Article

Determination of single mode condition in dielectric rib waveguide with large cross section by finite element analysis

Journal of Computational Electronics (Impact Factor: 1.52). 04/2007; 6(1):285-287. DOI: 10.1007/s10825-006-0124-4
ABSTRACT
The single mode condition in large cross section rib waveguides is of great interest because almost every kind of active and
passive integrated optoelectronic device or sensor is designed to sustain only the fundamental mode of propagation for better
matching with optical fibers. In this paper we present a criterion to determine the single mode condition for a large cross
section rib waveguides, by comparison between the numerical solutions found with Neumann boundary conditions and Dirichlet
boundaries conditions applied when solving the eigenvalues problem.

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Available from: Giovanni Breglio, Mar 04, 2014
Determination of Single Mode Condition
in Dielectric Rib Waveguides with Large Cross
Section by Finite Element Analysis
M. De Laurentis, A. Irace, G. Breglio
Dipartimento di Ingegneria Elettronica e delle Telecomunicazioni
Università degli Studi di Napoli “Federico II”
Via Claudio, 21I-80125 Naples, ITALY
e-mail: a.irace@unina.it
The single mode condition in large cross section rib
waveguides is of great interest because almost every
kind of active and passive integrated optoelectronic
device or sensor, is designed to sustain only the
fundamental mode of propagation for better matching
with optical fibers.
In this paper we present a criterion to determine the
single mode condition for a large cross section rib
waveguides, by comparison between the numerical
solutions found with Neumann boundary conditions
and Dirichlet boundaries conditions applied when
solving the eigenvalues problem.
I
NTRODUCTION
The main issue when solving the Helmholtz
equation with numerical techniques is that the
numerical solver may find solutions that are not
physical nor related to the geometries of the problem,
but “inspired” by the boundaries conditions. Such
solutions are usually caused by the unavoidable need
to limit the inspection domain to save computational
resources. Sometimes it can be difficult to distinguish
between physical solution and these “spurious”
solutions. Therefore, if we want to investigate the
single-mode condition in rib waveguides, we have
choose a robust criterium to understand weather a
numerical solution is either a guided mode or it is
leaking away from our guiding structure.
The rib waveguide guides modes are supposed to be
well confined nearby the rib region and insensible of
the lateral boundaries, so we suppose the non physical
solutions having larger spatial extension and, for these
reason, they are more sensible to lateral boundary
conditions. Therefore, by changing the rib section
geometrical dimensions, we expect a higher difference
between the eigenvalue of first mode solution found
with Dirichlet boundaries conditions the one found
with Neumann boundaries conditions, when these
solutions become not physical (i.e. the mode is not
longer guided).
S
INGLE MODE CONDITION: FEM ANALYSIS
Along this line of argument, we have developed a
numerical code based on FEMLAB and MATLAB
which, keeping fixed the rib height H, studies the
difference (|n
eff10D
- n
eff10N
|) between the first higher
order mode effective refractive index found with
Dirichlet boundaries conditions (n
eff10D
) and first mode
effective refractive index found with Neumann
boundaries conditions (n
eff10N
), by changing etching
value (i.e. changing the etching complement r, see
Fig.1) for each width-height ratio value, w/H, chosen
between 0.5 and 1.75. This has been done in order to
compare our results with recently published literature
data [1-3].
The typical outcome of this analysis is the plot
reported in the Fig. 2 where we observe, for r<r*, the
quantity |n
eff10D
- n
eff10N
| being essentially negligible,
while for r>r*, the difference
|n
eff10D
- n
eff10N
| increases as expected. The r* value is
what we expect to be the boundary between a single
mode waveguide and a multimode one. In Fig. 3 we
show the comparison between our results, Soref [1]
and Pogossian [2] results.
The analysis, originally performed for TE
polarization, can be extended to the TM case and to
different cross sections in order to evaluate if field
polarization or waveguide geometries affect the single
mode condition as they become comparable to the
wavelength of the propagating field.
R
EFERENCES
[1] R. A. Soref, J. Schimdtchen, K. Peterman, Large single-mode
rib waveguides in GeSi-Si and Si-on-SiO2, Journal of Quantum
electronics, 27 ,8, 1971-1974 (1991)
[2] S. P. Pogossian, L. Vescan, A. Vosonsovici, The single-mode
condition fot semiconductor rib waveguides with large cross
section, Journal of Lightwave technology, 16 ,10, 1951-1955 (1998)
[3] J. Lousteau, D. Furniss, A.B. Seddon, T. M. Benson, P.Sewell,
The single-mode condition fot Silicon-omInsulator optical rib
waveguides with large cross section, Journal of Lightwave
technology, 22,8, 1923 (2004)
11th International Workshop on Computational Electronics
TU Wien, 25-27 May 2006
ISBN 3-901578-16-1
313
Page 1
Fig. 1. Rib waveguide section. H is the rib height; w the rib
width and r the etching complement.
Fig. 2. Difference between first mode solution found with
Dirichlet boundaries conditions and first mode solution found
with Neumann boundaries conditions. Typically, when this
solutions become not physical (i.e. the mode is not longer
guided) the difference explodes, so we can observe a particular
value of r, r* , so that for r<r*, the quantity |neff10D- neff10N|
being essentially negligible, while for r>r*, the difference
|neff10D- neff10N| increases. The r* value is what we expect
to be the boundary between a single mode waveguide and a
multimode one.
Fig. 3. Comparison between our FEM analysis results (circle),
Soref’s formula [1] and Pogossian et al. results [2]. Above the
curves we define the multi mode region, while below the
single mode region.
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