Title: Wavelength dispersion compensating filter
Abstract: A 2-input, 2-output optical circuit is constructed by serially connecting two or more Mach-Zehnder interferometers possessing a structure in which two waveguides are embraced by two couplers. One output and one input of the two 2-input, 2-output optical circuit are connected by an optical propagation path to thereby construct a loop circuit. The waveguides of the Mach-Zehnder interferometers as well as the loop circuit are each provided with an optical path-length adjustment portion, thereby constructing a wavelength dispersion compensating filter.
Patent Number: 6,847,759 Issued on 01/25/2005 to Shibata
| Inventors:
|
Shibata; Kohei (Kawasaki, JP)
|
| Assignee:
|
Fujitsu Limited (Kawasaki, JP)
|
| Appl. No.:
|
375124 |
| Filed:
|
February 28, 2003 |
Foreign Application Priority Data
| Apr 24, 2002[JP] | 2002-121659 |
| Current U.S. Class: |
385/27; 385/24; 385/32 |
| Intern'l Class: |
G02B 006/26 |
| Field of Search: |
385/14,24,27,50,30-32,39-45
|
References Cited [Referenced By]
U.S. Patent Documents
| 4592043 | May., 1986 | Williams.
| |
| 6289151 | Sep., 2001 | Kazarinov et al.
| |
| 6389203 | May., 2002 | Jordan et al. | 385/50.
|
| 6766083 | Jul., 2004 | Bona et al. | 385/40.
|
| 2003/0086638 | May., 2003 | Frolov et al. | 385/17.
|
| 2003/0235367 | Dec., 2003 | Yamazaki | 385/39.
|
| Foreign Patent Documents |
| 57-66403 | Apr., 1982 | JP.
| |
| 57-089702 | Jun., 1982 | JP.
| |
| 1-306801 | Dec., 1989 | JP.
| |
| 6-276160 | Sep., 1994 | JP.
| |
| 2000-151513 | May., 2000 | JP.
| |
| 3112193 | Sep., 2000 | JP.
| |
| 2001-305497 | Oct., 2001 | JP.
| |
| 2001-318249 | Nov., 2001 | JP.
| |
Primary Examiner: Kim; Ellen E.
Assistant Examiner: Wood; Kevin S.
Attorney, Agent or Firm: Staas & Halsey LLP
Claims
What is claimed is:
1. A wavelength dispersion compensating filter having a 2-input, 2-output
optical circuit;
said 2-input, 2-output optical circuit being constructed by serially
connecting a plurality of Mach-Zehnder interferometers possessing a
structure in which two waveguides are embraced by two couplers;
one output and one input of said two 2-input, 2-output optical circuit
being connected by an optical propagation path to thereby construct a loop
circuit; and
the waveguides of the Mach-Zehnder interferometers as well as the loop
circuit each being provided with an optical path-length adjustment
portion.
2. The filter according to claim 1, wherein said optical path-length
adjustment portion has means for adjusting optical path length by an
electro-optic effect.
3. The filter according to claim 1, wherein said optical path-length
adjustment portion has means for adjusting optical path length by a
thermo-optic effect.
4. A wavelength dispersion compensating filter comprising two Mach-Zehnder
interferometers serially connected.
5. The filter according to claim 1, wherein a coupler having comparatively
little wavelength dependence is used as the couplers that construct the
Mach-Zehnder interferometers.
6. The filter according to claim 1, wherein the optical propagation paths
of the other input and output not used as the loop of said 2-input,
2-output optical circuit are made to intersect each other.
7. The filter according to claim 1, wherein the waveguides are made to
intersect each other in the vicinity of substantially the center of each
Mach-Zehnder interferometer in such a manner that built-in path length
differences between the two optical waveguides constructing the branches
of each MZI portion will be approximately equal.
8. The filter according to claim 1, wherein two or more of said dispersion
compensating filters are serially connected.
9. The filter according to claim 1, wherein the dispersion compensating
filters are created using a process for forming an optical waveguide layer
of SiO.sub.2 on a silicon substrate.
10. The filter according to claim 4, wherein a couple having comparatively
little wavelength dependence is used as the couplers that construct the
Mach-Zehnder interferometers.
11. The filter according to claim 4, wherein the optical propagation paths
of the other input and output not used as the loop of said 2-input,
2-output optical circuit are made to intersect each other.
12. The filter according to claim 4, wherein the way guides are made to
intersect each other in the vicinity of substantially the center of each
Mach-Zehnder interferometer in such a manner that built-in path length
differences between the two optical waveguides constructing the branches
of each MZI portion will be approximately equal.
13. The filter according to claim 4, wherein two or more of said dispersion
compensating filters are serially connected.
14. The filter according to claim 4, wherein the dispersion compensating
filters are created using a process for forming an optical waveguide layer
of SiO.sub.2 on a silicon substrate.
Description
BACKGROUND OF THE INVENTION
This invention relates to a wavelength dispersion compensating filter and,
more particularly, to a wavelength dispersion compensating filter which
compensates for wavelength dispersion produced at the time of a signal
pulse transmission in optical communication using wavelength division
multiplexing (referred to as "WDM" below).
In the transmission of optical signal pulses using optical fiber,
transmission rate in the fiber differs depending upon the wavelength of
light. As a consequence, the waveform of the signal pulses becomes less
steep as transmission distance increases. This phenomenon, referred to
as-wavelength dispersion, degrades the reception level to a great degree.
For example, with an SMF (Single-Mode Fiber), wavelength dispersion on the
order of 15 to 16 ps/nm/km is produced in the vicinity of a wavelength of
1.55 .mu.m often used in communication of optical pulses. Wavelength
dispersion compensation is for subjecting wavelength dispersion, which has
been produced in an optical fiber, to an equivalent amount of wavelength
dispersion in reverse.
What is used most often in dispersion compensation at the present time is
dispersion compensating fiber (referred to as "DCF" below). This fiber
produces reverse dispersion (structural dispersion), by a special
refractive index distribution, with respect to material dispersion
possessed by the fiber material, and is designed so as to exhibit
dispersion which, in total, is the reverse of that of ordinary SMF. It is
possible to achieve dispersion compensation that is five to ten times that
obtained with SMF of an equivalent length. Such DCF is connected to SMF in
a repeater office to make the dispersion zero overall.
Dispersion compensation using DCF involves two major problems in terms of
transmission system architecture. One is that the distance between
repeaters where DCF is inserted differs from system to system. This means
that it is necessary to provide a dispersion compensating module having a
specifically designed DCF length for each and every repeater node. The
second problem arises from the fact that the wavelength dependence of the
dispersion characteristic, which is referred to as "dispersion slope", is
not the same for DCF and SMF. Wavelength dispersion that could not be
subjected to dispersion compensation completely (such dispersion shall be
referred to as "residual dispersion" below) occurs at both ends of a
wavelength band used in WDM transmission, e.g., a wavelength band referred
to as the "C band" in which the wavelength of light is in the vicinity of
1530 to 1560 nm. This residual dispersion accumulates as transmission
distance increases and, as a result, it is necessary to compensate for
this residual dispersion channel by channel. For example, in the example
shown in FIG. 16, if a signal is transmitted through 10 km of SMF and
dispersion compensation is applied to the center wavelength (1545 nm)
using DCF having a dispersion slope of 0.2 ps/km/nm.sup.2, residual
dispersions of about 20 ps/nm and about -30 ps/nm occur in 1.sup.st and
40.sup.th channels, respectively, having a channel wavelength spacing of
100 GHz in the C band. As a consequence of these two problems, dispersion
compensating modules of a very large number of types must be prepared in
order to construct a single system, and designing the system becomes very
complicated. In order to solve these problems, there is compelling need
for implementation of a wavelength dispersion compensator in which the
amount of compensation is capable of being varied over a range of negative
to positive values.
One example that can be mentioned from the standpoint of good productivity
is a variable dispersion compensator that employs PLC (Planar Lightwave
Circuit) technology.
Filters used in wavelength dispersion compensation are classified broadly
into two types, namely IIR (Infinite Impulse Response) and FIR (Finite
Impulse Response). Both achieve variable compensation by changing the
optical path length of the portion of a waveguide that decides the amount
of compensation, using an EO (electro-optic) effect that produces a change
in dielectric constant within the waveguide, i.e., a change in effective
refractive index), by applying an electric field from outside the
waveguide, or a TO (thermo-optic) effect in which the refractive index of
the waveguide is changed by temperature.
The FIR-type filter controls frequency response by feed-forward. A typical
arrangement that can be mentioned is composed of serially connected
multiple MZIs (Mach-Zehnder interferometers) proposed by Takiguchi et al.
(see Variable Group-Delay Dispersion Equalizer, IEEE J. of Quant. Elect.),
illustrated in FIG. 17. As shown in FIG. 17, MZIs 1 each have a structure
in which two waveguides 1a, 1a are embraced by two couplers 1b, 1b. A
heater 1c for adjustment of the optical path length is provided on the
upper side of the central portion of the waveguide on the outer side of
each MZI, and electrodes 1d for applying voltage are formed on both sides
of the headers 1c. The FIR-type wavelength dispersion compensating filter
is obtained by building up an SiO.sub.2 clad 3 on an SiO.sub.2 substrate 2
and building up an SiO.sub.2 core layer 4 on the clad 3. Next, by
performing patterning, the two waveguides 1a, 1a are formed by the
SiO.sub.2 core 4, as depicted in FIG. 17, and the couplers 1b are formed
at suitable locations. Thereafter, a further clad layer is built up,
though this is not shown, the heater 1c is formed on this clad layer and
then the electrode 1d is formed on this heater to complete the device.
This FIR-type wavelength dispersion compensating filter has a highly stable
frequency characteristic. However, a large number of circuit elements (the
number of MZI stages) is needed to produce a steep frequency response.
Since this necessitates a large chip area, this filter is not very
desirable in terms of productivity.
The IIR-type filter, which is referred to also as a "rational filter", has
one or more feedback loops between the filter input and output. With the
IIR-type filter, the frequency (wavelength) characteristic has a peak
ascribable to the feedback loops, and it is possible to obtain a steep
frequency response with a small number of circuit elements (couplers,
etc.) by suitably engineering the position of the peak, as is known in
electrical circuit theory. The most simplest of the IIR-type filters is a
ring resonator. Though a ring resonator exhibits a very steep frequency
response, the FSR (Free Spectral Range, which corresponds to the spacing
of resonance peaks) thereof is proportional to 1/(ring length). As a
consequence, accuracy of the length of waveguides having little difference
in refractive index are limited by the minimum bending radius and there
are cases where the desired FSR cannot be obtained.
An all-pass optical filter (U.S. Pat. No. 6,289,151 B1, referred to as a
Madsen-type or prior-art filter below) according to R. F. Kazarinov and C.
K. Madsen, et al. has been proposed as a filter to solve this problem. As
shown in FIG. 18, this filter has a structure in which one input and one
output of an MZI 5 are connected by a loop. The MZI 5 has a structure in
which waveguides 5a, 5b are embraced by two couplers 5c, 5d, heaters 5e,
5f for adjusting amount of dispersion compensation are provided on the
upper side of the central portion of the waveguides 5a, 5b, and electrodes
(not shown) for applying voltage are formed on both sides of each of the
heaters. A heater 6b for adjusting center wavelength is provided on the
upper side of the central portion of a waveguide 6a of a loop portion 6
that forms the loop. Reference numeral 7 denotes a silicon (Si) substrate
and 8 an SiO.sub.2 clad. This all-pass optical filter is formed in a
manner similar to the filter shown in FIG. 17.
In accordance with the all-pass optical filter shown in FIG. 18, the amount
of change in phase at the design wavelength and the FSR can be designed
independently using two parameters, namely 1 loop length and 2 the
difference in optical path length between the two waveguides 5a, 5b in the
MZI. As a result, it is possible to realize a compact dispersion
compensator that uses an IIR filter at a design wavelength.
As mentioned above, dispersion compensation requires compensation even of
residual dispersion after compensation by DCF is applied. Accordingly, the
ability to perform positive compensation and negative compensation,
inclusive of an amount of dispersion compensation of zero, is sought. The
prior-art Madsen-type dispersion compensating filter cannot achieve an
amount of dispersion compensation of zero when manufacturability is taken
into account, and a problem which arises is that many products in which
the range of dispersion compensation is limited are produced.
The problems of the Madsen-type dispersion compensating filter will now be
described in detail through the following procedure: 1 The transfer
function of the Madsen-type dispersion compensating filter will be given,
the conditions that give dispersion compensation quantity=0 will be
indicated and the limitation imposed upon the design parameters by the
conditions for dispersion compensation quantity=0 will be indicated. 2 The
fact that many dispersion compensators which are limited in terms of
compensation range occur will be discussed, in which it will be pointed
out that it is difficult to reconcile both the conditions that give
dispersion compensation quantity=0 and design parameters exhibiting
variations in manufacture when the filter is actually manufactured, this
being ascribable to the range of fluctuation when manufacturing variations
in each of the design parameters are taken into account.
Design parameters of Madsen-type dispersion compensating filter
The design parameters and operation (see Table 1) of a prior-art
Madsen-type dispersion compensating filter (see FIG. 18) will be described
in simple terms. As shown in Table 1 below, the design parameters are loop
optical path length .DELTA.L.sub.r n(.lambda.), MZI optical path length
difference .DELTA.L.sub.m n(.lambda.) and MZI coupler splitting ratios
.theta..sub.1, .theta..sub.2.
TABLE 1
RELATIONSHIP BETWEEN PARAMETERS OF MADSEN-TYPE
FILTERS AND TRANSMISSION CHARACTERISTICS
RELATED DESCRIPTION
DESIGN CHARAC- OF
PARAMETER TERISTICS TENDENCY
1 OPTICAL FSR; CENTER FSR 0.8 nm
PATH FREQUENCY SPACING .fwdarw.
LENGTH OF ABOUT 2-mm
LOOP SPACING; CONTROL
.DELTA. L.sub.r n(.lambda.) OF CENTER
WAVELENGTH WITH
LINEAR CHANGE OF
.lambda. ORDER
2 MZI OPTICAL DISPERSION PHASE COMPENSATION
PATH COMPENSATION QUANTITY MAX FOR
LENGTH QUANTITY; LENGTH OF SEVERAL-
DIFFERENCE BANDWIDTH MICRON ORDER;
.DELTA. L.sub.m n(.lambda.) (TRADEOFF) COMPENSATION
QUANTITY IS
REDUCED IN
ACCORDANCE WITH
DEVIATION FROM THIS
LENGTH
3 MZI STRENGTH OF VARIATION IN PHASE
COUPLER PHASE IS REDUCED IF
SPLITTING CHANGE; COUPLING IS WEAK
RATIOS SETTING OF
.theta..sub.1, .theta..sub.2 DISPERSION
COMPENSATION
QUANTITY =
0 POINT
1 The FSR is set by the loop built-in optical path length (loop length
prior to adjustment) .DELTA.L.sub.r n(.lambda.), where .DELTA.L.sub.r
represents the loop optical path length and n(.lambda.) the effective
refractive index of the waveguide. The heater 6b is formed in the loop 6
and adjustment of the optical path length on the order of .lambda. (1.55
.mu.m) is performed by the TO effect, thereby controlling the center
wavelength position within the FSR.
2 Path length difference .DELTA.L.sub.m n(.lambda.) between the waveguides
5a and 5b of the MZI portion is related to the amount of dispersion
compensation, where .DELTA.L.sub.m represents the path length difference
and n(.lambda.) the effective refractive index of the waveguide. The
amount of dispersion compensation at non-heating of the heaters 5e, 5f
provided on the branches 5a, 5b of the MZI portion is decided by the
built-in path length difference (path length difference prior to
adjustment) .DELTA.L.sub.m n(.lambda.), and the amount of dispersion
compensation is controlled by controlling the heating of the heaters 5e,
5f. In a case where the amount of compensation applied is minimum when the
heaters are not producing heat, the built-in path length difference is
assumed to be zero.
3 (The coupling strengths (rotation angles .theta..sub.1, .theta..sub.2) of
the two couplers 5c and 5d exhibit a fixed relationship in order to
implement dispersion compensation quantity=0. In a case where the
dispersion compensation quantity is adjusted by changing .DELTA.L.sub.m
n(.lambda.) by the TO effect, etc., it will suffice to select the rotation
angles .theta..sub.1, .theta..sub.2 so as to satisfy Equation (11) (e.g.,
rotation angle rotation angles .theta..sub.1 =.theta..sub.2 =.pi./4, etc.)
described below.
Transfer function of Madsen-type dispersion compensating filter
The transfer function of a Madsen-type dispersion compensating filter is
given as follows:
First, a transfer matrix m(.lambda.) of an MZI (4-terminal circuit) is
expressed as follows using the path difference .DELTA.L.sub.m, coupler
rotation angles (couplings) .theta..sub.1 .theta..sub.2, effective
refractive index n(.lambda.) of the waveguide and input wavelength
.lambda.:
##EQU1##
Further, a phase shift h(.lambda.) produced by the loop-back portion 6 is
expressed as follows using the optical path length .DELTA.Lr:
h(.lambda.)=exp[-j2.pi..DELTA.Lrn(.lambda.)/.lambda.] (2)
A transfer function H(.lambda.) of the Madsen-type dispersion compensating
filter is expressed by the following equation using m(.lambda.) and
h(.lambda.):
##EQU2##
where m.sub.11 * represents the complex conjugate of m.sub.11. Group delay
D(.lambda.) is obtained by differentiating the phase part of the transfer
function of Equation (3) by .omega.(=2.pi.c/.lambda., where c represents
the velocity of light), and wavelength-dispersion DS(.lambda.) is obtained
by differentiating the group delay D(.lambda.) by wavelength .lambda..
That is, if we let the phase part of the transfer function be represented
by argH(.lambda.), then we have
D(.lambda.)=-(.lambda..sup.2 /2.pi.c)(d/d.lambda.)[argH(.lambda.)] (4)
DS(.lambda.)=(d/d.lambda.)D(.lambda.) (5)
Here argH(.lambda.) is expressed as follows:
##EQU3##
where the following holds:
.alpha.=cos [.pi..DELTA.L.sub.m n(.lambda.)/.lambda.] cos(.theta..sub.1
+.theta..sub.2) (7)
.beta.=sin [.pi..DELTA.L.sub.m n(.lambda.)/.lambda.] cos(.theta..sub.1
-.theta..sub.2) (8)
Conditions that give dispersion compensation quantity=0
Dispersion compensation quantity=0 means that DS(.lambda.)=0 holds in
Equation (5) and that D(.lambda.) in Equation (4) is a constant. This
signifies that it is required that argH(.lambda.) be expressed by the
following function:
argH(.lambda.)=C.sub.1 /.lambda.+C.sub.2 (C.sub.1, C.sub.2 are constants)
(9)
or
argH(.lambda.)=C.sub.3 (C.sub.3 is a constant) (10)
by the design parameters.
A condition that will satisfy Equation (9) is (.alpha.,.beta.)=(0,0), in
which we will have
argH(.lambda.)=-2.DELTA.L.sub.r n(.lambda.)/.lambda.
Further, examples of parameters are the following Equations (11), (12):
.DELTA.L.sub.m =0 and .theta..sub.1 +.theta..sub.2 =.pi.(2k+1)/2(k=0,1,2, .
. . ) (11)
n(.lambda.)=C.sub.4.lambda.+C.sub.5 (C.sub.4, C.sub.5 are constants) (12)
or the following equations (13), (14):
.theta..sub.2 =.pi./2 and .theta..sub.1 =.theta..sub.2
+.pi.(2m-1)/2(m=1,2,3, . . . ) (13)
n(.lambda.)=C.sub.4.lambda.+C.sub.5 (C.sub.4, C.sub.5 are constants,
.DELTA.L.sub.m.noteq.0) (14)
In case of a quartz-type waveguide, it is considered that Equations (13)
and (14) are approximations that will hold true satisfactorily in the C
band (in the vicinity of wavelengths 1530 to 1560 nm). This condition
means that signal light passes through the loop one time only.
On the other hand, a condition that will satisfy Equation (10) is
(.alpha.,.beta.)=(.+-.1,0), and the following Equation (15) is an example
of a parameter:
.DELTA.L.sub.m =0 and .theta..sub.1 +.theta..sub.2 =m.pi.(m=0,1,2,3 . . . )
(15)
This condition means that signal light is transmitted without entering the
loop.
Thus, in the prior-art example, it will be understood that the
relationships of Equations (11) to (15) are required for the two coupler
splitting ratios (rotation angles .theta..sub.1, .theta..sub.2) in order
to obtain dispersion compensation quantity=0.
Conditions that give dispersion compensation quantity=0, and manufacturing
variations
When manufacturability (the product of a variation in refractive index and
a variation in core machining) is taken into account, it is required that
a deviation of, e.g., .+-.10% from what is sought be allowed for the
coupler splitting ratio. In other words, owing to a variation in
manufacture, coupler splitting ratio deviates from the design value by a
maximum of .+-.10%. If the coupler splitting ratio deviates from this
design value by more than a predetermined percentage, it will no longer be
possible to obtain dispersion compensation quantity=0 even if the MZI
optical-path difference .DELTA.L.sub.m n(.lambda.) and feedback-loop path
length .DELTA.L.sub.r n(.lambda.), which are factors adjustable by the TO
effect, are varied. In other words, it is not possible to apply a range
extending from dispersion compensation quantity=0 to a minimum
compensation quantity (a minimum compensation quantity that corresponds to
deviation from the design condition of the two coupler branches). As a
result, the aforementioned problem arises, namely the occurrence of a
large number of products that cannot be compensated completely for
residual dispersion extending from positive to negative values.
FIG. 19 illustrates as an example of a group delay D(.lambda.) vs.
wavelength (.lambda.) characteristic, namely a wavelength dispersion
compensation characteristic, for a case where the rotation angle
.theta..sub.2 of the second coupler has deviated from the design value
(.theta..sub.1 =.theta..sub.2 =.pi./4) by 5%. The slope of this
characteristic is the wavelength dispersion DS(.lambda.). This is the
dispersion compensation quantity. In FIG. 19, the optical path length
difference .DELTA.L.sub.m n(.lambda.) (which is an adjustable parameter)
between the MZI branches is varied from the positive state, namely a state
in which the waveguide 5b on the outer side is long, to the negative
state, namely a state in which the waveguide 5a on the inner side is long.
However, it will be understood that even if the optical path length
difference .DELTA.L.sub.m n(.lambda.) is varied from 150 nm to -150 nm, a
range in which dispersion compensation quantity=0 (zero slope) holds is
not obtained anywhere in the necessary band (10 Gbps: 0.16 nm).
Further, the center wavelength (peak wavelength) also varies owing to the
effect of the deviation in the rotation angle .theta..sub.2 (there is no
change in the case of a value that is in accordance with the design
value), as indicated by FIG. 19. In order to compensate for this change,
it is necessary to adjust the optical path length .theta.L.sub.r
n(.lambda.) of the loop portion.
SUMMARY OF THE INVENTION
Accordingly, an object of the present invention is to so arrange that even
if the coupler splitting ratio (coupler rotation angle) of the MZI portion
deviates from the design value from one device to the next owing to
manufacturing variations or the like, dispersion compensation quantity=0
will be obtained by adjusting the value of optical path length difference
.DELTA.L.sub.m n(.lambda.) using the TO effect or EO effect.
Another object of the present invention is to make positive compensation
and negative compensation, inclusive of dispersion compensation
quantity=0, possible, thereby making it possible to compensate for
residual dispersion after dispersion compensation.
According to the present invention, the foregoing objects are obtained by
providing a wavelength dispersion compensating filter having a 2-input,
2-output optical circuit, in which the 2-input, 2-output optical circuit
is constructed by serially connecting two or more Mach-Zehnder
interferometers possessing a structure in which two waveguides are
embraced by two couplers, one output and one input of the two 2-input,
2-output optical circuit are connected by an optical propagation path to
thereby construct a loop circuit, and the waveguides of the Mach-Zehnder
interferometers as well as the loop circuit are each provided with a
optical path-length adjustment portion. The optical path-length adjustment
portion adjusts optical path length by the electro-optic effect or
thermo-optic effect.
If a wavelength dispersion compensating filter is thus constructed,
dispersion compensation quantity=0 can be obtained by adjusting the value
of optical path length difference .DELTA.L.sub.m n(.lambda.) using the TO
effect, etc., even if the coupler splitting ratio (coupler rotation angle)
of the MZI portion deviates from the design value from one device to the
next owing to manufacturing variations or the like. As a result,
wavelength dispersion compensation can be performed to deal even with
residual deviation irrespective of individual difference, device
manufacturability (yield) can be increased by a wide margin and the cost
of the dispersion compensating device can be reduced. In addition, the
size of the dispersion compensating filter can be reduced by serially
connecting two Mach-Zehnder interferometers.
A coupler having little wavelength dependence is used as the couplers that
construct the Mach-Zehnder interferometers. If this arrangement is
adopted, it is possible to endow each wavelength-division-multiplexed
optical signal with a splitting strength that is as designed and it
becomes possible to reduce variations in the amount of dispersion
compensation.
Further, if it is so arranged that the optical propagation paths of the
other input and output not used as the loop of the 2-input, 2-output
optical circuit are made to intersect each other, then it will be
unnecessary to bend the input and output propagation paths even if loop
length .DELTA.L.sub.r is shorter than a prescribed length. This means that
radiation loss is not increased at bent portions.
Further, the waveguides are made to intersect each other in the vicinity of
substantially the center of each Mach-Zehnder interferometer in such a
manner that the built-in path-length differences between the two optical
waveguides constructing the branches of each MZI portion will be
approximately equal. If this is done, one branch of the MZI portion will
extend from the inner side to the outer side, the other branch will extend
from the outer side to the inner side, the lengths of the two branches can
be made uniform and a path-length difference on the order to 0 to .lambda.
(1.55 .mu.m) can be achieved.
Further, if two or more of the above-described dispersion compensating
filters are connected serially, the dispersion compensation quantity per
filter can be reduced to broaden the pass band. As a result, the desired
dispersion compensation quantity can be generated overall and the band can
be broadened.
Other features and advantages of the present invention will be apparent
from the following description taken in conjunction with the accompanying
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram useful in describing the principles of a wavelength
dispersion compensating filter of the invention having a 2-input, 2-output
optical circuit;
FIG. 2 is a modification of FIG. 1 and is for illustrating the compensation
characteristic (group delay characteristic) of the present invention;
FIG. 3 is a group delay characteristic diagram of a wavelength dispersion
compensating filter according to the present invention;
FIG. 4 is a diagram showing the topology of a dispersion compensating
filter according to a first embodiment of the present invention;
FIG. 5 illustrates an example of the structure of means for adjusting
optical path-length difference in an SiO.sub.2 -type waveguide;
FIG. 6 illustrates an example of the structure of means for adjusting
optical path-length difference in an LiNbO.sub.3 -type waveguide;
FIG. 7 illustrates an example of the structure of an MMI-type coupler;
FIG. 8 illustrates an example of the structure of a WINC-type coupler;
FIG. 9 is a wavelength vs. transmission splitting intensity characteristic
diagram illustrating the wavelength dependence of the splitting
intensities of an MMI-type coupler, WINC-type coupler and directional
coupling-type coupler;
FIG. 10 is a diagram showing the topology of a dispersion compensating
filter according to a second embodiment of the present invention;
FIG. 11 is a diagram showing the topology of a dispersion compensating
filter according to a third embodiment of the present invention;
FIG. 12 is a diagram showing the topology of a dispersion compensating
filter according to a fourth embodiment;
FIG. 13 is a diagram showing the topology of a dispersion compensating
filter according to a fifth embodiment;
FIG. 14 illustrates a dispersion compensation characteristic in the case of
the 3-stage arrangement of FIG. 13;
FIG. 15 illustrates an example of the steps of a manufacturing process for
achieving the structure of a dispersion compensator according to the
present invention;
FIG. 16 is a diagram useful in describing residual dispersion;
FIG. 17 is a diagram showing a prior-art dispersion compensating filter
composed of serially connected multiple MZIs;
FIG. 18 is a Madsen-type prior-art dispersion compensating filter; and
FIG. 19 shows a group delay characteristic according to an example of the
prior art.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
(A) Principles of the Present Invention
Here it will be assumed that a wavelength dispersion compensating filter,
which is a 2-input, 2-output optical circuit, is obtained by serially
connecting two or more MZIs. As a result, even if the rotation angle of
the coupler in the MZI portion deviates from the design value from one
device to the next owing to manufacturing variations or the like,
dispersion compensation quantity=0 will be obtained by adjusting the value
of optical path length difference .DELTA.L.sub.mi n(.lambda.) (i=1, 2)
between the branches of the MZI using the TO effect. This makes it
possible to solve the problem encountered in the prior art. The fact that
the above problem is solved will be described taking as an example a case
where a 2-input, 2-output circuit (wavelength dispersion compensating
filter), which is the simplest arrangement, is constructed by connecting
two MZIs in series.
FIG. 1 is a diagram useful in describing the principles of the inventive
wavelength dispersion compensating filter having a 2-input, 2-output
optical circuit. MZIs 11, 12 each having a structure in which two
waveguides 11a, 11b; 12a, 12b are embraced by respective ones of two
couplers CPL1, CPL2; CPL2, CPL3 are serially connected to thereby
construct a 2-input, 2-output optical circuit. One output and one input of
the 2-input, 2-output optical circuit are connected by an optical
propagation path to construct a loop circuit 13, and the waveguides 11a,
11b; 12a, 12b of the MZIs 11, 12 as well as the loop circuit 13 are formed
to have heaters 14a to 14e, respectively, as path length adjustment
portions.
(a) Design Parameters and Driving Method According
to the invention (2-stage MZI structure)
The design parameters and operation (see Table 2) of the inventive
wavelength dispersion compensating filter having the two MZIs 11, 12 will
now be described in brief.
TABLE 2
RELATIONSHIP BETWEEN PARAMETERS OF PRESENT
INVENTION (2-MZI STRUCTURE) AND TRANSMISSION
CHARACTERISTICS
RELATED DESCRIPTION
DESIGN CHARACTER- OF
PARAMETER ISTICS TENDENCY
1 OPTICAL FSR; CENTER FSR 0.8 nm SPACING .fwdarw.
PATH FREQUENCY ABOUT 2-mm SPACING;
LENGTH OF CONTROL OF CENTER
LOOP WAVELENGTH WITH
.DELTA. L.sub.r n(.lambda.) LINEAR CHANGE OF
.lambda. ORDER
2 MZI OPTICAL DISPERSION COMPENSATION
PATH COMPENSATION QUANTITY IS
LENGTH QUANTITY; ADJUSTED BY
DIFFERENCE BANDWIDTH PERFORMING DRIVE
.DELTA. .sub.m1 (.lambda.) (TRADEOFF) SUCH THAT
.DELTA. .sub.m1 (.lambda.) .DELTA. L.sub.m2
n(.lambda.) = -.DELTA.
L.sub.m1 n(.lambda.) HOLDS AT
.theta..sub.1 = .theta..sub.3 =
.pi./4
3 FIRST AND STRENGTH OF VARIATION IN PHASE
THIRD PHASE CHANGE IS REDUCED IF
COUPLER COUPLING IS
SPLITTING WEAK
RATIOS
.theta..sub.1, .theta..sub.3
4 SECOND COMPENSATION COMPENSATION
COUPLER QUANTITY QUANTITY
SPLITTING (.theta..sub.1 = .theta..sub.3 = .pi./4, WHEN HEATER IS
NOT
RATIO .DELTA. L.sub.m1 = DRIVEN IS INCREASED
.theta..sub.2 .DELTA. L.sub.m2 = 0 AS COUPLING IS
WHEN MZI STRENGTHENED
HEATER IS
NOT DRIVEN
1 The FSR and control of center wavelength are similar to those of the
prior art. The FSR is set by the loop built-in optical path length (loop
length prior to adjustment) .DELTA.L.sub.r n(.lambda.), the heater 14e is
formed in the loop portion and adjustment of the optical path length on
the .lambda. order is performed by the TO effect, etc., thereby
controlling the center wavelength position within the FSR.
2 Path length difference .DELTA.L.sub.mi n(.lambda.) (i=1, 2) between the
two MZI portions 11 and 12 is related to the amount of dispersion
compensation. At rotation angles .theta..sub.1 =.theta..sub.3 =.pi./4 of
the first and third couplers CPL1, CPL3, drive is performed in such a
manner that .DELTA.L.sub.m2 n(.lambda.)=-.DELTA.L.sub.m1 n(.lambda.) will
hold, thereby controlling the amount of dispersion compensation with the
center wavelength being held fixed. It should be noted that the center
wavelength shifts when drive is performed asymmetrically. If
.theta..sub.1, .theta..sub.3 have deviated from their design values, the
values of .DELTA.L.sub.m1 n(.lambda.), .DELTA.L.sub.m2 n(.lambda.)
obtained by Equation 25, etc., described below, are applied beforehand as
offsets and the differences of the offsets are driven symmetrically.
3 The amount of dispersion compensation at non-heating of the heaters 14a,
14b, 14c, 14d in the MZI portions 11, 12 is substantially decided by the
rotation angle (coupling strength) .theta..sub.2 of the second coupler
CPL2.
4 In a case where .theta..sub.1 =.theta..sub.3 =.pi./4 holds, the amount of
dispersion compensation increases with an increase in coupling strength
starting from a coupling strength of zero and an amount of dispersion
compensation of zero. The amount of dispersion compensation attains the
maximum value in the vicinity of .theta..sub.2 =.pi./4 (the splitting
ratio is 1:1).
(b) Transfer Function of Optical Circuit According
to the invention (two MZIs serially connected)
The transfer function of the 2-stage MZI structure is expressed by
replacing the transfer matrix m(.lambda.) of the MZI (4-terminal circuit)
in Equation (3) by a transfer matrix M.sub.2 (.lambda.) (shown below) of
the MZI arranged in two stages.
The transfer matrix M.sub.2 (.lambda.) of the MZI arranged in two stages is
expressed as follows using each path length difference .DELTA.L.sub.mi
(i=1, 2), coupler rotation (coupling) .theta..sub.j (j=1, 2, 3), effective
refractive index n(.lambda.) of the waveguide and input wavelength
.lambda.:
##EQU4##
Here .DELTA.Lmi>0 corresponds to a case where the branch on the through
side is long with respect to the input port, and .DELTA.Lmi<0
corresponds to a case where the branch on the cross side is long. The
transfer function H.sub.2 (.lambda.) of the 2-stage MZI structure is
expressed as follows using M.sub.2 and a phase shift h(.lambda.) (path
length: .DELTA.L.sub.r) that is produced by the loop-back 13:
##EQU5##
h(.lambda.)=exp[-j2.pi..DELTA.L.sub.r n(.lambda.)/.lambda.] (18)
where M.sub.2 11* represents the complex conjugate of M.sub.2 11. From the
foregoing, the phase of the transfer function H.sub.2 (.lambda.) is as
follows:
##EQU6##
A=cos [.pi.(.DELTA.L.sub.m1 +.DELTA.L.sub.m2)n(.lambda.)/.lambda.]
cos(.theta..sub.2)cos(.theta..sub.1 +.theta..sub.3)-cos
[.pi.(.DELTA.L.sub.m1 -.DELTA.L.sub.m2)n(.lambda.)/.lambda.]
sin(.theta..sub.2)sin(.theta..sub.1 +.theta..sub.3) (20)
B=sin [.pi.(.DELTA.L.sub.m1 +.DELTA.L.sub.m2)n(.lambda.)/.lambda.]
cos(.theta..sub.2)cos(.theta..sub.1 -.theta..sub.3)-sin
[.pi.(.DELTA.L.sub.m1 -.DELTA.L.sub.m2)n(.lambda.)/.lambda.]
sin(.theta..sub.2)sin(.theta..sub.1 -.theta..sub.3) (21)
(c) Conditions that Give Dispersion Compensation Quantity=0 According to
the Invention
In order for the amount of dispersion compensation to become zero, it is
required that argH.sub.2 (.lambda.) be expressed by the following
function:
argH.sub.2 (.lambda.)=C.sub.6 /.lambda.+C.sub.7 (22a)
or
argH.sub.2 (.lambda.)=C.sub.8 (C.sub.6, C.sub.7, C.sub.8 are constants)
(22b)
by the design parameters, in a manner similar to that of the prior-art
example. A condition that will satisfy Equations (22a), (22b) is
(A,B)=(0,0) or (.+-.1,0), which is similar to the prior-art example.
The solution (A,B)=(0,0) will be described as one example. In the prior-art
example, (.alpha.,.beta.)=(0,0) cannot be satisfied only by selecting
.DELTA.L.sub.m, a fixed limitation is imposed with regard to the rotation
angle .theta. of the coupler and this becomes a problem in terms of
manufacturability. In order to simplify the discussion set forth below, a
description will be rendered in regard to minimum rotation. However, it
should be noted that this does not impose any particular limitation upon
the parameters of the present invention.
(c-1) Case 1: .theta..sub.1 +.theta..sub.3 =.pi./2
That .DELTA.L.sub.m1 n(.lambda.)/.lambda.=1/4, .DELTA.L.sub.m2
n(.lambda.)/.lambda.=-1/4 is a solution is readily verified.
(c-2) Case 2: .theta..sub.1 +.theta..sub.3.noteq..pi./2
The following equations are obtained by substituting A=0, B=0 into
Equations (20), (21), respectively, and transforming:
cos [.pi.(.DELTA.L.sub.m1 +.DELTA.L.sub.m2)n(.lambda.)/.lambda.]=cos
[.pi.(.DELTA.L.sub.m1 -.DELTA.L.sub.m2)n(.lambda.)/.lambda.]
tan(.theta..sub.2)tan(.theta..sub.1 +.theta..sub.3) (23)
sin [.pi.(.DELTA.L.sub.m1 +.DELTA.L.sub.m2)n(.lambda.)/.lambda.]=-sin
[.pi.(.DELTA.L.sub.m1 -.DELTA.L.sub.m2)n (.lambda.)/.lambda.]
tan(.theta..sub.2)tan(.theta..sub.1 +.theta..sub.3) (24)
In the process of the transformation, use is made of cos(.theta..sub.1
+.theta..sub.2).noteq.0 in view of .theta..sub.1
+.theta..sub.3.noteq..pi./2. An equation for selecting the value of
(.DELTA.L.sub.m1 -.DELTA.L.sub.m2)n(.lambda.) is obtained as follows using
the basic condition
cos .sup.2 [.pi.(.DELTA.L.sub.m1 +.DELTA.L.sub.m2)n(.lambda.)/.lambda.]+sin
.sup.2 [.pi.(.DELTA.L.sub.m1 +.DELTA.L.sub.m2)n(.lambda.)/.lambda.]=1
of the triangular function and Equations (23) and (24):
##EQU7##
It will be understood that if the values of .theta..sub.1, .theta..sub.2,
.theta..sub.3 are given in Equation (25), then the value of
(.DELTA.L.sub.m1 -.DELTA.L.sub.m2)n(.lambda.) is obtained. With regard to
(.DELTA.L.sub.m1 +.DELTA.L.sub.m2)n(.lambda.), it will suffice to
substitute the value of cos [.pi.(.DELTA.L.sub.m1
-.DELTA.L.sub.m2)n(.lambda.)/.lambda.], which is obtained from Equation
(25), into Equation (23). In order for Equation (25) to be established, it
is necessary in view of cos .sup.2 [.pi.(.DELTA.L.sub.m1
-.DELTA.L.sub.m2)n(.lambda.)/.lambda.].ltoreq.1 to previously decide the
values of .theta..sub.1, .theta..sub.2, .theta..sub.3 at the time of
design in such a manner that the condition
1.ltoreq.tan .sup.2 (.theta..sub.1 +.theta..sub.3).times.tan .sup.2
(.theta..sub.2) (26)
will hold even taking into consideration variations in .theta..sub.1,
.theta..sub.2, .theta..sub.3 at the time of manufacture. For this
condition it will suffice if the design is such that .theta..sub.1
+.theta..sub.3.apprxeq..pi./2 holds, and therefore this condition is
considered to be one that can be satisfied easily.
(c-3) Reconciling both conditions that give dispersion compensation
quantity=0 and variations in manufacture according to the invention
According to the present invention as described above, by adopting an
arrangement in which multiple MZIs are serially connected, dispersion
compensation quantity=0 can be achieved by selecting values of
.DELTA.L.sub.m1 n(.lambda.), .DELTA.L.sub.m2 n(.lambda.) in accordance
with values of .theta..sub.1, .theta..sub.2, .theta..sub.3. That is, even
if coupler rotation angle deviates from the design value owing to
manufacturing variations or the like, dispersion compensation quantity=0
is achieved by adjusting the values of .DELTA.L.sub.m1 n(.lambda.),
.DELTA.L.sub.m2 n(.lambda.) using the TO effect, etc. This means that the
aforementioned problems of the prior-art example can be solved.
In order afford a comparison with the prior-art example, FIG. 3 illustrates
the compensation characteristic (group delay characteristic) of a
dispersion compensating filter in FIG. 2, which is a modification of FIG.
1. Components of the dispersion compensating filter of FIG. 2 that are
identical with those of FIG. 1 are designated by like reference
characters. This modification differs in that loop length .DELTA.L.sub.r
of the loop circuit 13 is reduced and in that input and output waveguides
15 and 16 made to intersect.
FIG. 3 illustrates a compensation characteristic for a case where the
rotation angle .theta..sub.3 of the third coupler in FIG. 2 has deviated
from the design value (.theta..sub.1 =.theta..sub.2 =.theta..sub.3
=.pi./4, L.sub.r =4104 .mu.m) by 5%. The numerical value (nm) in FIG. 3 is
the path length difference .DELTA.L.sub.m1 n(.lambda.), -.DELTA.L.sub.m1
n(.lambda.) between the branches of each MZI. Since the deviation in
rotation angle is small in this example, the group delay characteristic of
FIG. 3, which is inclusive of dispersion compensation quantity=0
(slope=0), is obtained with almost no shift in the drive of the path
length difference .DELTA.L.sub.m1 n(.lambda.) between the MZI branches of
the first stage and of the path length difference .DELTA.L.sub.m2
n(.lambda.) between the MZI branches of the second stage from symmetrical
drive [.DELTA.L.sub.m2 n(.lambda.)=-L.sub.m1 n(.lambda.)]. Further, the
center wavelength also is almost unaffected by a deviation in the angle
.theta..sub.3, and it will be understood that this is sufficiently small.
(B) First Embodiment
FIG. 4 is a diagram showing the topology of a dispersion compensating
filter according to a first embodiment of the present invention, in which
two or more MZIs are serially connected. One output and one input of a
2-input, 2-output optical circuit are connected by an optical propagation
path (optical waveguide, optical fiber) to construct a loop circuit 20.
The 2-input, 2-output optical circuit is constructed by serially
connecting five MZIs 21 to 25. Each MZI has a structure identical with
that of the MZI in FIG. 1. The MZIs have two waveguides 21a, 21b to 25a,
25b embraced by two couplers CPLi, CPLj, and heaters HT serving as path
length adjustment portions formed on each of the waveguides.
The transfer function of the dispersion compensating filter illustrated in
FIG. 4 is expressed by replacing the transfer matrix m(.lambda.) of the
MZI (4-terminal circuit) in Equations (1) to (5) by a transfer matrix
M.sub.k (.lambda.) (shown below) of the MZI arranged in multiple (k)
stages.
The transfer matrix M.sub.k (.lambda.) of the MZI arranged in multiple
(.lambda.) stages is expressed as follows using each path length
difference .DELTA.L.sub.mi (i=1, 2, . . . k+1), coupler rotation
(coupling) .theta..sub.i (i=1, 2, . . . k+1), effective refractive index
n(.lambda.) of the waveguide and input wavelength .lambda.:
##EQU8##
Here .DELTA.Lmi>0 corresponds to a case where the branch on the through
side is long with respect to the input port, and .DELTA.Lmi<0
corresponds to a case where the branch on the cross side is long. The
transfer function Hk(.lambda.) of the arrangement obtained by serially
connecting k-number of MZIs is found using the transfer matrix
Mk(.lambda.) and the phase shift h(.lambda.) that is produced by the
loop-back. The phase argHk(.lambda.) of this transfer function is found.
In the first embodiment, positive compensation and negative compensation,
inclusive of dispersion compensation quantity=0, can be achieved using
k-number of path length differences .DELTA.Lmi (i=1, 2, . . . k) even if
.theta..sub.1 to .theta..sub.3 exhibit variations owing to manufacture.
Adjustment of optical path length
Methods of varying the path length difference .DELTA.Lmi of the MZI
portions 21 to 25 and the path length .DELTA.L.sub.r of the loop circuit
20 are 1 a method regarding the SiO.sub.2 -type waveguide, and 2 a method
regarding an LiNbO.sub.3 -type waveguide. As shown in FIG. 5, the method
of varying optical path length in an SiO.sub.2 -type waveguide includes
building up an upper clad UCL on the top side of waveguide core OWGs
formed on a lower clad LCL of a silicon substrate SPL, forming a heater HT
on the upper clad UCL and controlling-the optical path length by varying
the refractive index of the waveguides OWG through heating of the heaters.
(This method relies upon the TO effect.)
As shown in FIG. 6, the method of varying optical path length in an
LiNbO.sub.3 -type waveguide includes forming electrodes EL in parallel on
waveguides OWG formed by diffusing Ti in an LiNbO.sub.3 substrate LPL,
applying an electric field to the waveguide portions and controlling the
optical path length by varying the dielectric constant, namely the
refractive index. (This method relies upon the EO effect.)
The first embodiment shown in FIG. 4 is an example of an SiO.sub.2
waveguide, and means for adjusting path length difference is constructed
by the heaters HT. With regard to an LiNbO.sub.3 waveguide, the means for
adjusting path length difference can be constructed by adopting the
arrangement shown in FIG. 6.
Coupler
The coupler CPL in the dispersion compensating filter can be constructed by
either of two methods. A coupler based upon the first method of
construction is an MMI (Multi-Mode Interferometer) coupler obtained by
coupling two waveguides OWG1, OWG2 by a single core layer CR, as shown in
FIG. 7. FIG. 7 illustrates an example of the structure of an MMI-type
coupler. This is an example in which the distance between core centers of
the core waveguides OWG1, OWG2 is 14.9 .mu.m, splitting is 50% and the
core-clad difference in refractive indices is 0.8%.
A coupler based upon the second method of construction is one having little
wavelength dependence, such as a WINC (see Wavelength-Independent Coupler:
K. Jinguji et al., Journal of Lightwave Technology, vol. 14, No. 10 1996,
p. 2301), in which the parameters are coupling length L of MZI 22 and path
length difference .DELTA.Lm between the branches, as shown in FIG. 8. FIG.
8 illustrates an example of the structure of a WINC-type coupler. Here the
path length difference of the MZI 22 is 1900 .mu.m, coupling length of
unidirectional coupler CPL2 on the left side is 1900 .mu.m, distance
between the core centers is 9.2 .mu.m, coupling length of unidirectional
coupler CPL3 on the right side is 795 .mu.m distance between the core
centers is 9.2 .mu.m, splitting is 50% and the core-clad difference in
refractive indices is 0.8%.
FIG. 9 is a wavelength vs. transmission splitting intensity characteristic
diagram (simulation) illustrating the wavelength dependence of the
splitting intensities of an MMI-type coupler, WINC-type coupler and
directional coupling-type coupler. As evident from the characteristic
diagram, the splitting intensities of the MMI-type coupler and WINC-type
coupler are a substantially constant 50% and are independent of
wavelength. It is possible to endow each wavelength-division-multiplexed
optical signal with a splitting strength that is as designed and it
becomes possible to reduce variations in the amount of dispersion
compensation from wavelength to wavelength.
(C) Second Embodiment
FIG. 10 is a diagram showing the topology of a dispersion compensating
filter according to a second embodiment of the present invention. This
illustrates an example in which the number of MZIs connected in the first
embodiment is made two. Components identical with those of the first
embodiment in FIG. 4 are designated by like reference characters. The
second embodiment is the minimal structure of the present invention for
controlling the amount of dispersion compensation. This is a two-stage
arrangement in which the number of MZI stages is two. According to the
second embodiment, positive compensation and negative compensation,
inclusive of dispersion compensation quantity=0, can be achieved even if
manufacturing variations occur, as described above in accordance with FIG.
1. In other words, if the maximum value of positive compensation is +a and
the maximum value of negative compensation is -b, then any desired amount
of compensation can be achieved over the range -b to +a.
(D) Third Embodiment
FIG. 11 is a diagram showing the topology of a dispersion compensating
filter according to a third embodiment of the present invention. This is a
two-stage arrangement in which the number of MZI stages is two. Here input
and output optical propagation paths 20a, 20b not used as the loop of the
2-input, 2-output optical circuit are made to intersect at an angle of
10.multidot. or greater. Two waveguides 21a, 21b; 22a, 22b of the MZIs 21,
22 are embraced by two couplers CPL1, CPL2; CPL2, CPL3. This constructs a
2-input, 2-output optical circuit in which two MZIs are serially
connected.
One output and one input of the 2-input, 2-output optical circuit are
connected by an optical propagation path 23a to construct a loop circuit
23, and the waveguides 21a, 21b; 22a, 22b of the MZIs 21, 22 as well as
the loop circuit 23 are formed to have heaters HT as path length
adjustment portions. The dispersion compensating filter of the third
embodiment is a two-stage arrangement in which the number of MZIs is two
and is similar to the second embodiment of FIG. 10 except for the fact
that optical propagation paths 20a, 20b are made to intersect at an angle
of 10.multidot. or greater and the fact that the loop length
.DELTA.L.sub.r n(.lambda.) of the loop circuit 23 is small.
This arrangement is a layout in a case where a loop length .DELTA.L.sub.r
of sufficient size cannot be assured owing to the design value of the FSR.
In other words, the loop length .DELTA.L.sub.r of the loop circuit
diminishes when the FSR is small. If the loop length .DELTA.L.sub.r
becomes too small, the input and output propagation paths 20a, 20b must be
bent. In the actual manufacturing process, minimum bending radius r.sub.m
is limited owing to radiation loss at the bent portions. If the loop
length .DELTA.L.sub.r is less than a prescribed length, then the bending
radius at the bends of the propagation paths 20a, 20b falls below the
minimum bending radius r.sub.m and radiat
