Measurement of the frequency fluctuations of a laser with a nonlinear-absorbing cell using the Bershtein method

We propose to use the method of I. L. Bershtein for measuring the frequency fluctuations of an arbitrary type oscillator from the error signal at the output of the phase locking system for a laser with internal absorbing cell. The spectral density of the frequency fluctuations of a single-frequency He-Ne/CH₄ laser was measured. It is shown that in this case the method allows us to measure the low-frequency technical fluctuations of the laser frequency, which determine the width of the laser emission line. The measurements can be performed in the case of both suppression of low-frequency fluctuations of the laser frequency due to the phase locking system and the regime that is close to that of free generation. It is also shown that an increase in the operating frequency band of the phase locking system makes sense only in the case in which the reference spectral density of the laser frequency fluctuations multiplied by the slope of the frequency discriminator conversion (in this case, the power and photoreceiver peak) exceeds the noise level at the system input. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 11, pp. 1487–1494, November, 1998.     

Influence of fluctuations of the weight coefficients on the characteristics of adaptive antenna arrays

We analyze theoretically the influence of the weight-coefficient fluctuations on the characteristics of adaptive antenna arrays (AAAs) with gradient adjustment algorithms under the assumption that the useful and noise signals have different correlation times. We obtain expressions for the correlation function and the spectral power density of the AAA output signal, find the average radiation pattern (RP), and derive an expression for the correlation matrix of the weight-coefficient fluctuations. It is shown that the weight-coefficient fluctuations bring about distortions of the useful signal and decrease its output power compared with the case of no fluctuations. In the frequency spectrum, this “overcompensation” phenomenon results in the depression of the output signal spectrum of the antenna array in the frequency band where high-power noise exists. As an example, we calculate the spectral power density of the output signal for an AAA with single linear constraints and plot the fluctuation RP and the variance of the weight-coefficient fluctuations versus the noise arrival angle. N. I. Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 1, pp. 83–92, September 2000.     

Diffusion-induced Ramsey narrowing

Diffusion-induced Ramsey narrowing is characterized and identified as a general phenomenon, in which diffusion of coherence in and out of an interaction region such as a laser beam induces spectral narrowing of the associated resonance line shape. Illustrative experiments and an intuitive analytical model are presented for this spectral narrowing effect, which occurs commonly in optically interrogated atomic systems and may also be relevant to quantum dots and other solid-state spin systems.     

Level Dynamics and Universality of Spectral Fluctuations

The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics for the fictitious gas of particles associated with the parametric motion of levels yields spectral fluctuations of the random-matrix type. Previously known clues to that goal are an appropriate equilibrium ensemble and a certain ergodicity of level dynamics. We here complete the reasoning by establishing a power law for the dependence of the mean parametric separation of avoided level crossings. Due to that law universal spectral fluctuations emerge as average behavior of a family of quantum dynamics drawn from a control parameter interval which becomes vanishingly small in the classical limit; the family thus corresponds to a single classical system. We also argue that classically integrable dynamics cannot produce universal spectral fluctuations since their level dynamics resembles a nearly ideal Pechukas–Yukawa gas.     

Theoretical Approach to Energy Resolution of Semiconductor Detectors

All processes occurring in semiconductor detectors during detection of primary monoenergetic particles lead to broadening of spectral lines. In this work, a general expression for the energy resolution of semiconductor detectors is obtained using the theory of branching cascade processes. It is shown that the general formula involves all contributions to the spectral line broadening described in the literature and additional contributions associated with fluctuations of electron and hole lifetimes caused by inhomogeneity of traps in the semiconductor material and fluctuations of the electronic channel gain.     

Phase-amplitude characterization of a high-repetition-rate quantum dash passively mode-locked laser

We apply a novel phase-amplitude characterization method to a one-section quantum dash-based passively mode-locked laser at a 42.2 GHz repetition rate. The method relies on the measurement of the spectral phase of the longitudinal modes by the successive analysis of the correlation signal of a group of three adjacent modes. It provides both the temporal shape of the intensity and the phase of the emitted signal. A pulse of 1.5 ps of width is measured, and a pedestal is exhibited. Extinction ratio limitation is explained by investigating the origin of this pedestal. The accuracy of the method is estimated by comparing the measured autocorrelation signal and the calculated one from the phase analysis.     

Enhanced Landau-Placzek ratio in a heavy fermion metal observed by Brillouin scattering

Brillouin spectroscopy of the heavy fermion metal UPt₃ shows strong quasielastic scattering, which has no analogue in ordinary metals. An enhanced Landau-Placzek ratio relating the quasielastic to the inelastic scattering intensity is deduced from the line shape analysis. The quasielastic line is of nonmagnetic origin and is attributed to electron density fluctuations as predicted by a recent theory of hydrodynamic fluctuations in heavy fermion systems.     

Theoretical derivation of 1/f noise in quantum chaos

It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the power spectrum behavior of the excitation energy fluctuations, which is different for chaotic and integrable systems. Using random matrix theory, we derive theoretical expressions that explain without free parameters the universal behavior of the excitation energy fluctuations power spectrum. The theory gives excellent agreement with numerical calculations and reproduces to a good approximation the 1/f (1/f(2)) power law characteristic of chaotic (integrable) systems. Moreover, the theoretical results are valid for semiclassical systems as well.     

Theoretical expressions of temporal power spectra of irradiance fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

The temporal power spectra of irradiance fluctuations reflect the frequency distribution of temporal statistical property of irradiance fluctuation. In this paper, new analytical expressions of the temporal power spectral models of irradiance fluctuations are developed for optical waves propagating through weak non-Kolmogorov turbulence with horizontal path. They are derived with the general modified atmospheric spectral model, and they consider the finite turbulence inner and outer scales, and have a general spectral power law value in the range of 3 to 4 instead of the standard power law value of 11/3. Numerical calculations are conducted to analyze the influence of non-Kolmogorov weak turbulence on the temporal power spectra of irradiance fluctuations.     

Geometrical optimization of organic microlasers for microfluidic chemical sensing

We report the design, fabrication, and demonstration of a chemical sensor-based on the spectral shift of organic microcavity lasers. The shape of the cavity contour is used as a parameter and is optimized to improve the sensitivity. Analytical and numerical predictions are in good agreement with experiments performed in a microfluidic environment, showing sensitivities of up to 100 nm per refractive index unit for stadium-shaped microlasers on pedestal. Selective sensing of Hg²⁺ at a concentration down to 200 ppb is then demonstrated with cavities functionalized by ligands that are known to bind mercuric cations.     

Spectral line broadening in quantum wells due to Coulomb interaction of current carriers

A theoretical analysis of emission line broadening due to Coulomb interaction of carriers is performed. An analytical approximation for the spectral line shape function with exponential decays is derived by using the perturbation theory for many-body electron–hole systems for both non-degenerate and degenerate conditions. An explanation of the experimentally observed spectral line asymmetry and the linewidth change as a function of the temperature and the excitation level is given.     

Exact results of statistical analysis of multichannel adaptive systems with continuous gradient algorithms

We obtained some exact expressions for the power of the output signal of adaptive systems with continuous gradient adjustment algorithms. It is shown that fluctuations of weight coefficients result in a decrease in the signal power at the adaptive-system output as compared with the output-signal power in the absence of fluctuations of the weight coefficients. The “overcompensation” phenomenon is explained by the presence of a non-Gaussian statistical relation between the weight- coefficient and input-signal vectors. N. I. Lobachevskii State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 914–921, September, 1999.     

Conductance noise spectrum of mesoscopic systems

We investigate the shape as well as the size- and temperature-dependence of the conductance noise spectrum of a small system containing electrons and both fixed and mobile scatterers. If the number of mobile scatterers within a phase-coherent region is sufficiently large, the temporal variation of the conductance can be viewed as a random walk process limited by the universal conductance fluctuations, resulting in a practically Lorentzian power spectrum. We discuss the conditions under which the noise spectrum of a system consisting of many phase-coherent regions is either Lorentzian or 1/f-like. The temperature-dependence of the power spectrum is determined by the hopping mechanism and the variation of the phase breaking length. As a function of temperature the spectrum satisfies power law scaling relations with exponents depending on the dimension and the temperature range; the spectral intensity can both increase and decrease with decreasing temperature.     

Implications of Noise on Neural Correlates of Consciousness: A Computational Analysis of Stochastic Systems of Mutually Connected Processes

Random fluctuations in neuronal processes may contribute to variability in perception and increase the information capacity of neuronal networks. Various sources of random processes have been characterized in the nervous system on different levels. However, in the context of neural correlates of consciousness, the robustness of mechanisms of conscious perception against inherent noise in neural dynamical systems is poorly understood. In this paper, a stochastic model is developed to study the implications of noise on dynamical systems that mimic neural correlates of consciousness. We computed power spectral densities and spectral entropy values for dynamical systems that contain a number of mutually connected processes. Interestingly, we found that spectral entropy decreases linearly as the number of processes within the system doubles. Further, power spectral density frequencies shift to higher values as system size increases, revealing an increasing impact of negative feedback loops and regulations on the dynamics of larger systems. Overall, our stochastic modeling and analysis results reveal that large dynamical systems of mutually connected and negatively regulated processes are more robust against inherent noise than small systems.     

Localization and fluctuations in quantum kicked rotors

We address the issue of fluctuations, about an exponential line shape, in a pair of one-dimensional kicked quantum systems exhibiting dynamical localization. An exact renormalization scheme establishes the fractal character of the fluctuations and provides a method to compute the localization length in terms of the fluctuations. In the case of a linear rotor, the fluctuations are independent of the kicking parameter k and exhibit self-similarity for certain values of the quasienergy. For given k, the asymptotic localization length is a good characteristic of the localized line shapes for all quasienergies. This is in stark contrast to the quadratic rotor, where the fluctuations depend upon the strength of the kicking and exhibit local "resonances." These resonances result in strong deviations of the localization length from the asymptotic value. The consequences are particularly pronounced when considering the time evolution of a packet made up of several quasienergy states.     

Complex-number asymmetry parameters of the optical Fano effect in ring resonators

We studied the sharp asymmetric Fano line shape in fiber ring resonator systems and provided an explicit expression for asymmetry parameters using the physical parameters of the system. The fiber ring system was controllable and reconfigurable, allowing us to produce a variety of Fano line shapes in different configurations. Experimentally observed asymmetric spectral structures were fully reproduced using the complex-number asymmetry parameters, validating the approximations used to reduce the analytical expression for the line shape to the phenomenological Fano formula. The results may be useful in the design of on-chip application systems.     

Classical basis for quantum spectral fluctuations in hyperbolic systems

We reason in support of the universality of quantum spectral fluctuations in chaotic systems, starting from the pioneering work of Sieber and Richter who expressed the spectral form factor in terms of pairs of periodic orbits with self-crossings and avoided crossings. Dropping the restriction to uniformly hyperbolic dynamics, we show that for general hyperbolic two-freedom systems with time-reversal invariance the spectral form factor is faithful to random-matrix theory, up to quadratic order in time. We re late the action difference within the contributing pairs of orbits to properties of stable and unstable manifolds. In studying the effects of conjugate points, we show that almost self-retracing orbit loops do not contribute to the form factor. Our findings are substantiated by numerical evidence for the concrete example of two billiard systems.Received: 10 June 2003, Published online: 11 August 2003PACS: 05.45.Mt Quantum chaos; semiclassical methods - 03.65.Sq Semiclassical theories and applications     

Spectral analysis of a laser beam

The formulas of the dependence of the spectral laser power distribution and its spectral half-width on the physical parameters of its laser active medium are derived. In addition it is found that, if the gain line profile has a Lorentzian or Gaussian distribution, the spectral laser power distribution is of a Lorentzian profile. The spectral halfwidth of the laser beam in both cases are slightly different form each other. For a general gain line profile, the spectral laser power distribution behaves as a differential form like that of the gain line profile.The spectral halfwidth of He/Ne laser beam having powers (0·5 mW, 1·0 mW, 3·0 mW and 50 mW) and that of their longitudinal modes, the laser gain factor and the difference between the population atomic densities of the upper and lower energy levels for the laser line transition are experimentally determined.     

Ferromagnetic resonance in arrays of highly anisotropic nanoparticles

We present in this study computational simulations of the ferromagnetic resonance response of magnetic nanoparticles with a uniaxial anisotropy considerably larger than the microwave excitation frequency (in field units). The particles are assumed to be randomly oriented in a two dimensional lattice, and are coupled by dipolar interactions through an effective demagnetization field, which is proportional to the packing fraction. We have included in the model fluctuations in the anisotropy field (H_K) and allowed variations in the demagnetizing field. We then analyzed the line shape and line intensity as a function of both fields. We have found that when H_K is increased the line shape changes drastically, with a structure of two lines appearing at high fields. The line intensity has a maximum when H_K equals the frequency gap and decreases considerably for larger values of the anisotropy. The effects of fluctuations in H_K and variations in the packing fraction have been also studied. Comparison with experimental data shows that the overall observed behavior is dominated by the particles with lower anisotropy.     

Theoretical analysis of a PSK coherent heterodyne optical receiver using external cavity semiconductor lasers

The performance of a PSK heterodyne optical transmission system using external cavity semiconductor lasers as remote and local oscillators in evaluated theoretically. The actual shape of the instantaneous frequency fluctuations power spectral density of the optical oscillators is taken into account, obtaining indications for optimum design of the external optical feedback.