Fabrication and study of bent and coiled free silica nanowires: Self-coupling microloop optical interferometer

M. Sumetsky; Y. Dulashko; A. Hale

doi:10.1364/OPEX.12.003521

Optics Express
Vol. 12,
Issue 15,
pp. 3521-3531
(2004)
•https://doi.org/10.1364/OPEX.12.003521

Fabrication and study of bent and coiled free silica nanowires: Self-coupling microloop optical interferometer

M. Sumetsky, Y. Dulashko, and A. Hale

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M. Sumetsky, Y. Dulashko, and A. Hale, "Fabrication and study of bent and coiled free silica nanowires: Self-coupling microloop optical interferometer," Opt. Express 12, 3521-3531 (2004)

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Abstract

We fabricated nanometer- and micrometer-order diameter optical fibers (NMOFs) by drawing them in a microfurnace comprising a sapphire tube heated with a CO₂ laser. Using very short - a few mm long - fiber biconical tapers having a submicron waist, which can be bent locally in a free space by translation of the taper ends, we studied the effect of bending and looping on the transmission characteristics of a free NMOF. In particular, we have demonstrated an optical interferometer built of a coiled self-coupling NMOF.

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Fig. 1. Illustration of the setup for drawing NMOF using a sapphire tube heated with a CO₂ laser

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Fig. 2. SEM image of a NMOF drawn in sapphire microfurnace by translation of stage 1

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Fig. 3. Illustration of the setup for NMOF bending. The ends of biconical fiber taper are glued to the stages. The waist of taper can be bent by translation of one of the stages in three dimensions.

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Fig. 4. — variation of diameter of fiber tapers 1 and 2 used in our experiments as a function of length; insert shows variation of diameter for the NMOF parts of these tapers. b — transmission spectrum for the same fibers. Solid curves — fiber 1; dashed curves — fiber 2.

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Fig. 5. Transmission spectrum and digitally sharpened optical microscope images for different configurations of NMOF contained in taper 1. a — bent NMOF; b and c — coiled NMOF; d — NMOF with straight central part.

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Fig. 6. Comparison of the experimental transmission spectrum a, shown in Fig. 5 with theoretical fits obtained using Eqs. (1)–(3) for transmission loss. The bend radius, length of bent NMOF segment, and NMOF diameter for curves 1–5 are specified in the insert.

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Fig. 7. Illustration of two interfering waves (dashed) contributing to the transmission spectrum of the self-coupling microloop. 1 — a wave propagating through the loop; 2 — a wave propagating through the self-coupling region.

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Fig. 8. Transmission spectrum and sharpen optical microscope images for different configurations of NMOF contained in taper 2. a, b — bent and coiled NMOF without self coupling; c,d,e — self-coupling microcoils with successively decreasing bend radius. Fig. 8e shows comparison of the experimental data with theoretical dependence defined in the text.

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Equations (5)

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P (λ_{0}) = \exp (- γ (λ_{0}) L)

γ (λ_{0}) = \frac{U {(λ_{0})}^{2}}{2 V {(λ_{0})}^{2} W {(λ_{0})}^{3 ⁄ 2} K_{1}^{2} (W (λ_{0}))} {(\frac{π}{rR})}^{1 ⁄ 2} \exp [- \frac{4 W {(λ_{0})}^{3}}{3 V {(λ_{0})}^{2}} (1 - \frac{1}{n^{2}}) \frac{R}{r}] .

V (λ_{0}) = \frac{2 π r}{λ_{0}} {(n^{2} - 1)}^{1 ⁄ 2}, U (λ_{0}) = r {(\frac{4 π^{2} n^{2}}{λ_{0}^{2}} - β {(λ_{0})}^{2})}^{1 ⁄ 2}, W (λ_{0}) = r {(β {(λ_{0})}^{2} - \frac{4 π^{2}}{λ_{0}^{2}})}^{1 ⁄ 2}

[\frac{J_{1}^{'} (U)}{U J_{1} (U)} + \frac{K_{1}^{'} (W)}{W K_{1} (W)}] [\frac{J_{1}^{'} (U)}{U J_{1} (U)} + \frac{1}{n^{2}} \frac{K_{1}^{'} (W)}{W K_{1} (W)}] = {(\frac{β λ_{0}}{2 π n})}^{2} {(\frac{V}{UW})}^{4}

P (λ_{0}) = {∣ a_{1} (λ_{0}) \exp (i β (λ_{0}) S) + a_{2} (λ_{0}) ∣}^{2}

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Equations (5)

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