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Modeling of photonic crystal fiber with air holes sealed at the fiber end and its application to fluorescent light collection efficiency enhancement

Jianjun Ma and Wojtek J. Bock

Open Access Open Access

Abstract

A model of large core and multimode photonic crystal fiber (PCF) with sealed air holes at its end face is proposed for the first time. The model indicates that this PCF can be replaced by another equivalent fiber with complete holes at a new end-face position. Instead of a segment of glass rod between the old and new end faces, light rays travel in a virtual medium with the loss rating of pure glass but the refractive index of the immersion medium. For a two-fiber structure, this segment of pure glass has the capability of enhancing the light collection efficiency, which is investigated using a specifically designed fiber probe and fluorescent samples with different concentrations.

©2005 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. MM-HN-200 PCF from Crystal-Fiber A/S. (a). end face with complete air holes; (b). side view of (a); (c). side view of PCF having a segment of sealed air holes in the fiber end; (d). end face of (c) with light intensity distributed across the entire surface because of the missing air holes; (e). end face view of (d) obtained by focusing the camera on a deeper cross-section inside the PCF.

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Fig. 2.
Fig. 2. The PCF end with a segment of sealed air holes (between the plane A′-B′ and the plane D-G) and its equivalent PCF with complete air holes (end face on the plane C-H). Here, y stands for the sealed length; yeq is the end-face position of the equivalent fiber.

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Fig. 3.
Fig. 3. For different Γ, numerical results of δ/y vs. different incident angles θi from Eq. (2): (a) when the PCF is in the air immersion medium; (b) when the PCF is in the liquid immersion medium.

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Fig. 4.
Fig. 4. The end-face position of the equivalent PCF in the air and liquid immersion media vs. NA.

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Fig. 5.
Fig. 5. A PCF-conventional fiber probe for fluorescent light collection efficiency enhancement investigation. yeff : effective depth; yeq : end-face position of the equivalent PCF fiber; dashed lines ① and ②: determined by the NA of the PCF; V 0-1 and V 0-2 : overlap volumes with the same size. The virtual medium within the distance yeq (volume V ′) has a zero attenuation and the refractive index of immersion medium (n). Linking this advantage with additional overlap volumes of V 1, V 2 and V 3, PCF-2 is able to collect more fluorescent light than in the case of PCF-1. When yeff is reduced, the efficiency is enhanced further because of the larger difference of overlap volume between PCF-2 and PCF-1.

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Fig. 6.
Fig. 6. Experimental investigation of the fluorescent light collection enhancement capability of PCF with air holes sealed at its end. PCF-2 has a longer fused segment than PCF-1.

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

y e q = y n 2 2 − Γ 2 n 1 2 − Γ 2
δ = ∣ y sin θ i ( 1 cos θ i n 2 2 − Γ 2 n 1 2 − Γ 2 − n 2 n 1 2 − n 2 2 sin 2 θ i ) ∣
d e = d − 2 δ max
I r I e q > ( d e d ) 2 = ( 1 − 2 ( δ max d ) ) 2
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