Electro-optic coefficient

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. 

The electro-optic coefficient in a poled polymer film can be related to the second-order susceptibility as shown in Equation 5. 

Table II. The measured electro-optic coefficients and physical properties of copolymers of MAI and MMA...

Figure 5. Electro-optic coefficient (r33) vs. poling field for a 20 mol%...

KTiOAsOd. (KTA). Recent work on KTA shows a significant enhancement of the nonlinear optic and electro-optic coefficients versus those of KTP. (3 8) KTA is isostructural to KTP (39) and is also a 1-dimensional potassium ion conductor in the z-direction. KTA crystals have been grown using the flux technique. 

Group theory can tell us which elements of K are non-zero and about equalities between non-zero elements, but numerical factors (like /2 in the first row of K) are simply a matter of how the Kiq are defined in terms of the constants K, K, K, and Kq, this being usually done in a way that reduces the number of numerical factors. In LiNb03 the electro-optic coefficient r33 is more than three times r13, which gives rise to a relatively large difference in refractive index in directions along and normal to the optic (z) axis, thus making this material particularly useftd in device applications. 

The 18 ry are called electro-optic coefficients , and the problem starts to look a little complex and confusing. Fortunately, the symmetry and the physics of the crystal frequently reduce the complexity nicely. Look at four important examples ... 

Determination of material parameters gain factor T, effective electro-optic coefficient (( reff) and effective trap density AAir... 

The scattering pattern contains additional information about the scattering process itself as well as for the determination of material parameters. We will demonstrate in the following, that both the angular dependence of the holographic gain and the product of the effective linear electro-optic coefficient with the electron-hole competition factor as well as the effective trap density can be determined from the spatial distribution of the scattering pattern as a function of temperature [7],... 

Frequently, values of P for wavelengths where experimental data do not exist are estimated by extrapolation using a two-level model description of the resonance enhancement of P (see Appendix). Levine and co-workers [170] have also shown how to estimate the wavelength (frequency) dispersion of two-photon contributions to p. Because of the potential of significant errors associated with each measurement method, it is important to compare results from different measurement techniques. Perhaps the ultimate test of the characterization of the product of pP is the slope of electro-optic coefficient versus chromophore number density at low chromophore loading. It is, after all, optimization of the electro-optic coefficient of the macroscopic material that is our ultimate objective. 

As with the measurement of p, it is important to compare electro-optic coefficients determined by different methods. It is particularly important to establish consistency between electro-optic coefficients obtained from initially poled thin films and those existing in functional prototype devices. Such consistency not only adds credibility to reported material electro-optic activity, but also as-... 

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