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Higher order mode conversion via focused ion beam milled Bragg gratings in Silicon-on-Insulator waveguides

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We report the first Bragg gratings fabricated by Focused Ion Beam milling in optical waveguides. We observe striking features in the optical transmission spectra of surface relief gratings in silicon-on-insulator waveguides and achieve good agreement with theoretical results obtained using a novel adaptation of the beam propagation method and coupled mode theory. We demonstrate that leaky Higher Order Modes (HOM), often present in large numbers (although normally not observed) even in nominally single mode rib waveguides, can dramatically affect the Bragg grating optical transmission spectra. We investigate the dependence of the grating spectrum on grating dimensions and etch depth, and show that our results have significant implications for designing narrow spectral width gratings in high index waveguides, either for minimizing HOM effects for conventional WDM filters, or potentially for designing devices to capitalize on very efficient HOM conversion.

©2004 Optical Society of America

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Figures (9)

Fig. 1.
Fig. 1. Cross-sectional profile of a rib waveguide: (a) a schematic, showing simulated mode profile for the fundamental mode and (b) a scanning electron micrograph of the waveguide used in this paper.
Fig. 2.
Fig. 2. Experimental setup: (a) the FIB milled rib grating structure, (b) coupling to the grating waveguide, and (c) measuring the optical grating transmission spectrum.
Fig. 3.
Fig. 3. Experimental (top) and theoretical (bottom) optical transmission spectrum of the surface grating from 1300 nm to 1680 nm using an unpolarized LED and optical spectrum analyzer with 0.4 nm resolution. The dotted lines are an aid to the eye, and the red arrow indicates the position of the fundamental Bragg resonance.
Fig. 4.
Fig. 4. Grating transmission spectrum for the 1532 nm and 1554 nm resonances measured with a high power ASE-EDFA source for both TE and TM polarizations at a resolution of 80 pm.
Fig. 5.
Fig. 5. Effective index versus wavevector of the first 24 TE modes of the rib waveguide are represented by the colored lines. Intersection with the thick black line (λ/2) indicates a diagonal solution of the Bragg equation.
Fig. 6.
Fig. 6. Mode profiles for the first 21 modes of the rib waveguide. As the mode profiles are horizontally symmetric, only the right half of each profile is displayed
Fig. 7.
Fig. 7. (a) Top: Bragg grating coupling coefficient of the first 21 modes of the rib waveguide (b) Middle: leakage rates of the HOM as measured from BPM simulations and (c) Bottom: figure of merit representing how well the mode lobes fit in the both rib and slab regions (0.0 = poor, 1.0 = good spatial overlap).
Fig. 8.
Fig. 8. Schematic representation of the spatial overlap of the mode with the slab region. For modes that do not fit an integer number of lobes (a) in the slab, the figure of merit is defined as “0”, while for modes that fit an integer number of lobes in the slab (b) and hence have good overlap with the slab, the figure of merit is defined to be “1”.
Fig. 9.
Fig. 9. Theoretical coupling coefficients (κ) for grating depths of 40nm, 200nm and 400 nm. The overall envelop increases in strength and shifts to longer wavelength (and lower order modes) as the grating probes more of the fundamental mode. The arrow at the top right indicates the position of the fundamental grating resonance.

Equations (8)

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W H α + h / H 1 ( h / H ) 2 ,
h H 1 2 ,
λ = ʌ ( n inc + n scat ) ,
T i = 1 tanh 2 ( κ i L ) ,
κ i = ( π λ ) Δ n ( x , y ) E 0 ( x , y ) E i * ( x , y ) dxdy .
E ( x , y , 0 ) = Δ n ( x , y ) E 0 ( x , y ) .
P ( z ) = E ( x , y , 0 ) E * ( x , y , z ) dxdy ,
α i = ( λ π ) κ i .


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