Lez. 6 - Fisica At. Mol. Spec Carlo Altucci Consorzio Nazionale Interuniversitario di Struttura della Materia – CNISM Dipartimento di Scienze Fisiche, Università “Federico II”, Napoli, Italy UNIVERSITA’ DI NAPOLI “FEDERICO II” Brief introduction to Nonlinear Optics

Lez. 6 - Fisica At. Mol. Spec Nonlinear susceptibility 2.  (2) phenomena 3.  (3) phenomena 4.Brief mention to highly nonlinear optics OUTLINE

Lez. 6 - Fisica At. Mol. Spec Linear and nonlinear susceptibility In this case it is assumed that the polarization is an instantaneous response to the electric field. This, through the Kramers-Kronig relations, implies that the medium must be lossless and dispersionless. The theory is generalized to account for both losses and dispersion.

Lez. 6 - Fisica At. Mol. Spec  (2) occurs only in media that o not display inversion symmetry. Thus, liquids, gases, amorphous materials in general (glasses), some crystals, etc. etc. having inversion symmetry exhibit a  (2) which identically vanishes.  (3), instead, is not vanishing for both centrosymmetric and non-centrosymmetric media.

Lez. 6 - Fisica At. Mol. Spec This argument is quite accurate, despite its simplicity!

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8 Field progation through a nonlinear medium

Lez. 6 - Fisica At. Mol. Spec Even in non-resonant conditions an external field can strongly affect the response of the medium if its strength is approaching or even comparable with that of the atomic field! Nonlinear optics is typically triggerd at a much lower threshold..!

Lez. 6 - Fisica At. Mol. Spec Second order processes: SHG

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Lez. 6 - Fisica At. Mol. Spec Types of SHG in crystals SHG occurs in three types, denoted 0, I and II. In Type 0 SHG two photons having extraordinary polarization with respect to the crystal will combine to form a single photon with double the frequency/energy and extraordinary polarization. In Type I SHG two photons having ordinary polarization with respect to the crystal will combine to form one photon with double the frequency and extraordinary polarization. In Type II SHG, two photons having orthogonal polarizations will combine to form one photon with double the frequency and extraordinary polarization. For a given crystal orientation, only one of these types of SHG occurs. In general to utilise Type 0 interactions a quasi-phase-matching crystal type will be required, for example periodically poled lithium niobate (PPLN).

Lez. 6 - Fisica At. Mol. Spec SHG from planar surfaces Early experiments in the field demonstrated second harmonic generation from metal surfaces. Eventually, SHG was used to probe the air-water interface, allowing for detailed information about molecular orientation and ordering at one of the most ubiquitous of surfaces. It can be shown that the specific elements of  (2) : where N s is the adsorbate density, θ is the angle that the molecular axis z makes with the surface normal Z, and  (2) zzz is the dominating element of the nonlinear polarizability of a molecule at an interface, allow one to determine θ, given laboratory coordinates (x, y, z).

Lez. 6 - Fisica At. Mol. Spec Using an interference SHG method to determine these elements of  (2), the first molecular orientation measurement showed that the hydroxyl group of phenol pointed downwards into the water at the air-water interface (as expected due to the potential of hydroxyl groups to form hydrogen bonds). Additionally SHG at planar surfaces has revealed differences in pKa (dissociation constant) and rotational motions of molecules at interfaces.

Lez. 6 - Fisica At. Mol. Spec Applications of SHG from surfaces Second harmonic light can also be generated from surfaces that are ‘locally’ planar, but may have inversion symmetry (centrosymmetric) on a larger scale. Specifically, recent theory has demonstrated that SHG from small spherical particles (micro- and nanometer scale) is allowed by proper treatment of Rayleigh scattering. At a the surface of a small sphere, inversion symmetry is broken, allowing for SHG and other even order harmonics to occur. Cartoon depicting ordered molecules at a small spherical surface. An ultrafast pump laser pumps light with frequency ω which generates light at 2ω from the locally non- centrosymmetric media.

Lez. 6 - Fisica At. Mol. Spec SH generation: microscopic sources and formation/propagation of a macroscopic field

Lez. 6 - Fisica At. Mol. Spec SUM and DIFFERENCE frequency generation da “Nonlinear Optics”, R. W. Boyd

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Lez. 6 - Fisica At. Mol. Spec SUM frequency generation

Lez. 6 - Fisica At. Mol. Spec DIFFERENCE frequency generation fluorescence

Lez. 6 - Fisica At. Mol. Spec Optical parametric oscillation

Lez. 6 - Fisica At. Mol. Spec Third order processes When the input field has several spectral components the expression of the third order polarization becomes very complicated. Thus, let us consider a monochromatic input field.

Lez. 6 - Fisica At. Mol. Spec Parametric vs non-parametric processes

Lez. 6 - Fisica At. Mol. Spec Other examples

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Lez. 6 - Fisica At. Mol. Spec Remind: spontaneous Raman scattering

Lez. 6 - Fisica At. Mol. Spec Spontaneous vs stimulated Raman

Lez. 6 - Fisica At. Mol. Spec Highly nonlinear optics The lowest order perturbation theory (LOPT) holds true if the power series that gives the nonlinear polarization of the medium converges

Lez. 6 - Fisica At. Mol. Spec Bound-to-free transitions in atoms and molecules: highly nonlinear ionization In practice in the VIS-IR  bf   bb and if  < 1 we can use the LOPT. This implies that multi- photon ionization occurs within the LOPT for intensities not exceeding W/cm 2.

Lez. 6 - Fisica At. Mol. Spec Models for highly nonlinear ionization