Waveguide-type optical matrix switch

A waveguide-type optical matrix switch including as its switching element a Mach-Zehnder interferometer which includes two directional couplers and an optical phase shifter. The two directional couplers are arranged by placing two optical waveguides in close proximity at two positions on a substrate, and have an identical coupling ratio. The optical phase shifter is disposed over at least one of the two optical waveguides between the directional couplers. The two optical waveguides have an effective optical path length difference of half a wavelength of a light signal between the two directional couplers, and are intersected in the optical switch element. The waveguide-type optical matrix switch is little affected by fabrication errors in the coupling ratio of the directional couplers, and superior in the extinction ratio.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a waveguide-type optical matrix switch 
used in optical fiber communications, and more particularly, to a 
waveguide-type optical matrix switch which is little affected by 
fabrication errors, and has a high extinction ratio. 
2. Description of the Prior Art 
Recently, it has become essential for further spread of the optical fiber 
communications to develop optical circuit components such as optical 
splitters and couplers, optical multi/demultiplexers and optical switches 
in addition to the realization of higher performance and lower cost 
optical fibers, photo-detectors and emitters. Above all, optical switches 
are considered to play an important role in near future to freely switch 
optical fiber lines in response to demands or to establish alternate 
routes in case of line faults. 
As typical optical switch configurations, bulk-type and waveguide-type 
optical switches have been proposed. The bulk type optical switch is 
arranged by employing a movable prism and lenses as its parts, and has 
advantages that it has small wavelength dependence, and relatively low 
loss characteristics. The bulk-type optical switches, however, have not 
much spread because they are not suitable for mass production since their 
assembly and adjusting processes are complicated and expensive. On the 
other hand, the waveguide-type optical switches, which are mass-produced 
in the form of so-called integrated optical switches by utilizing the 
photolithography and fine pattern fabrication technique, are considered as 
a future-type optical switch. In particular, the waveguide-type optical 
switch is considered essential to realize a practical, rather large-scale 
M.times.N optical matrix switch having M input ports and N output ports. 
FIG. 1 is a schematic diagram showing an arrangement of a 4.times.4 optical 
switch as an example of an M.times.N optical matrix switch that will 
become the subject matter of the present invention. The 4.times.4 matrix 
switch are arranged in such a fashion that four input optical waveguides 
1a, 1b, 1c and 1d intersect four output optical waveguides 2a, 2b, 2c and 
2d at 16 places. Each of these 16 places is provided with a 2.times.2 
optical switch elements S00, . . . , or S33 as a minimum unit optical 
switch. Such an arrangement of the optical matrix switch is called "a 
strictly non-blocking optical matrix switch", and can switch four-channel 
light signals entering the input optical waveguides 1a, 1b, 1c and 1d to 
any one of the four output optical waveguides 2a, 2b, 2c and 2d. 
For example, when a light signal incident to the input optical waveguide 1a 
is to be outputted from the output optical waveguide 2b, an optical path 
passing through the optical switch elements S03, S02, S01, S11, S21 and 
S31 is formed. In this case, in the optical switch element S01, a bar path 
is established which guides a light beam incident to the bottom left 
waveguide to the bottom right waveguide. In the other switch elements, a 
cross path is established which guides a light beam incident to the bottom 
left waveguide (or to the top left waveguide) to the top right waveguide 
(or to the bottom right waveguide). To minimize the number of driven 
switch elements, it is necessary to establish a cross path when an optical 
switch element is in the OFF state, and a bar path when an optical switch 
element is in the ON state. In the above-mentioned example, only the 
switch element S01 is made ON state, and the other switch elements are 
made OFF state. This holds true for any other optical paths. For example, 
an optical path from the input optical waveguide 1a to the output optical 
waveguide 2a can be established by making the optical switch element S00 
ON, and the other optical switch elements S03, S02, S01, S10, S20 and S30 
OFF. Thus, the number of the optical switch element to be made ON to form 
a bar path is always one, whereas that of the optical switch elements to 
be made OFF to form a cross path varies from zero to six. In other words, 
in the 4.times.4 optical matrix switch, the number of the optical switch 
elements through which the light signal passes varies from a minimum of 
one to a maximum of seven. 
Many attempts have been conducted to constitute the optical matrix switch 
by using optical waveguides of various kinds of materials. Above all, a 
thermooptic matrix switch utilizing thermooptic effect of silica-based 
optical waveguide on a silicon substrate is expected as the most promising 
candidate of the practical optical matrix switches because it has no 
unfavorable polarization dependence, and has good joining characteristics 
to optical fibers. 
FIG. 2A is a plan view showing the entire arrangement of a conventional 
thermooptic 4.times.4 optical matrix switch constructed on a silicon 
substrate as an example corresponding to the 4.times.4 optical matrix 
switch as shown in FIG. 1, and FIG. 2B is an enlarged plan view showing an 
arrangement of a conventional optical switch element of FIG. 2A. In these 
figures, eight optical waveguides including the four input optical 
waveguides 1a, 1b, 1c and 1d constitute an input waveguide bundle 4a, and 
eight optical waveguides including the four output optical waveguides 2a, 
2b, 2c and 2d constitute an output waveguide bundle 4b. It is easily 
understood that the arrangement of FIG. 2A is topologically equal to that 
of FIG. 1. 
These waveguide bundles 4a and 4b are silica-based single-mode optical 
waveguide arrays formed on a substrate 3 by a known combination of the 
frame-hydrolysis deposition and the reactive ion etching technique. Each 
of the switch elements S00-S33 disposed at each one of the sixteen 
positions is a so-called Mach-Zehnder interferometer type 2.times.2 
optical switch as shown in FIG. 2B. 
In FIG. 2B, two optical waveguides 61a-61b and 62a-62b are placed in close 
proximity at two positions to form two directional couplers 63a and 63b. 
The coupling ratio of the directional couplers is set at 50% at the 
wavelength of a light signal. The optical path lengths of the two optical 
waveguides 61a-61b and 62a-62b between the two directional couplers 63a 
and 63b are set at an identical length (a symmetrical state) when 
thermooptic phase shifters 64a and 64b, which are made of thin film 
heaters and are disposed over the two optical waveguides, are not operated 
(in the OFF state). 
Assuming that the power coupling ratio of the directional couplers 63a and 
63b is k, the power of an input light signal to one optical waveguide is 
P10, the powers of output light signals from the bar path and the cross 
path are P1 and P2, respectively, and the phase difference taking place 
between the two waveguides connecting the two directional couplers 63a and 
63b is .DELTA..phi., the input and output switching characteristics of the 
Mach-Zehnder 2.times.2 optical switch element can be expressed by the 
following equations: 
EQU P.sub.1 /P.sub.10 =(1-2k).sup.2 cos.sup.2 (.DELTA..phi./2)+sin.sup.2 
(.DELTA..phi./2) (1) 
EQU P.sub.2 /P.sub.10 =4k (1-k) cos.sup.2 (.DELTA..phi./2) (2) 
When the coupling ratio k=1/2, that is, when the directional couplers 63a 
and 63b are a 3-dB coupler, the input-output characteristics are as 
follows: First, when the switch is in the OFF state where the thin film 
heaters 64a and 64b are not supplied with power, the phase difference 
.DELTA..phi. is zero, and hence, the light signal is transmitted through 
the cross path, that is, through the path 61a-62b or 62a-61b. On the other 
hand, when at least one of the phase shifters 64a and 64b is made ON by 
applying power to the thin film heater, the optical path length difference 
of 1/2 wavelength corresponding to .pi. radian is produced between the two 
waveguides connecting the directional couplers. The phase difference 
.DELTA..phi. of .pi. thus produced switches the optical switch element 
into the bar state so that the light signal is transmitted through the bar 
path 61a-61b or 62a-62b. In this way, switching between the cross/bar 
states of the optical switch element is achieved. The conventional 
waveguide-type optical matrix switch using the 2.times.2 optical switch 
elements with such an arrangement as a basic element, however, presents 
the following problem in a fabrication process: 
Although the coupling ratio of the directional couplers 63a and 63b must be 
exactly 50% at the wavelength of the light signal so as to achieve an 
ideal operation of the conventional Mach-Zehnder interferometer type 
optical switch element of FIG. 2B, it is difficult to set the coupling 
ratio at exactly 50% because some errors are inevitably involved in a 
practical fabrication process of the optical waveguides. This is because 
directional couplers are a very structure-sensitive optical device, and 
hence, the coupling ratio is readily varied by a width of the waveguides, 
by the separation between the two waveguides, and by very small process 
errors of the relative refractive index difference between the core and 
cladding of the waveguides, or the like. 
When the coupling ratio of the directional couplers deviates from 50%, the 
light signal is not transmitted in its entirety through the cross path 
61a-62b or 62a-61b in the OFF state, but leaks out of the cross path and 
enters the bar path 61a-61b or 62a-62b. In other words, so-called 
crosstalk takes place. This is an important problem to be solved in the 
fabrication process of the waveguide-type optical matrix switch. 
For example, when the coupling ratio deviates from 50% upward or downward 
by 5%, approximately 1% of the light signal power leaks to the bar path 
61a-61b or 62a-62b in each optical switch element so that only 15 dB 
extinction ratio can be achieved in the 4.times.4 optical matrix switch as 
shown in FIG. 2A. This becomes more serious as the scale of the matrix 
increases. In an 8.times.8 optical matrix switch, for example, the 
crosstalk characteristics deteriorates, and the extinction ratio declines 
to approximately 11 dB. 
In a practical fabrication process of the optical waveguides, errors of 
approximately .+-.5% commonly take place, and even errors on the order of 
.+-.10% are not rare in setting the coupling ratio of the directional 
couplers at 50%. Thus, the coupling ratio sensitivity of the 
waveguide-type optical matrix switch has been one of the most important 
problems in fabricating it with a high yield. 
SUMMARY OF THE INVENTION 
Accordingly, it is an object of the present invention to provide a 
waveguide-type optical matrix switch that can tolerate larger coupling 
errors of directional couplers and has a higher extinction ratio by 
eliminating the above-described disadvantages associated with the 
conventional techniques. 
In a first aspect of the present invention, there is provided a 
waveguide-type optical switch for switching a light signal inputted 
thereto, comprising: 
a substrate; 
two directional couplers arranged by placing two optical waveguides in 
close proximity at two positions on the substrate, and having an identical 
coupling ratio, the two optical waveguides having an effective optical 
path length difference of half a wavelength of the light signal between 
the two directional couplers; 
optical path length switching means disposed over at least one of the two 
optical waveguides between the two directional couplers for switching the 
effective optical path length difference to an integral multiple of the 
wavelength of the light signal; and 
a cross portion at which the two optical waveguides are intersected. 
Here, the optical path length switching means may be an optical phase 
shifter. 
In a second aspect of the present invention, there is provided a 
waveguide-type optical matrix switch having a plurality of input ports, 
and a plurality of output ports, and switching a light signal inputted to 
one the input ports to be produced from one of the output ports, the 
waveguide-type optical matrix switch comprising: 
a plurality of input optical waveguides each of which is connected to each 
one of the input ports; 
a plurality of output optical waveguides each of which is connected to each 
one of the output ports; and 
a plurality of optical switch elements each of which is disposed at each 
one of intersections of the input optical waveguides and the output 
optical waveguides; 
wherein each of the plurality of optical switch elements including: 
a substrate; 
two directional couplers arranged by placing two optical waveguides in 
close proximity at two positions on the substrate, and having an identical 
coupling ratio, the two optical waveguides having an effective optical 
path length difference of half a wavelength of the light signal between 
the two directional couplers; 
optical path length switching means disposed over at least one of the two 
optical waveguides between the directional couplers for switching the 
effective optical path length difference to an integral multiple of the 
wavelength of the light signal; and 
a cross portion at which the two optical waveguides are intersected. 
The optical path length switching means may be an optical phase shifter. 
The optical phase shifter may be a thermooptic effect phase shifter 
consisting of a thin film heater. 
The optical path length switching means may be two optical phase shifters 
each of which is disposed over each one of the two optical waveguides 
between the two directional couplers. 
The optical phase shifter may be disposed over a shorter waveguide of the 
two optical waveguides so that the effective optical path length 
difference is made zero when the optical phase shifter is driven. 
The optical phase shifter may be disposed over a longer waveguide of the 
two optical waveguides so that the effective optical path length 
difference is made one wavelength of the light signal when the optical 
phase shifter is driven. 
One of the optical phase shifters may compensate for an offset of the 
effective optical path length difference when the effective path length 
difference deviates from half a wavelength of the light signal. 
The cross portion may be disposed between the two directional couplers. 
The two optical waveguides may intersect at the cross portion with a cross 
angle of at least 15 degrees. 
The two optical waveguides may have tapered geometry in sections before and 
after the cross portion. 
The two optical waveguides may have tapered geometry at the cross portion. 
Each one of the two optical waveguides may be any one of a plastic 
waveguide, an ion-diffused glass waveguide, and a lithium niobate 
waveguide. 
The optical switch elements may be connected by curved waveguide bundles to 
form a serpentine layout. 
A waveguide-type optical switch may further comprise inactive switch 
elements placed at positions corresponding to the optical switch elements 
on the optical waveguides. 
Each of the inactive switch element may comprise: 
two directional couplers arranged by placing two optical waveguides in 
close proximity at two positions on the substrate, and having an identical 
coupling ratio, the two optical waveguides having an effective optical 
path length difference of half a wavelength of the light signal between 
the two directional couplers; and 
a cross portion at which the two optical waveguides are intersected. 
Centers of the optical waveguides may be offset at portions where each of 
the optical waveguides changes its geometry from a straight to a curve, 
and where each of the optical waveguides changes its radius of curvature, 
or changes its direction of a curve. 
A radius of curvature of a curve of the waveguides may be at least 4 mm. 
According to the present invention, an optical path length difference of 
1/2 wavelength is set in the OFF state between the two directional 
couplers of the Mach-Zehnder interferometer constituting the optical 
switch element. Thus, in the OFF state, the inputted light signal passes 
through the Mach-Zehnder interferometer without transferring to the other 
waveguide, that is, with maintaining the input state (in a through state). 
In addition, since the two waveguides cross in the switch element with an 
angle such that only negligible crosstalk will takes place, the light 
signal passes through the switch element in the cross path mode. These 
operations are accomplished as long as the coupling ratios of the two 
directional couplers are identical, regardless of their value. 
On the other hand, in the ON state, the optical phase shifter disposed over 
the optical waveguide constituting the Mach-Zehnder interferometer is 
driven so as to cancel the optical path length difference of 1/2 
wavelength. This enables the optical switch element including the cross 
portion to be switched to the bar path mode. 
The waveguide-type optical matrix switch according to the present invention 
differs from the conventional optical matrix switch in that it employs a 
Mach-Zehnder interferometer structure including the optical path length 
difference of 1/2 wavelength in the OFF state, and that the optical switch 
element includes a cross portion of the waveguides in the switch element. 
According to the present invention, the crosstalk to the bar path will not 
occur in the OFF state as long as the coupling ratios of the two 
directional couplers are equal even if the value of the coupling ratios 
deviates from 50%. When the value of the coupling ratios deviates from 
50%, the light signal is not switched in its entirety to the bar path, 
leaving a small amount of the light signal in the cross path. The 
remaining light signal, however, is led to an unused waveguide terminal of 
the output waveguide bundle, and hence, the degradation of the extinction 
ratio of the optical matrix switch can be prevented. 
Furthermore, when the cross portion is provided between the two directional 
couplers, the length of the switch element can be reduced to a minimum. 
This is because two positions where the separation of the two waveguides 
must be widen, that is, the section between the two directional couplers 
and a cross portion, can be unified. Thus, dimensions of the optical 
matrix switch formed by integrating many optical switch elements can be 
reduced. 
In the waveguide-type optical matrix switch according to the present 
invention, even when the coupling ratios deviate from 50%, the light 
signal transmits a switch element in its entirety through the cross path 
in the OFF state as long as the two coupling ratios of the directional 
couplers in the switching element are identical. Therefore, precise 
adjustment required for fabricating the directional couplers can be 
greatly reduced, and the optical matrix switch with a high extinction 
ratio can be readily provided. In addition, in the optical matrix switch 
of the present invention comprising the switch elements can reduce the 
setting accuracy of the wavelength of the light signal, thus enabling to 
introduce a low cost, low wavelength accuracy signal source. The optical 
matrix switch of the present invention is expected to make a great 
contribution to constructing optical fiber communications systems in which 
a great number of light signals are communicated. 
The above and other objects, effects, features and advantages of the 
present invention will become more apparent from the following description 
of the embodiments thereof taken in conjunction with the accompanying 
drawings.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
The invention will now be described with reference to the accompanying 
drawings. In the following embodiments, silica-based single-mode optical 
waveguides formed on a silicon substrate are used as optical waveguides, 
and thermooptic Mach-Zehnder interferometer type 2.times.2 optical switch 
devices are employed as optical switch elements of an optical matrix 
switch. This is because this combination is superior in joining to 
single-mode optical fibers, and can provide an optical matrix switch 
without polarization dependence. The present invention, however, is not 
restricted to this combination. 
EMBODIMENT 1 
FIGS. 3A-3C show an arrangement of an optical switch element constituting a 
4.times.4 optical matrix switch as a first embodiment of a waveguide-type 
optical matrix switch according to the present invention: FIG. 3A is a 
plan view; FIGS. 3B and 3C are enlarged cross-sectional views taken along 
lines 3B--3B and 3C--3C of FIG. 3A. A plan view showing the entire 
arrangement of the 4.times.4 optical matrix switch is identical to FIG. 1, 
and so it is omitted here. Two silica-based-glass optical waveguides 
31a-31b and 32a-32b are placed in close proximity separated approximately 
several micrometers apart at two positions on a silicon substrate 11, 
thereby forming two directional couplers 33a and 33b as shown in FIGS. 3A 
and 3B. The coupling ratios of the directional couplers are set to become 
50% by adjusting the separation of the waveguides at the coupling section 
and the coupling length. The effective optical path lenght of the optical 
waveguides 31a-31b and 32a-32b between the two directional couplers 33a 
and 33b are set such that the waveguide 32a-32b is longer than the 
waveguide 31a-31b by half the light signal wavelength of 1.3 .mu.m, that 
is, by 0.65 .mu.m. In addition, a thin film heater 34a is disposed on top 
of a cladding layer 14 in such a manner that the heater 34a is located 
just over the waveguide 31a-31b as shown in FIG. 3C. The waveguides 
31a-31b and 32a-32b intersect with a cross angle of .theta. at a cross 
portion 35. The cross angle .theta. is set at such a value as crosstalk 
caused by the intersection is negligible. 
The region between the directional couplers 33a and 33b constitutes a 
slightly asymmetric Mach-Zehnder interferometer having an optical path 
length difference of half a wavelength. In the OFF state when no current 
flows through the thin film heater 34a, a light signal inputted to the 
input port 31a of the waveguide 31a-31b passes through the directional 
couplers 33a and 33b being confined in the waveguide 31a-31b, and is 
outputted from the output port 31b. The light signal passing through the 
interferometer region intersects at the cross portion 35, and hence, the 
cross path can be achieved when the optical switch element is in the OFF 
state. 
Here, the output state of the Mach-Zehnder interferometer is visually 
explained in terms of interference between the modes of the electric field 
when the optical path length difference of zero and .lambda./2 is given to 
the waveguide arms linking the two directional couplers. 
The optical power transfer in the directional coupler sections can be 
expressed in terms of the interference between an even mode and an odd 
mode of the electric field, that is, in terms of the superimposition of 
the two modes. Each mode is represented in the real and imaginary space to 
express phase states. 
FIGS. 4A-4D illustrate the mode behavior at various stages of the 
conventional switch element where the optical path length difference 
.DELTA.L=0. Assuming that an incident light signal is E.sub.10, the 
composite electric fields on the axes of the two waveguides are 
represented by vectors. The behavior of the light signal at positions 
(1)-(4) in FIG. 4A are as follows: 
(1) It is supposed that the even mode and odd mode are in such a state as 
shown in FIG. 4B when the light signal is in the waveguide I: in the 
waveguide I, the two modes are in the same phase, and hence, they are 
added to each other; in the waveguide II, on the other hand, they are in 
opposite phase, and hence, they are canceled. 
(2) Since the odd mode has a lower phase velocity (a smaller propagation 
constant) than the even mode, it rotates toward the imaginary axis when 
the even mode is supposed to be fixed on the real axis. When the phase 
difference between the two modes becomes 90.degree., the electric field 
intensities in the two waveguides become equal. Here, it should be noted 
that although the electric field intensities are equal, the phase leads 
90.degree. in the waveguide II as shown by the vectors of FIG. 4C. 
(3) The state of (2) is maintained because there is no optical path length 
difference between the two waveguide arms linking the two directional 
couplers. 
(4) When the light signal passes through the other 3-dB directional 
coupler, the phase difference between the two modes adds another 
90.degree., thus resulting in the opposite state to that of (1): in the 
waveguide I, the two modes are in opposite phase, and hence, they are 
canceled; whereas in the waveguide II, the two modes are in the same 
phase, and hence, they are added to each other. Thus, the light signal 
transfers from the waveguide I to the waveguide II in its entirety. 
As explained above, when the optical path length .DELTA.L=0, the phase 
difference between the even mode and the odd mode is produced only in the 
directional coupler sections, and unless the phase difference is exactly 
.pi., the complete power transfer does not take place so that a part of 
the light signal leaks to the through path. 
FIGS. 5A-5C illustrate the mode behavior at various stages of the switch 
element of the present invention where the optical path length difference 
.DELTA.L between two directional couplers is .pi./2. The behavior of the 
light signal at positions (1)-(4) in FIGS. 5A-5C are as follows: 
(1) and (2) are identical to those of FIGS. 4B and 4C where the optical 
path length difference .DELTA.L=0. 
(3) Since the phase delay of .pi. occurs only in the waveguide II, the 
electric field in the waveguide II rotates by 180.degree.. The resultant 
electric field vector can be considered as the composition of the even 
mode and the odd mode as shown in FIG. 5B. 
(4) The phase difference between the two modes is increased by another 
90.degree. by passing through the second 3 dB directional coupler, and the 
entire light signal returns to the waveguide I as shown in FIG. 5C. 
These phenomena occur without fail as long as the coupling ratios of the 
two directional couplers are equal, regardless of the value of the 
coupling ratios. The reason for this is as follows: when the light signal 
enters the second directional coupler, the phase of the odd mode in the 
waveguide I leads, as shown in FIG. 5B, by .theta. degrees corresponding 
to the coupling ratio of the first directional coupler, with regard to the 
phase of the even mode because of the optical path length difference of 
.pi.; the phase lead of the odd mode, however, is canceled by the second 
directional coupler which delays the odd mode by the same .theta. degrees 
as shown in FIG. 5C; and thus, the relation of the two modes is returned 
to the first state as shown in FIGS. 4B. 
Let us express the above-mentioned operation by equations. Parameters of 
the Mach-Zehnder interferometer are defined as shown in FIG. 6: .delta. 
denotes a coupling coefficient of each directional coupler; d, a coupling 
length; k (=2.pi.neff/.lambda.0), a wave number. The characteristic matrix 
of a single directional coupler is expressed by 
##EQU1## 
Here, .delta.d, when expressed in terms of the above-mentioned modes, 
denotes the difference between the phases of the even and odd modes. 
Accordingly, in a 3 dB directional coupler, 
EQU .delta.d=.pi./4 
The phase difference produced by the waveguide arms of the interferometer 
is expressed by 
##EQU2## 
Therefore, the matrix of the electric field of the entire interferometer 
can be expressed as follows: 
##EQU3## 
Expanding equation (5), and expressing it in terms of power, the output 
characteristics can be expressed as follows: 
EQU P.sub.1 =P.sub.10 [cos.sup.2 (2.delta.d) cos.sup.2 (k.DELTA.L/2)+sin.sup.2 
(k.DELTA.L/2)]+P.sub.20 [sin.sup.2 (2.delta.d) cos.sup.2 (k.DELTA.L/2)](6) 
EQU P.sub.2 =P.sub.10 [sin.sup.2 (2.delta.d) cos.sup.2 (k.DELTA.L/2)]+P.sub.20 
[cos.sup.2 (2.delta.d) cos.sup.2 (k.DELTA.L/2)+sin.sup.2 (k.DELTA.L/2)](7) 
When only P.sub.10 is inputted to the conventional interferometer where the 
optical path length difference .DELTA.L=0, the output powers are expressed 
by 
EQU P.sub.1 =P.sub.10 cos.sup.2 (2.delta.d) (8) 
EQU P.sub.2 =P.sub.10 sin.sup.2 (2.delta.d) (9) 
In contrast, when only P.sub.10 is inputted to the interferometer of the 
present invention, where the optical path length difference 
.DELTA.L=.lambda./2 (k.DELTA.L/2=.pi./2), the output powers are expressed 
by 
EQU P.sub.1 =P.sub.10 (10) 
EQU P.sub.2 =0 (11) 
As clearly seen from equation (8), when the optical path length difference 
.DELTA.L=0 as in the conventional directional couplers, the inputted power 
P.sub.10 leaks to the output power P.sub.1 unless .delta.d=.pi./4, that 
is, unless the directional couplers are a precise 3 dB coupler. 
On the other hand, when the optical path length difference 
.DELTA.L=.lambda./2 as in the present invention, no power leak occurs on 
principle to the output power P.sub.2, regardless of the coupling ratio of 
directional couplers as expressed by equation (11). This result agrees 
with the above-described superimposition of the two modes. 
From these results, it is found that even if the coupling ratios of the 
directional couplers deviate from the ideal value of 50%, the crosstalk of 
the optical matrix switch can be sharply reduced as long as the coupling 
ratios of the two directional couplers are made equal, regardless of the 
value of the coupling ratios, when the optical path length difference 
.DELTA.L is set at .lambda./2 in the OFF state. In an optical matrix 
switch, however, the number of the switch elements to be driven becomes 
minimum when the input light signal is outputted from the cross port as 
stated before. To achieve this, the output ports must be exchanged. In the 
present invention, this is carried out by intersecting the two waveguides 
31a-31b and 32a-32b at the cross portion 35 with such an angle that no 
interference will occur between the two waveguides. 
In contrast with this, when the effective optical path length difference 
.DELTA.L of the interferometer is adjusted to zero by increasing the 
refractive index of the waveguide 31a-31b under the thin film heater 34a 
by supplying power to the heater, the coupling ratios of the two 
directional couplers 33a and 33b act in such a fashion that they are added 
to each other as shown in FIGS. 4A-4D. Accordingly, if the coupling ratio 
of each directional coupler is set at the ideal value of 50%, the 
interferometer takes an equivalent coupling ratio of 100% so that the 
light signal passes through the interferometer with exchanging the 
waveguides as shown in FIG. 4D. Following this, the light signal is 
transmitted through the cross portion 35, and thus, is switched to the bar 
path. Hence, the optical switch element satisfies a condition required for 
the ON state. When the coupling ratio of the directional couplers 33a and 
33b deviates from the ideal value of 50%, not the entire light signal 
transfers to the bar path, but a part of the light signal remaining in the 
cross state appears. The remaining light signal, however, is eventually 
outputted from an unused output side waveguide other than those associated 
with the output ports 2a, 2b, 2c and 2d of FIG. 2A. Consequently, the 
extinction ratio of the optical matrix switch suffers no deterioration 
although the loss is increased. 
FIG. 7 is a graph illustrating characteristics of the excess loss caused by 
the crosstalk in the 4.times.4 optical matrix switch: values of the excess 
loss were obtained when the light signal passed through seven switch 
elements. In FIG. 7, a solid curve indicates the characteristics of the 
optical matrix switch of the present invention, whereas a broken curve 
represents that of the conventional optical matrix switch. When the 
coupling ratio of the directional couplers deviates upward or downward by 
5% from the ideal coupling ratio of 50%, the excess loss of the 
conventional optical matrix switch is 0.25 dB, while that of the optical 
matrix switch of the present invention is only 0.05 dB. Furthermore, when 
the coupling ratio of the directional couplers deviates by 15% from the 
ideal coupling ratio, such as 35% or 65%, the excess loss of the 
conventional optical matrix switch increases to no less than 2.5 dB, while 
that of the optical matrix switch of the present invention increases by a 
very small amount of 0.4 dB. 
It must be noted here that although the loss increases sharply as the scale 
of the optical matrix switch augments in the conventional optical matrix 
switch, the loss is maintained at a fixed value as shown by the solid 
curve of FIG. 7, in the optical matrix switch of the present invention, 
regardless of the scale of the matrix switch, when the coupling ratio of 
the switch elements is fixed. The reason for this is as follows: In an 
optical matrix switch, each input light signal passes through one or more 
switch elements. In this case, only one of the switch elements is made ON 
state, and the other switch elements are kept OFF state. In the 
conventional optical matrix switch, the light signal leaks even when it 
passes through the OFF state switch elements when the coupling ratio of 
the directional couplers deviates from 50%. Therefore, the excess loss 
increases as the scale of the matrix augments, and hence, the number of 
the OFF state switch elements through which the light signal passes 
increases. In the optical matrix switch of the present invention, however, 
the light signal does not leak from the OFF state switch elements, but 
leaks from only one ON state switch element. Thus, the excess loss is 
caused by the loss of that ON state switch element. As a result, the 
excess loss takes the same value regardless of the scale of the matrix. 
Next, the dependence of the crosstalk on the wavelength will be explained. 
FIGS. 8A and 8B show the optical path length difference .DELTA.L in the ON 
state and OFF state of the switch element of the present invention, and 
that of the conventional switch element, respectively. It is found that 
the optical path length differences of the two are reversely related. 
FIGS. 9A and 9B are graphs illustrating the dependence of the transmittance 
of the cross path of the optical switch elements on the wavelength of the 
light signal: FIG. 9A is a graph about the optical switch element of the 
present embodiment; and FIG. 9B is a graph concerning the conventional 
switch element shown in FIG. 2B. In FIGS. 9A and 9B, respective two solid 
curves indicate the dependence of the cross path transmittance on the 
wavelength in the OFF state and ON state, and each broken curve indicates 
a coupling ratio of the directional couplers constituting the 
interferometer. It is assumed that the coupling ratio of the directional 
couplers are set at the ideal coupling ratio of 50% at the 1.3 .mu.m 
wavelength. It is noticed here that in FIG. 9A associated with the present 
invention, the wavelength dependence in the OFF state is small, whereas 
that in the ON state is large, and conversely, in FIG. 9B associated with 
the conventional switch element, the wavelength dependence in the OFF 
state is large, whereas that in the ON state is small. In the practical 
4.times.4 optical matrix switch, the light signal passes through up to 
seven optical switch elements, and only one of them is in the ON state and 
the others are in the OFF state. Accordingly, it is clearly understood 
that the optical switch element of the present invention having smaller 
wavelength dependence in the OFF state as shown in FIG. 9A is superior to 
the conventional switch element in reducing the wavelength dependence of 
the entire optical matrix switch. 
Next, the dependence of the cross path transmittance on the wavelength of 
the light signal is described by using mathematical equations. 
First, the wavelength dependence of the conventional switch element in the 
cross path is explained. In the conventional switch element, the optical 
path length difference .DELTA.L=0 in the OFF state. Accordingly, the 
output characteristic is expressed as follows from equation (9): 
EQU P.sub.2 =P.sub.10 sin.sup.2 (2.delta.d) (12) 
Thus, the conventional switch element has wavelength characteristics as 
shown in FIG. 9B corresponding to the wavelength dependence of the 
coupling ratio of the directional couplers. 
On the other hand, in the ON state of the conventional type switch element, 
the wavelength dependence is caused not only by the wavelength dependence 
of the directional couplers but also by the optical path length difference 
between the waveguide arms linking the two directional couplers. Thus, the 
output characteristic is expressed as follows from equation (7): 
EQU P.sub.2 =P.sub.10 [sin.sup.2 (2.delta.d) cos.sup.2 (k.DELTA.L/2)](13) 
The dependence of the optical path length difference on the wavelength of 
the light signal is no more than 8% for the wavelength of 1.2-1.4 .mu.m, 
and hence, cos .sup.2 (k.DELTA.L/2) becomes approximately zero. 
Consequently, the output to the cross path in the ON state in the 
conventional switch element is nearly zero, and is little affected by the 
wavelength dependence of the directional couplers. 
Next, the cross path output of the switch element of the present invention 
is considered. As shown in FIGS. 8A and 8B, the relationship between the 
ON/OFF state and the optical path length difference is opposite between 
the switch element of the present invention and the conventional type 
switch element. In addition, the relationship between the output ports are 
opposite in the two switch elements. Consequently, the output 
characteristics of the switch element of the present invention can be 
obtained by reversing the curves of FIG. 9B with regard to the 50% 
transmittance line, together with the ON and OFF indications of FIG. 9B. 
Thus, FIG. 9A is obtained as a graph representing the output 
characteristics of the switch element of the present invention. 
As clearly seen from these figures, although the conventional type switch 
element exhibits considerable wavelength dependence in the OFF state, the 
switch element of the present invention exhibits little wavelength 
dependence in the OFF state. 
FIG. 10 illustrates calculation results about the crosstalk when the light 
signal passes through seven switch elements in the 4.times.4 matrix 
switch. Here, the crosstalk is defined as the total sum of the leaked 
light from the remaining three input?? ports when the main light signal is 
incident onto one input port. The calculations were performed on the basis 
of the wavelength dependence described above. The crosstalk of the switch 
element of the present invention, which is shown by solid curves in FIG. 
10, exhibits smaller wavelength dependence than that of the conventional 
type switch element, which is shown by broken curves. For example, 
although the wavelength range in which crosstalk is less than -15 dB is 50 
nm in the conventional optical matrix switch, it expands to 170 nm in the 
present embodiment. The smaller wavelength dependence of the optical 
matrix switch of the present invention is closely related to the fact that 
the optical matrix switch of the present invention is little affected by 
fabrication errors. 
More practical fabrication procedures of the present embodiment will be 
described below. The 4.times.4 optical matrix switch of this embodiment 
was formed on a 1 mm thick, 3 inch diameter silicon substrate 11. 
FIGS. 11A-11F are cross-sectional views illustrating the process for 
simultaneously fabricating 16 optical switch elements arranged as shown in 
FIG. 2A. Each switch element includes silica-based single-mode optical 
waveguides having cross-sectional structure as shown in FIGS. 3B and 3C. 
First, fine glass particle layer 12a for a bottom cladding layer 12, whose 
base component was pure silica (SiO.sub.2), was deposited on the silicon 
substrate 11 by the frame-hydrolysis deposition. The frame-hydrolysis 
deposition used, as a raw material, mixture gas composed of silicon 
chloride (SiCl.sub.4) as a base component, together with small amounts of 
boron chloride (BCl.sub.3) and phosphorus chloride (PCl.sub.3). 
Subsequently, by switching the mixture gas to that composed of the 
above-mentioned components plus an appropriate amount of germanium 
chloride (GeCl.sub.4), fine glass particle layer 13a for a core layer 13, 
whose base component was SiO.sub.2 -GeCl.sub.4, was deposited as shown in 
FIG. 11A. Then, the silicon substrate 11 on which the two fine glass 
particle layers 12a and 13a had been deposited was heated at approximately 
1350.degree. C. in an electric furnace to consolidate the fine glass 
particles, thus forming the bottom cladding layer 12 and the core layer 13 
as shown in FIG. 11B. After that, unnecessary portions of the core layer 
13 were removed by the photolithography process and the reactive ion 
etching process to form cores 31 and 32 as shown in FIG. 11C. 
Subsequently, fine glass particle layer 14a for a top cladding 14 was 
deposited by utilizing the frame-hydrolysis deposition using an SiCl.sub.4 
-BCl.sub.3 -PCl.sub.3 mixture gas as a raw material so that the cores 31 
and 32 were embedded in the layer 14a as shown in FIG. 11D. Then, the 
silicon substrate 11 was heated again in the electric furnace so as to 
consolidate the fine glass particle layer 14a for the top cladding 14, 
thus forming single-mode optical waveguides as shown in FIG. 11E. Finally, 
as shown in FIG. 11F, a thin film heater 34a as an optical phase shifter 
was deposited on a predetermined position on the top cladding 14 over the 
optical waveguide 31 of each optical switch element formed on the silicon 
substrate 11 through the above-mentioned procedures. 
The cross section of the cores 31 and 32 of the optical waveguides was 6 
.mu.m.times.6 .mu.m, and the relative refractive index difference .DELTA. 
between the cores and the cladding layers 12 and 14 was 0.75%. The 
4.times.4 optical matrix switch of the present embodiment has a basic 
structure in which eight silica-based-glass optical waveguides are 
parallely disposed at a 250 .mu.m pitch. Each optical switch element 
employs as its integral parts a linear optical waveguides and curved 
waveguides whose radius of curvature is approximately 4 mm. 
FIG. 12 is a graph plotting experimental values about the dependence of the 
bending loss on the radius of curvature of a 90 degree arc silica-based 
single-mode optical waveguide, which will serve as guidelines for 
appropriately setting the radius of curvature of the curved waveguides. In 
the optical waveguides whose relative refractive index difference .DELTA. 
between the cladding layers 12 and 14 is 0.75%, which were employed in 
this embodiment, the minimum allowable radius of curvature was 
approximately 4 mm, and this value was used so that the whole optical 
matrix switch could be accommodated on the substrate with a limited area. 
In addition, the cross angle at the cross portion 35 was set at 30 degrees. 
The effective optical path length difference between the two directional 
couplers was exactly set at 0.65 .mu.m, or half the light signal 
wavelength of 1.3 .mu.m, by using the photolithography process. 
Considering that the refractive index of the silica-based glass was 
approximately 1.45, the waveguide length difference on a real mask pattern 
was set at 0.45 .mu.m (=0.65 .mu.m/1.45). The thin film heater 34a was 
formed by depositing a 0.3 .mu.m thick, 50 .mu.m wide, 4 mm long chromium 
thin film on each optical switch element by the vacuum evaporation method 
using chromyl as an evaporation source. The total length of each optical 
switch element including the two directional couplers 33a and 33b, the 
thin film heater 34a and the cross portion 35 was about 15 mm. 
The optical matrix switch formed on a silicon wafer through the 
above-described procedures was cut into 10 mm.times.110 mm rectangular 
chip by using a dicing-saw. A heat-sinker was disposed on the bottom of 
the silicon substrate 11, optical fiber arrays were joined to the input 
and output optical waveguides, and leads for power supply were connected 
to the thin film heater 34a. Thus, the optical matrix switch was 
completed. By supplying power currents to selected thin film heaters, 
switching operation of the 4.times.4 matrix switch was confirmed. The 
power consumption of each thin film heater 34a required for the switching 
operation was about 0.5 W, and hence, the total consumption power was a 
maximum of 2 W because up to four thin film heaters operated at the same 
time. The total loss of the optical matrix switch was 3-4 dB including the 
loss at the optical fiber joints, and the extinction ratio thereof was 
greater than 25 dB even when the coupling ratios of the directional 
couplers largely deviated from the ideal value of 50% by .+-.10% owing to 
fabrication errors. 
EMBODIMENT 2 
FIG. 13 is a plan view showing an entire arrangement of an 8.times.8 
optical matrix switch as a second embodiment of a waveguide-type optical 
matrix switch according to the present invention. In this figure, 
reference numeral 11 denotes a silicon substrate, and a reference numeral 
21a-21b designates a waveguide bundle consisting of 16 (=8+8) silica-based 
optical waveguides. Midway between the input port and output port of the 
waveguide bundle 21a-21b, 15 optical switch groups #1-#15 are disposed. 
The switch groups #1-#15 include 1, 2, . . . , 7, 8, 7, . . . 2, and 1 
optical switch elements, respectively. This arrangement is characterized 
in that waveguide bundles 22a, 22b, 22c, 22d, 22e, 22f, 22g, and 22h, each 
of which includes 90 or 180 degree curve, are provided to connect between 
the switch groups #2 and #3, #4 and #5, #6 and #7, #7 and #8, #8 and #9, 
#9 and #10, #11 and #12, and #13 and #14, respectively. In other words, 
the 15 optical switch groups are arranged on the limited area substrate in 
a serpentine layout by using the curved waveguide bundles. 
FIG. 14 is a plan view showing the arrangement of each optical switch group 
#1-#15 of the optical matrix switch as shown in FIG. 13: it shows the way 
how optical switch elements are arranged on the way from the input port to 
the output port of the waveguide bundle 21a-21b. The switch groups include 
1, 2, . . . , 7, 8, 7, . . . , 2, and 1 optical switch elements as denoted 
by ellipses in FIG. 14. The left end of the optical switch group #1 is 
joined to the input port of the waveguide bundle 21a-21b including eight 
input optical waveguides 1a, 1b, 1c, 1d, 1e, 1f, 1g and 1h. The optical 
switch groups #1 and #2 are directly connected, and the optical switch 
groups #2 and #3 are joined by the curved waveguide bundle 22a, and the 
like. Finally, the right end of the optical switch group #15 is led to the 
output port of the waveguide bundle 21a-21b including eight output optical 
waveguides 2a, 2b, 2c, 2d, 2e, 2f, 2g and 2h. 
FIG. 15 is a plan view showing an arrangement of an optical switch element 
constituting the optical matrix switch as shown in FIGS. 13 and 14. Two 
silica-based optical waveguides 31a-31b and 32a-32b are placed in close 
proximity separated approximately several micrometers apart at two 
positions on a silicon substrate, thereby forming two directional couplers 
33a and 33b. A cross portion 35 is provided between the two directional 
couplers 33a and 33b. The coupling ratios of the directional couplers are 
set to become 50% by adjusting the separation of the waveguides at the 
coupling section and the coupling length. The effective optical path 
length of the optical waveguides 31a-31b and 32a-32b between the two 
directional couplers 33a and 33b are set such that the waveguide 32a-32b 
is longer than the waveguide 31a-31b by half the light signal wavelength 
of 1.3 .mu.m, that is, by 0.65 .mu.m. In addition, thin film heaters 34a 
and 34b are disposed on top of a cladding layer in such a manner that the 
heaters 34a and 34b are placed just over the waveguides 31a-31b and 
32a-32b, respectively. The waveguides 31a-31b and 32a-32b intersect with a 
cross angle of .theta. (30 degrees, for example) at the cross portion 35. 
The optical switch element shown in FIG. 15 is 12 mm long. In the optical 
switch element of this embodiment, since the cross portion 35 is provided 
between the directional couplers 33a and 33b, two locations (between the 
two directional couplers and at the cross portion 35) at which the two 
waveguides are rather separated from each other in FIG. 3A can be unified. 
As a result, the length of the optical switch element can be reduced to 
about 12 mm, which is shorter than that of the first embodiment, where it 
is 15 mm long. 
The 8.times.8 optical matrix switch formed on a silicon wafer was cut into 
55 mm.times.55 mm square chip by using a dicing-saw. A heat-sinker was 
disposed on the bottom of the silicon substrate, optical fiber arrays were 
joined to the input and output optical waveguides, and leads for power 
supply were connected to the thin film heaters 34a and 34b. Thus, the 
optical matrix switch was completed. By supplying currents to selected 
thin film heaters, switching operation of the 8.times.8 matrix switch was 
confirmed. The power consumption of each thin film heater required for the 
switching operation was about 0.5 W, and hence, the total consumption 
power was a maximum of about 4 W because up to eight thin film heaters 
operated at the same time. The total loss of the optical matrix switch was 
5-7 dB including the loss at the optical fiber joints, and the extinction 
ratio thereof was greater 20-25 dB even when the coupling ratios of the 
directional couplers largely deviated from the ideal value of 50% by 
.+-.10% owing to fabrication errors. 
In the present embodiment, the optical switch element includes two thin 
film heaters 34a and 34b as shown in FIG. 15. Although the thin film 
heater 34a disposed over the shorter waveguide 31a-31b is sufficient in a 
normal operation, the thin film heater 34b serves to compensate an optical 
path length difference error by lightly supplying power to the thin film 
heater 34b even if the error has been caused by an accident during the 
fabrication. 
In the arrangement of the optical matrix switch of the second embodiment, 
the number of optical switch elements through which the light signal 
passes is different. For example, when the light signal incident onto the 
input optical waveguide 1h is produced from the output optical waveguide 
2h, it passes through only one optical switch element, whereas when the 
light signal incident onto the input optical waveguide 1a is produced from 
the output optical waveguide 2a, it passes no less than 15 optical switch 
elements. Consequently, when each optical switch element produces a 
constant transmission loss, the output level of the light signal 
fluctuates in accordance with the traveling path of the light signal. This 
will present a problem in some cases. In such a case, the following 
embodiment can be employed to eliminate the problem. 
EMBODIMENT 3 
FIG. 16 shows an arrangement of optical switch groups used in a third 
embodiment of the present invention. The third embodiment is identical in 
its basic structure to the second embodiment described with reference to 
FIGS. 13 and 14, but is different in that inactive optical switch elements 
S.sub.D are disposed in addition to optical switch elements S in each 
optical switch group. The inactive switch element S.sub.D has the same 
geometry as that of the optical switch element of FIG. 15 except that the 
thin film heaters 34a and 34b are omitted, and the coupling ratios of 
directional couplers are equal, regardless of the value of the two 
coupling ratios. By adding such inactive optical switch elements S.sub.D, 
the fluctuations of the output level of the optical matrix switch due to 
the traveling path difference was reduced. The total loss of the optical 
matrix switch was 6.5-7 dB, and the extinction ratio equal to or greater 
than 20 dB was achieved even if the coupling ratios of the directional 
couplers deviated from the ideal value of 50% by about .+-.10% owing to 
fabrication errors. 
In the above-described embodiments, the cross angle .theta. of the two 
waveguides is set as 30 degrees. The setting of the cross angle .theta. is 
considered in terms of the crosstalk and cross loss. 
FIG. 17 is a graph illustrating the dependence of the crosstalk on the 
cross angle, that is, an amount of the light signal leaked to a 
counterpart optical waveguide at a single cross portion. The optical 
waveguides used here has a relative refractive index difference .DELTA. of 
0.75% between the core and cladding, and has the cross section of 6 
.mu.m.times. 6 .mu.m. As the cross angle increases, the crosstalk 
declines. In the present invention, the two optical waveguides in an 
optical switch element must intersect at such an angle that the crosstalk 
can be ignored. An angle such that the crosstalk due to the intersection 
of the two waveguides falls less than -30 dB is considered appropriate. 
Although such an angle depends on the relative refractive index difference 
between the core and cladding of the waveguides, the crosstalk between the 
two waveguides is practically negligible when the cross angle is greater 
than approximately 15 degrees owing to the contribution of the direct 
propagation characteristic of light. At the cross angle of 30 degrees 
employed in the above-described embodiments, the crosstalk was small as 
less than -60 dB. 
FIG. 18 is a graph illustrating the dependence of the cross loss on the 
crossangle. The optical waveguides used here also has a relative 
refractive index difference .DELTA. of 0.75% between the core and 
cladding, and has the cross section of 6 .mu.m.times.6 .mu.m. As the cross 
angle increases, the crosstalk decreases: the loss less than 0.2 dB can be 
achieved when the cross angle is greater than approximately 15 degrees 
where the crosstalk is negligible. At the 30 degree cross angle employed 
in the embodiments, the loss for each cross portion is 0.06 dB, which is 
very small. The total excess loss due to the cross portions in the 
8.times.8 optical matrix switch is less than 1 dB, which is also small. 
As seen from the two results described above, the loss and the crosstalk at 
the cross portion are decreased as the cross angle approaches 90 degrees. 
Accordingly, it is preferable that the cross angle be greater than 15 
degrees, and be as close to 90 degrees as possible. A large cross angle, 
however, is liable to increase occupation areas of curved sections, 
resulting in the increase in sizes of the optical switch element. 
Consequently, the amount of the cross angle is determined taking account 
of the required performance of an optical matrix switch, allowable radius 
of curvature of optical waveguides, or the like. 
Next, geometry of optical waveguides at a cross portion will be considered. 
FIGS. 19A-19E are schematic diagrams for explaining the geometry of the 
cross portions. In the above embodiments, width of the waveguides was 
uniform throughout the circuits as shown in FIG. 19A. The geometry of a 
cross section of the waveguides, however, can be modified to reduce the 
loss at the cross portion. 
One method of the modifications is shown in FIGS. 19B and 19C: waveguides 
are tapered in sections before and after the cross portion. More 
specifically, optical waveguides 41a, 41b, 42a and 42b of a common width, 
which constitute the circuit of a switch element except the cross portion, 
are joined to tapered optical waveguides 43a, 43b, 44a and 44b for 
transforming the waveguide width, respectively. The tapered waveguides 43a 
and 43b, and 44a and 44b are joined in turn to waveguides 45 and 46, which 
constitute the cross portion, and whose width serves to reduce the cross 
loss. When the cross portion is made up of the common waveguides whose 
relative refractive index difference .DELTA. between the core and cladding 
is 0.75%, and whose width is 6 .mu.m, the cross loss is 0.06 dB as stated 
before. In contrast, when the waveguides whose width is 4 .mu.m or 10 
.mu.m are used to constitute the cross potion, the cross loss is reduced 
to 0.05 dB. It indicates that the cross loss can be reduced by 
appropriately setting the width of the waveguides at the cross portion. In 
this case, the tapered waveguides 43a, 43b, 44a and 44b for transforming 
the waveguide width must be gradually tapered so that radiation loss or 
the like do not occur. 
Another method of the modifications is shown in FIGS. 19D and 19E: tapered 
waveguides 47a-47b and 48a-48b are extended to the cross portion so that 
the width at the cross portion is reduced or increased. When the cross 
portion is made up of the common waveguides whose relative refractive 
index difference .DELTA. between the core and cladding is 0.75%, whose 
width is 6 .mu.m, and which cross at an angle of 30 degrees, the cross 
loss is 0.06 dB as stated before. In contrast, when the waveguides whose 
width is gradually narrowed from 6 .mu.m to 5 .mu.m over a tapered length 
of 50 .mu.m as shown in FIG. 19D, the cross loss is reduced to 0.03 dB. 
This indicates that the method is effective for reducing the cross loss. 
In the above embodiments, all the optical waveguides are smooth. 
Considering the eigen electric field distribution in an optical waveguide, 
however, the shape and center of the electric field distribution differ in 
accordance with the shape of the waveguide: in accordance with a straight 
or curved waveguide; or with a radius of curvature. For this reason, when 
the optical waveguides of different geometry are joined with aligning the 
center thereof, not only the radiation loss due to mismatch of the eigen 
electric field distributions, but also the light undulation that 
unstabilizes the characteristics of directional couplers and a 
Mach-Zehnder interferometer will occur. Accordingly, a method is effective 
where optical waveguides of different geometry, such as a straight 
waveguide and a curved waveguide, or curved waveguides of different radii 
of curvature or of different curved directions, are joined with a small 
amount of offset: the centers of the waveguides are joined with offsets in 
such a fashion that no tilt between the center axes of the waveguides will 
occur so that the eigen electric field distributions of the two joined 
waveguides are matched as perfect as possible. This method is effective 
not only to reduce the loss, but also to restrict the light undulation. 
FIG. 20 is a schematic diagram showing an arrangement of a directional 
coupler having an offset structure. The offset structure is applied to 
joints 53a, 53b, 53c, 53d, 54a, 54b, 54c and 54d, where a straight 
waveguide and a curved waveguide are joined, and to joints 53e, 53f, 54e 
and 54f, where curved waveguides of different directions are joined. An 
amount of the offset is generally on a submicron order, although it 
differs depending on the relative refractive index difference between the 
core and cladding, the geometry of optical waveguides, and the wavelength 
of a light signal. 
Although in the above-described embodiments, the optical phase shifter (a 
thin film heater) is disposed over a shorter waveguide by half a 
wavelength than the other, so that the optical path length difference of 
1/2 wavelength is canceled to change the switch element to the ON state, 
the ON state can be realized by increasing the optical path length 
difference to one wavelength. This, however, presents a disadvantage that 
the wavelength dependence in the ON state increases. 
Furthermore, although in the above-described embodiments, a light signal 
whose wavelength is 1.3 .mu.m is used, the structure of the present 
invention can be readily applied to other light signals of different 
wavelengths, such as 1.55 .mu.m. 
Although it has been stated that the optical matrix switch of the present 
invention is little affected by fabrication errors of directional 
couplers, it must also be emphasized that the present invention has a 
subsidiary effect that it is little affected by the polarization 
dependence of directional couplers. 
Furthermore, although in the above embodiments, the structure and operation 
of the optical matrix switch based on the silica-based optical waveguides 
on a silicon substrate have been explained, the present invention can also 
be applied to other materials, such as plastic waveguides, ion-diffused 
glass waveguides, or lithium niobate waveguides with an optical phase 
shifter using an electrooptic effect, which can constitute a Mach-Zehnder 
interferometer type optical switch element. 
The present invention has been described in detail with respect to various 
embodiments, and it will now be apparent from the foregoing to those 
skilled in the art that changes and modifications may be made without 
departing from the invention in its broader aspects, and it is the 
intention, therefore, in the appended claims to cover all such changes and 
modifications as fall within the true spirit of the invention.