Random fluctuations in the phase and the amplitude of a source field induce random fluctuations in the field intensity at the network output, which in turn give rise to electrical noise in the detector current. The characteristics of this source-induced noise depend on the properties of the source and on the network transfer function. In the present study we consider a stationary optical source with a finite coherence time coupled to an arbitrary, linear, time-independent network. General expressions for the power-spectral density of the source-induced noise are derived in terms of the network transfer function and the second- and the fourth-order correlation functions of the source field in the frequency domain. The incoherent limit and the case of a source that has two uncorrelated polarization modes are considered in detail, and a simple method for the estimation of the source-induced noise is suggested.
Random fluctuations in the phase and the amplitude of a source field induce random fluctuations in the field intensity at the network output, which in turn give rise to electrical noise in the detector current. The characteristics of this source-induced noise depend on the properties of the source and on the network transfer function. In the present study we consider a stationary optical source with a finite coherence time coupled to an arbitrary, linear, time-independent network. General expressions for the power-spectral density of the source-induced noise are derived in terms of the network transfer function and the second- and the fourth-order correlation functions of the source field in the frequency domain. The incoherent limit and the case of a source that has two uncorrelated polarization modes are considered in detail, and a simple method for the estimation of the source-induced noise is suggested.
A field noise spectral density matrix for the noise from a linear optical device, modeled as an optical multiport, is derived semi-classically. The noise is formulated in the scattering parameters, population inversion factor, and internal efficiency of the device. From this noise expression, a new equation for the amplified spontaneous emission spectral density from an optical amplifier is derived. This equation is more general than those previously published. The derivations are accomplished with the aid of methods from ordinary (classical) electrical network theory and only one quantum mechanical result regarding the noise from a conductance. As a result, the first-mentioned noise expression also includes the so-called vacuum field fluctuations. Further, the current noise spectrum of a square-law detector is derived with classical methods. The optical input to the detector includes the vacuum field fluctuations, which are shown to be the cause of the detector shot noise. Here, a second quantum mechanical result has to be employed, viz., that the vacuum field fluctuations cannot be detected alone. The results in this paper agree with the special cases found in the literature. The noise expressions are well suited for examination of the optical noise performance of arbitrary linear optical networks including, e.g., amplifiers, attenuators, isolators, reflections, filters, and couplers.>
We calculate the intensity fluctuations of the light transmitted by a Fabry-P\'erot interferometer when a broadband laser is incident upon it. The laser field is assumed to have a Lorentzian spectrum and to be broadened by random amplitude fluctuations (real or complex) or random frequency fluctuations. In each case we obtain closed-form expressions for the intensity autocorrelation function, from which we can obtain the magnitude of the intensity fluctuations, as well as the power spectrum. These results indicate a strong dependence of the transmitted intensity fluctuations on the higher-order statistical properties of the incident field. Agreement with similar results concerning atomic fluorescence fluctuations is very good.
The optical response of a two-site system driven by a pair of optical pulses in an interferometric set up has been studied theoretically by applying the density operator formalism. The one-exciton approach is taken for modeling two coupled two-level systems (TLS), the external field is presented semiclassically and bath-induced dissipative processes are included. In the δ-pulse limit the population of the excited state has been formulated to the lowest order perturbation expansion in the external field. In the limit of slow luminescence the interferogram of time-integrated total fluorescence has been calculated for pulses with constant relative phase. For phase-randomized pulses the variance of the correlated fluorescence signal as a function of the pulse delay allows direct interrogation of coherent transients and dephasing processes. Our analysis follows the principle of coherence observation by interference noise, COIN [O. Kinrot, I. Sh. Averbukh, and Y. Prior, Phys. Rev. Lett. 75, 3822 (1995)], but is a generalization of this concept to expand on electronically interacting TLS. The theoretical results demonstrate that analysis of fluorescence interference fluctuations may provide a powerful diagnostic tool for probing the initial quantum coherence of energy transfer, i.e., excitation oscillations by employing fs-fluorescence correlation measurements in stable interferometric configurations.
Photoelectric correlation measurements of optical fields are now becoming commonplace and, as is well known, they require fourth order correlation functions of the field for a description. Nevertheless, the fourth order theory of optical coherence has not received a great deal of attention. This is the subject of the present paper. When interference effects are combined with intensity correlations, we encounter correlation functions of the general form Γ(2,2) ≡〈V* (r−1,t1)V* (r−2,t2)V (r−3,t 3)V (r−4,t4)〉, which are functions of four space‐time arguments. Some properties of such fourth order correlations, as they relate to interference and intensity correlation effects, are derived. The space arguments are generally suppressed in the calculation. The correlation functions are expressible as multiple Fourier transforms of certain fourth order spectral densities, which are functions of three frequencies in the stationary state. The superposition law for fourth order spectral densities is derived for independent light beams, and it is shown that the fourth order spectral densities exhibit the reproducing property under superposition only when the light obeys thermal statistics. Next the superposition law is found for the spectral densities of the photoelectric signals generated by light beams falling on photodetectors. Investigation of the photoelectric signal spectrum yields information on the spectrum of the light intensity fluctuations, and removes the measurement from the domain of optics to the domain of electronics. It is shown that the photoelectric spectral densities reproduce under superposition when the two light beams in question obey a certain factorization condition, that is analogous to the cross‐spectral purity condition for second order correlations. Finally, it is shown that, under certain circumstances, all the relevant fourth order correlation properties of the optical field are expressible in terms of simpler two‐frequency spectral functions.
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.