After introducing linear optics from the perspective of polarizability and linear susceptibility, the authors cover incoherent second-harmonic generation. They then deal with the study of surfaces and interfaces, exploiting the intrinsic surface sensitivity of second-harmonic generation and sum-frequency generation. The final chapter discusses second-order imaging techniques, including confocal microscopy and two-photon excited fluorescence microscopy. Accessible to a wide range of scientists, this concise book stresses the reliability of nonlinear optical processes for probing surfaces and interfaces.

Drawing on the insight offered in the text, scientists from many disciplines can now clearly understand and use second-order nonlinear optical methods. Read more Read less.

Combining Eqs. Here c is the free space light velocity. Suppose that the electric field is a group of monochromatic plane waves given by [ 1 ]. Then, the Fourier transform of the nonlinear polarization 1 yields [ 1 ]. We do not present here the analytical properties of the nonlinear susceptibilities which are discussed in detail in Ref.

In some simple cases, the nonlinear susceptibilities can be evaluated by using the anharmonic oscillator model [ 1 , 8 ]. It is assumed that a medium consists of N classical anharmonic oscillators per unit volume [ 1 ]. Such an oscillator may describe an electron bound to a core or an infrared-active molecular vibration [ 1 ]. The nonlinear terms become essential when the electromagnetic power is large enough in such a way that a medium response cannot be considered linear anymore [ 8 ]. We limit our analysis with quadratic and cubic nonlinearities proportional to x 2 and x 3 , respectively [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ].

In general case, the microscopic expressions for nonlinear susceptibilities of a medium are calculated by using the quantum mechanical approach.

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In particular, the density matrix formalism is a powerful and convenient tool for such calculations [ 1 , 2 , 7 , 8 ]. Electromagnetic waves in a medium interact through the nonlinear polarization 8 [ 1 ]. Typically, a nonlinear optical effect that occurs due to such an interaction is described by the coupled wave equations of the type 7 with the nonlinear susceptibilities 12 as the coupling coefficients [ 1 ].

In general case, the coupled wave method can also include waves other than electromagnetic [ 1 ]. For instance, in the case of SBS process, the acoustic waves are taken into account, and in the case of SRS process, the molecular vibrations are typically considered [ 1 , 2 , 4 ].

The coupled wave equations are usually solved by using SVEA 2 [ 1 ]. We start with the sum-frequency, difference-frequency, and second harmonic generation. Similarly, in the case of the difference-frequency generation, we obtain [ 1 ]. The efficient nonlinear wave mixing can occur only under the phase-matching conditions. The detailed analysis of the sum-frequency generation, difference-frequency generation, and SHG in different configurations may be found in [ 1 , 3 , 6 ].

It can be shown that the efficient sum-frequency generation can be realized under the following conditions [ 1 ]. The length of the nonlinear crystal must provide the required conversion efficiency. The efficient SHG can be realized with the single-mode laser beams focused into the nonlinear optical crystal [ 1 ]. Sum-frequency generation, difference-frequency generation, and SHG can be also carried out in the waveguide nonlinear optical devices [ 3 ].

Waveguide SHG devices can be used in optical signal processing such as laser printer, laser display, optical memory, short pulse, multicolor, and ultraviolet light generation [ 3 ]. These phenomena are much weaker than the second-order ones. Self-focusing is an induced lens effects caused by the self-induced wavefront distortion of the optical beam propagating in the nonlinear medium [ 1 ]. In such a medium, a refractive index n has the form [ 1 ]. Consequently, the central part of the beam travels at a smaller velocity than the beam edge. As a result, the gradual distortion of the original plane wavefront of the beam occurs, and the beam appears to focus by itself [ 1 ].

The self-focusing results in the local increase of the optical power in the central part of the beam and possible optical damage of transparent materials limiting the high-power laser performance [ 1 ]. SPM is also caused by the positive refractive index change It is the temporal analog of self-focusing which leads to the spectral broadening of optical pulses [ 4 ].

In optical fibers, for short pulses and sufficiently large fiber length L f , the combined effect of the group velocity dispersion GVD and SPM should be taken into account [ 4 ]. In such a case, the pulse propagates in the optical fiber as an optical soliton, i. The optical solitons can propagate undistorted over long distances, and they can be applied in fiber-optic communications [ 4 ].

Consider now THG. Unlike SHG, it is always allowed [ 1 ]. For this reason, the laser intensity required for the efficient THG is limited by the optical damage in crystals [ 1 ]. THG can be realized in highly nonlinear optical fibers where the phase matching can be accomplished [ 4 ]. SBS is a nonlinear optical effect related to parametric coupling between light and acoustic waves [ 1 ].

The acoustic wave enhanced by the interacting pump and signal Stokes wave modulates the mass density of the medium which in turn modulates the refractive index [ 1 , 3 , 4 ].

## Electric field-induced second-order nonlinear optical effects in silicon waveguides

In quantum electrodynamics the interpretation of phase conjugation is much simpler compared to classical electrodynamics. The photon reflected from phase conjugating-mirror out has opposite directions of linear and angular momenta with respect to incident photon in :. Optical fields transmitted through nonlinear Kerr media can also display pattern formation owing to the nonlinear medium amplifying spatial and temporal noise. The effect is referred to as optical modulation instability.

The early studies of nonlinear optics and materials focused on the inorganic solids. With the development of nonlinear optics, molecular optical properties were investigated, forming molecular nonlinear optics [30]. Recently, many novel directions were proposed for enhanced nonlinearity and light manipulation, including twisted chromophores, combining rich density of states with bond alternation, microscopic cascading of second-order nonlinearity, etc.

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Due to the distinguished advantages, molecular nonlinear optics have been widely used in the biophotonics field, including bioimaging [31] , phototherapy [32] ,biosensing [33] , etc. From Wikipedia, the free encyclopedia. See also: Second-harmonic generation. Physical Review Letters. Bibcode : PhRvL November A Study of the Phosphorescent State". Journal of the American Chemical Society. Nonlinear Optics. Bibcode : Natur. Submitted manuscript.

Bibcode : PhRvL.. Retrieved July 4, Nat Phys. Bibcode : NatPh Physica D: Nonlinear Phenomena. Bibcode : PhyD..

## Buy Second Order Nonlinear Optical Characterization Techniques: An Introduction

Kouzov, N. Egorova, M. Chrysos, F. Encyclopedia of Laser Physics and Technology. Boyd 3rd ed. Boyd, Nonlinear optics, Third edition, Chapter 2. Bijlani; Amr S. Helmy Optics Express. Bibcode : OExpr.. Optics Letters. Bibcode : OptL CLEO ' Pepper, Jack Feinberg, and Nicolai V. Okulov, "Angular momentum of photons and phase conjugation", J. B: At. JETP Lett. The Journal of Physical Chemistry C. ACS Macro Letters. Advances in Optics and Photonics. Bibcode : AdOP Scientific Reports. Bibcode : NatSR Advanced Materials. Coordination Chemistry Reviews. Branches of physics.