The current status of organic low-molecular weight and polymeric materials for third-order nonlinear optics is reviewed. The importance of organic materials lies in their promise of large nonlinear optical figure of merit, high optical damage thresholds, ultrafast optical responses, architectural flexibility, and ease of fabrication. Organic materials exhibiting interesting third-order nonlinear optical properties are discussed to illustrate the importance of structure–property correlations. Results on emerging organic materials that include liquids, dyes, fullerenes, charge-transfer complexes, π-conjugated polymers, dye-grafted polymers, organometallic compounds, composites, and liquid crystals are presented. Organic nonlinear optical materials seem promising for a wide range of applications and their potential for integrated optics should be further explored.

Organic Materials for Third‐Order Nonlinear Optics

Publisher Summary This chapter describes the symmetry aspects of the crystal field and the parametrization of the energy level scheme. It provides an overview of the experimental data of trivalent lanthanide ions doped into crystalline host matrices. The selection rules for induced electric dipole (ED) and magnetic dipole (MD) transitions for systems with even or odd numbers of f electrons in different site symmetries are presented. Methods for the assignment of crystal-field levels are discussed and the determination of phenomenological crystal-field parameters is described. Such a set of crystal-field parameters in combination with a suitable set of free-ion parameters allows calculating crystal-field energy levels and reconstructing the energy diagram of the 4fn configuration. In this way, it is not only possible to check the validity of the crystal-field model but also to get information about energy levels, which cannot be detected experimentally.

Chapter 155 Rationalization of crystal-field parametrization

Calculations of the nonlinear-optical behavior are developed for model composites of nanospheres with a metallic core and nonlinear shell or with a nonlinear core and metallic shell suspended in a nonlinear medium. Optical phase conjugation is shown to be enhanced from each nonlinear region because the optical field can be concentrated in both the interior and the exterior neighborhoods of the particle and magnified at the surface-mediated plasmon resonance. For the model composite with a metallic core, a limited range of resonance tunability can be achieved by adjustment of shell thickness; the frequency range is dependent on the dielectric dispersion of the metal. For the composite with a metallic shell instead of a metallic core, this restriction is reduced so that tunability from ultraviolet to infrared can be attained. Enhancement of the phase-conjugate signal is calculated for the electrostrictive mechanism dominant in the microsecond time scale and for the electronic mechanism dominant in the picosecond time scale. Calculations based on the dielectric functions for gold and for aluminum indicate that phase-conjugate reflectivity enhancements of 108 can be achieved. The imaginary components of the composite dielectric functions are shown to limit the magnitude of the field enhancement at the surface-plasmon resonance and determine the absorption and figure of merit of the composite.

Composite structures for the enhancement of nonlinear-optical susceptibility

The physics of the photorefractive effect is briefly discussed. A coupled-mode theory is then developed to analyze the coupling of two coherent electromagnetic waves inside a photorefractive medium. Both codirectional and contradirectional coupling are considered. The coupled-mode theory is then extended to consider the case of nondegenerate two-wave mixing. A discussion of the fundamental limit of the speed of photorefractive effect is then introduced. The coupling of two polarized beams inside photorefractive cubic crystals is considered. The formulation is focused on the cross-polarization two-beam coupling in semiconductors such as GaAs. The coupling of two electromagnetic waves inside a Kerr medium and the electrostrictive Kerr effect are discussed. A new concept of nonlinear Bragg scattering is introduced. The similarity among various kinds of two-wave mixing, including stimulated Brillouin scattering and stimulated Raman scattering are pointed out. Several applications of two-wave mixing are discussed. These include photorefractive resonators, optical nonreciprocity, resonator model of self-pumped phase conjugators, real-time holography, and nonlinear optical information processing. >

Two-wave mixing in nonlinear media

We review the main works in the field of nonlinear interferometers, which has been developing ever since the start of nonlinear optics and has seen growing interest in recent years due to the applications in quantum information and quantum metrology. Because the class of schemes that are referred to as nonlinear interferometers is too broad, we restrict the consideration to the cases in which crystals, fibers, or atomic systems producing the nonlinear effect are placed inside the interferometer, and only linear phase shifts are imposed. As a nonlinear effect, we consider four-wave mixing and parametric down-conversion, at both low and high gain.

Nonlinear interferometers in quantum optics

Fluorescein-doped boric acid glass is a material characterized by an extremely low saturation intensity of \ensuremath{\sim}15 mW${\mathrm{?}}^{\mathrm{\ensuremath{-}}2}$ and a nonlinear susceptibility ${\ensuremath{\chi}}^{(3)}$ as large as \ensuremath{\sim}1 esu. The saturated absorption of this material is shown both theoretically and experimentally to depend on the state of polarization of the saturating beam, even though the unsaturated absorption is polarization insensitive. Phase-conjugate reflectivities as large as 0.6% have been obtained through use of degenerate four-wave mixing in this material. These measured reflectivities are in good agreement with the predictions of a theory that includes the effects of excited-state absorption and grating washout. In addition, two-beam coupling due to the nonlinearity of saturable absorption has been demonstrated in this material. The magnitude of the coupling is maximized by inducing a frequency shift between the two beams of \ensuremath{\sim}0.1 Hz.

Nonlinear-optical interactions in fluorescein-doped boric acid glass.

This paper presents the results of a study of resonantly enhanced, three-, photon absorption in Nd-doped yttrium aluminum garnet (Y3Alg0~2) or Nd: YAG. The trivalent ions of the rare-earth elements, such as Nd'+, are characterized by energy levels which remain relatively sharp even in a crystalline environment, and thus crystalline solids doped with rare-earth ions present interesting systems in which to study resonantly enhanced optical nonlinearities. While a number of different types of optical nonlinearity can be studied in impurity-doped crystals, such as two-photon absorption, "saturated absorption, ' degenerate four-wave mixing, ' and polarization spectroscopy, this paper focuses on. the process of three-photon absorption. 'Through the absorption of three visible photons we are able to excite Nd'+ energy levels which lie approximately 40000 to 70000 cm ' above the ground state, and hence belong to the 4f'Sd' electron configuration. Since Nd: YAG is essentially opaque for radiation of wave numbers greater than 42000 cm ', the technique of three-photon absorption allows us to probe regions of the 4 f '5d' configuration which are inaccessible using one-photon techniques. Some of the single=photon spectroscopic properties of Nd: YAG that are needed for the interpretation of the three-photon-absorption results are presented here. An absorption spectrum of our 1 wt. %, Nd:YAG taken on a Carey model 14 recording spectrophotometer is shown in Fig. 1. The numerous sharp absorption features in the range 2500 to 9000 A are due to the Nd'+ ion. Since the fundamental absorption edge of YAG occurs' at 1920 A, the observed 2400 A cutoff wavelength in Nd:YAG has been interpreted by Krupke' as due to a distortion of the host lattice by the Nd dopant. Figure 2 shows an energy-level diagram of Nd: Y AG which combines our results of Fig. 1 with previously published data. The region between 0 and 70000 cm ' contains a large pumber of energy levels belonging to the 4f 3 electron configuration. Since the 4f electrons are shielded from the crystalline electrostatic field by the closed outlying Ss and Sp shells, energy levels in this region are very narrow. For energies below 21000 cm ', we have plotted the energy levels determined by Koningstein and Geusic including their level identifications. For energies in the range 27000 and 40000 cm ', we have plotted

Three-photon absorption in Nd-doped yttrium aluminum garnet

The propagation of a weakly modulated light beam through a nonlinear material is treated. The optical field representing such a beam consists of a strong carrier-frequency component and two weak, symmetrically displaced sidebands that combine to form a field, which may be purely amplitude modulated (AM), frequency modulated (FM), or some combination of these two modulation forms. It is shown that, for any optical nonlinearity, two modulation forms exist that have the property that the form of modulation is invariant under propagation of the beam. If a modulation form other than one of these natural modes is injected into the nonlinear medium, the modulation form will change as the beam propagates, asymptotically approaching the natural mode that experiences the lower attenuation. Explicit expressions for these natural modes are presented for the case in which the nonlinear medium can be modeled as a collection of two-level atoms. For the special case of an on-resonance pump beam, the natural modes correspond to pure amplitude modulation and pure frequency modulation. This formalism provides a general description of saturation spectroscopy for both AM and FM fields. Formulas are derived for the rate at which a pure FM beam is converted to an AM beam owing to its interaction with a two-level atomic medium. We also consider the variation that is due to propagation of the depth of modulation of an AM wave interacting resonantly with two-level atoms. The formalism predicts the existence of spectral features whose shape depends sensitively on the internal relaxation processes of the material. Experimental spectra are presented for ruby, alexandrite, and fluorescein in glass and are interpreted.

Propagation of modulated optical fields through saturable-absorbing media: a general theory of modulation spectroscopy

Theoretical predictions have been made by Gavrielides et al.1 concerning the image processing capabilities of an optical parametric amplifier (OPA). They predicted that an OPA could be used to amplify selectively small portions of the spatial frequency distribution of an image. This effect occurs when a small negative phase mismatch (Δk = kp− ks − ki) is induced. As the magnitude of this mismatch is increased, the optical transfer function of the OPA shifts its peak to higher spatial frequencies, and the passband of the transfer function narrows. This paper reports experimental observations that confirm these analytical results.

Mark A. Kramer

Papers

Nonlinear-optical interactions in fluorescein-doped boric acid glass.

Three-photon absorption in Nd-doped yttrium aluminum garnet

Propagation of modulated optical fields through saturable-absorbing media: a general theory of modulation spectroscopy

Spatial frequency selection using down- conversion optical parametric amplification

Nonlinear optical properties of fluorescein in boric-acid glass