Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

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

V.G. Ta’eed, D.J. Moss, B.J. Eggleton, D. Freeman, S. Madden, M. Samoc, B. Luther-Davies, S. Janz, and D.-X. Xu

Open Access Open Access

Abstract

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

Full Article  |  PDF Article
More Like This
Mode conversion and birefringence adjustment by focused-ion-beam etching for slanted rib waveguide walls

Po Shan Chan, H. K. Tsang, and C. Shu
Opt. Lett. 28(21) 2109-2111 (2003)

Tunable Bragg reflectors on silicon-on-insulator rib waveguides

Ivano Giuntoni, Andrzej Gajda, Michael Krause, Ralf Steingrüber, Jürgen Bruns, and Klaus Petermann
Opt. Express 17(21) 18518-18524 (2009)

Diffraction grating couplers milled in Si3N4 rib waveguides with a focused ion beam

Kirill E. Zinoviev, Carlos Dominguez, and Anna Vilà
Opt. Express 13(21) 8618-8624 (2005)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


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.

Download Full Size | PDF

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.

Download Full Size | PDF

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.

Download Full Size | PDF

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.

Download Full Size | PDF

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.

Download Full Size | PDF

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

Download Full Size | PDF

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).

Download Full Size | PDF

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”.

Download Full Size | PDF

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.

Download Full Size | PDF

Equations (8)

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

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 .

Metrics

Select as filters
Select Topics Cancel
Top
       
© Copyright 2023 | Optica Publishing Group. All Rights Reserved
Privacy | Terms of Use