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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.

**Benefits**

This course will enable you to:

- Understand the physical meaning behind each of the Maxwell equations.
- Convert the four Maxwell equations to a nonlinear wave equation.
- Appreciate when the susceptibility expansion is appropriate.
- Understand how fundamental excitations of materials lead to scattering
- Understand the operation of Pockels cells.
- Learn how phase matching and index matching control second harmonic generation.
- Understand the fundamentals of optical parametric oscillators (OPO's).
- Understand how the Kerr effect produces self-focusing, sideband generation, self-phase modulation, etc.
- Appreciate the unusual behavior of solitons if fiber optic systems.
- Understand the many ways in which the Kerr effect can change the color content of signals.
- Understand chirped pulse compression techniques.
- Understand the nonlinear behavior of multi-photon transitions.
- Learn to use stimulated scattering as a tool to produce new signals at new wavelengths.
- Appreciate how fluid properties lead to atmospheric Rayleigh scattering and estimate its strength.
- Understand photorefractive fanning, two-beam coupling, and cat-corner conjugators.
- Understand special signal processors made from photorefractors
- Appreciate the vast variety of nonlinear optical phenomena and the strong similarities among them.

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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