Effective nonlinear coefficients of organic powders measured by second-harmonic generation in total reflection: numerical and experimental analysis

R. Kremer, A. Boudrioua, J. C. Loulergue, and A. Iltis

Author Affiliations

R. Kremer,^{1} A. Boudrioua,^{1} J. C. Loulergue,^{1} and A. Iltis^{2}

^{1}Laboratoire des Matériaux Optiques à Propriétés Spécifiques, Centre Lorrain d’Optique et Electronique des Solides, Université de Metz, Supelec, 2, Rue Edouard Belin, 57070 Metz, France

^{2}Société Crismatec, 104 Route de Larchant, B.P. 521, 77794 Nemours Cedex, France

R. Kremer, A. Boudrioua, J. C. Loulergue, and A. Iltis, "Effective nonlinear coefficients of organic powders measured by second-harmonic generation in total reflection: numerical and experimental analysis," J. Opt. Soc. Am. B 16, 83-89 (1999)

A second-harmonic wave generated by an evanescent wave (SHEW) is used to measure the effective nonlinear coefficient of organic materials in powder form. The SHEW signal is less sensitive than the powder method to the phase-matching conditions of the material. For this reason, the SHEW technique can be used to survey a wide variety of samples. The effective nonlinear coefficient and the refractive indices of the sample are obtained as fitting parameters. The influence of experimental conditions on the fitting process is discussed. The results obtained from our powders are compared with the nonlinear coefficients of the same materials in bulk crystal form. Good agreement is found between experimental results and literature values.

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The reference curve is shifted by ±0.05°, ±0.1°, and ±0.6° to simulate these errors. The fit results are compared with the parameters of the reference curve ($n_{s}{}^{\omega}=1.906,$$n_{p}{}^{2\omega}=2.262,$${d}_{\mathrm{eff}}=84\mathrm{pm}/\mathrm{V}$). $\mathrm{\Delta}n_{s}{}^{\omega}=n_{s}{}^{\omega}(\mathrm{fit}\hspace{0.5em}\mathrm{result})-n_{s}{}^{\omega}(\mathrm{reference}),$$\mathrm{\Delta}n_{s}{}^{2\omega}=n_{s}{}^{2\omega}(\text{fit result})-n_{s}{}^{2\omega}(\mathrm{reference}),$$\mathrm{\Delta}{d}_{\mathrm{eff}}={d}_{\mathrm{eff}}\hspace{0.5em}(\text{fit result})-{d}_{\mathrm{eff}}\hspace{0.5em}(\mathrm{reference}).$

Table 2

Influence of Incident Laser Power Fluctuations on Fit Resultsa

The distribution of the fluctuation is determined by the random parameter ${R}_{i}.$ For several distributions the corresponding curves are fitted. The results are compared with the parameters of the reference curve ($n_{s}{}^{\omega}=1.906,$$n_{p}{}^{2\omega}=2.262,$${d}_{\mathrm{eff}}=84\mathrm{pm}/\mathrm{V}$). The effective nonlinear coefficient is the most sensitive parameter to these fluctuations

Table 3

Influence of Angular Range Detection of SHEW Power after Total Reflection for a SH Wavea

When the measurements are performed far beyond the angle of total reflection for the SH wave $({\theta}_{\mathrm{SHTR}}),$ the parameters obtained with the fitting process are in good agreement with the theoretical values ($n_{s}{}^{\omega}=1.906,$$n_{p}{}^{2\omega}=2.262,$${d}_{\mathrm{eff}}=84\mathrm{pm}/\mathrm{V}$). For a narrow angular range of detection after ${\theta}_{\mathrm{SHTR}}$ (curve 10), the results deviate widely from theoretical values

Table 4

Comparison between SHEW Results and Literature Values of Refractive Indices and Effective Nonlinear Coefficients of NPP, POM, MMONS, and NPAN

The reference curve is shifted by ±0.05°, ±0.1°, and ±0.6° to simulate these errors. The fit results are compared with the parameters of the reference curve ($n_{s}{}^{\omega}=1.906,$$n_{p}{}^{2\omega}=2.262,$${d}_{\mathrm{eff}}=84\mathrm{pm}/\mathrm{V}$). $\mathrm{\Delta}n_{s}{}^{\omega}=n_{s}{}^{\omega}(\mathrm{fit}\hspace{0.5em}\mathrm{result})-n_{s}{}^{\omega}(\mathrm{reference}),$$\mathrm{\Delta}n_{s}{}^{2\omega}=n_{s}{}^{2\omega}(\text{fit result})-n_{s}{}^{2\omega}(\mathrm{reference}),$$\mathrm{\Delta}{d}_{\mathrm{eff}}={d}_{\mathrm{eff}}\hspace{0.5em}(\text{fit result})-{d}_{\mathrm{eff}}\hspace{0.5em}(\mathrm{reference}).$

Table 2

Influence of Incident Laser Power Fluctuations on Fit Resultsa

The distribution of the fluctuation is determined by the random parameter ${R}_{i}.$ For several distributions the corresponding curves are fitted. The results are compared with the parameters of the reference curve ($n_{s}{}^{\omega}=1.906,$$n_{p}{}^{2\omega}=2.262,$${d}_{\mathrm{eff}}=84\mathrm{pm}/\mathrm{V}$). The effective nonlinear coefficient is the most sensitive parameter to these fluctuations

Table 3

Influence of Angular Range Detection of SHEW Power after Total Reflection for a SH Wavea

When the measurements are performed far beyond the angle of total reflection for the SH wave $({\theta}_{\mathrm{SHTR}}),$ the parameters obtained with the fitting process are in good agreement with the theoretical values ($n_{s}{}^{\omega}=1.906,$$n_{p}{}^{2\omega}=2.262,$${d}_{\mathrm{eff}}=84\mathrm{pm}/\mathrm{V}$). For a narrow angular range of detection after ${\theta}_{\mathrm{SHTR}}$ (curve 10), the results deviate widely from theoretical values

Table 4

Comparison between SHEW Results and Literature Values of Refractive Indices and Effective Nonlinear Coefficients of NPP, POM, MMONS, and NPAN