Jay R. Ackerhalt

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.

Chaos in quantum optics

Abstract We describe how chaotic dynamics may appear in some fundamental as well as practical problems of quantum optics. This essay is intended for researchers in the general areas of quantum optics and laser physics, especially those unfamiliar with the basic ideas and implications of “chaos” . Our aim is to describe what chaos is, how it may be identified, and why it may be important. We suggest that quantum optics offers an attractive arena for the study of chaotic behavior. To support this suggestion we consider several examples involving Maxwell-Bloch equations, lasers, nonlinear optics, and infrared laser-molecule interactions.

Modeling laser instabilities and chaos

We summarize some previous work on the analysis of laser instabilities and chaos and present new results on routes to chaos and field-correlation functions.

Analysis of 3ν3 in SF6

Studies of the 3ν3 absorption band in SF6 in the spectral region from 2800 to 2850 cm−1 have been completed with a FT–IR spectrometer at a spectral resolution of 0.04 cm−1. This study confirms the results reported earlier by Kildal on the general shape of this absorption band. The absorption has been studied as a function of temperature, allowing a definite assignment to be made of the ground state features observed in this spectrum at room temperature. The ground state absorption to 3ν3 appears with a double Q branch [estimated band origins at 2830.22 and 2827.62 (±0.06) cm−1]. The intensities and temperature dependence studies confirm the assignment by Fox of these two Q branches to the two F1u components of the 3ν3 state.

Calculation of the temperature dependence of the multiphoton absorption spectrum of SF 6

The temperature dependence of the theoretical multiphoton absorption spectrum of SF6 gas is obtained by forming a superposition of ν3-ladder spectra properly shifted and weighted by the vibrational Boltzmann factor for temperatures of 150 and 300 K. First-order rotational effects are included, and all levels up to three-photon absorption are contained in the model. Over 70 hotbands (95% of total population) are included at 300 K. The calculations show general broadening and a red shift to the absorption spectrum at room temperature, which is not, however, great enough to account for the experimentally observed dissociation-rate spectrum. We conclude that resonant absorption in the quasi-continuum occurs at or below 940 cm−1.

Phase-pulling effects in forward Raman scattering

Phase-pulling effects in transient stimulated Raman scattering of forward-propagating plane-wave fields are examined both analytically and numerically. The Stokes temporal phase profile is found to lock very quickly to a final (output) temporal phase profile, once the Stokes-field intensity has grown to roughly 1 order of magnitude greater than the initial Stokes seed intensity. The final temporal phase profile of the output Stokes field is pulled to the phase of the input pump (Stokes) field when the medium relaxation time is large (small) relative to the time scale of the input phase variations. For intermediate relaxation times, the output Stokes temporal profile also locks quickly but to a profile that is that of neither the input pump nor the input Stokes. The output Stokes phase is found to be relatively insensitive to pump transverse intensity variations.

Self-focusing in SF 6

We calculate the susceptibility responsible for self-focusing in SF6 in two parts, the ν3-ladder contribution and the quasi-continuum contribution. Our ν3-ladder vibrational model is a classical triply degenerate anharmonic oscillator in the Cartesian basis with the anharmonicity parameters chosen to be consistent with the latest spectroscopic analysis of the 3ν3-overtone spectrum. The rotational structure is represented by a distribution of these oscillators in which the distribution is chosen to correspond to the spectrum of the ν3 fundamental. Using our previously published model, we find that the quasi-continuum contribution is much smaller than the ν3-ladder contribution to the susceptibility and always decreases with increasing laser energy. We find that the ν3 ladder is entirely responsible for self-focusing in SF6. The susceptibility curves show qualitative agreement with the 300-K self-focusing data of Nowak and Ham [Opt. Lett. 6, 185 (1981)] at CO2P(28), P(20), and P(10) in SF6. Calculations with a two-dimensional diffraction-propagation code show good quantitative agreement with the Nowak and Ham data at CO2P(20) and P(10).

Coherent pumping in a weakly coupled quasicontinuum model

We construct and solve a model of laser photon absorption in polyatomic molecules which is related to the onset of effective intramolecular mode coupling (quasicontinuum). We find coherent absorption of the laser photons despite the many‐level nature of the system, however, all of the features of intramolecular vibrational relaxation are also evident if the populations of the pure pumped mode states are monitored as a function of time. The model is also found to be quite stable with respect to an asymmetry in the intramolecular mode coupling constant.

The dynamics of pulse compression in synchronously pumped fiber Raman lasers

Dynamical equations describing the amplification and propagation of an initial Stokes seed pulse in a synchronously pumped fiber Raman laser configuration are formulated, and analytic solutions are derived. A train of Stokes shifted pulses is produced. Their individual characteristics eventually evolve on successive round trips through the fiber into subpicosecond pulses having constant fluence and decreasing temporal duration. Raman pulse compression stops when it is counterbalanced by the effects of group velocity dispersion and phase modulation in the normal dispersion regime. Pulse breakup due to soliton formation can occur in the anomalous dispersion regime. Simple expressions for the rate of pulse compression, the steady-state pulse fluence, and the minimum steady-state pulse duration are obtained. >

Collisionless self-focusing of CO 2 10 µm P(20) laser light in SF 6

We develop a simple intuitive picture of the vibration-rotation structure of the SF 6 molecule such that the molecular susceptibility responsible for self-focusing can be calculated. We treat the propagation dynamics by generalizing the standard steady-state Gaussian propagation equations to include the important effect of absorption in the wings of the spatial profile. By calibrating the model to absorption data at CO 2 10 μm P(2) we find good agreement with beam waist data at the same wavelength. Absorption in the wings is dominant at low laser fluences, and the real part of the susceptibility is responsible for the defocusing-to-focusing turnover in the beam waist near 100 mJ/cm2, consistent with the interpretation of Nowak and Ham [6].