The learning outcomes of this course are :

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Transfer – Students will be able to…

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- Model any 2nd or 3rd order nonlinear effects

- Evaluate nonlinear interaction performances/efficiencies under approximations that should be specified, explained and justified

- Design and specify the beam-related quantities (direction, polarization, intensity, CW or pulsed, transverse extension, power) and nonlinear material (crystal orientation, effective nonlinear susceptibility, size) to be used to meet given performances. The approach and values shall be justified and presented in a written or oral report.

- Determine in a situation involving the propagation of at least one light beam through a dielectric material medium (solid or guided), whether non-linear effects can be neglected.

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Understanding – Students will understand that..

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- Nonlinear effects are a key points in the development of many photonics applications

- Understand interplays between linear and nonlinear effects

- Nonlinear interactions lead to energy transfer between optical beams, and/or between matter and beams, enabling in some cases the realization of nonlinear optical amplification and/or oscillation.

- Nonlinear optics is an essential tool to create novel optical frequencies generated through the interaction of incident beams within nonlinear materials

- Nonlinear effects are subject to phase matching conditions

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Essential Questions - The course will address the following questions

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- Capability of light matter interactions in modifying light properties : frequency generation, self-action or cross-actions of light on beam propagation, optical amplification, phase shift, rectification…

- Use of a perturbative approach in describing and deriving a NON LINEAR problem in physics

- Link between the microscopic and macroscopic terms in Maxwell’s equations (induced dipole, macroscopic polarization and fields)

- Link between the frequency relation and the law of energy conservation, the phase matching relation and the law of momentum conservation

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Knowledge – Students will know…

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- the constitutive relations of nonlinear optics

- the nonlinear effects that arise in a 2nd and 3rd order nonlinear materials

- the origin of the nonlinear susceptibilities (classical origin)

- the basic properties of nonlinear susceptibility tensors

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Skill – Students will be skilled at…

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- Manipulating the nonlinear susceptibility tensor components and, with given incident fields, calculate the components of nonlinear polarisation vector

- Determining the phase matching conditions for a given nonlinear interaction

- Solving the nonlinear equation in parametric situations and derive analytical solutions under the undepleted pump approximation

- Calculating nonlinear interaction performances/efficiencies in situations governed by analytical solutions or expressions