Femtosecond visible and infrared analogues of multiple-pulse nuclear magnetic resonance techniques provide novel snapshot probes into the structure and electronic and vibrational dynamics of complex molecular assemblies such as photosynthetic antennae, proteins, and hydrogen-bonded liquids. A classical-oscillator description of these spectroscopies in terms of interacting quasiparticles (rather than transitions among global eigenstates) is developed and sets the stage for designing new pulse sequences and inverting the multidimensional signals to yield molecular structures. Considerable computational advantages and a clear physical insight into the origin of the response and the relevant coherence sizes are provided by a real-space analysis of the underlying coherence-transfer pathways in Liouville space.

Multidimensional femtosecond correlation spectroscopies of electronic and vibrational excitations.

Control of multistability

Part 1 Theory: probability elementary introduction to the theory of stable laws characteristic functions probability densities integral transformations special functions and equations multivariate stable laws simulations estimation Part 2 Applications: some probabilistic models correlated systems and fractals anomalous diffusion and chaos physics radiophysics astrophysics and cosmology stochastic algorithms financial applications miscellany Appendix

Chance and Stability: Stable Distributions and Their Applications

We describe a novel photonic oscillator that converts continuous-light energy into stable and spectrally pure microwave signals. This optoelectronic oscillator (OEO) consists of a pump laser and a feedback circuit including an intensity modulator, an optical-fiber delay line, a photodetector an amplifier, and a filter. We present the results of a quasi-linear theory for describing the properties of the oscillator and their experimental verifications. Our findings indicate that the OEO can generate ultrastable, spectrally pure microwave-reference signals up to 75 GHz with a phase noise lower than -140 dBc/Hz at 10 KHz. We show that the OEO is a special voltage-controlled oscillator with an optical-output port and can be synchronized to a reference source by means of optical injection locking, electrical injection locking, and a phase-locked loop. Other OEO applications include high-frequency reference regeneration and distribution, high-gain frequency multiplication, comb frequency and pulse generation, carrier recovery, and clock recovery.

Optoelectronic oscillator for photonic systems

High-dimensional chaotic behavior in systems with time-delayed feedback

Optical turbulence and periodic oscillations are easily seen with a hybrid optically bistable device with a delay in the feedback. The behavior of these instabilities is in good agreement with the recent work of Ikeda, Daido, and Akimoto, who predicted them for both ring-cavity and delay-line hybrid devices.

Observation of Chaos in Optical Bistability

Bifurcations to chaos in optical bistability

We extend the technique of quantum-beat spectroscopy to the infrared region by utilizing the strong, directional absorption and emission which occurs in photon echoes and optical nutation. Using a vibrational transition of N${\mathrm{H}}_{2}$D, we have made the first observations of infrared quantum beats in these phenomena. The hyperfine splitting which produces the quantum beats has not been observed in Lamb-dip spectroscopy but is clearly resolved in these time domain studies.

Observation of Quantum Beats in Photon Echoes and Optical Nutation

We have observed periodic oscillations and optical turbulence in hybrid optical bistable systems having a delay in the feedback, as predicted by Ikeda et al. The period-two output is essentially a square wave of period equal to twice the feedback delay time. Most of the measurements in our hybrid system have been made with a detector-amplifier-modulator response time T of 0.8 ms, much less than the 36 ms computer-generated delay time tR, as required for Ikeda instabilities. Period-two oscillations have also been seen with an optical fiber providing a tR of 6 ps. These hybrid systems have enabled us to study the path to chaos as the input intensity or feedback gain is increased. In all-optical bi-stable devices, such as semiconductor etalons, the feedback time is the cavity round-trio time, which can be made very short (approximately picoseconds), so that many-gigahertz all-optical oscillators can be contemplated. However, such oscillations also require that the medium response time be shorter than the delay time, so realization of high-frequency optical oscillators must await the discovery of high-speed bistable optical devices. In the meantime, use of fast nonresonant nonlinearities in guided-wave configurations could lead to gigahertz optical oscillators.

Periodic Oscillations And Chaos In Optical Bistability: Possible Guided-Wave All-Optical Square-Wave Oscillators

We describe a method of directly determining transition dipole matrix elements which we have used to make the first measurements of this quantity in an asymmetric rotor. A low pressure gas (a few mtorr NH2D) which is subjected to a cw CO2 laser beam is suddenly Stark switched into resonance. An optical nutation signal is detected whose frequency yields ‐E0/h/, where ‐ is the transition dipole matrix element of interest and E0 is the optical field strength which may be determined from power and beam profile measurements. Thus an observation of the nutation frequency along with the power measurements yields ‐. This was done for two transitions of NH2D giving transition dipole matrix elements along two axes in the molecule: 〈ν2=0a‖ (∂μa/∂Q) Q‖ν2=1a〉=0.112±0.009 D and 〈0a‖ (∂μc/∂Q) Q‖1s〉=0.158±0.009 D. The extension of this technique to nonpolar molecules and its advantages over conventional steady state laser methods are discussed.

R. L. Shoemaker

Papers

Observation of Chaos in Optical Bistability

Bifurcations to chaos in optical bistability

Observation of Quantum Beats in Photon Echoes and Optical Nutation

Periodic Oscillations And Chaos In Optical Bistability: Possible Guided-Wave All-Optical Square-Wave Oscillators

Direct measurements of transition dipole matrix elements using optical nutation