Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Introduction to Nonlinear Optics H. R. Khalesifard Institute for Advanced Studies in Basic Sciences Email: [email protected] Contents 1. 2. 3. 4. 5. 6. Introduction The essence of nonlinear optics Second order nonlinear phenomena Third order nonlinear phenomena Nonlinear optical materials Applications of nonlinear optics Introduction input Answer: Not without a laser light NLO sample Question: Is it possible to change the color of a monochromatic light? output 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 E2 h Absorption h h E1 E2 E1 Spontaneous Emission h E2 E1 Stimulated Emission h Light (Microwave) Amplification by Stimulated Emission of Radiation LASER (MASER) 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) 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. (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 Maiman and the first ruby laser Ali Javan and the first He-Ne Laser 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 Applications of Laser (1960s) “A solution looking for a problem” (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 Output When the intensity of the incident light to a material system increases the response of medium is no longer linear Input intensity 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 h h h h Nonlinear Susceptibility Dipole moment per unit volume or polarization Pi Pi ij E j 0 The general form of polarization Pi Pi χ E j χ 0 (1) ij (2) ijk E j Ek χ E j Ek El (3) ijkl Nonlinear Polarization Permanent Polarization First order polarization: Second order Polarization Third Order Polarization P Ej 1 i (1) ij Pi E j Ek 2 ( 2) ijk Pi E j Ek El 3 ( 3) ijkl How does optical nonlinearity appear The strength of the electric field of the light wave should be in the range of atomic fields h a0 N Eat e / a 2 0 a0 / me 2 e 2 7 Eat 2 10 esu Nonlinear Optical Interactions The E-field of a laser beam ~ E (t ) Eeit C.C. 2nd order nonlinear polarization ~ ( 2) P (t ) 2 ( 2) EE* ( ( 2) E 2e 2it C.C.) 2 ( 2) 2nd Order Nonlinearities The incident optical field ~ i1t i 2t E (t ) E1e E2e C.C. Nonlinear polarization contains the following terms 2 1 P(21 ) E (SHG) P(2 2 ) ( 2 ) E22 (SHG) ( 2) P(1 2 ) 2 E1 E2 (SFG) P(1 2 ) 2 ( 2 ) E1 E2* (DFG) ( 2) P(0) 2 ( 2) ( E1 E1* E2 E2* ) (OR) Sum Frequency Generation 2 2 ( 2) 1 Application: Tunable radiation in the UV Spectral region. 1 3 1 2 2 1 3 Difference Frequency Generation 2 2 1 ( 2) 1 Application: The low frequency photon, 2 amplifies in the presence of high frequency beam . This 1 is known as parametric amplification. 3 1 2 1 2 3 Phase Matching ( 2) 2 •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. Third Order Nonlinearities When the general form of the incident electric field is in the following form, ~ i3t i1t i 2t E (t ) E1e E2e E3e The third order polarization will have 22 components which their frequency dependent are i ,3i , ( i j k ), ( i j k ) (2 i j ), (2 i j ), i, j, k 1,2,3 The Intensity Dependent Refractive Index The incident optical field ~ it E (t ) E ( )e C.C. Third order nonlinear polarization P ( ) 3 ( ) | E ( ) | E ( ) ( 3) ( 3) 2 The total polarization can be written as P TOT ( ) E ( ) 3 ( ) | E ( ) | E ( ) (1) ( 3) 2 One can define an effective susceptibility eff 4 | E ( ) | (1) 2 ( 3) The refractive index can be defined as usual n 1 4eff 2 By definition n n0 n2 I where n0c 2 I | E ( ) | 2 12 2 ( 3) n2 2 n0 c Typical values of nonlinear refractive index Mechanism n2 (cm2/W) ( 3) 1111 (esu) Response time (sec) Electronic Polarization 10-16 10-14 10-15 Molecular Orientation 10-14 10-12 10-12 Electrostriction 10-14 10-12 10-9 Saturated Atomic Absorption 10-10 10-8 10-8 Thermal effects 10-6 10-4 10-3 Photorefractive Effect large large Intensity dependent Third order nonlinear susceptibility of some material 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 20 ns (1-100)×10-14 Very fast Optical glass 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. ( 3) Wave mixing 2n0Sin( /2) Optical Phase Conjugation Phase conjugation mirror PCM M s M PCM Aberration correction by PCM Aberrating medium s Aberrating medium PCM PCM What is the phase conjugation The signal wave ~ it Es (r, t ) Es e C.C. Es ε̂ s As e The phase conjugated wave ~ * it Ec (r , t ) rEs e C.C. iks .r Degenerate Four Wave Mixing A1 A2 ( 3) A3 A4 •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 Mathematical Basis The four interacting waves ~ i ( ki .r t ) Ei (r.t ) Ai (r )e C.C. The nonlinear polarization P NL * i (( k1 k 2 k3 ).r t ) 3 6 E1E2 E 6 A1 A2 A e ( 3) * 3 ( 3) The same form as the phase conjugate of A3 Holographic interpretation of DFWM A1 A2 ( 3) A3 A4 Bragg diffraction from induced dynamic gratings