟了外部光注入光强度、频差以及激光器线宽增强参数、驱动电流对分岔的影响,分别得到激光由分岔、周期、多周期进入混沌的过程以及激光混沌频谱.给出了多量子阱激光器静态锁模最大频域公式,导出了注入多量子阱激光器四维系统的一次近似下扰动方程和本征值方程及解,给出了该系统的Hopf分岔条件,理论和数值分析了系统的动力学稳定性行为,并进一步模拟得出激光单周期、双周期、六周期时振荡频率等值.     

An optoelectronic self-oscillatory circuit with an optical fiber delayed feedback and its injection locking technique

An optoelectronic self-oscillatory circuit with a constant time delay and its injection locking have been theoretically and experimentally described. The oscillation circuit incorporates a delayed feedback path by utilizing an optical fiber and is characterized by a differential-difference equation. The oscillation waveform and amplitude have been investigated by computing the equation. It is also shown that a stable frequency locking region exists and expands with an increase in the injection amplitude. By employing a carrier signal, two methods for optoelectronic oscillation, an AM and an FM type, are proposed and have been demonstrated to obtain more stable oscillation.     

Computer simulation of Adler's generalized equation for the interaction of oscillators with injected signals

A computer simulation that solves Adler's generalized equation describing the interaction of an injected signal with a free running oscillator is presented [1]. The simulation, performed on a digital computer, offers the advantage of a fast turn-around, great flexibility, and a high degree of accuracy. In contrast to analog computer simulations, no scaling is required. The simulation is demonstrated by determining the injection locking properties of an avalanche diode oscillator and of a pulsed magnetron with injected CW signals. The results concerning avalanche diode oscillator injection locking are in good agreement with other computational methods reported in current literature. The injection locking simulation of pulsed magnetrons, the results of the simulation, appear to confirm experimental data reported in the literature.     

Influence of amplitude-phase coupling on the injection locking bandwidth of a semiconductor laser

The strong amplitude-phase coupling in a semiconductor laser is well known to induce an enhancement linewidth factor (1 + ?2) It is shown that it also produces an enhancement of the injection locking bandwidth proportional to (1 + ?2)1/2. The connection with the usual locking bandwidth derived from Adler's equation is pointed out by considering the carrier dependence of the injected cavity resonance frequency.     

Studies on injection locking of a TEA-CO2laser for stable high-power operation

Optimum Conditions for stable operation of an injected TEA-CO2laser with high-power output have been pursued both theoretically and experimentally. The stability of injection locking as well as the obtainable peak power was analyzed based on a transient mathematical model which deals with buildup of the electric fields. Predicted dependence of injection locking on the injection intensity, the output coupling, and the resonator length was tested and verified in the experiments.     

Synchronization Effects in a Submillimeter Josephson Self-Oscillator

We present an experimental and theoretical study of injection locking in an oscillator in the presence of noise. The experiment is performed with a Josephson point-contact self-oscillator heterodyne receiver irradiated by a very weak = 1-THz signal. A general calculation of the oscillator response at low injection level is made based on the theoretical treatment of Stratonovitch. We show that the Josephson oscillator described by the RSJ model obeys the general locking equation in the presence of noise. We assume a simple evolution law of the oscillator spectrum as a fnnction of detuning and calculate its response. The experimental results are compared with computer calculations and the implications are discussed.     

Injection locking of oscillators

An oscillator can be locked in frequency by an external signal which is injected into the oscillator. In the oscillator model developed by Adler [1], the mechanism of the locking process depends upon the following. 1) The initial frequency difference between the oscillator and external signals. 2) The relative amplitude between the injected and the oscillator signals. 3) The circuit parameters. There are cases when the time required for locking must be known, particularly when an oscillator is being locked to a pulsed signal. In this paper, the work of Adler is extended to develop an equation which is useful for higher levels of locking signal, a case often encountered when an oscillator is being injection locked by a pulsed signal. Because the solution of this equation is unwieldy and difficult to understand intuitively, except in very special cases, curves describing the locking mechanism were obtained using a digital computer. These curves enable a designer to construct oscillators which will provide a desired performance. The curves were checked experimentally and showed a close agreement between predicted and measured results. The experimental data indicates that the theory describes the locking time remarkably well even at high levels of locking signal.     

Phase locking and chaos synchronization in injection-locked semiconductor lasers

We theoretically studied synchronization of chaotic oscillation in semiconductor lasers with chaotic light injection. Feedback-induced chaotic light generated from a master semiconductor laser was injected into a solitary slave semiconductor laser. The slave laser subsequently exhibited synchronized chaotic output for a wide parameter range with strong injection and frequency detuning within the injection-locking regime. Our numerical simulation revealed that the synchronized slave laser exhibits remarkable phase locking, even for chaotic light injection. Consequently, synchronization in phase fluctuations becomes dominant over intensity fluctuations. We found that there exists a parameter range where the slave can synchronize in phase only, with no intensity synchronization. However, synchronization can be completely destroyed, both in phase and in intensity, when the phase locking becomes unstable due to four-wave mixing or excited resonance oscillation. The phase locking was studied analytically and the correspondence between numerical and analytical results was shown. We also analytically examined chaos synchronization based on a linear stability analysis from the viewpoint of modulation response of injection-locked semiconductor lasers to a chaotic light signal. As a result, we verified that such injection-locking-induced chaos synchronization results from a quasilinear response of the bandwidth-broadened slave laser due to strong optical injection.     

Injection locking of CW ring dye lasers

An analytical treatment of the injection locking of CW dye lasers, taking into account the Fabry-Perot enhancement of the laser cavity is presented. The analysis, restricted to the case where the injected radiation is resonant within the injected resonator, is based on a set of rate equations for the population densities and photon flux. Analytical solutions are found which allow the injection threshold conditions to be easily determined, and which describe the different intracavity intensities characterizing the system. The dependence of these quantities on various parameters such as input coupler transparency, pump intensity, injected intensity, and wavelength is analyzed. These results correct, in the case of steady-state laser operation, the theoretical predictions obtained by Ganiel et al. from a model where only the field intensities were considered instead of the field amplitudes. The experimental feasibility of CW ring dye laser injection locking is discussed and the conditions for an optimum system, in terms of intracavity power are determined.     

Propagation equation based theory of intermodal injection lockingin semiconductor lasers

Intermodal injection locking is analyzed theoretically through the use of propagation equations inside the amplifying semiconductor medium and the boundary conditions on the laser facets. In particular, the stability analysis is performed by considering the oscillation threshold of sideband waves generated inside the laser via intracavity nearly degenerate four-wave mixing processes. This study of injection locking is performed by taking into account the dispersion relationship of both the optical gain and linewidth enhancement factor. As a consequence, in intermodal injection locking, the injected-locked power is shown to be, in certain cases, lower than that of the free-running laser, and the frequency zones of stable injection locking broader than those obtained in the intramodal injection-locking case usually considered     

Injection locking properties of a semiconductor laser

Injection locking properties of a semiconductor laser have been analyzed, taking into account the injected carrier density dependent refractive index in the active region. It has been found that this dependence significantly affects the injection locking properties, giving rise to a peculiar asymmetric tuning curve and dynamic instability. The instability originates from the intermode interaction via the modulation in the injected carrier density caused by intensity beat. The detuning dependence of the direct modulation response characteristics inside and outside of the locking range have also been examined.     

Distortion of FM modulation in detuned injection phase-locked oscillator-amplifiers

A solution of a generalized Adler's equation for injection locking phenomena is discussed. The results of calculations for both tuned and detuned injection phase-locked oscillator-amplifiers are presented graphically. These results are shown to serve as a convenient means to theoretically evaluate the distortion properties of a single-stage injection phase-locked oscillator-amplifier.     

Injection locking in AlGaAs semiconductor laser

Injection locking of AlGaAs double-heterostructure (DH) lasers was studied with respect to locking bandwidth, required power, and coherence. The relation of the locking bandwidth versus the ratio of locked laser power to injected power was consistent with the classical analysis on injection locking phenomena reported by Adler [2]. The measured maximum locking bandwidth was 5.8 GHz when the locking gain was 18 dB. A maximum gain of 40 dB was observed with a 500 MHz locking bandwidth. The power increase in the injected mode agrees well with theoretical values calculated with the van der Pol equation. The interference pattern was observed between an injecting beam and a locked laser beam. Visibility was the same as that obtained by the interference between forward and backward emitted beams in an identical free-running laser. Spurious mode suppression was observed when a single-frequency optical power is injected into an RF-modulated laser. Single longitudinal mode operation was obtained at a sufficiently high injecting level.     

一种毫米波宽锁定范围的注入锁定倍频器设计

为提高毫米波段倍频器在低功耗下的工作带宽,采用IHP130 nm SiGe BiCMOS 工艺,设计了一种采用双端注入技术的毫米波宽锁定范围注入(DEI)锁定倍频器。该注入锁定倍频器主要由谐波发生器和带有尾电流源的振荡器构成,由巴伦产生差分信号双端注入振荡器的形式提高三次谐波注入强度,使其在E、W 等波段输出宽锁定范围和良好相位噪声性能的三倍频信号。仿真结果表明,注入锁定倍频器在工作电压为1.2 V,输入信号功率为0 dBm时,其锁定范围在57~105 GHz 内。在相同工作电压和输入信号功率下,输入频率为32 GHz 时,一次、二次和四次谐波抑制大于20 dBc,功耗为9.1 mW。