Masashi Kiguchi, "Comparison of error properties of techniques used for measuring second-order nonlinear optical coefficients with least-squares fitting," J. Opt. Soc. Am. B 12, 871-875 (1995)
The technique of second-harmonic generation with an evanescent wave (SHEW) and the Maker fringe technique were examined by simulation of least-squares fitting. The calculations were made for correlation among parameters in a fit and error-propagation coefficients between parameters. Correlation among parameters for the SHEW technique is lower and the parameter value for the second-order nonlinear optical coefficient d is less sensitive to errors of refractive indices than for the Maker fringe technique. As a result, use of the SHEW technique can provide more-accurate values for the d coefficient than use of the Maker fringe technique.
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Correlation Coefficients and Error-Propagation Coefficients with Least-Squares Fitting for Maker Fringe and SHEW Techniques in Sample A: nsω = 1.6 and ns2ω = 1.7, a Case of Small Dispersiona
Two cases of sample length L, M1 and M2, are examined for the Maker fringe technique, and three cases of the fitting range, S1-S3, are examined for the SHEW technique. r(ai − aj) is the correlation coefficient between parameters ai and aj.
Δd/Δai is the error-propagation coefficient from parameter ai to the d value.
Table 2
Correlation Coefficients and Error-Propagation Coefficients with Least-Squares Fitting for Maker Fringe and SHEW Techniques in Sample B: nsω = 1.8 and ns2ω = 2.2, a Case of Large Dispersiona
Some cases of the conditions are examined as well in Table 1. r(ai − aj) is the correlation coefficient between parameters ai; and aj.
Δd/Δai is the error-propagation coefficient from parameter ai to the d value.
Tables (2)
Table 1
Correlation Coefficients and Error-Propagation Coefficients with Least-Squares Fitting for Maker Fringe and SHEW Techniques in Sample A: nsω = 1.6 and ns2ω = 1.7, a Case of Small Dispersiona
Two cases of sample length L, M1 and M2, are examined for the Maker fringe technique, and three cases of the fitting range, S1-S3, are examined for the SHEW technique. r(ai − aj) is the correlation coefficient between parameters ai and aj.
Δd/Δai is the error-propagation coefficient from parameter ai to the d value.
Table 2
Correlation Coefficients and Error-Propagation Coefficients with Least-Squares Fitting for Maker Fringe and SHEW Techniques in Sample B: nsω = 1.8 and ns2ω = 2.2, a Case of Large Dispersiona
Some cases of the conditions are examined as well in Table 1. r(ai − aj) is the correlation coefficient between parameters ai; and aj.
Δd/Δai is the error-propagation coefficient from parameter ai to the d value.