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Introduction to Nonlinear Optics

Introduction to Nonlinear Optics . Azita Emami May 2002. Outline . General Introduction Photorefractive Effect Wave Mixing Phase Conjugation Stimulated Back Scattering Other Applications. Introduction. What does the index of refraction mean?

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Introduction to Nonlinear Optics

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  1. Introduction to Nonlinear Optics Azita Emami May 2002

  2. Outline • General Introduction • Photorefractive Effect • Wave Mixing • Phase Conjugation • Stimulated Back Scattering • Other Applications

  3. Introduction • What does the index of refraction mean? • Linear Region : Efield << Intra-Atomic field. “n” is independent from the light intensity, “I”. • Nonlinear Region: Efield ~ Intra-Atomic field. Modified electron distribution, “n” depends on “I”.

  4. Introduction (2) • Nonlinear Optics: Study of interaction of light in matter • We can control “n” by the light itself or manipulate one beam with the other. • Leads to a Great variety of technical innovations.

  5. Material Response to the Light • P = e0c(1)E + e0c(2)EE + e0c(3)EEE + … • P: induced polarization of medium • e0: dielectric constant of vacuum • E: electric field • c(i): constant • D = e0E + P = eE • In linear optics: n2 = 1 + c(1)

  6. Nonlinear Terms • Second-order term, c(2)EE : frequency doubling sum/difference generation • Third-order term, c(3)EEE : 3rd harmonic generation Raman & Brillouin Scattering Self focusing Optical Phase Conj.

  7. Nonlinear terms (2) • Now consider an optical beam with frequency w and a DC field: E=E0 + Ewcos(wt) • c(2) E0 Ewcos(wt) linear electro-optic effect discovered by Pockels in 1883, modifying n with a DC field used for optical switching used for phase modulation of light

  8. More Terms • c(2)Ew2 static voltage appears across the sample • c(2)Ew2 cos(2wt) • c(3) E02 Ew cos(wt) quadratic electro-optic effect(DC Kerr effect) • c(3) E0Ew2 cos(2wt) • c(3) Ew3 cos(3wt)

  9. Last term… Kerr effect • c(3) Ew3 cos(wt) = c(3) Ew2 (Ewcos(wt)) optical (or AC) Kerr effect looks like a refractive index which depends on the optical field strength n= n0+n2I self-focusing and self-phase modulation

  10. Photorefractive Effect • Change of the local index of refraction by illumination of a beam with spatial variation of Intensity. • First discovered in 1966, study of laser beams through electro-optic crystals • LiNbO3, BaTiO3, KNbO3, LiT aO3, …

  11. Simple Model for Photorefractive effect • There are impurities with energy levels around the middle of band gap (donors). • With enough photon energy, electrons get excited. • Electrons migrate and get trapped at nearby sites in the dark side • Space charge separation, E field, change in “n”.

  12. Periodic Media • A periodic media can be created using the photorefractive effect • Many important phenomena involve the scattering of light from gratings or holograms • Wave mixing, phase conj., dynamic holography, etc.

  13. Wave in Periodic Media • Grating, when dielectric constant is a periodic function of position.

  14. Two Wave Mixing • Two beams with same frequency create a stationary interference pattern. • There will be energy coupling between the two beams. • Can be used for beam amplification, one beam pumps the energy in to the other

  15. Photorefractive Resonators

  16. Optical Phase Conjugation • Generation of a time-reversed replica of the wave, like a mirror • E = A cos(wt-kz-f) Ec = A cos(wt+kz+f) • Lensless imaging, distortion correction, associated with a frequency shift • With nonlinear techniques this can be done real-time

  17. Phase Conjugation

  18. Generation of Phase-Conj. waves • FWM • Degenerate Four-Wave Mixing (similar to holography) • Nondegenerate FWM, gives large freq shift • Stimulated Scattering processes • Brillouin scattering: involves acoustic waves, small freq shift • Raman Scattering: molecular vibration or optical phonons, larger shift

  19. DFWM • A 3rd order nonlinear optical process • The induced grating by 2 input waves scatters the 3rd and generates the 4th • Inputs are 2 antiparallel, high-power pumps and a weaker probe wave, the output could be amplified besides being conjugated • In conventional holography gratings are recorded in a photographic emulsion

  20. Holography • Record object beam A1 with the reference beam A2 • Read out by A3 which is A2’s phase conj.

  21. Raman & Brellouin Processes • Mixing of mechanical oscillations with a light beam in a nonlinear media • Mechanical var. : intra-atomic dis in a molecule or density in a solid or liquid • Freq spectrum of light is modified while phonons are emitted or absorbed

  22. Brillouin Scattering • “n” is a function of density, Debye-Sears effect (acoustic wave scatters light with a Doppler shift) • In turn electronic polarization creates pressure variations • Light can pump a sound wave • Then it is scattered back with slightly different freq.

  23. Raman Scattering • Intra-atomic distance within the molecule is changed when the electron cloud is displaced • Involves the vibration state of molecules • Here variables are microscopic while in Brillouin macroscopic

  24. More… • Optical Computing Fourier Optics using FWM, Image Subtraction • Optical Interconnection Amplification, Dispersion cancellation, Optical switches with dynamic holography (1 ms recording time), …

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