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Comparative analysis of ferroelectric domain statistics via nonlinear diffraction in random nonlinear materials

B. Wang, K. Switkowski, C. Cojocaru, V. Roppo, Y. Sheng, M. Scalora, J. Kisielewski, D. Pawlak, R. Vilaseca, H. Akhouayri, W. Krolikowski, and J. Trull

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Abstract

We present an indirect, non-destructive optical method for domain statistic characterization in disordered nonlinear crystals having homogeneous refractive index and spatially random distribution of ferroelectric domains. This method relies on the analysis of the wave-dependent spatial distribution of the second harmonic, in the plane perpendicular to the optical axis in combination with numerical simulations. We apply this technique to the characterization of two different media, Calcium Barium Niobate and Strontium Barium Niobate, with drastically different statistical distributions of ferroelectric domains.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Corrections

6 February 2018: A typographical correction was made to the author listing.

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Figures (14)
Fig. 1
Fig. 1 (a) Schematic plot of planar SHG from an as-grown ferroelectric crystal with a random distribution of domains with inverted sign of the quadratic nonlinearity. (b) Phase-mismatch compensation diagram via the use of RLV of modulus G (z corresponds to the optical axis)

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Fig. 2
Fig. 2 (a) SH emission over a plane perpendicular to the optical axis for a structure made with normal distribution of domains with a mean value ρo = 0.9μm and standard deviation σ = 0.3μm as a function of the incident fundamental wavelength. The 0° direction corresponds to emission in the forward direction of the incident beam. (b) The angle of maximum SH emission as a function of wavelength.

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Fig. 3
Fig. 3 Modulus of G needed to compensate the phase mismatch at a given wavelength and emission angle within the plane transverse to the optical axis for SBN crystals.

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Fig. 4
Fig. 4 Experimentally measurement of the SH emission pattern from sample 1 (CBN) and sample 2 (SBN) for two different fundamental wavelengths: 800 nm (blue line; circles) and 1064 nm (green line; triangles). Below each figure we show a picture of the SH pattern at 400 nm for each sample, recorded with a CCD camera placed behind the crystal.

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Fig. 5
Fig. 5 Schematic representation of the experimental setup. HW - half-wave plate, P - polarizer, F - IR blocking filter, S - diffusive screen.

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Fig. 6
Fig. 6 Experimental results for CBN sample. Normalized SH intensity as a function of the emission angle

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Fig. 7
Fig. 7 Overview of experimental results for oo-e and ee-e interactions in the CBN sample. The map of colors shows the modulus of G needed to compensate the phase mismatch at a given wavelength and emission angle (see Fig. 3). Circles represent the maximum SH angle and the bars the angular width of the SH emission, for all different wavelengths used in the experiment.

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Fig. 8
Fig. 8 Experimentally measured angular SH intensity distribution for sample 2 (SBN61). The data was normalized for clarity of presentation.

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Fig. 9
Fig. 9 Overview of experimental results for SBN sample for oo-e and ee-e interactions. The map of colors shows the modulus of G needed to compensate the phase mismatch at a given wavelength and emission angle (see Fig. 3). Circles represent the maximum SH angle and the bars show the angular width of the SH emission, for all different wavelength used in the experiment.

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Fig. 10
Fig. 10 SHG microscopy images corresponding to: (a) as grown CBN crystal (sample 1); (b) artificially poled SABN crystal (sample 2). Note that the scale is different in the two pictures.

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Fig. 11
Fig. 11 (a) 2D domain pattern simulation in real space for the as grown CBN crystal (sample 1); (b) the corresponding Fourier spectrum in the reciprocal space for sample 1; (c) 2D domain pattern simulation in real space for the artificial poled SBN crystal (sample 2) and (d) the corresponding Fourier spectrum in the reciprocal space for sample 2.

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Fig. 12
Fig. 12 (a) Far field SH angular pattern as a function of propagating distance. (b) Far field intensity distribution after x = 70 μm propagation distance within the crystal.

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Fig. 13
Fig. 13 Comparison between the experimental results for as-grown CBN crystal (top) and numerical simulations (bottom) at different wavelengths for the domain distribution shown in Fig. 11(a)

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Fig. 14
Fig. 14 Comparison between the experimental results for SBN crystal, sample 2 (top) and the numerical simulations (bottom) at different wavelengths for the domain distribution shown in Fig. 11(c)

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Equations (2)

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G ( λ , θ ) = k 2 ω 2 + ( 2 k ω ) 2 − 2 k 2 ω ( 2 k ω ) cos ( sin − 1 ( sin θ / n 2 ω ) )
I ( 2 ω ) ∝ I ( ω ) d e f f k ω 2 n ω 4 · n 2 ω · 4 L G 2 · 1 − e − G 2 σ 2 1 + e − G 2 σ 2 + 2 cos ( G ρ o ) e − G 2 σ 2 / 2 .
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