Einstein relations for gain-guided semiconductor lasers

The Einstein equations which relate the transition rates for stimulated emission, spontaneous emission and stimulated absorption in a laser active medium are re-examined for the special case of a semiconductor laser with complex wave-guiding. It is shown that, owing to the nonorthogonality of the gain-guided laser modes, the Einstein relations have to be modified. In particular, the spontaneous emission rate per laser mode no longer equals the stimulated emission rate per laser photon.     

Spatio-temporal dynamics of gain-guided semiconductor laser arrays

A continuous model based on the coupled field-matter Maxwell-Bloch equations for a two-level homogeneously broadened single mode laser is developed. The model includes a Langevin formulation to model thermal and spontaneous emission noises and accounts for carrier diffusion, optical field diffraction and current spreading. Our model is flexible enough to simulate any gain-guided longitudinally uniform laser geometry and is applied to both a single-stripe and a four-stripe gain-guided semiconductor lasers where the influence of the injection current, the interstripe distance and carrier diffusion is discussed within the context of the laser dynamics. We show that an array operating with quasi-independent stripes may be achieved at low pumps and larger interstripe distances. However, as injection current is increased or the interstripe distance is decreased, the device passes through a variety of dynamical instabilities which can be analyzed in the context of lateral cavity modes. Moreover, we also show that the array dynamics is strongly influenced by carrier diffusion which may also lead to different thresholds for each element of the array     

Quantum mechanical explanation of spontaneous emission K-factor

The rate of spontaneous photon emission in an injection laser depends on whether the laser modes are gain-guided or index-guided. For gain-guided modes the ratio of spontaneous to stimulated emission is greater by a factor K to the corresponding ratio for index-guided modes. Recently, the validity of the K-factor was questioned by means of a quantum mechanical argument. It is the purpose of this letter to show that quantum theory does not contradict the classical derivation of the K-factor but instead confirms its validity and sheds new light on the physics of spontaneous emission into gain-guided laser modes.     

Dynamic analysis of multiple wavelength DFB fiber lasers

The behavior of multi- and single-wavelength distributed feedback fiber lasers is simulated in a comprehensive dynamic model. The evolution of the spatial distribution of gain, saturation-induced gain gratings, and spontaneous emission is taken into account. Stability and relative intensity noise (RIN) of the different laser types and laser modes are compared, and the effect of varying degree of pump RIN and quenching of spontaneous emission lifetimes is analyzed     

On the "Excess spontaneous emission factor" in gain-guided laser amplifiers

Petennann [1] computed an "excess spontaneous emission factor" for gain-guided laser. In this paper, we investigate further the role of this factor. Such a factor also appears in the treatment of thermodynamic equilibrium in an attenuating medium-a seeming paradox. Further investigation shows that the excess spontaneous emission excitation at thermal equilibrium is cancelled by the excitations in the other modes which are correlated with that in the fundamental mode. In a medium with gain, cancellation also occurs in a short amplifier in which there is no gain discrimination among modes. The "excess spontaneous emission factor" is fully present only in a system in which the different higher order modes have an appreciably smaller gain than the lowest order mode, a high gain amplifier. An analysis of the signal-to-noise ratio of a high gain amplifier reveals that the excess noise factor can be fully compensated by proper input excitation by a lens arrangement. The lens arrangement provides the signal with an "excess gain" factor. An "excess gain" factor is also present when a thermal source is used.     

一种新型结构的单纵模光纤激光器

单纵模掺铒光纤激光器在光通信和光传感等方面有着广泛的应用前景。设计了一种新型的光纤激光器，在光纤环形镜中嵌入未抽运的掺铒光纤作为可饱和吸收体以抑制多纵模，用光纤环谐振腔作为滤波器抑制拍频噪声，用光纤光栅作为波长选择器件，最终得到了单纵模输出并消除了拍频噪声。使用零拍法测量其线宽小于频谱仪的低频极限5kHz。实验结果证明了可饱和吸收体和光纤环的功能。     

Accuracy of Fabry-Perot method of semiconductor laser gain measurement

The Fabry?Perot (FP) method of semiconductor laser gain measurement, first proposed by Hakki and Paoli (1975), is widely used. It is based on the measurement of the FP resonances excited by spontaneous emission. Its validity rests on the assumption that a single mode is significant. We show, using a simplified laser model, that this assumption is valid only when the power mirror reflectivity is very small, or near the laser oscillating frequency. For example, the error is in the order of 20% when the power facet reflectivities are equal to 37% and the modal gain is unity. These results apply to both index-guided and gain-guided lasers.     

Coherence properties of gain- and index-guided semiconductor lasers

The spectral linewidth of the longitudinal laser modes has been measured as a function of mode power for different types of gain-guided as well as index-guided (GaAl)As double heterostructure laser diodes. Various effects contributing to line broadening, such as spontaneous emission, carrier density fluctuations, changes of the resonator parameters, and mode competition are discussed.     

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.     

Dynamical noise in single-mode distributed feedback fiber lasers

The dynamics of erbium distributed feedback fiber lasers close to steady state is analyzed taking into account spatial hole burning and the nonuniform modefield distribution. A set of linearized equations is derived and used to obtain theoretical amplitude and frequency noise spectra for spontaneous emission noise and generic pump power noise. Analytic formula for important laser characteristics including pump slope efficiency and relaxation oscillation frequency are also obtained. It is found that the spatial distribution of the laser mode plays and important role in determining the output characteristics of the laser.     

Transverse-mode competition effects observed in the numericalsimulation of transients in gain-guided semiconductor laser arrays

A numerical analysis of transient turn-on in a gain-guided semiconductor laser array is presented. The self-consistent approach, valid in the strong-coupling limit, treats the array as a single waveguide laser with a transversely varying refractive index. The program first solves for the modes of this system without considering stimulated emission. The overall modal gain is then inserted into the rate equations in order to calculate a photon density; this results in a new spatial gain distribution, which in turn causes changes to the modal intensity profiles. This analysis is used to find both steady-state results and instabilities which result from mode competition. The approach is to solve instantaneous eigenvalue equations     

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.     

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     

Analysis of diode laser properties

An analytic model of diode lasers applicable to both the lasing and the nonlasing states is described. For these homogeneously broadened devices, spectral envelope widths for TE00and TM00modes are related to power in each modal family and are shown to depend critically on spontaneous emission coupling into the transverse modes. Thus, lasers with real-refractive index waveguiding (and associated weak spontaneous emission coupling) operate single longitudinal mode above threshold, whereas gain-guided devices run multimode. After connecting gain and spontaneous emission, a charge conservation equation, containing optical power in the form of a stimulated emission term, pumping current, spontaneous emission, and spectral width, is derived. These equations are then demonstrated to suffice for determination of the completeLversusIcharacteristic. For lasers in which both charge and mode confinement exist, such as the buried heterostructure (BH) and channelled-substrate narrow stripe (CNS) types, it is shown that both TM00power and spectral envelope width approach limiting values at threshold, whereas TE00mode power grows in conjunction with TE00spectral envelope narrowing.     

Spectral linewidth in oxide-confined vertical-cavitysurface-emitting lasers

We present a model to compute the linewidth in vertical-cavity surface-emitting lasers (VCSELs), by accounting for the 3-D structure of real devices. To this aim, we include the noise source in the field equations and treat both the noise and the structural characteristics by means of coupled-mode theory. In this way, we obtain an expression for the linewidth that is given as the standard relation, modified by two correction factors that account for spatial effects and modal dispersion of the resonator. In the numerical results, we study for oxide-confined VCSELs the transition from index to gain-guided regime, where the standard linewidth theory does not hold, and we give some guidelines for narrow-line emission devices     

On crosstalk and noise in an optical amplifier with gain clamping by vertical laser field

We have calculated the transient behavior and noise figure of a semiconductor optical amplifier (SOA) with the gain clamped by a vertical cavity laser (VCL). The characteristic behavior of the more conventional gain-clamped SOAs and SOAs with no gain-clamping is also studied and compared with the vertically gain-clamped amplifier. The calculations are based on a numerical stochastic rate equation model including several forward- and backward-propagating channels that are coupled to the vertical laser field through the active medium. The noise model takes into account the input noise, randomly amplified spontaneous emission, and random gain. Numerical simulations have been carried out to study the relaxation oscillations, crosstalk, and noise in a system with a strong input signal switched on and off while observing the output signals, VCL photon density, and carrier density. Results show that the VCL field captures most of the disturbances, in agreement with available experimental data.     

The starting mechanism in coupled-cavity modelocked laser systems

We present what we believe to be the starting mechanism in coupled-cavity additive pulse modelocked (APM) laser systems. The etalon effect of the coupled cavity forces the main cavity to lase at two separate frequencies, thus producing short and strong mode beating “noise bursts” that can overcome dynamic gain saturation in large emission cross-section gain media. As a result, self-starting is possible for the NaCl:OH coupled-cavity color center laser. The dependence of the etalon effect on the cavity length detuning and its role in the dynamics of the APM process and in self-stabilized picosecond coupled-cavity lasers are discussed. The experimental observation of THz-mode beating fluctuations produced by the mode structure of a coupled-cavity NaCl:OH color center laser supports our model     

Near-threshold behavior of the intrinsic resonant frequency in a semiconductor laser

The excitation-dependence of the resonant frequency intrinsic to a semiconductor laser is analyzed in terms of a spatially uniform laser model which takes into account radiative and nonradiative recombination as well as spontaneous emission into the lasing modes. The analysis reveals that the frequency of the resonance excited by internal quantum noise approaches a minimum value as the excitation level approaches threshold in contradiction to the behavior expected from a small-signal analysis of the external modulation spectrum or the relaxation oscillations. This distinctly different behavior of the noise-excited resonance is shown to result from the presence of noise fluctuations in the optical field, which are sensed only by the noise-excited spectrum. Experimental observations made with a stripe-geometry (AlGa)As double-heterostructure laser confirm the predicted behavior of the noise-excited resonant frequency in the near-threshold regime.     

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.