Directional photon transfer between two wires
L. Dobrzynski,
1
A. Akjouj,
1
B. Djafari-Rouhani,
1
J. O. Vasseur,
1
M. Bouazaoui,
2
J. P. Vilcot,
3
A. Beaurain,
3
and S. McMurtry
3
1
LDSMM, UMR 8024, UFR de Physique, Universite ´ de Lille1, 59655 Villeneuve d’Ascq Ce ´dex, France
2
PHLAM, UMR 8523, UFR de Physique, Universite ´ de Lille1, 59655 Villeneuve d’Ascq Ce ´dex, France
3
IEMN, UMR 8520, Universite ´ de Lille1, 59655 Villeneuve d’Ascq Ce ´dex, France
Received 21 January 2003; published 28 May 2003
The directional transfer of a single photon from one wire to another, leaving all other neighbor states
unaffected, is of great importance. We present a simple coupling structure that makes such transfer possible, for
any given photon wavelength and linewidth. We give closed-form expressions for the parameters necessary to
build such a structure. An illustration of our analytic study is given for the directional transmission of a
telecommunication signal between two lines.
DOI: 10.1103/PhysRevE.67.057603 PACS numbers: 42.79.Sz, 73.40.Gk, 78.67.Lt
The directional transfer of photons 1–3 between two
wires has been intensively investigated in the recent years.
Applications of such transfer processes are, in particular, im-
portant for wavelength multiplexing in communication de-
vices.
In order to allow a directional transfer of one photon with
a given energy between two monomode wires, one has to
build an appropriate coupling structure to permit all incom-
ing particles of different energies to continue to travel with-
out perturbation along the input wire and to transfer success-
fully one to the output wire in a given direction. The criteria
for such transfers were given on the basis of symmetry argu-
ments and were illustrated by applications to structures de-
signed in photonic materials by rod removal and perturbation
2. We proposed other structures 3 made of resonating
finite wires. All the above structures require very precise
definition of their parameters.
In this paper we propose a simpler structure and give
closed form expressions for all the parameters that are nec-
essary for the device fabrication. Another advantage of the
present structure is that it requires less tuning accuracy than
the earlier ones.
Let us consider the system presented in Fig. 1. The two
continua are the two infinite lines passing by, respectively,
points (1,2) and (3,4). The distance d
0
between points 1 and
2 is the same as between points 3 and 4. Four identical
monomode structures are branched between points (1,5),
(5,4), (2,6), and (6,3). These structures have one finite wire
of length d
2
branched in the middle of the lines of length 2 d
1
situated between the above-given points. The wave function
associated with the particles traveling in this structure is sup-
posed to vanish at the free end of the dangling wires. Such
structures enable transmission gaps to be opened in the de-
sired frequency range in the same manner as in similar stub
structures 3. Between points 5 and 6 is fixed a waveguide
of length 3 d
1
with two finite wires of length d
2
in its middle,
which acts as a resonant cavity with a localized mode in the
above-mentioned gap.
The reflection and transmission coefficients as a function
of wavelength associated with the particles traveling in the
monomode wires were found to be given by the following
expressions:
R =| z
1
+z
2
+z
3
+z
4
+1 |
2
, 1a
T
12
=| z
1
+z
2
-z
3
-z
4
|
2
, 1b
T
13
=| z
1
-z
2
+z
3
-z
4
|
2
, 1c
T
14
=| z
1
-z
2
-z
3
+z
4
|
2
, 1d
where
z
n
=
i
2
y
n
-i
-1
, n =1,2,3,4, 2
y
1
= y
2
-
2 B
1
4
2 A
1
+A
2
2
3 A
1
-
2 B
1
2
2 A
1
+A
2
-
B
1
2
2 A
1
+A
2
+B
1
,
3a
FIG. 1. The multiplexer design.
PHYSICAL REVIEW E 67, 057603 2003
1063-651X/2003/675/0576034/$20.00 ©2003 The American Physical Society 67 057603-1