The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]

Quantum noise in photonics

A general theory of linewidth for single-frequency semiconductor lasers is presented. The effects of spatially distributed noise sources together with spatially varying carrier and photon densities and injection current are analyzed in a rigorous manner by solution of the scalar wave equation. A new rate equation for the electric field is derived, in which the longitudinal effects are represented in the form of the weight functions C/sub N/(z) and C/sub S/(z). These functions express the sensitivity of the (output) field to local changes in carrier and photon density at the position z. For Fabry-Perot laser's the z dependence of the C factors is shown to be negligible, in agreement with the fact that spatial hole burning is not considered to be important for Fabry-Perot lasers. For distributed-feedback (DFB) lasers, however, the z dependence is shown to be very significant. >

Theory of linewidth for multielectrode laser diodes with spatially distributed noise sources

We show theoretically, that the detuning between the resonance frequencies of differently pumped DFB sections gives rise to two different pulsation mechanisms, 1) dispersive self Q-switching of a single-mode and 2) beating oscillations between two modes of nearly equal threshold gain. Our analysis is based on the dynamic coupled wave equations accomplished with carrier rate equations. We demonstrate the existence of certain isolated values of the detuning between both sections, at which two longitudinal eigenmodes become degenerate. In the degeneration point, the longitudinal excess factor of spontaneous emission has a singularity and the system of eigenmodes becomes incomplete. We derive reduced equations governing the dynamics in the vicinity of degeneration points. For an example device, the numerical integration of these equations clearly demonstrates the two different self pulsations with repetition rates of more than 100 GHz.

Mechanisms of fast self pulsations in two-section DFB lasers

Large signal dynamic responses of temporal and spectral characteristics for gain-coupled distributed feedback (DFB) lasers are calculated by a computer model based on power matrix methods. Spontaneous emission, longitudinal ef- fects of spatial hole burning and carrier induced variations of the coupling coefficient have been taken into account. Both an- tireflection (AR) coated and cleaved facet devices are analyzed for the purely gain-coupled DFB. For partly gain-coupled DFB's, it is found that the dynamic behavior is dependent on the phase of the index and gain coupling. Low chirp operation can be achieved by having index and gain coupling in anti- phase.

http://ieeexplore.ieee.org/iel1/3/6035/00234427.pdf

Dynamic Response of the

We present a traveling wave analysis of a general class of semiconductor lasers, which includes multisection DFB/DBR lasers and gain-coupled DFB lasers. The analysis leads to new semianalytic expressions for the small-signal IM and FM modulation responses, the intensity and FM noise spectra, and the linewidth. The expressions are given in terms of solutions to four coupled linear homogeneous differential equations and can easily be evaluated numerically. We also derive a stability parameter /spl sigma/, for which /spl sigma/ >

Traveling wave analysis of semiconductor lasers: modulation responses, mode stability and quantum mechanical treatment of noise spectra

In DFB (distributed feedback) lasers, the shape of the longitudinal intensity and carrier density distributions changes above threshold as a result of spatial hole burning. The longitudinally distributed coupling of spontaneous emission into the lasing mode also plays an important role for the noise properties. The authors demonstrate how both effects can be included in a dynamic analysis. They extend their previously developed theory for multielectrode lasers to enable calculation of stability properties as well as small-signal modulation responses and noise spectra. The theory is used to study global and local stability of the stationary solutions (modes). The numerical results for several laser structures are presented. It is shown that symmetric DFB lasers are likely to exhibit pitchfork bifurcations in their static tuning characteristics as the current is increased. The authors discuss how the presence or proximity of such instabilities can affect the modulation and noise properties, and in particular, the spectral linewidth. >

Stability and dynamic properties of multi-electrode laser diodes using a Green's function approach

Results of a detailed linewidth theory for DFB lasers are presented. We show that fluctuations in the longitudinal distributions of photon and carrier densities can have a significant effect on the linewidth. A new type of linewidth rebroadening is identified, which is attributed to modal instability. This may explain the rebroadening observed in cases with high sidemode suppression.

Mode instability and linewidth rebroadening in DFB lasers

The authors present a new traveling wave method for calculating the linewidth, the frequency tuning efficiency, and a mode stability parameter for a general class of laser-diode structures. The method leads to simple semianalytic expressions which allow an easy numerical determination of the three parameters. >

Traveling wave method for calculation of linewidth, frequency tuning, and stability of semiconductor lasers

The Bragg grating induced by the pattern of standing waves in a Fabry-Perot laser diode is shown to give a significant contribution to nonlinear gain. An analytic expression is derived for the contribution leading to a simple universal relation between the damping rate of relaxation oscillations, the square of the relaxation resonance frequency, and the carrier diffusion time. The effect of the standing wave grating cannot explain present data from various experiments, which indicated that there must be additional important contributions to nonlinear gain. >

H. Olesen

Papers

Traveling wave analysis of semiconductor lasers: modulation responses, mode stability and quantum mechanical treatment of noise spectra

Stability and dynamic properties of multi-electrode laser diodes using a Green's function approach

Mode instability and linewidth rebroadening in DFB lasers

Traveling wave method for calculation of linewidth, frequency tuning, and stability of semiconductor lasers

Gain compression and asymmetric gain due to the Bragg grating induced by the standing waves in Fabry-Perot lasers