Peter W. Milonni

Chaos in Laser-Matter Interactions

This is a set of lecture notes given by the authors at the Universities of Rochester, Arkansas and Puerto Rico. This volume introduces the main ideas of chaos and its applications to a broad range of problems in quantum optics, electronics and laser physics. Contents: Introduction; Nonlinearity; The Period Doubling Route to Chaos; The Duffing Oscillator; Strange Attractors; Two-Frequency Route to Chaos; Intermittency; Dimensions of Attractors; Noise, The Lorenz Model and the Single-Mode Laser; Chaotic Lasers: Theory and Experiment; Hamiltonian Systems; The Henon-Heiles System; The Standard Mapping; Fat Fractals; Ergodicity and Mixing; Chaos and the Microwave Ionization of Hydrogen; The Kicked Pendulum: Classical Theory and Quantum Theory; Chaos and Multiple-Photon Excitation of Molecular Vibrations; Chaos and Molecular Rotations; Ideas in Quantum Chaos; Outlook.

Influence of local-field effects on the radiative lifetime of liquid suspensions of Nd:YAG nanoparticles

We measured the radiative lifetime of Nd:YAG nanopowder with an average particle size of 20nm suspended in different organic and inorganic liquids. To extract information regarding local-field effects, we fitted the experimental data to three different local-field models: the virtual-cavity (or Lorentz) model, the real-cavity model, and the no-local-field-effects model. The real-cavity model and the no-local-field-effects model can both be adequately fitted to our experimental results, while the virtual-cavity model can be ruled out.

Electromagnetic momenta and forces in dispersive dielectric media

When the effects of dispersion are included, neither the Abraham nor the Minkowski expression for electromagnetic momentum in a dielectric medium gives the correct recoil momentum for absorbers or emitters of radiation. The total momentum density associated with a field in a dielectric medium has three contributions: (i) the Abraham momentum density of the field, (ii) the momentum density associated with the Abraham force, and (iii) a momentum density arising from the dispersive part of the response of the medium to the field, the latter having a form evidently first derived by Nelson (1991) [8]. All three contributions are required for momentum conservation in the recoil of an absorber or emitter in a dielectric medium. We consider the momentum exchanged and the force on a polarizable particle (e.g., an atom or a small dielectric sphere) in a host dielectric when a pulse of light is incident upon it, including the dispersion of the dielectric medium as well as a dispersive component in the response of the particle to the field. The force can be greatly increased in slow-light dielectric media.

Noise properties of propagation through slow- and fast-light media

We consider the fundamental noise properties of propagation through slow- and fast-light optical media based on gain or loss processes. For purely quantum mechanical reasons, any gain or loss process will add noise to a transmitted light field. We derive a relation between the noise figure describing the decreased signal-to-noise ratio of the transmitted laser pulse and the fractional delay or advancement of the pulse. We apply these results explicitly to the situation of operation on the line center of a gain or loss line. We find that for an ideal gain medium the noise figure never exceeds a factor of two. For a loss medium, there is no limit as to how large the noise figure can become. The increased noise in this case is the result of the random loss of photons from the optical field.

Spontaneous emission between mirrors

Some of the physics of spontaneous emission in cavities is revisited, including the enhancement of the decay rate by the cavity Q, the nature of inhibited spontaneous emission, and the ‘excess noise’ in lossy laser cavities.

Retardation in two-atom systems

Abstract We consider the old problem of two identical two-level atoms a fixed distance r apart, one excited at t = 0, the other unexcited, and the field in the vacuum state. We are interested specifically in the higher order retardation effects, which have not previously been discussed. We show the existence of an unexpected interference term in the probability for atom 1 to be excited which sets in two retardation times after atom 1 begins to decay.

Fourier processing with partially coherent fields

We describe how Fourier signal processing techniques can be generalized to partially coherent fields. Using standard coherence theory, we first show that focusing of a partially coherent beam by a lens modifies its coherence properties. We then consider a 4f imaging system composed of two lenses and discuss how spatial filtering in the Fourier plane allows one to tune the coherence properties of the beam. This, in turn, provides control over the beams directionality, spectrum, and degree of polarization.

Instabilities in the Propagation of Arbitrarily Polarized Counterpropagating Waves in a Nonlinear Kerr Medium

The stability of strong optical waves counterpropagating in a nonlinear optical material has important implications for nonlinear optical processes such as optical bistability and phase conjugation. Nonlinear Kerr media are perhaps the simplest nonlinear optical material to model, yet the interaction of light waves in these materials can exhibit very rich and complicated behavior [1–5]. SILBERBERG and BAR-JOSEPH [3] have predicted that the output intensities of two strong waves with parallel polarization, counterpropagating in a nonlinear Kerr medium with finite response time, can show oscillatory as well as chaotic behavior. KAPLAN and LAW [5] have recently demonstrated that multistable polarization states are possible in the steady-state outputs of two counterpropagating vector fields in a nonlinear Kerr medium with an infinitely fast response time. This complicated steady-state behavior has motivated us to study the time dependence of the output polarizations of counterpropagating vector fields in a nonlinear Kerr medium. The inclusion of temporal effects enables us to study theoretically the stability of the polarization of the transmitted waves in order to determine whether oscillatory, hysteretic, or chaotic behavior occurs. In this paper, we present numerical results that demonstrate the existence of hysteretic bistability in the output polarizations.

The effects of local fields on laser gain of composite optical materials

We develop a simple theoretical model for calculating the effective linear susceptibility of composite optical materials with a gain resonance in one of their components. We distinguish two cases of resonant components: the case of “pure resonant emitters,” in which all the atoms or molecules of the resonant medium are of the same sort, and the case of “resonant emitters in a background,” in which only a fraction of the molecules or atoms comprising the resonant component of a composite material are in resonance with the optical field. Analysis of the model suggests that local‐field effects in composite materials can provide a useful means for controlling the optical properties of laser gain media.

Comment on «Spontaneous emission: vacuum fluctuations or radiation reaction» by R. R. Puri

It has recently been claimed that the vacuum field does not contribute explicitly, in any operator ordering, to spontaneous emission. This claim is based on a trivial observation that misses the point of a whole series of independent investigations.