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Course Description:

AN INTRODUCTION TO NONLINEAR OPTICS draws from many different nonlinear optical phenomena to elucidate the basic components of the subject. The course notes contain copies of each vuegraph used so that participants can spend a maximum amount of time listening and understanding. Margins are extra large so that participants may write additional notes, making their experiences as useful as possible. As an option, examples can include fiber nonlinear optic phenomena such as spontaneous occurrence of second harmonic generation, cross-phase modulation, soliton concepts, fiber SBS, fiber pulse compression, and other fiber phenomena.

The Introduction will develop the general topic via the Maxwell equations and the "reduced" or "Slowly-Varying Envelope Approximation (SVEA)". Expansions for the nonlinear susceptibility will be described, and specific third order effects will be introduced. The transformation to a moving frame, and the scattering from elementary excitations will be presented.

Next, specific nonlinear optical effects will be studied in detail to illustrate specific points.

The Pockels Effect and its role in the modulation of optical signals will be presented first, showing how one of the simplest nonlinearities works. Phase matching conditions will be introduced in our discussion of Second Harmonic Generation. Here Type I and Type II phase matching will be presented for uniaxial doubling crystals, along with a recipe for quickly making one's own doubler. Optical Parametric Oscillators (OPO's) and Optical Parametric Amplifiers (OPA's) will next be addressed, showing the circumstances under which they are a time-reversed generalization of the second-harmonic generation process.  Shown will be the concepts of signal and idler, basic configurations, and issues of growth from noise.

To become conversant with the slowly-varying envelope approximation, the Optical Kerr Effect will be discussed. Here the basic Kerr nonlinearity will be described, along with its relationship to spontaneous depolarized Rayleigh wing scattering, stimulated Rayleigh wing scattering, weak-wave retardation, and self-focusing. Furthermore, plane-wave Kerr propagation effects such as self-steepening, self-phase modulation, and dispersive self-phase modulation (including optical shocks, extralinear chirping, and optical solitons) will all be described. To show the connection of nonlinear optics to spectroscopy, For courses with durations longer than one day, Two-Photon Transitions will be discussed. Doppler-free spectroscopy and other practical applications will be described, and detailed examples will be provided for transitions in atomic Sodium.

The concept of stimulated nonlinear scattering is introduced in Stimulated Brillouin Scattering. The electrostrictive nonlinearity is described, and both stimulated and spontaneous aspects are reviewed, including the SBS gain coefficient, the concept of threshold, polarization issues, phase coherence issues, backward seeding, and the manipulation of expressions for the SBS frequency shift, the gain coefficient, and the threshold intensity. Next covered is Stimulated Raman Scattering, which further advances our understanding of stimulated scattering. Here, issues of narrowband versus broadband gain are addressed, along with the closely related issue of "correlating up".

Atmospheric Rayleigh Scattering is discussed as an example of unavoidable nonlinear optical noise in optical systems. The Photorefractive Effects are discussed in considerable detail. Here the basic photorefractive mechanism is described, leading to the 90 degree shifted index gratings and their role in two-beam coupling. Issues of frequency offset, and their applicability to understanding two-beam coupling in Kerr media are described.  Note:  As an alternative, the specialization to the Photorefractive effect is also available as a separate in-house course.

If time permits, Resonance Nonlinearities will be presented to aid in the understanding of nonlinear behavior of absorbers and amplifiers. The two-level absorbing system is cast in the Bloch formalism, and this formalism is used to show that an inhomogeneously broadened absorber can emit a "Photon Echo".

Finally, Optical Phase Conjugation will be introduced as a means of using nearly any nonlinear optical effect to produce from a distorted wave a phase-conjugate wave, one which will propagate backwards through a system while undoing virtually any distortion that the originally distorted wave had picked up.  Examples of popular conjugators will be presented.  Note:  As an alternative, the specialization to Optical Phase conjugation is also available as a separate in-house course.

A Nonlinear Optics Bibliography is provided so that participants can pursue other topics in this richest of fields.

Each idea is explained in clear and simple terms with an emphasis on underlying physical principles and with a minimum of mathematics. Pertinent references and review material are identified. The course notes contain copies of each vuegraph used during the day so that participants can spend a maximum amount of time listening and understanding.

This course will enable you to:

Intended Audience
Researchers, scientists, engineers, and managers who need a fundamental understanding of nonlinear optics and of nonlinear optical systems.

Continuing Education Units (CEU's) available upon request.

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