Physics 568 (ECE 568), Nonlinear Optics
Mondays and Wednesdays, 11:00 to 12:15 pm, CHTM Room 103
Spring 2026
Instructor
- Jean-Claude Diels
- Physics & Astronomy room PAIS 2236, phone 277 4026
- CHTM, room 114A, phone 272 7830 email: jcdiels@unm.edu
Reference material
Lecture content, followed by a link to the powerpoint file, and homework assignments will be posted on my personal Web site dielslab.unm.edu/courses.
References will be made to textbooks and articles, when appropriate. I follow the notations of the book “Ultrafast Phenomena” of which a link can be found before the first lecture.
Other reference material:
- Robert W. Boyd. Nonlinear optics. Academic Press, third edition, 2008.
- Shen
- "Fundamentals of attosecond optics" (Chang)
- Ultrafast Phenomena
Assignments
- Homework problems will be assigned on a regular base, due generally on Wednesdays. They will count for 50% of the final grade.
- Some problems will be treated in class.
- Final Oral presentation and written report on a topic related to the class. The report should be in the format of Optics letter. It will be graded as moch for the form as for the content.
THIS COURSE: AN UNCONVENTIONAL APPROACH
The approach taken in this class is to proceed from the most general formalism and proceed by successive approximation to specific phenomena. Some of you may have been exposed in high-school to a similar method in your course of analytical geometry. The old school taught only cartesian coordinates, in which circles, ellipses hyperbolae are totally unrelated objects. Going from cartesian to projective coordinates one realizes that circles, ellipses and hyperbolae are just one object. Teaching analytical geometry in particular-izing from the general projective coordinates towards the more narrow minded cartesian gives one a much richer and elegant understanding of geometry.
In this course, successive approximations from the more general response of the electron in time varying high electric field, to linear optics, is a journey that will bring us through all the aspects of nonlinear optics. The classical situation treated in the first chapter(s) of most nonlinear optics books results from a stationary “weak field” approximation of a more general interaction, with all real atomic level off-resonance with the radiation frequency.
While different aspects of nonlinear optics may be taught in a different order, the material covered will be the same as that of previous nonlinear optics classes. The last chapter of the class will deal with quantum aspects of nonlinear optics, with a study of solitons, noise in measurements, and squeezing.
Nearly all problems of linear and nonlinear optics are treated in a stationary approximation. Ultrashort pulses are bringing the awareness that not all situation can be treated as “steady-state”, the latter being an asymptotic limit of a transient behavior.
CHAPTER 3 OF THE BOOK ULTRAFAST PHENOMENA:
The free Electron
A. Multiphoton ionization {Jumped the fence of St Quentin and ran)
Above Threshold Ionization (ATI); Measuring ion and electron energy and velocity distribution (VMI)
B. Tunnel ionization {Dugged its way out of Guantanamo and waited...)
lecture 1 multiphoton.ppt
Keldysh parameter; Tunneling, attosecond generation, polarization dependence, single attosecod pulse generation by (i) polarization gating (ii) pulse synthesis; attosecond measurerment, Wigner distribution; the molecular centrifige. synthesis of attosecond -pulse from chirped fs pulses.
lecture 2 attosecond 2-Feb1.pptx
C. The plasma {Free but with the field marshal in hot pursuit)
Re-radiatio of the moving electron into the applied field, Creation of an isotropic incompressible electron plasma; Plasma frequency, the Drude model; bound electron resonances versus plasma resonance.
lecture attosecond 3-Feb3.pptx
The bound Electron: Coherent Nonlinear Optics
The general approach is to derive the wave function of atomic/molecular system interaction with the light fied. Only dipole allowed transition are considered. Levels close to resonance are treated exactly, while an adiabatic approxiation is used for levels off-resonace
multilevel interaction equations.pptx
2 examples of why AI is AS! Resonant versus non resonant harmonic generation
AI is AS.pptx
Two-photon resonant third harmonic. Considering a two-photon resonant two level system. There is an intermrediate level detuned by Delta1 from single photon resonance. An adiabatic approximation is made to model the contribution of that level to the interaction. One defines a two photon Rabi frequency which is the product of the two single photon Rabi frequencies for the transitions 0-1 and1-2, divided by the detuning Delta1. Level 2 is detuned from 2-photon rresonance by Delta2, augmented by a Stark shift. If there is a level 3 detued from 3 photon resonance by Delta 3, one can have efficient third harmonic generation if Delta 2 issmall and Delta3 < or equal to Delta 1. Thee third harmonic will saturate at lower intensity if Delta 1 << Delta 3.
Two-photon resonant Kerr effect. The same system as above, but larger Delta 2. The resonant Kerr effect can be positive or negative depending on the sign of Delta 2.
Example of application of coherent optical pumping: the sodium guidestar
The nonlinear coherent interaction formalism automatically satisfies the Kramers Kronig relations
Kerr-nonlinearity-self-foc.pptx
HOMEWORK
Homework 1: Electron trajectories.pdf
Homework 2 HW2-Uncertainty relation for a radiating level.pdf:
Homework 3 nonlinear susceptibility HW3.pdf