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

Contents 1.Introduction 2.The essence of nonlinear optics 3.Second order nonlinear phenomena 4.Third order nonlinear phenomena 5. Nonlinear optical materials 6.Applications of nonlinear optics

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

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

E1E1 E2E2 Absorption E1E1 E2E2 Spontaneous Emission E1E1 E2E2 Stimulated Emission

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

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)

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

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

The LASER (1951) V. A. Fabrikant “A method for the application of electromagnetic radiation (ultraviolet, visible, infrared, and radio waves)” patented in Soviet Union. (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) 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” (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) Schawlow and Townes U. S. Patent No. 2,929,922 (1960) Theodore Maiman Invention of the first Ruby Laser (1960) Theodore Maiman Invention of the first Ruby Laser (1960) Ali Javan The first He-Ne Laser (1960) Ali Javan The first He-Ne Laser

Maiman and the first ruby laser Maiman and the first ruby laser

Ali Javan and the first He-Ne Laser Ali Javan and the first He-Ne Laser

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

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

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)

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

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

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

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

How does optical nonlinearity appear The strength of the electric field of the light wave should be in the range of atomic fields The strength of the electric field of the light wave should be in the range of atomic fields N a0a0 e

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

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

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

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

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. 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.

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

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

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

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

By definition where

Mechanism n 2 (cm 2 /W) (esu) (esu) Response time (sec) Electronic Polarization Molecular Orientation Electrostriction Saturated Atomic Absorption Thermal effects Photorefractive Effect largelarge Intensity dependent Typical values of nonlinear refractive index

Material  1111 Response time Air 1.2× CO 2 1.9× Ps GaAs (bulk room temperature) 6.5× ns CdS x Se 1-x doped glass ps GaAs/GaAlAs (MQW) ns Optical glass (1-100)× Very fast Third order nonlinear susceptibility of some material

Processes due to intensity dependent refractive index 1.Self focusing and self defocusing 2.Wave mixing 3.Degenerate four wave mixing and optical phase conjugation

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

Wave mixing

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

Aberration correction by PCM PCM Aberrating medium PCM s Aberrating medium

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

Degenerate Four Wave Mixing A1A1 A2A2 A3A3 A4A4 All of the three incoming beams A 1, A 2 and A 3 should be originated from a coherent source. The fourth beam A 4, will have the same Phase, Polarization, and Path as A 3. It is possible that the intensity of A 4 be more than that of A 3 All of the three incoming beams A 1, A 2 and A 3 should be originated from a coherent source. The fourth beam A 4, will have the same Phase, Polarization, and Path as A 3. It is possible that the intensity of A 4 be more than that of A 3

Mathematical Basis The four interacting waves The nonlinear polarization The same form as the phase conjugate of A 3

Holographic interpretation of DFWM A1A1 A2A2 A3A3 A4A4 Bragg diffraction from induced dynamic gratings Bragg diffraction from induced dynamic gratings