1 / 24

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?

briana
Download Presentation

Introduction to Nonlinear Optics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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), …

More Related