Optics of One-Dimensional Periodic Structures

Lecture: 34 hours

Practical studies: ---

Self-instruction: 7 hours

2 master course (3 term)
Course program: 


One-dimensional periodic media.

Methods of  solving of wave equation in one-dimensional periodic structures.

Floke - Bloch method. Integral equation method. Born approximation:  Raman - Nath multiple diffraction. Two-wave  dynamic theory of diffraction: Bragg djffraction.

Coupled mode theory. Relationship between diffraction dynamic theory and coupled mode theory.  Usability conditions for  coupled mode theory.

Modified coupled mode theory.  Application of modified coupled mode theory for periodic and nearly-periodic nonlinear media.

Photonic crystals. 

Dispersion law and band strucuture of one-dimensional photonic crystals. Light  propagation in photonic crystals:  methods of matrices and effective media for calculation of light reflection and transmission by  bounded crystals.

Periodic waveguides.

Modes of dielectric waveguide. Theory of waveguide coupled modes. Solution for coupled modes in periodic waveguide.

Photorefractive crystals. 

Photorefractive nonlinear optics. Electro-optic effects. Band transport model. Space-charge field. Stationary solutions. Photorefractive volume gratings. Time evolution of space-charge field.

Photovoltaic effect. Modification of equations for space-charge field.

Optical two-wave mixing of coherent laser beams on photorefractive grating. Degenerate and nondegenerate mixing. Set of coupled mode equations and their solutions. Approximation of slowly varying amplitudes and undepleted-pump approximation.

Optical four-wave mixing of coherent laser beams on photorefractive grating. 

Knowledge tests: 




1. С.Ю. Карпов, С.Н. Столяров. Распространение и преобразование волн в средах с одномерной периодичностью. УФН, т.163, с.63-89, 1993.

2. J.D. Joannopoulos, R.D. Meade, and J.N. Winn. Photonic Crystals:Molding the Flow of Light. Princeton: Princeton University Press, 1995.

3. A. Yariv,  P. Yeh. Optical waves in crystals.-  1985.

4. P. Yeh. Introduction to photorefractive nonlinear optics. Wiley, New York, 1993.


1. Photorefractive Optics. Materials, Properties, and Applications. Ed. F.Yu and S.Yin, Academic Press, 2000.

2. Photorefractive Materials and their Applications 1. Basic Effects.- Springer, 2006.

3. J. Frejlich. Photorefractive Materials. Fundamental Concepts, Holographic Recording and Materials Characterization. - Wiley, New Jerse, 2007.