2024 Light and Matter IV

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Academic unit or major
Graduate major in Physics
Satoh Takuya 
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Lecture    (Face-to-face)
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Course description and aims

This lecture focuses on nonlinear optical effects, which are optical phenomena that do not vary linearly with the intensity of light, and explores various phenomena and theories related to the nonlinear interaction of light. Firstly, it discusses nonlinear optical effects, where the intensity of light interacts with nonlinear optical materials, giving rise to phenomena such as second-harmonic generation and sum- and difference-frequency generation. It also examines how nonlinear optical phenomena, such as optical parametric oscillation and third-harmonic generation, contribute to the amplification of light and the generation of new frequency components. This involves discussing the classical nonharmonic oscillator model, Miller's rule, Kleinman's symmetry, and the Kramers–Kronig relation, all of which play important roles. Furthermore, it delves into understanding the behavior of light and the energy conservation laws in nonlinear optical systems through concepts such as coupled-wave equations, phase matching, and the Manley-Rowe relation.

Student learning outcomes

The objective of this course is to understand the basic principles and phenomena of nonlinear optics and to acquire knowledge of specific effects and related theories. Students will gain an understanding of the types and characteristics of nonlinear optical effects and will be able to explain specific phenomena such as second-harmonic generation, sum- and difference-frequency generation, and optical parametric oscillation. Moreover, they will explore theoretical backgrounds such as Miller's rule and Kleinman's symmetry, thus obtaining fundamental knowledge of nonlinear optics. Additionally, students will grasp concepts like coupled-wave equations and phase matching and develop the ability to consider practical applications in optical systems. Graduates of this course are expected to possess the foundational knowledge and theories necessary to address problems related to nonlinear optics.


nonlinear optical effect, second-harmonic generation, sum- and difference-frequency generation, optical parametric oscillation, third-harmonic generation, classical anharmonic oscillator, Miller’s rule, Kleinman’s symmetry, Kramers–Kronig relations, coupled-wave equations, phase matching, Manley–Rowe relations

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

lasses are held face-to-face. However, the 4th will be on-demand type.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Nonlinear Optical Processes Explain nonlinear optical processes.
Class 2 Classical Anharmonic Oscillator Explain classical anharmonic oscillator.
Class 3 Properties of the Nonlinear Susceptibility Explain properties of the nonlinear susceptibility.
Class 4 Time-Domain Description Explain time-domain description.
Class 5 Coupled-Wave Equations Explain coupled-wave equations.
Class 6 Second-Harmonic Generation Explain second-harmonic generation.
Class 7 Optical Parametric Oscillators Explain optical parametric oscillators.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


Robert W. Boyd, Nonlinear Optics, 4th ed. (Academic Press, 2020)

Reference books, course materials, etc.

Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, 2002).

Assessment criteria and methods

Learning achievement is evaluated by reports.

Related courses

  • PHY.C446 : Light and Matter I
  • PHY.C447 : Light and Matter II
  • PHY.C448 : Light and Matter III
  • PHY.C441 : Crystal Physics

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites.

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