Two-dimensional high-precision fiber waveguide arrays for coherent light propagation

U. Röpke; H. Bartelt; S. Unger; K. Schuster; J. Kobelke

doi:10.1364/OE.15.006894

Optics Express
Vol. 15,
Issue 11,
pp. 6894-6899
(2007)
•https://doi.org/10.1364/OE.15.006894

Two-dimensional high-precision fiber waveguide arrays for coherent light propagation

U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke

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U. Röpke, H. Bartelt, S. Unger, K. Schuster, and J. Kobelke, "Two-dimensional high-precision fiber waveguide arrays for coherent light propagation," Opt. Express 15, 6894-6899 (2007)

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Abstract

Fiber waveguide arrays can be applied as a very useful tool for the investigation of effects in discrete optics. The observation of coherent propagation in such discrete waveguide arrays requires, however, high structural precision and great material homogeneity. The fabrication of such a fiber array with close tolerances compared to conventional fiber technology is discussed. Linear propagation effects are modeled for an ideal fiber waveguide array and are compared with experimental results. The good agreement of these results with each other indicates the applicability of such fiber waveguide arrays in studying linear and non-linear properties in discrete optics.

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Fig. 1. Cross-sections of a high-precision waveguide array: white light transmission microscopy (left), reflected-light/differential interference contrast microscopy image of an etched cleaved facet (right).

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Fig. 2. Eigenvalues of the supermodes of a 61-core array (left), and field distribution of the supermodes with the highest symmetry (right). The colors (yellow and blue) indicate the sign of the real-valued amplitudes u_i .

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Fig. 3. Output distribution of light launched at specific cores: array center (upper row), boundary corner (middle row) and middle of a boundary line (lower row); columns (a) and (c) show experimental results for sample lengths z_A = 26.5 mm and 55 mm, respectively; columns (b) and (d) show computer simulations of an ideal array with ζ = 0.42 and 0.85, respectively.

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Equations (5)

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L_{C} = \frac{λ_{0}}{{4 Δ n}_{0}} \frac{\int_{A \infty} E_{0}^{2} dA}{\int_{AR} E_{0} (x + Λ, y) E_{0} (x, y) dA} .

i \frac{λ_{0}}{2 π} \frac{du}{dz} + (M_{D} + \frac{λ_{0}}{4 L_{C}} M_{C}) u = - \frac{n_{2} ∙ 1 W}{A_{eff}} diag ({∣ u_{i} ∣}^{2}) u + \dots,

M_{D} = \frac{{Δ n}_{0} diag (\frac{{δn}_{i}}{{Δ n}_{0}} \int_{A \infty} E_{0}^{2} dA + 2 πRδ R_{i} E_{0} {(R)}^{2} + Γ_{i} \int_{AR} E_{0} {(x + Λ, y)}^{2} dA)}{\int_{A \infty} E_{0}^{2} dA} .

i \frac{λ_{0}}{2 π} \frac{du}{dz} + (\frac{λ_{0}}{{4 L}_{C}} M_{C}) u = 0 .

u (z) = \exp (i \frac{π z}{2 L_{C}} M_{C}) ∙ u (0) .

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