Nonlinear optics

The non-linear optics ( NLO short ) is a branch of physics Optics of the electromagnetic waves, in which the relationship between electric field and electric polarization in a medium is not linear but is of higher degree.

Basics

The starting point of modern optical descriptions form the Maxwell equations, which form a mathematical formalism for the description of electromagnetic waves in vacuum and in matter, among others. Propagates an electromagnetic wave in a medium, which excites electrons in it to vibrate and in turn send new waves. This will be described by the electric flux density:

Here, the electric field constant, the electric field of the shaft and the electrical polarization. To a first approximation for low intensities that the polarization increases linearly with the electric field:

Wherein the electrical susceptibility represents. However, this no longer holds for very high intensities and it must be taken into account higher-order terms, since the intensity is proportional to the square of the electric field and the electric polarization can not rise any linear:

It is generally a tensor higher level. The wave equation, the higher order terms results from the introduction, is:

It is the Laplace operator, n is the refractive index of the medium, c is the speed of light, and the sum of all non- linear terms of the polarization.

Effects and applications

Light as an electromagnetic wave is generally represented by a spatially and temporally oscillating function:

With the place of the time t, the wave vector, the angular frequency and amplitude. Substituting this function or overlays of different light waves with different frequencies in the nonlinear electric polarization provides different terms where new frequencies are included. Not all the effects occurring in this bill, however, occur simultaneously in appearance. Light with different frequencies has different phase velocities due to the frequency dependence of the refractive index, that is the dispersion in a medium. This results in a destructive interference of the waves. So that the desired effect occurs, the phase matching condition for the involved frequencies must be met:

That is, the refractive indices of the two light waves having the angular frequencies, and must be identical. This condition can only be achieved by means of birefringent materials by the optical polarizations of light waves are suitably chosen.

Some non-linear optical effects are:

• Frequency doubling (English second harmonic generation, SHG)
• Sum-frequency generation (English sum frequency generation, SFG )
• Difference frequency generation ( engl. difference frequency generation, DFG)
• Parametric process, even down conversion ( engl. down conversion ) called, for example, with an optical parametric oscillator.
• And self-focussing Kerr effect
• Self-phase modulation ( SPM), cross-phase modulation (English cross phase modulation, XPM )
• Four - wave mixing ( engl. four wave mixing FWM )

Nonlinear optics and nonlinear optical materials find use in the construction of optical switches and components. Such are, for example, green laser pointers frequently diodes which emit infrared light, which for the pumping of Nd: (1064 nm, an infrared wavelength) is used YVO4 lasers, which in turn is frequency doubled with a nonlinear crystal (wavelength 532 nm, green). They can also data and image processing are used as memory in the ( digital ) optical.

Media with non-linear effects

Nonlinear optical effects occur only in media where the terms do not disappear with susceptibilities higher order than 1, ie are equal to zero. For second-order effects are mostly around crystals also exhibit a piezoelectric effect. The crystals most commonly used with non-linearity in the second order are beta - barium borate ( BBO ), potassium dihydrogen phosphate ( KDP), ammonium dihydrogen phosphate (ADP), lithium niobate, lithium iodate, Silberthiagolat.

Postgraduate

• Robert W. Boyd: Nonlinear Optics. 3rd edition. Academic Press, New York 2008, ISBN 978-0123694706.
• Nonlinear Optics in the Encyclopedia of Laser Physics and Technology (English )