G. Debarge

Time-bandwidth product of chirped sech 2 pulses: application to phase-amplitude-coupling factor measurement

An exact analytical expression for the time-bandwidth product DeltatDeltaf of chirped sech(2) pulses is derived. The relation can be expressed by DeltatDeltaf = 0.1786 arcosh(cosh pialpha + 2) as a function of the lasers phase-amplitude coupling factor alpha. An experimental measurement of the alpha factor that relies on this formula is discussed.

Analysis of frequency chirping of semiconductor lasers in the presence of optical feedback

The frequency chirping of a single-mode semiconductor laser in the presence of optical feedback is studied by rate-equation analysis. The model includes the amplitude-phase-coupling and spectral-hole-burning effects. A simple analytical formula is obtained in the small-signal regime that shows that the amplitude-phase-coupling effect also enhances the chirp-reduction ratio and that the maximum reduction of frequency chirping can be achieved at the same time as maximum line narrowing in the in-phase condition.

Phase jitter in an injection-locked semiconductor laser

An expression for the mean-square phase jitter of an injection-locked semiconductor laser is derived. It leads to the determination of the power spectrum of the locked laser. The theoretical results are in good agreement with experimental results reported previously [IEEE J. Quantum Electron. 24, 148 (1988)].

Optimum conditions for soliton launching from chirped sech2 pulses.

Simple and exact analytical formulas are derived for the optimum power and width of chirped sech2 pulses that maximize the energy transfer to the fundamental soliton. The maximum achievable energy transfer is shown to be equal to 2/(1+1+α2), normalized relative to the initial pulse energy, where α is the laser phase-amplitude coupling factor. The critical values of the α factor for the fundamental soliton are given simply in terms of the normalized pulse amplitude A by αcr = (4A2 − 1)1/2.

Numerical resolution of the Fokker-Planck equation for the study of phase noise filtering in coherent optical systems

Laser phase noise deteriorates the high sensitivity of heterodyne optical receivers. To reduce phase noise influence, the intermediate frequency signal resulting from the coherent detection is filtered by a narrow bandpass filter (BPF). The phase noise at the input of the BPF generates an amplitude and phase noise at the output of the BPF. The joint probability density function of these noises is evaluated in the case of a first order filter by numerical resolution of a Fokker-Planck equation. A finite difference operator splitting scheme is used. The accuracy of the numerical solution is checked comparing numerically and analytically calculated moments. In addition, a new very efficient method for the analytical calculation of moments is developed. Contour plots of the probability density for both a finite time integrator and a first order filter are compared in order to show the impact of different filter types on phase noise filtering. The marginal pdf of the amplitude and phase noise at the output of the above filters are also calculated.

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

RésuméCet article présente un formalisme général permettant de décrire les propriétés de bruit et de modulation des lasers à semiconducteur de structure complexe. Les lasers à contre-réaction distribuée et les lasers multisection accordables de type réflecteur Bragg distribué sont examinés à titre d’exemple. Le taux d’émission spontanée couplée au mode et le couplage phase-amplitude y sont discutés. Les résultats obtenus montrent en particulier l’influence respective des propriétés du matériau et des propriétés de la structure dont il faudra maîtriser les interactions pour développer des composants de très hautes performances.AbstractThis 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.

Propriétés spectrales d’un laser semiconducteur soumis à une rétroaction optique externe

ResumeLes équations d’évolution d’un laser semiconducteur soumis à une rétroaction optique sont résolues numériquement. La méthode est appliquée à une rétroaction optique simple produite par un miroir externe unique et au couplage du laser à un résonateur externe de finesse élevée. La réduction de largeur spectrale, l’ amortissement des oscillations de relaxation et l’influence des fréquences propres du résonateur externe sont discutés et comparés pour ces deux configurations.AbstractThe rate equations of a semiconductor laser with external optical feedback are solved numerically. The method is applied to the case of simple optical feedback and to that of a high finesse external resonator. The spectral linewidth reduction, the damping of the relaxation oscillations and the influence of the resonant frequencies of the external resonator are discussed and compared for these two configurations.