Thermal poling of thin silica glass films: Design rules for optical fibers and waveguides
Yves Quiquempois
*
Université des Sciences et Technologies de Lille, Laboratoire PhLAM, Bâtiment P5, 59655 Villeneuve d’Ascq Cedex, France
Nicolas Godbout and Suzanne Lacroix
Centre d’optique, photonique et lasers, Laboratoire des fibres optiques, Département de génie physique, École Polytechnique de
Montréal, C.P. 6079, Succ. Centre-ville, Montréal (Québec) H3C 3A7 Canada
Received 2 January 2005; published 16 June 2005
The charge migration models which account for the creation of a second-order nonlinear susceptibility in
poled silica glasses give significant results if the sample thickness is at least 1 order of magnitude larger than
the induced nonlinear layer thickness. We present herein a model valid for thin samples applicable to twin-hole
optical fibers or waveguides.
DOI: 10.1103/PhysRevA.71.063809 PACS numbers: 42.65.An, 42.70.Ce, 66.30.Dn, 72.20.Ht
It is now well established that the creation of a second-
order nonlinear susceptibility in silica glasses by thermal
poling is mainly due to charge migration occurring during
the process. The existing models predict that a cation deple-
tion region is induced near the anode. The thickness of this
region depends mainly on the initial concentration of cations
c
0
and on the applied voltage V
app
1–3. If we neglect charge
injection, the thickness of the cation depletion region is
given by the following equation:
x
a
=
2
ec
0
V
app
- V
t
, 1
where is the material permittivity and e is the elementary
charge. V
t
is a threshold voltage below which no
2
suscep-
tibility is induced 3. The expression of x
a
in Eq. 1 is
identical to that of x
a
in Eqs. 19 of Ref. 3. The superscript
is added to emphasize the fact that this expression is valid
when the total thickness of the sample is at least 1 order of
magnitude larger than x
a
. For example, in high purity silica
glasses, x
a
is typically larger than 20 m. The value given
by Eq. 1 is then a good approximation for larger than
about 200 m, i.e., bulk silica samples. In the opposite case
x
a
, the spatial electric field distribution is expected to
strongly depend on the thickness of the sample. This fact
raises an important question about the efficiency of poling
experiments in thin silica samples such as twin-hole optical
fibers or waveguides in which the distance between elec-
trodes could be smaller than 20 m 4. The blocking elec-
trode condition assumed in the present paper, i.e., the fact
that the charge injection phenomenon is neglected, is a valid
assumption in the case of short poling duration. Indeed, there
exists experimental observation 5 and theoretical demon-
stration 6 of the existence of an optimum poling duration
for maximizing the magnitude of the recorded electric field.
Beyond this optimum, the maximal value of the built-in elec-
tric field decreases due to charge injection phenomena 5.
For poling durations shorter than this optimum, the charge
injection can be neglected in first approximation.
The purpose of this paper is to give a model for the de-
termination of the
2
spatial distribution within thin silica
samples after they are thermally poled and to propose some
simple rules for the design of the optimal geometry of
waveguides and twin-hole optical fibers.
The electric field EF Ex inside the sample during pol-
ing is related to i the chemical composition of the glass
through the initial concentration of alkali ions c
0
and the
threshold voltage V
t
, ii the poling conditions through the
applied voltage V
app
and the poling temperature T, and iii
the geometric characteristics of the sample via its thickness
.
According to the charge migration model introduced in
Ref. 3, specifically Eqs. A36, A37, and A43 therein,
the steady-state EF distribution Exduring poling can be
expressed as
Ex =
2c
0
e
V
app
- V
t
+ E
min
2
-
c
0
e
x 0 x x
a
E
min
x
a
x ,
2
where E
min
is the value of Ex outside the anodic layer of
thickness x
a
. A sketch of the electric-field distribution during
poling external electric field applied is shown in Fig. 1. E
in Fig. 1 corresponds to the difference between the maximal
*Electronic address: yves.quiquempois@univ-lille1.fr
FIG. 1. General shape of the electric-field distribution during the
poling process while the external electric field is applied. The
sample thickness can be larger or smaller than x
a
.
PHYSICAL REVIEW A 71, 063809 2005
1050-2947/2005/716/0638094/$23.00 ©2005 The American Physical Society 063809-1