Diffractive self-imaging based on selective etching of a ferroelectric domain inversion grating

Yunlin Chen; Tianwei Fan; Man Tong

doi:10.3788/COL201513.020502

Journals >Chinese Optics Letters >Volume 13 >Issue 2 >Page 020502 > Article

Chinese Optics Letters
Vol. 13, Issue 2, 020502 (2015)

Diffractive self-imaging based on selective etching of a ferroelectric domain inversion grating

Yunlin Chen^*, Tianwei Fan, and Man Tong

Author Affiliations

Institute of Applied Micro-Nano Materials, School of Science, Beijing Jiaotong University, Beijing 100044, China

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DOI: 10.3788/COL201513.020502 Cite this Article Set citation alerts

Yunlin Chen, Tianwei Fan, Man Tong. Diffractive self-imaging based on selective etching of a ferroelectric domain inversion grating[J]. Chinese Optics Letters, 2015, 13(2): 020502 Copy Citation Text

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Abstract

A hexagonal array grating based on selective etching of a 2D ferroelectric domain inversion in a periodically poled MgO-doped

{LiNbO}_{3}

crystal is fabricated. The effects to the diffractive self-imaging as a function of diffraction distance for a fixed phase difference and array duty cycle of the grating is theoretically analyzed. The Talbot diffractive self-imaging properties after selective etching of a 2D ferroelectric domain inversion grating under a fixed phase difference are experimentally demonstrated. A good agreement between theoretical and experimental results is observed.

u (x, y) = \sum_{m n} A_{m n} \exp [i 2 π (\frac{m x}{t_{x}} + \frac{n y}{\sqrt{3} t_{x}})],

(1)

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A_{00} = \exp [- i (Δ φ)] + c {\exp [i (Δ φ)] - \exp [- i (Δ φ)]},

(2)

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A_{m n} = i {1 + \exp [i π (n + m)]} \times \frac{{(- 1)}^{n} \sin (Δ φ)}{n (n^{2} - m^{2}) π^{2}} \times [(n + m) \cos (\frac{2 m - 3 n}{5} π) - 2 n \cos (\frac{n π}{5}) + (n - m) \cos (\frac{2 m + 3 n}{5}) π] .

(3)

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u_{z} (Δ φ, x, y) = \sum_{m n} A_{m n} \times \exp [i 2 π (\frac{m x}{t_{x}} + \frac{n y}{\sqrt{3} t_{x}})] \times \exp [i π λ z (\frac{3 m^{2} + n^{2}}{3 t_{x}^{2}})] .

(4)

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u_{z} (Δ φ, x, y) = \sum_{m n} A_{m n} \times \exp [\frac{i 2 π D}{l} (m x + \frac{n y}{\sqrt{3}})] \times \exp [i \frac{π β}{2} (3 m^{2} + n^{2})] .

(5)

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Yunlin Chen, Tianwei Fan, Man Tong. Diffractive self-imaging based on selective etching of a ferroelectric domain inversion grating[J]. Chinese Optics Letters, 2015, 13(2): 020502

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