Università degli Studi dell'Insubria

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Nonlinear optics - SCC0476

Master's Degree Course in Physics - A.Y. 2014-15, 2015-16 

Professor: Alessia Allevi





Exercise sessions






48 hours






Aims and outcomes

  • knowledge of the fundamental nonlinear optical phenomena (parametric and non-parametric ones)
  • understanding the requirements and conditions to be met to achieve these processes
  • ability to discriminate the different nonlinear processes, by understanding their origin and distinguishing between linear and nonlinear phenomena
  • knowledge of the main applications of nonlinear optics to science and technology



For a better understanding of the topics covered in the course, it is required that students have already attended courses of Electromagnetism and Physics of Matter. In addition, it is advisable that students have inserted the course of Optics in their learning program and that they have already attended it.



  • Historical background and introduction to the main nonlinear optical phenomena (parametric and non-parametric ones) (4 hours); 
  • Passive mode-locking techniques obtained by means of nonlinear processes (Kerr lens mode-locking and saturable absorbers) (2 hours); 
  • Symmetry properties of the second-order nonlinear susceptibility tensor (2 hours);
  • Linear optical systems and Kramers-Kronig relations in linear and nonlinear optics (2 hours);
  • Second-order nonlinear processes under plane-wave approximation: second-harmonic generation, sum-frequency generation, parametric amplification and spontaneous parametric down conversion, optical parametric oscillator (7 hours); 
  • Phase-matching conditions and generation in phase-mismatch condition (3 hours); 
  • Generation of nonlinear processes by means of focused Gaussian beams (2 hours); 
  • Symmetry properties of third-order nonlinear susceptibility (1 hour); 
  • Description of the intensity-dependent refractive index of the non-linear medium (1 hour); 
  • Processes resulting from the intensity-dependent refractive index: self-phase modulation, self focusing, filamentation, temporal solitons, phase conjugation (8 hours); 
  • Optically induced damage and multiphoton absorption (2 hours);
  • Ultrafast and ultra-intense optics: nonlinear Schrödinger equation, white-light continuum and high-harmonic generation (4 hours).

The laboratory activities (roughly 10 hours) aim at directly observing and investigating some nonlinear optical phenomena, especially those related to second-order nonlinearity, already presented from the theoretical point of view.  

In fact, on the basis of the available laser sources and instruments, the following processes can be studied:

  • second-harmonic generation in collinear and non-collinear geometry: application to the measurement of short-pulse duration using the autocorrelation technique
  • quantitative analysis of second-harmonic generation in phase-mismatch condition
  • Sum- and difference-frequency generation: study of the processes as functions of the polarization of the input optical fields
  • spontaneous parametric down conversion (SPDC): observation of SPDC cones and quantitative analysis of their spatial and spectral properties
  • passive mode-locking technique: use of a laser source in which such a technique can be easily obtained and observed.


Teaching methods

The course is essentially based on lectures (38 hours). In order to improve the quality of teaching and to make the content of theoretical lessons much more understandable, the remaining 10 hours will be devoted to the experimental observation and characterization of nonlinear optical processes in the laboratory.


Textbooks and references

Lectures are based on the following textbooks: R. W. Boyd, “Nonlinear Optics”, Academic Press (2008); B. E. A. Saleh and M. C. Teich, “Fundamentals of Photonics”, John Wiley & Sons, Inc. (1991); V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, “Handbook of Nonlinear Optical Crystals”, Springer (1999). Moreover, when it is the case, copies of some articles are provided during lessons.


Final examination

The exam is oral. Usually, students are asked to choose and talk about a topic among those mentioned in the course. Then, some questions about some of the remaining topics are asked, through which the professor will check if the students have not only acquired a sufficient knowledge of nonlinear optical phenomena, but have also learnt skills in recognizing and understanding them.


Office hours

Monday-Friday 10:00-17:00.

[aggiornato il 23-06-2016]
Università degli Studi dell'Insubria - Via Ravasi 2, 21100 VARESE - NUMERO VERDE 800 011 398 - P.I. 02481820120 - C.F. 95039180120