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Iterative processing of second-order optical nonlinearity depth profiles

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Abstract

We show through numerical simulations and experimental data that a fast and simple iterative loop known as the Fienup algorithm can be used to process the measured Maker-fringe curve of a nonlinear sample to retrieve the sample’s nonlinearity profile. This algorithm is extremely accurate for any profile that exhibits one or two dominant peaks, which covers a wide range of practical profiles, including any nonlinear film of crystalline or organic material (rectangular profiles) and poled silica, for which an excellent experimental demonstration is provided. This algorithm can also be applied to improve the accuracy of the nonlinearity profile obtained by an inverse Fourier transform technique.

©2004 Optical Society of America

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Figures (7)

Fig. 1.
Fig. 1. Flow chart of the iterative Fienup algorithm.
Fig. 2.
Fig. 2. Examples of possible physical nonlinearity profiles that can be recovered from their FT magnitudes only by using the Fienup algorithm assuming zero initial FT phase.
Fig. 3.
Fig. 3. The same buried-Gaussian profile as in Fig. 2 with uniform noise added (blue trace). The result of the recovery with 100 iterations is shown in red. The green curve is the difference between the original noisy profile and the recovered profile.
Fig. 4.
Fig. 4. An arbitrarily three-peaked profile (solid blue curve) and the profile recovered (black dashed curve) with the Fienup algorithm after 100 iterations. The red curve shows the recovered profile when d(0) is increased to d(0)=10·max{d(z)}.
Fig. 5.
Fig. 5. Measured MF curve of the poled sample (circles) compared with the theoretically computed MF curve of the processed nonlinearity profile.
Fig. 6.
Fig. 6. Recovered FT phases with the two-sample technique (blue) and with the Fienup algorithm (green) assuming zero initial FT phase.
Fig. 7.
Fig. 7. Nonlinearity profiles recovered with the two-sample technique and with the Fienup algorithm.

Equations (1)

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n = 0 m 1 d min ( n ) 2 n = 0 m 1 d ( n ) 2
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