Optical materials constants

The interest in efficient optical frequency doubling has stimulated a search for new nonlinear materials. Kurtz 316) has reported a systematic approach for finding nonlinear crystalline solids, based on the use of the anharmonic oscillator model in conjunction with Miller s rule to estimate the SHG and electro optic coefficients of a material. This empirical rule states that the ratio of the nonlinear optical susceptibility to the product of the linear susceptibilities is a parameter which is nearly constant for a wide variety of inorganic solids. Using this empirical fact, one can arrive at an expression for the nonlinear coefficients that involves only the linear susceptibilities and known material constants. 

This review summarizes the current state of materials development in nonlinear optics. The relevant properties and important materials constants of current commercial, and new, promising, inorganic and organic molecular and polymeric materials with potential in second and third order NLO applications are presented. 

In anisotropic materials, the electronic bonds may have different polarizabilities for different directions (you may think of different, orientation-dependent spring constants for the electronic harmonic oscillator). Remembering that only the E-vector of the light interacts with the electrons, we may use polarized light to test the polarizability of the material in different directions, lno is one of the most important electro-optic materials and we use it as an example. The common notations are shown in Figure 4.7. If the E-vector is in plane with the surface of the crystal, the wave is called a te wave. In this example, the te wave would experience the ordinary index na of LiNbOs (nG 2.20). If we rotate the polarization by 90°, the E-ve ctor will be vertical to the surface and the wave is called tm. In lno, it will experience the extraordinary index ne 2.29. Therefore these two differently polarized waves will propagate with different phase velocities v c/n. In the example of Figure 4.7, the te mode is faster than the tm mode. 

Assessing thermal and photochemical stability is important. Thermal stability can be readily measured by measuring properties such as second harmonic generation as a function of heating at a constant rate (e.g., 4-10 °C/min) [121]. The temperature at which second-order optical nonlinearity is first observed to decrease is taken as defining the thermal stability of the material [2,3,5,63,63]. It is important to understand that the loss of second-order nonlinear optical activity measured in such experiments is not due to chemical decomposition of the electro-optic material but rather is due to relaxation of poling-induced acentric... 

Clausius-Mossotti equation — Named after Clausius and Ottaviano Fabrizio Mossotti (1791-1863). It relates the electron -> polarizability a of an individual molecule to the optical -> dielectric constant (relative permittivity) r of the bulk material. 

The same formula applies if the electron polarizability is replaced by the total polarizability, and the optical dielectric constant is replaced by the static dielectric constant, provided attention is then restricted to nonpolar materials. 

The selection rules governing photon absorption in solids determine the oscillator strength of the optical transition and its energy dependence. The expressions obtained for the imaginary component of the optical dielectric constant depend on whether the transition is allowed in the dipole approximation and on whether the simultaneous absorption or emission of a phonon is involved. In pure single-crystal materials, the absorption coefficient can be described conveniently by relationships that take the general form [4]... 

Optical materials refractive index n (to) n (2nonlinear optical constant d hi xlO (esu) 2nd-order molecular polarizability 0 xlO 30 (esu) 3rd-order nonlinear susceptibility X xlO 14 (esu)... 

The excitation of the surface plasmon is found to be an extinction maximum or transmission minimum. The spectral position v half-width (full width at half-maximum) T and relative intensity f depend on various physical parameters. First, the dielectric functions of the metal and of the polymer Cpo(v) are involved. Second, the particle size and shape distribution play an important role. Third, the interfaces between particles and the surrounding medium, the particle-particle interactions, and the distribution of the particles inside the insulating material have to be considered. For a description of the optical plasmon resonance of an insulating material with embedded particles, a detailed knowledge of the material constants of insulating host and of the nanoparticles... 

Over the past five years, a new class of electro-optic polymeric materials has evolved which provides for the first time the capability to fabricate simple and inexpensive electro-optic devices on a variety of substrates. More importantly, these materials possess optical dielectric constants (or refractive indexes) comparable to radio-frequency dielectric constants allowing for fabrication of devices in which the electric field and the optical field propagate at the same velocity. Finally, the low dielectric constant of these materials relative to inorganic ionic crys s provides for operation of devices at much higher efficiency. Although the above facts have been clear for some time, the practical applications of these materials cannot be realized until materials can be created which satisfy a host of practical requirements and until device architectures and fabrication techniques appropriate for these materials can be developed. We will describe here research directed toward both of these ends. 

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