Linewidth enhancement for DFB lasers due to longitudinal field dependence in the laser cavity

To calculate the linewidth for an index-guided semiconductor laser, one usually neglects a correction factor for the spontaneous emission rate, which is introduced by the longitudinal field distribution within the laser cavity. For FabryPerot lasers with cleaved facets the correction factor is small. However, for DFB lasers this correction factor may become quite significant, yielding a linewidth enhancement for DFB laser diodes.     

Noise analysis of injection-locked semiconductor injection lasers

The noise of injection-locked semiconductor lasers is analyzed by rate equations including the spontaneous emission noise. The side mode suppression and the relative intensity noise (RIN) of the locked laser (slave laser) are given for different wavelengths detuning between the master and slave laser and for different linewidth enhancement factors α. For large α, locking is difficult to achieve, whereas extremely low noise may be obtained for injection-locked lasers with a low linewidth enhancement factor.     

半导体激光器的微腔结构调制及其脉码在光纤中的传输

采用腔量子电动力学(QED)方法,定量讨论了平面结构微腔半导体激光器的自发发射特征物理量随腔结构的变化规律.在微腔半导体激光器自发发射因子调制、自发发射寿命调制以及一些实验依据的基础上,提出了微腔结构调制方法.数值模拟了其脉码在光纤中的传输图形.结果表明,微腔结构调制方法在提高脉码比特率方面优于同参数下的电流调制方法.     

Transfer-matrix formulation of spontaneous emission noise of DFBsemiconductor lasers

A unified formulation of the spontaneous emission noise in semiconductor DFB (distributed feedback) lasers is presented by using a transfer-matrix approach. Analytical expressions for the noise power per unit frequency bandwidth below threshold and the spontaneous emission rate into the lasing mode are obtained based on the Green's function method. Three DFB laser structures are analyzed: (1) a standard DFB structure with facet reflectivities, (2) a multisection DFB structure composed of n sections which models a phase-shifted DFB laser and a multielectrode (tunable) DFB laser, and (3) a periodic layered DFB structure which models a surface-emitting DFB laser. It is shown that the spontaneous emission noise of a complicated DFB laser structure can be calculated easily by the transfer matrix of each section of the structure and its derivative to frequency     

Spontaneous emission model of surface-emitting DFB semiconductorlasers

A general spontaneous emission model is developed for surface-emitting (SE) distributed feedback (DFB) semiconductor lasers. The frequency distribution of spontaneous emission noise below lasing threshold and the spontaneous emission rate in lasing operation are formulated by using a transfer matrix method combined with the Green's function method. The effective linewidth enhancement factor is obtained from this model in terms of the elements of the transfer matrix. By way of example, the author applies the formulation to a standard SE DFB laser, and a SE λ/4-shifted DFB laser with a distributed Bragg reflector (DBR) mirror. In particular, the author analyzes the below-threshold spectrum, the threshold current density, the differential quantum efficiency, and the spectral linewidth of these lasers     

A quasi-three-dimensional large-signal dynamic model of distributedfeedback lasers

A simple, but powerful, quasi-three-dimensional large-signal dynamic model of distributed feedback semiconductor laser is presented. The transient response of lasers is analyzed by using a combined beam propagation method and time-domain algorithm that is capable of including the longitudinal and lateral variation of the optical-mode and carrier density profiles. In addition, the spontaneous emission noise, the nonuniform current injection resulting from the variation of Fermi-voltage as well as that of the refractive index distribution are also taken into consideration. Using this model, the influence of nonuniform waveguide structure on the static and dynamic responses of distributed feedback lasers is analyzed. In addition, a novel double tapered waveguide distributed feedback laser is proposed for stable single-mode operation at high power     

Variation of intensity noise and frequency noise with thespontaneous emission factor in semiconductor lasers

The intensity noise level and the spectral line-width of semiconductor injection lasers are theoretically analyzed. Approximated but simple forms representing these characteristics are found to give criteria for various types and sizes of cavity, including microcavity lasers. The noise and the line-width are reduced by operation with high injection current or high optical power in general. For operation at a low-power level in the microcavity laser, increase of the spontaneous emission factor as well as reduction of the threshold current level and the threshold gain level are important to get a low noise level and narrow line-width     

Detailed model and investigation of gain saturation and carrier spatial hole burning for a semiconductor optical amplifier with gain clamping by a vertical laser field

A detailed model for semiconductor linear optical amplifiers (LOAs) with gain clamping by a vertical laser field is presented, which accounts the carrier and photon density distribution in the longitudinal direction as well as the facet reflectivity. The photon iterative method is used in the simulation with output amplified spontaneous emission spectrum in the wide band as iterative variables. The gain saturation behaviors and the noise figure are numerically simulated, and the variation of longitudinal carrier density with the input power is presented which is associated with the on-off state of the vertical lasers. The results show that the LOA can have a gain spectrum clamped in a wide wavelength range and have almost the same value of noise figure as that of conventional semiconductor optical amplifiers (SOAs). Numerical results also show that an LOA can have a noise figure about 2 dB less than that of the SOA gain clamped by a distributed Bragg reflector laser.     

Wide-range tunable semiconductor lasers using asymmetric dualquantum wells

Using asymmetric dual quantum wells for the laser material, the semiconductor lasers are broadly tunable. In a grating coupled ring cavity, the semiconductor laser is continuously tunable from 766 to 856 nm using a 400-μm semiconductor laser amplifier in the cavity. This letter also demonstrates that the grating coupled ring cavity could well eliminate the amplified stimulated emission noise and about 40-dB amplified spontaneous emission (ASE) suppression ratio is obtained over the entire tuning range     

Influence of spontaneous frequency fluctuations on lineshape of semiconductor laser modulated by a pseudorandom pumping current

The lineshape of a single-mode semiconductor laser is studied numerically for fast pseudorandom current modulation. We analyze the contribution of frequency fluctuations originated from spontaneous emission to the laser spectrum. The expression is derived for the nonstationary phase increment determining the influence of frequency noise on the lineshape. The obtained results show that spectral characteristics of laser radiation substantially depends on the spontaneous emission factor as well as on parameters of modulation.     

自发发射因子在外腔半导体激光器的模式选择和线宽压缩过程中的作用

本文提出并论证外腔模式自发发射因子急剧减小使模式选择所需的增益差和光场相位噪声皆急剧减小是外腔半导体激光器具有优异的纵模选择和线宽压缩性能同时又具有严重不稳定性的统一的关键性物理根源。     

Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers

A theory of spontaneous emission noise is presented based on classical electromagnetic theory. Unlike conventional theories of laser noise, this presentation is valid for open resonators. A local Langevin force is added to the wave equation to account for spontaneous emission. A general expression is found relating the diffusion coefficient of this force to the imaginary part of the dielectric function. The fields of lasers and amplifiers are found by solving the wave equation by the Green's function method. The lasing mode is a resonant state associated with a pole in Green's function. In this way, noise in lasers and amplifiers is treated by a unified approach that is valid for either gain guiding or index guiding. The Langevin rate equations for the laser are derived. The theory is illustrated with applications to traveling wave and Fabry-Perot amplifiers and Fabry-Perot lasers. Several new results are found: optical amplifier noise increases inversely with quantum efficiency; spontaneous emission into the lasing mode is enhanced in lasers with low facet reflectivities; and the linewidth of a Fabry-Perot laser with a passive section decreases as the square of the fraction of the cavity optical length that is active.     

Couplage phase-amplitude et taux d’émission spontanée dans les lasers à semiconducteur à contre-réaction distribuée ou à cavité composite

This article presents a formalism which describes the noise and modulation properties of a complex structure semiconductor laser. As an example, the distributed feedback lasers and the distributed Bragg reflector lasers are examined. The rate of the spontaneous emission coupled to the lasing mode and the phase-amplitude coupling factor are discussed. The obtained results show particularly the influence of both the materials properties and the structure. The interactions between these two factors should be controlled to develop high performance laser diodes.     

半导体微腔激光器中的自发辐射耦合增强效应

针对半导体微腔激光器的结构特点,以及腔量子电动力学中自发辐射增强效应,采用光增益与载流子密度的对数关系,引入增益饱和项和非辐射复合项的贡献,指出即便是对于理想的封闭微腔,由于非辐射衰减速率的影响,光输出并不随泵浦线性变化。结合频谱和相图分析,给出了自发辐射耦合因子与微腔激光器的辐射阈值、开关延迟时间、驰豫振荡频率和光输出等参量关系的仿真结果,这对于微腔激光器的理论研究和优化器件结构有所裨益。     

Transfer-matrix analysis of the intensity and phase noise ofmultisection DFB semiconductor lasers

A general small-signal model for the intensity and phase noise spectra of multisection distributed feedback (DFB) semiconductor lasers is developed by using the transfer-matrix approach based on the Green's function method. The spontaneous emission enhancements due to nonuniform longitudinal field distribution and the effective amplitude-phase coupling effect (the effective linewidth enhancement factor) are taken into account in the formulation. Analytical expressions for the spectra of the relative intensity noise and the FM noise of the main mode in the multimode operation are presented by using the transfer functions in a flow-graph representation. Facet reflectivities and external optical feedback are included in the model. The effects of the grating coupling coefficient, the random grating-phase at the facets, the phase-shift position, the external optical feedback, and the side mode on the noise spectra are analyzed systematically for a λ/4-shifted DFB laser     

Semiconductor laser noise in an interferometer system

The noise of semiconductor laser light after passing a Michelson interferometer has been measured for gain guided as well as index guided double-heterostructure injection lasers. This noise is mainly due to the partition noise and the frequency noise of the laser emission. Unless the interferometer is perfectly balanced, the observed noise is several orders of magnitude larger than the usual intensity noise of semiconductor lasers.     

Analysis of the phase-amplitude coupling factor and spectrallinewidth of distributed feedback and composite-cavity semiconductorlasers

A Green's function approach to the analysis of semiconductor lasers is formulated in a form suitable for complex cavity structures. Both the spontaneous emission rate and the effective phase-amplitude coupling factor can be accurately evaluated. For distributed-feedback (DFB) lasers, the spontaneous emission rate is strongly dependent on both the facet reflectivities and the grating coupling coefficients. The effective phase-amplitude coupling factor depends on the wavelength detuning from the gain maximum. The calculated linewidth of DFB lasers differs considerably from previous calculated results and gives better agreement with experimental results. For composite-cavity lasers, the frequency dependence of the equivalent reflectivity has a strong impact on the phase-amplitude coupling factor and the spontaneous emission rate. Distributed Bragg reflector (DBR) lasers are investigated as an example of a composite-cavity structure     

Noise in an AlGaAs semiconductor laser amplifier

The noise characteristics in a Fabry-Perot (FP) cavity type semiconductor laser amplifier, biased at just below its oscillation threshold current, have been studied theoretically and experimentally. Quantum mechanical multimode rate equations containing a Langevin shot noise source and an input signal term were numerically solved for an exponential band-tail model with nok-selection rule. Noise power calculated using this rate equation was compared with a simpler photon statistic master equation method. The experimental results on noise power for an AlGaAs laser amplifier are in reasonable agreement with the two different theoretical predictions. Dominant noise powers in a semiconductor laser amplifier are beat noise powers between signal and spontaneous emission, and between spontaneous emission components. Noise characteristics in a Fabry-Perot cavity type laser amplifier can be improved both by the reduction of the facet mirror reflectivities and by use of an asymmetric cavity configuration with low-input and high-output mirror reflectivities. Two beat noise powers are expressed in simple analytic form by introducing an equivalent noise bandwidth and an excess noise coefficient as figures of merit in an optical amplifier.     

Noise in an AlGaAs Semiconductor Laser Amplifier

The noise characteristics in a Fabry-Perot (FP) cavity type semiconductor laser amplifier, biased at just below its oscillation thresh-old current, have been studied theoretically and experimentally. Quantum mechanical multimode rate equations containing a Langevin shot noise source and an input signal term were numerically solved for an exponential band-tail model with no k-selection rule. Noise power calculated using this rate equation was compared with a simpler photon statistic master equation method. The experimental results on noise power for an AlGaAs laser amplifier are in reasonable agreement with the two different theoretical predictions. Dominant noise powers in a semiconductor laser amplifier are beat noise powers between signal and spontaneous emission, and between spontaneous emission components. Noise characteristics in a Fabry-Perot cavity type laser amplifier can be improved both by the reduction of the facet mirror reflectivities and by use of an asymmetric cavity configuration with low-input and high-output mirror reflectivities. Two beat noise powers are expressed in simple analytic form by introducing an equivalent noise bandwidth and an excess noise coefficient as figures of merit in an optical amplifier.     

Characterizing relative intensity noise in InGaAsP-InP triangular ring lasers

This paper discusses relative intensity noise (RIN) characterization of triangular ring lasers, fabricated through a self-aligned dry etching process in InGaAsP-InP. Unusual low frequency noise enhancement was observed in each of the output beams, that is strongly dependent on the mirror backscattering strength. We explain the physical origin of the unusual RIN results as a partition noise effect between the two output beams of the ring laser, which can be best interpreted as superposition of two incoherent spatially bidirectional modes, generated by incoherent spontaneous emission photons traveling in clockwise and counterclockwise directions. This effect is unique to the ring laser geometry, and reported here for the first time. General noise predictions of our analysis are consistent with experimental measurements. This partition noise enhancement is expected to be present in the entire class of bidirectional semiconductor ring lasers, affecting the noise performance of not only the triangular ring laser, but also circular and square geometries, and possibly microdisk type lasers, in integrated photonic circuit applications.