Introduction to Nonlinear Optics

1. Introduction to Nonlinear Optics H. R. Khalesifard Institute for Advanced Studies in Basic Sciences Email: khalesi@iasbs.ac.ir

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

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

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

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

7. The Maser Two groups were working on Maser in 50s • AlexanderM. 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 Frankenet 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 Output Input intensity

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

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

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

33. Third order nonlinear susceptibility of some material

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

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

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

40. A1 A2 A3 A4 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 morethan that of A3

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

42. A1 A2 A3 A4 Holographic interpretation of DFWM Bragg diffraction from induced dynamic gratings