1. Introduction to Nonlinear Optics
H. R. Khalesifard
Institute for Advanced Studies in Basic Sciences

2. Contents Introduction The essence of nonlinear optics
Second order nonlinear phenomena
Third order nonlinear phenomena
Nonlinear optical materials
Applications of nonlinear optics

3. Introduction Question:
Is it possible to change the color of a monochromatic light?
Answer:
Not without a laser light
output
NLO sample
input

4. Stimulated emission, The MASER and The LASER
(1916) The concept of stimulated emission Albert Einstein
(1928) Observation of negative absorption or stimulated emission near to resonant wavelengths, Rudolf Walther Ladenburg
(1930) There is no need for a physical system to always be in thermal equilibrium, Artur L. Schawlow

5. E1 E2
Absorption E1 E2
Spontaneous
Emission E1 E2
Stimulated
Emission

6. Light (Microwave) Amplificationby
Stimulated
Emission of Radiation
LASER
(MASER)

7. The Maser Two groups were working on Maser in 50s
Alexander M. Prokhorov and Nikolai G. Bassov (Lebedev institute of Moscow)
Charles H. Townes, James P. Gordon and Herbert J. Zeiger (Colombia University)

8. Left to right: Prokhorov, Townes and Basov at the Lebede institute (1964 Nobel prize in Physics for developing the “Maser-Laser principle”)

9. Townes (left) and Gordon (right) and the ammonia maser they had built at Colombia University

10. The LASER
(1951) V. A. Fabrikant “A method for the application of electromagnetic radiation (ultraviolet, visible, infrared, and radio waves)” patented in Soviet Union.
(1958) Townes and Arthur L. Schawlow, “Infrared and Optical Masers,” Physical Review
(1958) Gordon Gould definition of “Laser” as “Light Amplification by Stimulated Emission of Radiation”
(1960) Schawlow and Townes U. S. Patent No. 2,929,922
(1960) Theodore Maiman Invention of the first Ruby Laser
(1960) Ali Javan The first He-Ne Laser

11. Maiman and the first ruby laser

12. Ali Javan and the first He-Ne Laser

13. Properties of Laser Beam
A laser beam
Is intense
Is Coherent
Has a very low divergence
Can be compressed in time up to few femto second

14. Applications of Laser (1960s) “A solution looking for a problem”
(Present time) Medicine, Research, Supermarkets, Entertainment, Industry, Military, Communication, Art, Information technology, …

15. Start of Nonlinear Optics
Nonlinear optics started by the discovery of Second Harmonic generation shortly after demonstration of the first laser.
(Peter Franken et al 1961)

16. 2. The Essence of Nonlinear Optics
When the intensity of the incident light to a material system increases the response of medium is no longer linear
Input intensity
Output

17. Response of an optical Medium
The response of an optical medium to the incident electro magnetic field is the induced dipole moments inside the medium

18. Nonlinear Susceptibility
Dipole moment per unit volume or polarization
The general form of polarization

19. Nonlinear Polarization
Permanent Polarization
First order polarization:
Second order Polarization
Third Order Polarization

20. How does optical nonlinearity appear
The strength of the electric field of the light wave should be in the range of atomic fields N a0 e

21. Nonlinear Optical Interactions
The E-field of a laser beam
2nd order nonlinear polarization

22. 2nd Order Nonlinearities
The incident optical field
Nonlinear polarization contains the following terms

23. Sum Frequency Generation
Application:
Tunable radiation in the
UV Spectral region.

24. Difference Frequency Generation
Application:
The low frequency photon, amplifies in the presence of high frequency beam This is known as parametric amplification.

25. Phase Matching Since the optical (NLO) media are dispersive,
The fundamental and the harmonic signals have
different propagation speeds inside the media.
The harmonic signals generated at different points
interfere destructively with each other.

26. SHG Experiments
We can use a resonator to increase the efficiency of SHG.

28. Third Order Nonlinearities
When the general form of the incident electric field is in the following form,
The third order polarization will have 22 components which their frequency dependent are

29. The Intensity Dependent Refractive Index
The incident optical field
Third order nonlinear polarization

30. The total polarization can be written as
One can define an effective susceptibility
The refractive index can be defined as usual

31. By definition
where

32. Typical values of nonlinear refractive index
Mechanism
n2 (cm2/W)
(esu)
Response time (sec)
Electronic Polarization
10-16
10-14
10-15
Molecular Orientation
10-12
Electrostriction
10-9
Saturated Atomic Absorption
10-10
10-8
Thermal effects
10-6
10-4
10-3
Photorefractive Effect
large
Intensity dependent

33. Third order nonlinear susceptibility of some material
 1111
Response time
Air
1.2×10-17
CO2
1.9×10-12
2 Ps
GaAs (bulk room temperature)
6.5×10-4
20 ns
CdSxSe1-x doped glass
10-8
30 ps
GaAs/GaAlAs (MQW)
0.04
Optical glass
(1-100)×10-14
Very fast

34. Processes due to intensity dependent refractive index
Self focusing and self defocusing
Wave mixing
Degenerate four wave mixing and optical phase conjugation

35. Self focusing and self defocusing
The laser beam has Gaussian intensity profile. It can induce a Gaussian refractive index profile inside the NLO sample.

36. Wave mixing

37. Optical Phase Conjugation
Phase conjugation mirror M
PCM
PCM s M

38. Aberration correction by PCM
Aberrating
medium
PCM s
Aberrating
medium

39. What is the phase conjugation
The signal wave
The phase conjugated wave

40. Degenerate Four Wave Mixing
All of the three incoming beams A1, A2 and A3 should be originated
from a coherent source.
The fourth beam A4, will have the same Phase, Polarization, and
Path as A3.
It is possible that the intensity of A4 be more than that of A3

41. Mathematical Basis The four interacting waves
The nonlinear polarization
The same form as the phase conjugate of A3

42. Holographic interpretation of DFWM
Bragg diffraction from
induced dynamic gratings