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Numerical modeling of femtosecond laser inscribed IR gratings in photonic crystal fibers

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Abstract

During grating inscription in photonic crystal fibers (PCFs) the intensity of the inscribing laser beam is non-uniformly distributed over the core region due to the interaction with the air holes in the fiber’s microstructure. In this paper we model and study the non-uniformity of the index modification and its influence on the grating reflection spectra, taking into account the non-linear nature of the index change. For femtosecond laser inscription pulses at 800 nm, we show that the intensity redistribution in the PCF core region can result in Type II index changes even if the peak intensity of the incident beam is well below the corresponding threshold. Our coupled mode analysis reveals that the non-uniform nature of the index change can seriously affect the reflectivity of the grating due to a limited overlap of the guided mode with the transverse index modulation profile for almost all angular orientations of the PCFs with respect to the inscription beam. We also evaluate the influence of PCF tapering and we found that for the considered PCF a significant increase in the induced index change and reflectivity is observed only for taper diameters below 40 μm.

© 2015 Optical Society of America

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Supplementary Material (6)

Media 1: MP4 (377 KB)     
Media 2: MP4 (313 KB)     
Media 3: MPEG (1612 KB)     
Media 4: MPEG (1458 KB)     
Media 5: MPEG (1612 KB)     
Media 6: MPEG (1458 KB)     

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Figures (9)

Fig. 1
Fig. 1 Illustration of (a) two interfering beams that transversely propagate to the PCF core region, (b) and (c) cross sections of the considered PCFs with wave vector decomposition of the transverse beam into in- and out-of-plane components.
Fig. 2
Fig. 2 Proposed simplified model for the refractive index change as a function of the optical intensity at 800 nm.
Fig. 3
Fig. 3 (a) Outline of the multiple beam scanning modeling approach for PCFs and process for obtaining the distribution of maximal intensities in the fiber core region for (b) a conventional step-index fiber and (c) a photonic crystal fiber.
Fig. 4
Fig. 4 (a) Maximum intensity distribution for PCF-1 and (b) modeled refractive index change in PCF core for the incident beam peak intensity I = 3x1013 W/cm2.
Fig. 5
Fig. 5 Modeled average of the induced transverse refractive index change depending on the angular orientation for (a) PCF-1 and (b) PCF-2 (ESM-12-01).
Fig. 6
Fig. 6 Schematic illustration of the simulation approach used to model the spectral response of a fiber Bragg grating in photonic crystal fiber.
Fig. 7
Fig. 7 Simulated FBG reflectivity as a function of the angular orientation for PCF-1 and PCF-2 (ESM-12-01), and incident beam peak intensity I = 4.3x1013 W/cm2.
Fig. 8
Fig. 8 Dependence of (a) the average of the induced index change in the core region and (b), (c) the resulting grating reflectivity on the fiber taper diameter for gratings written in PCF-2 along the ΓK and ΓM directions of the hexagonal lattice.
Fig. 9
Fig. 9 Refractive index modification profile modeled for different values of fiber taper diameter for PCF (ESM-12-01) orientation along (a) ΓK (Media 1) and (b) ΓM direction of hexagon (Media 2).

Equations (4)

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Δn=C I 5
λ xy = λ cos(α)
κ= ω 4 Δε(x,y) E t E t * dxdy
R=tan h 2 (κL)
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