JPS63223709A - Space distribution detecting element for light signal - Google Patents

Abstract

PURPOSE:To permit detection of the space part of light signals by constituting the titled element of a multimode trunk light guide, plural branch light guides which are branched therefrom and are different in width size from each other and photoelectric converters which detect the light propagating in the respective branch light guides. CONSTITUTION:Modes of the prescribed order propagating in the trunk light guide 10 are guided to the prescribed branch light guides 11-13 predetermined by the width sizes of the branch light guides 11-13. Namely, one mode or plural modes are separated from the plural modes. The modes of the order corresponding to the space distribution of the light signals are guided to the branch light guides 11-13 such a manner and, therefore, the space distribution of the light signals is detected by recognizing to which of the light guides 11-13 the light is guided by the output signals of the photoelectric converters 41-43.

Description

DETAILED DESCRIPTION OF THE INVENTION Summary of the Invention A multimode core leading waveguide, at least two branched optical waveguides branching from the leading waveguide and having mutually different width dimensions, and a photoelectric conversion element that detects light propagating through each branched optical waveguide. It consists of When a spatially distributed optical signal is guided to the main waveguide, the optical signal is excited in a mode corresponding to the spatial distribution and guided to a branch optical waveguide corresponding to that mode.

Therefore, the spatial distribution of the optical signal can be detected depending on which branched optical waveguide the light is guided to.

BACKGROUND OF THE INVENTION The present invention relates to an optical signal spatial distribution detection element that can classify and detect the form of spatial distribution of optical signal intensity.

When detecting the spatial distribution of optical signals, C is used as a detector.
It is necessary to use elements such as OD and PSD. In this configuration, an optical system (
(lens system) and the signal processing system that processes the output signals of these elements become complicated.

The shape becomes larger. The problem is that it is expensive.

SUMMARY OF THE INVENTION An object of the present invention is to provide an optical signal spatial distribution detection element with a relatively simple configuration.

A spatial distribution detection element for optical signals according to the present invention.

a multi-mode core leading waveguide having one end surface into which a detected signal is incident and having a width to hold a plurality of optical modes; a core leading waveguide connected to the other end of the core leading waveguide so as to extend substantially on its extension; At least two branched optical waveguides having a smaller number of retained modes than the above, and having width dimensions such that the branching angle between them is sufficiently small and the orders of the retained modes are different from each other, and each branching It is characterized by comprising a photoelectric conversion element that detects light propagating through an optical waveguide.

This invention utilizes the fact that the propagating light incident on the basic optical waveguide is photographed frame-by-frame in different modes depending on the spatial distribution of the optical signal. A mode of a predetermined order propagating through the main optical waveguide is guided to a predetermined branch optical waveguide predetermined by the width dimension of the branch optical waveguide. That is, one mode or multiple modes are separated from multiple modes. In this way, the mode of the order corresponding to the spatial distribution of the optical signal is guided to the branched optical waveguide corresponding to that mode, so which branched optical waveguide the light is guided to is determined by the output signal of the photoelectric conversion element. By recognizing, the spatial distribution of the optical signal can be detected.

Since the above-mentioned main waveguide two-branch optical waveguide and, if necessary, a photoelectric conversion element can be integrated on one substrate, it is possible to achieve reduction in size and weight. Furthermore, since it is only necessary to couple optical signals distributed in space to the main waveguide, the lens system for this purpose can be simplified. Furthermore, since the spatial distribution can be determined simply by looking at which photoelectric conversion element outputs the detection signal, the signal processing system does not become complicated.

DESCRIPTION OF EMBODIMENTS First, a basic optical mode separation/synthesis element will be described, and then an example of an optical signal spatial distribution detection element will be described.

(1) Single mode three-branch optical waveguide (1,1) Structure and manufacturing method First, a single mode three-branch optical waveguide will be explained.

FIG. 1 perspectively shows an example of a single mode three-branch optical waveguide element. A 5IO2 buffer layer 2 is formed on an St substrate 1, and a glass waveguide layer 3 is further formed on this buffer layer 2. Ridge-shaped optical waveguides 10.11 to 13 are formed in the glass optical waveguide layer 3. The main waveguide 10 is a multi-mode optical waveguide capable of guiding light in three modes of 0 and 1° second order, and from one end of this optical waveguide 10 are three single-mode branch optical waveguides each having a different width. 11, 12, and 13 are branched. The optical waveguide 11 has the widest width, and the optical waveguide 13 has the narrowest width.

The branch angles θ (see FIG. 2) of these optical waveguides 11, 12, and 13 are sufficiently small. The fact that the branching angle θ is sufficiently small means that when the light propagates a minute distance along the branching optical waveguides 11, 12 or 13, the change in the interval between the branching optical waveguides is negligible compared to the distance traveled. It means that. The single mode branch optical waveguides 11 to 13 are parallel to each other when the distance between them is sufficiently large. Branch optical waveguides Il~13 are the main leading waveguide O
The part from the point where the two parts diverge to the part where they become parallel to each other is called a branch part.

FIG. 2 shows an example of the dimensions of these leading waveguides 10-13, such as the width of two intervals. For example, the branching angle θ is 1
150.1/100.1/200.1/400 (ra
d) fj, which can be set in degrees, and the length L of the branch part for these branch angles θ is 1.025.2. (15,
4, 10, 8, 20 (related).

Such a guiding waveguide element can be manufactured, for example, as follows.

FIG. 3 shows the manufacturing process, in which the leading waveguide 12
The cross section of the section is shown.

(100) n-type Si with a resistivity of 8 to 12 Ω·1 was used as the substrate 1 (Fig. 3 (A)), and this Si was heated to a temperature of 110 Ω.
Wet thermal oxidation at 0°C, 1.5μm thick SiO2
A buffer layer 2 is produced (FIG. 3(B)). On top of this
A glass optical waveguide layer 3 is prepared by sputtering Corning 7059 glass to a thickness of 1 μm (FIG. 3(C)).

Furthermore, a photoresist 4 (Az-
1350J) was uniformly spin-coated and baked at 90°C (Fig. 'M3 (D)). When the resist 4 is exposed to the leading waveguide pattern to be produced and then developed, the resist 4 in the portion that is to become the optical waveguide is removed (Fig. 3 (H)
) (photolithography).

When Al1 is sputtered onto this (FIG. 3(P)) and the resist 4 is melted, an optical waveguide pattern AJ5 remains (FIG. 3(G)) (lift-off).

Then, the portion of the glass layer 3 other than the Aj7 pattern 5,
For example, dry etching is performed by 0.1 μm using CHF3 gas (Fig. 3 (■)). Finally, the A-o pattern 5 is removed by wet etching. Etching liquid is HPO
;HNO3;CH3COOH-12:1:1 may be used.

The thickness of the glass layer in parts such as the optical waveguide 12 is 1 μm, and the thickness in other parts is 0.9 μm.

(1, 2) Operation of mode separation and synthesis In the branch portion of the three-branch optical waveguide device as described above,
When the three single mode optical waveguides 11, 12, 13 are sufficiently close together, the light waves propagating through each optical waveguide are mutually influenced. Therefore, we consider one branch part as one optical waveguide, and perform analysis using the local normal mode within it.

First, consider a model of a rib-shaped channel leading waveguide as shown in FIG. 4, and use the two-equivalent refractive index method to examine changes in equipolarized refractive index due to branching and field distribution. This model is equivalent to the device shown in FIG. 1 with the branched portions cut off. The rib refers to a portion that forms part of the optical waveguide 11, 12, 13 and protrudes above the surrounding area.

In FIG. 4, first consider the confinement of the light wave mode field in the longitudinal direction (X direction) of the leading waveguide. It can be considered that there are two types of slab optical waveguides I and It depending on the presence or absence of ribs.

The TE mode will be considered with the propagation direction of the light wave as the Z axis and the respective coordinate axes as shown in FIG.

It is assumed that the equipolarized refractive index of the leading waveguide layer (the optical waveguide layer or the part marked ■) is n, and the equipolarized refractive indexes of the air layer above it and the SlO□ buffer layer below are n and n, respectively. The upper surface of the optical waveguide layer is xmO, and the thickness of the optical waveguide layer is t or t
2) is represented by t.

(2) The Y-direction component E of the electric field in each of these layers is expressed as follows.

E-Aexp(kxlx)
(-oo<x<0)I E -B cos (kx2x-φ)
(0<X<t)E −Cexp(−kxa(x−t
)) (t<x<+oo) where k −1
2-β2-l (1-1,2,3)Xl in n2
i.

ko−2π/λo(2) nl: equipolarized refractive index of the i-th layer β: Phase constant in two directions λ0 = free space wavelength k - wave number in the X direction of the 1st layer xl.

Since the electric and magnetic fields must be continuous at each x-0 and x-t boundary, we obtain a characteristic equation that determines the second-order wave number by eliminating the amplitude terms.

k x2 i 2-mπ-tan (kxl/kx2)
+tan (kx3/kx2) Let the equipolarized refractive index of the portion where the layer thickness is 1-1 be n. This 2
el'f'2, the model shown in FIG. 4 can be considered as a seven-layer slab guided waveguide as shown in FIG.

Next, based on the 7-layer model shown in Figure 5,
We consider the confinement of the light wave mode field and find the final equipolarized refractive index.

The width of the part corresponding to the leading waveguide 13.12.11 is d
, d, and de, and the leading waveguide spacing is h. Consider the 7M mode.

Letting the X-direction component of the magnetic field in each optical waveguide be H, the stiffness is given by the following equation.

HX, ""A eO8φt exp (kx y) (-
ω<y<0) Hx27A cos (k2y +φ1) (0<y<
d2) HX3-B"exp fk3[y-(d2+h)El
+B-oxp [-3(y-d2)] (d2<y<
d2+h) H, -Ceos fk4[y -(d2+d4+h)]
-φ2) (d2+h<y<d2+d4+h) H, -D exp lk5[y-(d2+d4+2h)
110D-exp (-5 [y-(d2 +
d4 +h) ko1(d2+d4+h<y<d2+d4+
2h) HX6-EcoS(k6 [y-(d2+d4+
dB+2h)]-φ3)(d2+64+2h<y<d2
+d4+d6+2h)Hx7=E eosφ38xp
7[V-(d2+d, +d, +2h)]1(
d2+d4+d8+2h<y<10 flashes) However, k -1
n2 to 2-β2]cx-1,2,-, r>, -2π/
λ (5) Since the electric and magnetic fields must be continuous at each boundary, the equation for determining the first-order wavenumber is obtained by eliminating the terms related to amplitude.

Φ1Φ2Φ8-Φ3Φ4Φg exp (2k 3h
) - Φ1Φ5Φ7exp (-2k5h) -Φ4Φ5ΦSθxpl 2 (ka + ks)
h) −〇However, Φ −k n2(n2k +n2k )+ [0
2 k l k s ~(n r n a k2 ) ]
tan k 2 d 2Φ −k n2(n2k
+n2k )+ [nt ka to 5- (n3n5
4)] tan k4d4Φ −k n2Cn2k
+rx2k )+ [ne ks k7-(ns
n7 ke ) ]tan ke d6Φ −k
n (-n k +n2k ) ten [n k
k + (n n k ) Fltank dΦ −
k n2(n2k −n2k )5 B[
i 75 57+ [nk
k + (n n k)2 ta
nkd857 570 B111
Φ −k n2(n2k +n2k )+[−n
'k k + (n n k )21 tank
dΦ −k n2(n2k −n2k )+[n
4 to 3 to 5+ (n3r15 to 4)] tank k
4d4Φ −k n2(n2k −n2k )+
[n'k k + (n n k )21ta
nk dhere nl ” ” 3- n5- n7
- nof'f12 4 8
The thickness of the leading waveguide part with the arr2 rib is tl-1
μm, and the thickness of the part without ribs is t2 - 0.9 μm.

The width of the three single mode leading waveguides 13.12.11 is d
-2μm, d4-2.5μm, dB-3μm (
(Slightly different from that shown in FIG. 2), equation (6) is solved, and FIG. 6 shows the equipolarized refractive index β/ko of each optical waveguide with respect to the waveguide spacing.

From this graph, it can be seen that as the leading waveguide spacing increases, the equipolarized refractive index approaches a constant value.

The first term of equation (6) is the 73 single mode leading waveguides 11
．． This is the product of characteristic equations when 12.13 are each independent (the interval is sufficiently large). Namely.

If the spacing between the optical waveguides is sufficiently large, the second term and subsequent terms in equation (6) can be ignored and the three optical waveguides can be considered to be in a single state.

FIG. 7 shows how the equipolarized refractive index changes with respect to the optical waveguide width d of a single waveguide in an independent state where they do not influence each other. However, tl - 1 μm, tl 0
．． It was set to 9 μm.

In FIG. 7, the points where the solid line ■ intersects with each dispersion curve of equipolarized refractive index represent the propagation constant (equal polarized refractive index) of each mode in the multimode leading waveguide IO.

The point where the broken lines ■, ■, ■ intersect is the single mode optical waveguide 11
~13 propagation constants, respectively. Furthermore, arrows indicate the behavior of the waveguide mode in the three-branch optical waveguide element shown in FIG.

By the way, in the first branch part, the spacing between the optical waveguides changes, and independent modes in the original strict sense cannot exist. However, in the case of ideal branching in which the first branching angle is sufficiently small and there is no loss of optical power in the second branching portion, and the wavefront of the mode is approximately perpendicular to the Z axis, each mode may be considered to be independent.

Therefore, if we stand on the front run that the bifurcation angle is sufficiently small,
FIG. 6 shows the variation of the propagation constants of three independent local-normal modes in the bifurcation section. Further, the equivalent refractive indices of these three modes are independent without intersecting with each other.

As can be seen from FIG. 7, the zero-order mode is coupled to the optical waveguide 11 having the largest waveguide width among the three single-mode leading waveguides 11-13, and so on.

The first-order and second-order modes are respectively coupled to the optical waveguide 12° having an intermediate width and the leading waveguide 13 having a minimum width.

FIG. 8 shows how the field distribution changes. FIG. 8(A) shows how the zero-order mode propagating through the optical waveguide 10 advances to the leading waveguide 11, and FIG. 8(B) shows the change in field distribution when the first-order mode advances to the optical waveguide 12. Figure 8 (
C) shows changes in the field distribution of the secondary mode.

The above explanation also applies to light traveling in the opposite direction. That is, it propagates through the optical waveguide LL and reaches the optical waveguide lO.
The light entering the optical waveguide 10 becomes the zero-order mode, and similarly, the light propagating through the optical waveguides 12 and 13 and proceeding to the leading waveguide 10 becomes the first-order mode and the second-order mode, respectively, in the optical waveguide lO.

(2) Multimode Y-branch optical waveguide Next, the multimode Y-branch optical waveguide will be explained. An example of the configuration of a multimode Y-branch optical waveguide is shown in FIG.

Two branch optical waveguides 21 and 22 are branched from the main optical waveguide 20. One optical waveguide 21 is a multimode optical waveguide, and extends straight from the main optical waveguide 20, but for convenience of explanation, this will also be called a branch optical waveguide.

The other optical waveguide 22 is a single mode optical waveguide and is separated from the optical waveguide 21 by a very small angle. In FIGS. 10 to 12, the factors related to these leading waveguides 20, 21, 22 are referred to in the following description.
They are simply indicated by a, b, and c, respectively.

In this embodiment, the main optical waveguide 20 can propagate four modes of 0, 1.2, and 3rd order, one of these four modes branches off to the branch optical waveguide 22, and the rest The three modes propagate through the leading wavepath 21.

Such a Y branch portion can also be analyzed using the local normal mode described above.

Although the behavior of the light wave mode can be understood by determining the propagation constant of the local normal mode of the five-layer slab optical waveguide, the details of the analysis will be omitted and only the results will be described below.

Three cases are possible depending on the width of the leading waveways 21 and 22. If the mode guided to the single-mode optical waveguide 22 is the third-order mode in the multi-mode optical waveguide 20 one branch before (case 1), if it is the second-order mode (case 2), if the mode is the first-order mode, mode (case 3).

Figure 10 shows Case 1. Figure 10 (A) shows the change in the equivalent refractive index with respect to the change in the normalized optical waveguide spacing, and Figure 10 (B) shows the value of the equivalent refractive index before and after branching. Figure 10 (C) shows the behavior of the waveguide mode plotted on the dispersion curve with arrows.
(c)) shows the field distribution of the mode guided by (shown in (c)).

As an example of the normalized optical waveguide width of each branch optical waveguide in case 1, the leading waveguide 21(b) has a width of 14.2. The leading waveguide 22(c) is 1.58. In FIG. 10(B), the intersection of the solid line a and each dispersion curve is the equivalent refractive index in the optical waveguide 20 of each mode. 0 out of these points,
The first and second-order points move to a point corresponding to the width of the optical waveguide 21, as shown by the intersection of the broken lines. Only the tertiary mode point moves to a point corresponding to the width of the leading waveguide 22, as shown by the intersection with the broken line C. As mentioned above, since the branching angle is set at °C on the condition that it is sufficiently small, the equipolarized refractive indices of the four modes are independent without intersecting each other. It can be seen that only the 3rd order mode branches off into the optical waveguide 22 and the other 0.1 and 2nd order modes propagate in the leading waveguide 21.

FIG. 11 shows, for case 2, the change in the equipolarized refractive index, the behavior of the propagation mode, and the field distribution of the mode proceeding to the leading waveguide 22, respectively. An example of the normalized optical waveguide width of the leading waveguides 21 and 22 is 14.2. 3.1
It is 8. Among the 0th to 3rd order modes propagating through the optical waveguide 20, the 2nd order mode is split into the leading waveguide 22, and the remaining 0, 3, and
The first and third-order modes propagate through the optical waveguide 21.

FIG. 12 shows case 3. The normalized leading wave widths of the optical waveguides 21 and 22 are respectively 11.1.
It is 4.74. The first-order mode branches into the optical waveguide 22, and the remaining 0.2- and third-order modes propagate through the optical waveguide 21.

As described above, by appropriately selecting the width of the one-branch optical waveguide on the dispersion curve of equipolarized refractive index, any higher-order mode can be selectively extracted from the multimode leading waveguide.

By repeating the above idea in several lines, as shown in FIG. 0, 1 propagating through wave path 20
, 2.3 mode can be separated from each other.

In FIGS. 9 and 13, the light propagating through the single mode branch optical waveguides 22.31 to 34 and entering the main optical waveguide 20 passes through the optical waveguide 20 in the mode set in the propagating branch optical waveguide. It is also easy to understand that it is propagated.

(3>Summary There are two methods to consider when considering the characteristics of a waveguide branch. One is an analysis using local normal mode, which solves the characteristic equation and analyzes each section of the leading waveguide. This is a method to consider the change in the refractive index of
The first method is to consider changes in the equipolarized refractive index using a dispersion curve of the equipolarized refractive index with respect to the width of the leading waveguide. In the method of considering using a dispersion curve, as shown in FIG. 14, the equipolarized refractive index at each normalized leading waveguide width of the main leading waveguide before one branch and each branch optical waveguide after branching is plotted.

When the branching angle is sufficiently small compared to the wavelength, the change in the 1-equivalent refractive index is slow and continuous. Therefore, the equipolarized refractive index of each mode does not cross during the change,
The refractive index changes to an equipolarized refractive index of the normalized width of each branch waveguide. This situation is indicated by an arrow. 2 before and after branching
There is no change in the order of the equivalent refractive index. According to this method of considering the characteristics of optical waveguide branches using dispersion curves, by determining the width of the leading waveguide before and after the 9th branch, it is possible to know which mode before the 1st branch is separated into which branching optical waveguide. .

In the above example, a ridge-type leading waveguide using a glass material was described, but an optical waveguide can be made using any optical material, and the type of leading waveguide is a buried type (thermal diffusion, ion exchange, etc.).

It can be applied to all types including ion implantation, light/electron beam irradiation, etc.), loaded type, and voltage induced type.

(4) Optical signal spatial distribution detection element FIGS. 15(A) to 15(C) show examples of optical signal spatial distribution detection elements. In these figures, the same parts as those described above are given the same reference numerals.

The branched optical waveguides 11 to 13 terminate halfway on the substrate 1, and the branched optical waveguides 11 to 1
Photoelectric conversion elements 41 to 43 are provided, respectively, for detecting light propagating through 3 and converting it into an electrical signal. The photoelectric conversion elements 41 to 43 are, for example, a-Si (amorphous silicon).

CdS and CdTe can be used, and in this case, these materials may be deposited on the ends of the branched optical waveguides 11 to 13. It is also possible to use a photodiode or phototransistor using an I pn junction.

A hole may be formed at the end position of the optical waveguides 11 to 13, and a photodiode or the like may be inserted therein and bonded.
When is St, the pn junction can be formed integrally.

The optical signal is passed through a condenser lens 40 if necessary.

The signal is incident on one end of the main waveguide IO. As shown in FIG. 15(A), the intensity distribution of the optical signal has a Gaussian distribution,
The spot diameter is adjusted by the lens 40 to the core leading waveguide 10.
When the main optical waveguide 10 is positioned so that the light is focused to approximately the same extent as the width and the central part of the main optical waveguide 10 is excited, mainly zero-order mode light propagates through the main optical waveguide 10. Since this zero-order light travels to the branched optical waveguide 11 as described above, the largest electrical signal is output from the photoelectric conversion element 41. This shows that the spatial distribution of the optical signal is a Gaussian distribution.

In addition, as shown in FIGS. 15(B) and 15(C), there is a distribution of optical signals that strongly excite both sides of the incident end face of the core guiding waveguide 10, and an optical signal that excites the center and both sides of the incident end face of the core guiding waveguide 10. In the case of a distribution of
．． Since the mode is separated into 13, the photoelectric conversion element 42.4
A large electrical signal can be obtained from each of the three.

In addition, for example, in the case of an optical signal having a spatial distribution such that the incident lights shown in FIGS. 15(A) to 15(C) are superimposed, detection signals can be obtained from all the photoelectric conversion elements 41 to 43. . Furthermore, even if the spatial distribution of the optical signal is Gaussian, in the case of light whose spot diameter is larger than the width of the main leading waveguide 10, the secondary mode is mainly excited in the main leading waveguide 10, so the photoelectric conversion line A detection signal is obtained from the child 43. When the incident light beam spot is smaller than the width of the main optical waveguide lO, mainly the zero-order and second-order modes are excited, and detection signals are obtained from the photoelectric conversion elements 41 and 43.

In this way, it becomes possible to detect the spatial distribution of optical signals based on the detection signals of the photoelectric conversion elements 41 to 43.

It goes without saying that the optical waveguide fabricated on the substrate 1 may be a Y-branch optical waveguide as shown in FIG. Furthermore, the ends of the single-branch optical waveguides 11 to 13 are extended to the end surface of the substrate 1 as shown in FIG. 1, and the light emitted from this end surface is detected by a photoelectric conversion element arranged outside the substrate 1. You can also do it.

[Brief explanation of drawings]

1 to 8 are for explaining a single mode three-branch optical waveguide. FIG. 1 is a perspective view showing a single mode three-branch optical waveguide element. FIG. 2 is a plan view showing its dimensions. Figures 3A to 3 are cross-sectional views showing the manufacturing process. Figure 4 is a cross-sectional view used to explain the operation. Figure 5 is a diagram showing a model of a seven-layer slab guided waveguide. The figure is a graph showing the change in the equipolarized refractive index with respect to the normalized optical waveguide spacing. Fig. 7 is a graph showing the dispersion curve of the equipolarized refractive index, which shows the behavior of the propagation mode. Fig. 8 is (A) ~<C> are diagrams each showing the field distribution of the branching modes. Figures 9 to 13 are for explaining the multimode Y-branch optical waveguide. Figure 9 is a plan view. Figure 10 From FIG. 12, the branching modes F are 3.
2. This is to explain the operation in the first-order case. In each figure, (A) is a graph showing the change in the equipolarized refractive index with respect to the normalized optical waveguide spacing, and (B) is a graph showing the dispersion curve. Graph showing the behavior of the propagation mode; (C) is a diagram showing the field distribution of the mode guided to the branched optical waveguide. FIG. 13 is a plan view showing another example of a multimode Y-branch optical waveguide. FIG. 14 is a graph showing a dispersion curve of equipolar refractive index, and is used to explain the summary. FIGS. 15(A) to 15(C) are plan views showing an embodiment of the present invention. 10...Key guiding waveway. 11, 12.13... Branch optical waveguide. 41, 42.43...Photoelectric conversion element. that's all

Claims (2)

[Claims] (1) A multimode backbone optical waveguide having one end face into which the detected signal is incident and having a width capable of holding a plurality of optical modes; At least two branched optical waveguides that have a smaller number of retained modes than the main optical waveguide, and have width dimensions such that the branching angle between them is sufficiently small and the orders of the retained modes are different from each other; and a photoelectric conversion element that detects light propagating through each branched optical waveguide. (2) The optical signal spatial distribution detection element according to claim (1), wherein the branched optical waveguides are single mode optical waveguides having different width dimensions.