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

Mode field patterns and preferential mode coupling in planar waveguide-coupled square microcavities

Chung Yan Fong and Andrew W. Poon

Open Access Open Access

Abstract

We report a numerical and analytical study of mode field patterns and mode coupling in planar waveguide-coupled square microcavities, using two-dimensional (2-D) finite-difference time-domain (FDTD) method and k-space representation. Simulated mode field patterns can be identified by k-space modes. We observe that different mode number parities permit distinctly different mode field patterns and spectral characteristics. Simulation results suggest that k-space modes that nearly match the waveguide propagation mode have a relatively high coupling efficiency. Such preferential mode coupling can be modified by the mode number parity.

©2003 Optical Society of America

Full Article  |  PDF Article
More Like This
Planar corner-cut square microcavities: ray optics and FDTD analysis

Chung Yan Fong and Andrew W. Poon
Opt. Express 12(20) 4864-4874 (2004)

Dispersion-guided resonances in two-dimensional photonic-crystal-embedded microcavities

Kevin K. Tsia and Andrew W. Poon
Opt. Express 12(23) 5711-5722 (2004)

Waveguide-coupled octagonal microdisk channel add–drop filters

Chao Li, Ning Ma, and Andrew W. Poon
Opt. Lett. 29(5) 471-473 (2004)

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 (6)
Fig. 1.
Fig. 1. Schematic of a planar waveguide-coupled square µ-cavity channel add-drop filter.

Download Full Size | PDF

Fig. 2.
Fig. 2. FDTD simulated throughput (blue), drop (green) and add (red dashed line) spectra (normalized with input intensity) of a planar waveguide-coupled square µ-cavity filter. a=2.2 µm, w=0.2 µm, g=0.2 µm and TM-polarized. The dominant resonances in the throughput spectrum are indexed as (mx, my) modes according to the corresponding mode-field patterns. The indexed (mx, my) modes are clustered according to the integer number of wavelengths M.

Download Full Size | PDF

Fig. 3.
Fig. 3. FDTD simulated odd M (=15) mode field patterns of a planar waveguide-coupled square µ-cavity filter at (6,9) mode (λ=1538 nm). a=2.2 µm, w=0.2 µm, g=0.2 µm and TM-polarized. (a) t=t0, (b) t≈t0+T/8, (c) t≈t0+T/4, (d) t≈t0+3T/8 and (e) t≈t0+T/2.

Download Full Size | PDF

Fig. 4.
Fig. 4. FDTD simulated odd M (=15) mode field patterns of a planar waveguide-coupled square µ-cavity filter at (7,8) mode (λ=1562.5 nm). a=2.2 µm, w=0.2 µm, g=0.2 µm and TM-polarized. (a) t=t0, (b) t≈t0+T/6, (c) t≈t0+T/4, (d) t≈t0+2T/6 and (e) t≈t0+T/2. Calculated mode field patterns of a discrete square cavity using Eq. (2) with A=0.7 for (7,8) mode, B=0.3 for (8,7) mode, and δ=π/2. (f) ωt=0, (g) ω t=2π/6, (h) ωt=π/2, (i) ωt=4π/6 and (j) ωt=π.

Download Full Size | PDF

Fig. 5.
Fig. 5. FDTD simulated even M (=16) mode field patterns of a planar waveguide-coupled square µ-cavity filter. a=2.2 µm, w=0.2 µm, g=0.2 µm and TM-polarized. (a) (7,9)π mode (λ=1446.5 nm), (b) (6,10)π mode (λ=1417.1 nm), (c) (7,9)0 mode (λ=1454.5 nm) and (d) (8,8) mode (λ=1461.2 nm). Calculated mode field patterns of a discrete square cavity using Eq. (2) with A=B. (e) (7,9)π mode, (f) (6,10)π mode, (g) (7,9)0 mode and (h) (8,8) mode. The dashed-line box in (b) and (f) denotes a “vortex.”

Download Full Size | PDF

Fig. 6.
Fig. 6. Calculated k-space (mx, my) modes (filled and open dots) of a discrete square cavity of a=2.36 µm. The y-axis is the mode angle θ and the x-axis is the wavelength λ. Only the modes that satisfy θc<θ <90°-θc are represented (θc≈16.6° for n=3.5). The modes of the same M values are distributed along various parabola curves. The dominant modes in Fig. 2 are represented by filled dots. The dashed line shows the waveguide fundamental mode angle ϕ (w=0.2 µm) in TM polarization.

Download Full Size | PDF

Equations (3)

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

E mx , my ( x , y ) e iωt = A e iωt sin ( m x π x a ) sin ( m y π y a ) ,
E mx , my ( x , y ) e iωt = A e iωt sin ( m x π x a ) sin ( m y π y a )
+ B e i ( ω t − δ ) sin ( m y π x a ) sin ( m x π y a ) ,
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use