Optics: measuring and testing – By light interference
Reexamination Certificate
2001-03-06
2003-07-01
Bruce, David V. (Department: 2882)
Optics: measuring and testing
By light interference
C359S199200
Reexamination Certificate
active
06587204
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to optical communication, and more specifically, it relates to methods and apparatuses for interleaving frequencies in optical communication systems.
2. Description of Related Art
In dense wavelength division multiplexing (DWDM) optical communication, various frequencies (wavelengths) of laser light are coupled into the same optical fiber. The information capacity is directly proportional to the number of channels in the fiber. Since the total usable wavelength range is limited (about a few tens of nanometers), the smaller the channel spacing, the more channels can fit into the same optical fiber, therefore enabling more communication capacity.
The minimum possible channel spacing is limited by the capability of the multiplexer (MUX) and the de-multiplexer (de-MUX). Currently, the standard channel spacing is 100 GHz (0.8 nm). The manufacturing costs increase dramatically when the channel spacing is less than 100 GHz. A cost-effective method is desirable for interleaving channels thereby enabling the use of higher bandwidth filters with lower channel spacing in an optical communication system. For instance, one can use 100 GHz filters with 50 GHz channel spacing for using a one-stage interleave. Furthermore, if a two-stage interleave is implemented, 100 GHz filters can be used in 25 GHz channel spacing communication system.
FIG. 1A
shows a conventional Michelson interferometer. The incident light
10
from the left-hand side of a 50—50 beam-splitter
12
is separated into two beams; 50% of the power is reflected from the beam splitter in beam
14
and the rest of light is transmitted in beam
16
. After those two beams are reflected from mirror
18
and mirror
19
, they are reflected by and transmitted through the beam-splitter again. The interference takes place at both the bottom and the left of the beam-splitter. The constructive interference takes place when the optical path length difference (OPD) of the two interference beams is an integer multiplication of wavelength. Since the total energy is conserved, the summation of optical power at the bottom arm and the left arm should be equal to the optical power delivered from the light source. In other words, when the constructive interference occurs at the bottom arm, the destructive interference should take place at the left arm and vise verse.
For the interferometer shown in
FIG. 1
, the amplitudes of the two interference beams are the same and their phase difference depends on the OPD. The various phase functions are listed in Table 1.
Table 1
Definition of Phase
&psgr;
RTM
:reflected by BS→reflected by mirror→transmit through BS.
&psgr;
TMR′
:transmitted through BS→reflected by mirrors→reflected by BS.
&psgr;
RMR
:reflected by BS→reflected by mirror→reflected by BS
&psgr;
TMT′
:transmitted by BS→reflected by mirror→transmit through BS
&psgr;
ST
:phase introduced by the BS for S-polarized light, transmitted beam with front side incidence
&psgr;
ST′
:phase introduced by the BS for S-polarized light, transmitted beam with rear side incidence
&psgr;
SR
:phase introduced by the BS for S-polarized light, reflected beam with front side incidence
&psgr;
SR′
:phase introduced by the BS for S-polarized light, reflected beam with rear side incidence
&psgr;
PT
:phase introduced by the BS for P-polarized light, transmitted beam with front side incidence
&psgr;
PT″
:phase introduced by the BS for P-polarized light, transmitted beam with rear side incidence
&psgr;
PR
:phase introduced by the BS for P-polarized light, refleced beam with front side incidence
&psgr;
PR′
:phase introduced by the BS for P-polarized light, reflected beam with rear side incidence
&psgr;
B
=&psgr;
TRM′
−&psgr;
RMT
(phase difference of the two interference beams in the bottom arm)
&psgr;
L
=&psgr;
TMT′
−&psgr;
RMR
(phase difference of the two interfereince beams in the left arm)
Power Definition
P
B
:optical power in the bottom arm
P
L
: optical power in the left arm
Assuming that the incident polarization is S-polarized, the two electric fields at the bottom arm can be expressed as follows.
E
→
TMR
′
=
s
^
2
exp
(
ⅈ
Ψ
TMR
′
)
E
→
RMT
=
s
^
2
exp
(
ⅈ
Ψ
RMT
)
The power at the bottom arm is as follows.
P
B
=
&LeftDoubleBracketingBar;
E
→
TMR
′
+
E
→
RMT
&RightDoubleBracketingBar;
2
=
&LeftDoubleBracketingBar;
s
^
cos
[
ψ
TMR
′
-
ψ
RMT
2
]
&RightDoubleBracketingBar;
2
=
cos
2
(
ψ
2
)
With
Equation
(
1
)
ψ
TMR
′
=
2
π
(
v
v
1
)
+
ψ
ST
+
ψ
SR
′
ψ
RMT
=
2
π
(
v
v
2
)
+
ψ
SR
+
ψ
ST
ψ
B
=
ψ
B
(
s
)
≡
ψ
TMR
′
-
ψ
RMT
=
2
π
(
v
v
0
)
+
(
ψ
SR
′
-
ψ
SR
)
where
&IndentingNewLine;
v
1
=
C
2
L
1
;
v
2
=
C
2
L
2
;
v
0
=
C
2
(
L
1
-
L
2
)
Equation
(
2.1
)
In Equation (1), the total power on the bottom arm is dependant on the phase difference between the two interference beams.
When the incident polarization is P-polarized,
ψ
B
=
ψ
B
(
p
)
≡
ψ
TMR
′
-
ψ
RMT
=
2
π
(
v
v
0
)
+
(
ψ
PR
′
-
ψ
PR
)
Equation
(
2.2
)
The phase difference of the two interference beams at the bottom arm for S-polarized light, &psgr;
(s)
B
, and that of P-polarized light, &psgr;
(p)
B
, will be the same when &PSgr;
SR
−&PSgr;
SR′
=&PSgr;
PR
−&PSgr;
PR′
. In the following analysis at this section, it is assumed that the coating of beam splitter has been made such that &PSgr;
SR
−&PSgr;
SR′
=&PSgr;
PR
−&PSgr;
PR′
=0. Under such condition, &psgr;
B
=&psgr;
(s)
B=&psgr;
(p)
B
. Notice that in the derivation of equations (2.1) and (2.2), the phase introduced from the two reflection mirrors is neglected. Those phases do not have polarization dependence due to the fact that the incident angles at those surfaces are close to normal.
FIG. 2
shows the phase difference &psgr;
B
and &psgr;
L
. Both of them are a linear function of frequency with slope 2 Πv
−1
o
. As a result of energy conservation, there is a phase offset &pgr; between them.
FIG. 3
shows the corresponding optical power at the bottom (upper curve at 0 normalized frequency) and left arm (bottom curve at 0 normalized frequency). In these plots, the horizontal axis is normalized by frequency v
o
. When the normalized frequency is an integer, all the light goes to the bottom; In contrast, as that is a half integer, the light goes to the left In other world, the light is interleaved in the frequency domain with half of the channels (integer frequency) to the bottom arm and the other half to the left arm.
The Michelson interferometer shows the fundamental requirement of interleaving. However, it is not practical to apply such an interferometer to a real interleave device since it is too sensitive to the central frequency and the line width of light source. Referring to
FIG. 3
, as the frequency is slightly off from the integer, part of the optical power will leak from the bottom arm towards the left arm, causing cross talk between channels. In other words, in order to make this device work, the laser line width should be zero and its central frequencies have to be perfectly locked over all the operation condition. Such frequency locking is very hard to achieve in the real world.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide an optical filtering method to separate/merge the odd and even channels in an optical comm
Bruce David V.
Optoplex Corporation
Wooldridge John P.
LandOfFree
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