Interactions between Light Waves in a Nonlinear Dielectric

Abstract

The induced nonlinear electric dipole and higher moments in an atomic system, irradiated simultaneously by two or three light waves, are calculated by quantum-mechanical perturbation theory. Terms quadratic and cubic in the field amplitudes are included. An important permutation symmetry relation for the nonlinear polarizability is derived and its frequency dependence is discussed. The nonlinear microscopic properties are related to an effective macroscopic nonlinear polarization, which may be incorporated into Maxwell's equations for an infinite, homogeneous, anisotropic, nonlinear, dielectric medium. Energy and power relationships are derived for the nonlinear dielectric which correspond to the Manley-Rowe relations in the theory of parametric amplifiers. Explicit solutions are obtained for the coupled amplitude equations, which describe the interaction between a plane light wave and its second harmonic or the interaction between three plane electromagnetic waves, which satisfy the energy relationship ws = wi+<u>2, and the approximate momentum relationship k 3 = ki+k 2 -]-Ak. Third-harmonic generation and interaction between more waves is mentioned. Applications of the theory to the dc and microwave Kerr effect, light modulation, harmonic generation, and parametric conversion are discussed.

Tunable diffraction-free array in nonlinear photonic crystal

“…In a typical QPM configuration, SHG can be greatly enhanced by using the reciprocal vectors in a PPLT crystal to compensate for the phase mismatch between the fundamental wave and the SH wave26. Luckily, there exist abundant non-collinear reciprocal vectors in a 2D domain structure, which can realize non-collinear QPM SHG2728 as shown in Fig.…”

“…PPLT crystals have been extensively investigated because they can realize highly-efficient frequency conversions through the quasi-phase-matching (QPM) technique26. Since the concept of nonlinear photonic crystal, i.e., 2D PPLT crystal, was proposed by Berger27 in 1998, numerous interesting phenomena have been discovered such as non-collinear second-harmonic generation (SHG)28, nonlinear Čerenkov radiations293031, and nonlinear Talbot self-imaging32.…”

Temperature- and wavelength-insensitive parametric amplification enabled by noncollinear achromatic phase-matching

“…To address the advantages of the NAPM over the wavelength-insensitive noncollinear PM in parametric amplification, both the conversion efficiency and the signal pulse profiles are numerically investigated based on the nonlinear coupled-wave equations32 (see Methods for detail). In the simulations, both the pump and chirped signal durations (full width at half maximum) are designated to be 10 ps with a Gaussian profile.…”

Nonlinear Optics and Spectroscopy

“…In the same manner the term in x (3) causes a coupling between four electromagnetic waves. A general formulation of three-and fourwave light mixing was developed by our group at Harvard (21). The quantum mechanical calculation of the complex nonlinear susceptibilities, based on the evolution of the density matrix, was also quickly applied to optical problems (22).…”

“…This was demonstrated independently by Giordmaine (30) and Terhune and co-workers (31). For = 0, the polarization in all unit cells in the crystal contributes in phase to the second harmonic field, and if the crystal is long enough and the light intensity high enough, the fundamental power may be quantitatively converted to second harmonic power (21). Phase coherence is essential.…”