Electronics Letters, Volume 27, Issue 19, 12 September 1991, p. 1756 – 1758
ABSTRACT
For frequency-independent gain and loss, the circuit theory of photonic noise based on the Nyquist noise sources reduces to a corpuscular theory that postulates independent shot-noise fluctuations of the particle rates. For linear gain, the corpuscular theory coincides with standard rate equations (SREs). When the relative gain compression is comparable with unity, however, SREs are in error by a large factor. The exact theory shows that in the presence of nonlinear gain, photonic noise may be less than shot noise, even when the injected current exhibits shot-noise fluctuations. This new effect cannot be predicted by SREs.
The small-signal modulation and noise properties (electrical voltage, optical power and phase) of laser diodes depend on ten real parameters relating to the semiconductor material employed. Among these, the phase-amplitude coupling factor α is of particular importance. These parameters are evaluated for GaAs at 0.87 μm, GaInAsP at 1.55 μm and InAsSb at 3.87 μm at room temperature. Revised expressions for the optical gain are used. The light-hole contribution, the plasma effect and band-gap shrinkage are taken into account. The latter leads to a significant reduction of α, particularly below the peak-gain frequency. The α-factors for the three materials listed above are found to be, respectively, 2.9, 3.85 and 8.3 for conventional diodes
The circuit theory of laser diode modulation and noise is based only on the energy and electron-number conservation laws, and on the well known expression hv(Gb+Ga) for the spectral density of Nyquist noise currents. The conductances G b and Ga represent stimulated absorption and stimulated emission, respectively. This theory leads to results that are in exact agreement with the predictions of quantum optics, even in the case of electronic feedback and non-classical states of light, but the optical field is not quantised. The theory is presented in a general form, applicable to arbitrary optical and electrical configurations, but is exemplified for only a single active element model of laser diode. For independent electron-hole injection, the results are the same as those obtained from standard rate equations, except for a phase-noise term. Important differences do occur for more realistic laser models.
A general theory of noise and small-signal modulation of multielement laser diodes in the saturated regime is established. Nonlinear elements are connected to the ports of a linear-optical circuit oscillating in a single electromagnetic mode. The laser amplitude and phase fluctuations are expressed simply in terms of the scattering matrix of the linear-optical circuit at any baseband frequency and for an arbitrary electronic feedback. The case of a single laser diode and a single detector is treated to demonstrate this method. The correlation between optical power and electrical voltage fluctuations is shown to disappear at large output powers, in agreement with recent experiments.
IEEE Journal of Quantum electronics, vol 25 n° 4, april 1989
ABSTRACT
The linewidth of a laser diode having a phase-amplitude factor α that varies arbitrarily alongt he path is calculated. For simplicity, an ideal single-mode ring-type laser diode with only one wave circulating is considered. The theory is exact in the limit of large injected currents, provided parameters such as the carrier temperature do not vary and the gain or loss per wavelength is small. It is found that when the electron-hole pairs are injected independently of each other (that is, when the pump fluctuations are spatially uncorrelated shot noises) the linewidth is half the value obtained earlier for the linear regime multiplied by (1 + α2)av where the round-trip averaging is affected with respect to the reciprocal of the power gain. Specific examples, in particular a sequence of amplifiers and partially reflecting mirrors, are considered.
Electronics Letters, Volume 25, Issue 1, 5 January 1989, p. 1 – 2
ABSTRACT
It is generally believed that the amplitude fluctuations of a light beam initially in the coherent state cannot be squeezed below those of shot noise by the simple arrangement of a beamsplitter and a detector, the current from the detector being fed back to the light source or to a modulator. A simple semiclassical theory shows that arbitrary amounts of squeezing can in fact be obtained if a negative opticalconductance device such as a constant-voltage-driven (nonself-oscillating) laser diode is used in place of a conventional detector.
The amplitude noise of a laser diode submitted to electronic feedback is evaluated using a new circuit theory. It is postulated that the electron-hole injection rate equals the photon generation rate at any time, and Nyquist-like noise sources are introduced. Previous results based on quantum mehcanics are recovered. It is found that the amplitude fluctuations of an optical beam in the coherent state can be squeezed below shot noise by feeding back the driving current of a laser amplifier.
Yamamoto and others are shown when the pump (or injected current) fluctuations of a laser diode are suppressed, the optical power fluctuations are much reduced, but the laser linewidth remains essentially unchanged. We find that for a realistic extended laser model, the linewidth may in fact be importantly reduced. Our finding is based on a semiclassical theory. With full shot-noise in the injected current, the linewidth is proportional to (1 + α2) av, where α (z) denotes the phase-amplitude factor, and the average is evaluated along the diode z-axis. Without injected current fluctuations, one must substract from this expression half the variance (α2) av – (αav)2 of α. The linewidth reduction thus occurs only if α varies significantly along the diode.
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.