e-book The principles of nonlinear optics

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One undesirable effect of angle tuning is that the optical frequencies involved do not propagate collinearly with each other. This is due to the fact that the extraordinary wave propagating through a birefringent crystal possesses a Poynting vector that is not parallel to the propagation vector. This would lead to beam walk-off, which limits the nonlinear optical conversion efficiency. These methods are called temperature tuning and quasi-phase-matching.

Temperature tuning is used when the pump laser frequency polarization is orthogonal to the signal and idler frequency polarization. The birefringence in some crystals, in particular lithium niobate is highly temperature-dependent. The crystal temperature is controlled to achieve phase-matching conditions. The other method is quasi-phase-matching. Hence, these crystals are called periodically poled. This results in the polarization response of the crystal to be shifted back in phase with the pump beam by reversing the nonlinear susceptibility. This allows net positive energy flow from the pump into the signal and idler frequencies.

Quasi-phase-matching can be expanded to chirped gratings to get more bandwidth and to shape an SHG pulse like it is done in a dazzler. SHG of a pump and self-phase modulation emulated by second-order processes of the signal and an optical parametric amplifier can be integrated monolithically.

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At high peak powers the Kerr effect can cause filamentation of light in air, in which the light travels without dispersion or divergence in a self-generated waveguide. When a noble gas atom is hit by an intense laser pulse, which has an electric field strength comparable to the Coulomb field of the atom, the outermost electron may be ionized from the atom.

Once freed, the electron can be accelerated by the electric field of the light, first moving away from the ion, then back toward it as the field changes direction. The electron may then recombine with the ion, releasing its energy in the form of a photon.

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The light is emitted at every peak of the laser light field which is intense enough, producing a series of attosecond light flashes. The photon energies generated by this process can extend past the th harmonic order up to a few K eV. This is called high-order harmonic generation. The laser must be linearly polarized, so that the electron returns to the vicinity of the parent ion. High-order harmonic generation has been observed in noble gas jets, cells, and gas-filled capillary waveguides.

One of the most commonly used frequency-mixing processes is frequency doubling , or second-harmonic generation. Practically, frequency doubling is carried out by placing a nonlinear medium in a laser beam. While there are many types of nonlinear media, the most common media are crystals. These crystals have the necessary properties of being strongly birefringent necessary to obtain phase matching, see below , having a specific crystal symmetry, being transparent for both the impinging laser light and the frequency-doubled wavelength, and having high damage thresholds, which makes them resistant against the high-intensity laser light.

It is possible, using nonlinear optical processes, to exactly reverse the propagation direction and phase variation of a beam of light. The reversed beam is called a conjugate beam, and thus the technique is known as optical phase conjugation [17] [18] also called time reversal , wavefront reversal and is significantly different from retroreflection.

One can interpret this nonlinear optical interaction as being analogous to a real-time holographic process. The third incident beam diffracts at this dynamic hologram, and, in the process, reads out the phase-conjugate wave. In effect, all three incident beams interact essentially simultaneously to form several real-time holograms, resulting in a set of diffracted output waves that phase up as the "time-reversed" beam.

In the language of nonlinear optics, the interacting beams result in a nonlinear polarization within the material, which coherently radiates to form the phase-conjugate wave. The most common way of producing optical phase conjugation is to use a four-wave mixing technique, though it is also possible to use processes such as stimulated Brillouin scattering.

A device producing the phase-conjugation effect is known as a phase-conjugate mirror PCM. As above, the phase-matching condition determines which of these waves is the dominant. This results in the retroreflecting property of the effect. Further, it can be shown that for a medium with refractive index n and a beam interaction length l , the electric field amplitude of the conjugate beam is approximated by.

If the pump beams E 1 and E 2 are plane counterpropagating waves, then. Since the imaginary part of the amplitude contains the phase of the beam, this results in the reversal of phase property of the effect.

Nonlinear Optics

Note that the constant of proportionality between the signal and conjugate beams can be greater than 1. The power for this comes from the two pump beams, which are depleted by the process. The frequency of the conjugate wave can be different from that of the signal wave. This is known as frequency flipping. Optical phase conjugation in the near field performs the reversal of classical rays, or retroreflection. In classical Maxwell electrodynamics a phase-conjugating mirror performs reversal of the Poynting vector :.

The above identities are valid locally , i. 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.

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Non-linear optical processes

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