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Physical Review A

Corpuscular theory of intensity noise with gain compression

Jacques Arnaud

Published Feb 1, 1992• 16 citations
Publisher

Abstract

When light from a laser is fully absorbed by an ideal detector, the detected current exhibits a fluctuation called here ``photonic noise.'' The spectral density of Iintensity noiseR, defined as the difference of the photonic-noise spectral density and a term corresponding to the shot-noise level, is negative for sub-Poissonian statistics. The usefulness of the relative-intensity-noise concept is that it is independent of any linear attenuation. A simple circuit theory of intensity noise based only on energy conservation and the Nyquist formula (zero-point fluctuation) leads to expressions of the spectral densities that agree with quantum theory even for sub-Poissonian photon statistics. When the optical gain and loss are frequency independent, the circuit theory reduces to a corpuscular theory that keeps track of the time rates of change of electron and photon numbers treated as continuous variables. Consideration is given to laser diodes in which the rate of electron-photon conversion depends nonlinearly on both the carrier and photon densities. The cross-spectral density between electrical-voltage and relative photonic fluctuations is independent of internal or external optical losses. Standard rate equations are inaccurate in the case of gain compression. Very general yet simple formulas for intensity noise are applied to room-temperature GaAs laser diodes, using recently calculated optical parameters.

DOI
10.1103/physreva.45.1775

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When light from a laser is fully absorbed by an ideal detector, the detected current exhibits a fluctuation called here ``photonic noise.'' The spectral density of Iintensity noiseR, defined as the difference of the photonic-noise spectral density and a term corresponding to the shot-noise level, is negative for sub-Poissonian statistics. The usefulness of the relative-intensity-noise concept is that it is independent of any linear attenuation. A simple circuit theory of intensity noise based only on energy conservation and the Nyquist formula (zero-point fluctuation) leads to expressions of the spectral densities that agree with quantum theory even for sub-Poissonian photon statistics. When the optical gain and loss are frequency independent, the circuit theory reduces to a corpuscular theory that keeps track of the time rates of change of electron and photon numbers treated as continuous variables. Consideration is given to laser diodes in which the rate of electron-photon conversion depends nonlinearly on both the carrier and photon densities. The cross-spectral density between electrical-voltage and relative photonic fluctuations is independent of internal or external optical losses. Standard rate equations are inaccurate in the case of gain compression. Very general yet simple formulas for intensity noise are applied to room-temperature GaAs laser diodes, using recently calculated optical parameters.
Fluctuations of the stored energy and the emitted power of a semiconductor laser are derived by classical corpuscular optical theory. The fundamental noise sources are the shot noise associated with a field’s conversion to emitting or absorbing atoms and the mirror loss noise. The latter is taken into account in the form of partition noise forces linked to laser facet reflection. The theory permits the description of the nonclassical states of light, and its results agree with quantum theory. For quiet pumping conditions and for a high-reflection coated Fabry–Perot laser, 50% of internal photon noise suppression is obtained, whereas nonfluctuating optical output is possible for negligible internal loss. The influence of gain suppression on amplitude squeezing is discussed. The effect of attenuation on the propagation of laser fluctuations is studied by use of the concept of optical partition noise. This leads to the invariance of a suitably defined relative intensity noise, which becomes negative for sub-Poissonian photon statistics. The setup for the intensity noise measurement with the balanced detection technique is analyzed by use of optical partition noise.
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]
Adopting a new classical approach, the additive noise power generated in optical amplifiers is calculated in terms of power spectral density. The classical formalism used combines a coruscular approach to a phase-amplitude description of the optical field. The noise contributions of the input field fluctuations, including zero-point fluctuations, and of the electron momentum fluctuations at optical frequency linked to the amplifier itself, are clearly identified. The excess of noise associated to coupling or built-in losses is determinated. The well-known result of the Amplified Spontaneous Emission (ASE) is obtained for the laser amplifiers. This description is applied to linear phase-insensitive amplifiers and to inhomogeneous, nonlinear phase-insensitive Raman amplifier, pointing out the effects of gain compression and gain distribution. This new approach makes possible the treatment of the squeezed-state of light and the quadrature reduced noise amplifications.
'l*he noise is the was a saying of Rolf Landauer, l one of the founding fathers of mesoscopic physics. What he meant was that fluctuations in time of a measurement can be a source of Information that is not present in the time-averaged value. As figure l reminds us, some types of noise are more interesting than others. A physicist with access to sensitive ways of distinguishing the granularity in a signal may delight in the noise. Noise plays a uniquely informative role in the particle-wave duality. In 1909, Albert Einstein realized that electromagnetic fluctuations vary depending on whether the energy is carried by waves or by particles. The magnitude of energy fluctuations scales linearly with the mean energy for classical waves, but it scales with the square root of the mean energy for classical particles. Since a photon is neither a classical wave nor a classical particle, the linear and square-root contributions coexist. Typically, the square-root (particle) contribution dominates at optical frequencies and the linear (wave) contribution takes over at radio frequencies. If Isaac Newton could have measured noise as the time-dependent fluctuations from the mean intensity, he would have been able to settle his dispute with Christiaan Huygens on the corpuscular nature of light—without actually needing to observe an individual photon. Such is the power of noise. The diagnostic power of photon noise was further developed in the 1960s, when it was discovered that one can teil the difference between radiation from a laser and that from a black body on the basis of their fluctuating Signals: The wave contribution to the fluctuations is entirely absent for a laser; it is merely small for a black body. Noise measurements are now a routine technique in quantum optics, and Roy Glauber's quantum mechanical theory of photon statistics is textbook material. Because electrons share the particle—wave duality with photons, one might expect fluctuations in the electrical current to play a similar diagnostic role. Current fluctuations due to the discreteness of the electrical charge are known as shot noise. Although the first observations of shot noise date from work on vacuum tubes in the 1920s,
Using an extension of the Scully—Lamb laser theory we show that by insertion of nonlinear elements in the cavity, laser light with nonclassical sub—Poissonian photon statistics can be generated. For an N—photon absorber in the limit of small saturation the variance of the photon number distribution can be reduced by a factor of (+1/N) compared to Poissonian limit of the usual laser. When we generalize the type of such nonlinear elements to the case of a nonlinear feedback or Raman type nonlinear transition, the noise in the laser intensity can be reduced even further and approach the ideal limit, characterized by a Mandel Q parameter of Q = —1. Furthermore we show how this noise reduction via nonlinearities can be combined with a regular pump mechanism, which recently has been sugessted as a way to generate sub—Poissonian light. It turns out that in certain configurations the effect of both methods can be combined. Finally we show how this nonclassical behaviour is also reflected in a reduction of the output intensity power spectra below the shot noise level.