A simple formula is presented for the linewidth-power product of multielement laser diodes, under the condition that the active elements are submitted to the same field. The theory is particulalrly applicable to laser diodes incorporating two thin active layers of different composition. Such diodes can be moduled by two active conducttances in parrallel with a linear admittance. If the injected current exhibits full shot noise, the laser linewidth is given by the same expression as for a single active element , except that α and α2 must be replaced by their average values weighted by the injected bias currents, where α denotes that phase-amplitude coupling factor. The same result is applicable to conventional index-guided laser diodes.
Electronics Letters, Volume 24, Issue 6, 17 March 1988, p. 302 – 303
ABSTRACT
The standard rate equations are incomplete when the optical cavity conductance depends on the optical frequency at the operating point. Corrected rate equations are given in the paper, that involve an action of frequency back on the amplitude. The number of relaxation oscillations is found to be much smaller than that calculated from standard rate equations when the optical wave is weakly index guided, as in CSP lasers. The revision of the rate equations proposed in the paper may affect most laser characteristics.
Electronics Letters, Volume 24, Issue 2, 21 January 1988, p. 116 – 117
ABSTRACT
A theory is given for the frequency noise of saturated laser diodes having arbitrary geometry. The frequency noise is expressed in terms of integrals of the unperturbed resonating field. The formula simplifies considerably when the shot noise contribution, in addition to the spontaneous emission contribution, is taken into account. The validity of the perturbation formula used is verified by comparison with a direct exact calculation for a two-active-element electrical circuit.
Electronics Letters, Volume 23, Issue 9, 23 April 1987, p. 450 – 451
ABSTRACT
The classical Schawlow–Townes formula for the linewidth of a laser should be multiplied by a factor K’ = (1+αA2)K/2. In this formula, αA, is the ratio of changes in the real and imaginary parts of the compl resonant frequency resulting from a change in carrier density, and K is Petermann’s factor. It is shown here that this factor is identical to a result reported in 1971 by other authors in connection with impact oscillators.
IEE Proceedings J (Optoelectronics), Volume 134, Issue 1, February 1987, p. 2 – 6
ABSTRACT
A general and simple expression for the natural linewidth of lasers with high, spatially inhomogeneous gain, such as semiconductor lasers, has recently been reported by the author in a short paper. In the present paper, the relation is applied to a number of circuits relevant to semiconductor injection lasers. Its significance is clarified by considering simple lumped circuits. It is further generalised to anisotropic materials which may be nonreciprocal, and the role of dispersion inside and outside the laser cavity is discussed. The theory is restricted to single-mode operation (well above threshold operation), but saturation is neglected.
Optical and Quatum Electronics, 18, 335-346, mai 1986
ABSTRACT
The natural linewidth of lasers is shown to be enhanced with respect to the value predicted by the Schawlow-Townes formula whan the gain is high and inhomogeneous in transverse or longitudinal directions. A general formula for the linewidth enhancement is derived from first principles : Maxwell’s equations and the fluctuation-dissipation theorem, for media with arbitrary bi-anisotropy and dispersion. The result is expressed in terms of an integral of the resonating fiels over the cavity volume. For isotropic media (scalar ε and μ), thos formula generalizes previous results by Petremann for gain-guided lasers, by Ujihara for lasers with low reflectivity mirrors, and results obtained by others authors for lasers coupled to long external cavities. The role of non-reciprocity is discussed.
IEEE Journal of Quantum Electronics, vol QE-22, n°4, avril 1986
ABSTRACT
Petermann has proposed that the classical formula for the linewidth of a laser be multiplied by a factor K ≥≥ 1 in the case of gain-guided semiconductor lasers (1). The concept of power in the mode used by that author, however, is not well defined in a waveguide with gain, and his theory is therefore opened to question. The analysis given here avoids this difficulty ans nevertheless agrees with Petermann’s result. This is because spatial mode filtering is strong in oscillating lasers.
IEEE Journal of Quantum Electronics, vol QE-21, n°6, juin 1985
ABSTRACT
In a mode matched configuration, spontaneous emission in semiconductor laser amplifier sis enhanced by a factor which is larger that unity but which is significantly smaller than the K-factor calculated by Petermann. Using thin-slab model, we find that in typical situations, the factor is about K/2.
The theory presented indicates that when the active region of a semiconductor laser is very thin the linewidth enhancement factor differs significantly from Henry’s 1 + α2 factor and can be reduced by a factor of 4. Petermann’s K-factor may also play a role in the plane perpendicular to the junction.