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Low radiation loss Y-junctions in planar dielectric optical waveguides
Volume 51, number 4
OPTICS COMMUNICATIONS
15 September 1984
LOW RADIATION LOSS Y-JUNCTIONS IN PLANAR DIELECTRIC OPTICAL WAVEGUIDES Osamu HANAIZUMI, Mitsunobu MIYAGI and Shojiro KAWAKAMI Research Institute o f Electrical Communication, Tohoku University, Sendai, 980 Japan Received 15 June 1984
A simple structure is proposed to reduce radiation losses of Y-junctions in planar optical waveguidesby decreasingrefractive indices near the branchingregions. The losses of the properly designed Y-junctions can be reduced by around an order of magnitude compared with those of conventional ones when the branching angles are large.
1. Introduction Branching waveguides are important structures in planar optical waveguides as power dividers and switches [1,2]. One of the most important problems in the branching waveguides is the radiation loss at the junctions. When the refractive index difference between the core and the cladding is large, power of the guided mode is divided into the branches with relatively small losses. However, in some situations, the refractive index difference cannot be made large [3], because it is necessary to match the spot size in the planar waveguides with that in fibers, and one wants to realize waveguides with large branching angles in order to avoide long waveguide sections for the separation of the waveguides. In this paper, we propose a simple structure to reduce radiation losses of Y-junctions in planar optical waveguides by decreasing refractive indices near the branching regions. A principle to reduce radiation losses is presented and the junction losses are calculated by means of the propagating beam method (PBM) [4,5]. It is theoretically possible to realize the Y-junctions with large branching angles with small junction losses.
2. Principle to reduce radiation losses Fig. 1 shows a basic structure for reducing radia236
x
n 2T
J
n2 ~3~
~Z
T n
z=O
TcosecO (2TsecO -T)cot 0
Fig. 1. Symmetricplanar optical waveguide with a Y-junction with decreased index distributions, where the refractive index in region A and B is n3. tion losses which we propose. For simplicity, a twodimensional symmetric slab geometry is assumed. The regions (A and B) near the branching point are assumed to have lower refractive indices than that of the cladding. A principle to reduce the junction loss is to match the direction of each elementary wave of the guided mode to that in the branches to introducing regions with lower refractive indices. We assume that a waveguide with a refractive index n 2 of the core and core width 2T is followed by branches with a refractive index h 2 of the core and core width 21r, which are embedded in the cladding with a refractive index n 1 and a total branching angle 0 030-4018/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 51, number 4
OPTICS COMMUNICATIONS
o,
I
15 September 1984
n,
Fig. 2. Ray trajactory in the proposed Y-junction. 20. Let the angles between the elementary waves of the guided modes and the propagation a~xesbe ~0and ~b, and the refraction angles at the media with refractive indices n 3 and h 2 be 01 and 02, respectively, as shown in fig. 2. By Snell's law, one has
n 2 sin ~0=n 3 sin01
,
n 3 cos 01 = h 2 cos 0 2 .
(1) (2)
By using the relation 0
+ ~ =
02,
(3)
3. Analysis and numerical results In order to evaluate the branching loss, the propagating beam method (PBM) [4,5] is employed. To show the effectiveness of decreasing the refractive indices near the branching region described above, we only show the case of the TE 0 mode incident to the single-mode waveguide, i.e., the normalized frequency o defined by [2(n2/n 1 - 1)] 1/2nlkoTis less than ,r/2. Let the field distributions obtained by the PBM be E(x, z), which is symmetric around x = 0, and the dominant modal field be Co(X):
we can express n 3 as n 3 = [n22sin2t.0 + n22cos2(O + ~b)]1/2 .
(4)
~oand ~ are determined from the corresponding char. acteristic equations of the guided modes. One might think that the above discussion can only be applied to over.moded waveguides, i.e., waveguides with a large normalized frequency. However, as shown later, this can suecessfuUy apply to single-mode waveguides and the radiation losses of Y-junctions designed by use of eq. (4) can be reduced drastically A simple discussion shows that eq. (4) can only be applied to the waveguide structure 0> ~
(5)
for reducing radiation losses, because the ray refracted to the branches should not appear in the central region at all.
60(x)-- [ ~ 1 + =
I[W)I-1/2COS(UX/:/);
IX[< :/,
[:/(I+ 11g,)]-l[2costJ
Ixl> :/, (6)
X e x p [ - ~ ( [ x L / : / - 1)] ;
where t~/:/and jff/:/are the transverse phase constants in the core and the cladding, respectively. Then the power transmission coefficient n is expressed by
~=41!E(x,z)~O(X-x X exp(jk0h2x sin 0) dx
c) ,
(7)
where x c is the x coordinate corresponding to the center of the upper branch. The power transmission coefficient is numerically evaluated at some distance 237
Volume 51, number 4 15
'
OPTICS COMMUNICATIONS Power
'
/
conventional
ca
•o
15 September 1984
/
/
10
-5'0
ii
Ao.it_ii
~core -
o
X
~core -
~o
, ~iTI
th
o
Fig. 5. Power distributions of the proposed ( - - )
u_.
//
//
z/~ 2
4 2e
proposed 6
8
10
12
4
, degrees
Fig. 3. Junction losses of the proposed and conventional Y-
junctions as functions of 20 for nl = 1.5, h = 1 #m, and 2T = 2T = 5 #m. Solid and dashed lines correspond to o = o = 1.57 and o = 1.4, o = 1.2, respectively. Arrows indicate the angle of 20 = 2~ showing lower limits of the angle predicted by eq. (5). where the coupling between the branches is negligible. Fig. 3 shows the junction losses - 1 0 log r / o f the proposed Y-junction as well as those o f the conventional one where the refractive index is h 2 in region A and n 1 in region B as functions of the total branching angle 20 for two cases o f o = b= 1.57 and o = 1.4, b= 1.2, where n 1 = 1.5, k = 1 grn, and 2 T = 2 J ' = 5 p m are assumed. One can see that the junction losses can be drastieaUy reduced in the proposed structure when the branching angle is large. This fact shows that the junction with large angles can be realized in planar optical waveguides. In this particular examples, if the allowed junction loss is 1 dB, maximum branching
.8
.
.6
.
.
.
.
,/
.2
A simple structure has been proposed to reduce radiation losses o f Y-junctions in planar optical waveguides. The principle described in this paper can be applied to some other similar derivatives and threedimensional waveguides with branches in i n t e g r a t e d optical circuits.
References [ 1] I. Anderson, IEE J. Microwaves, Optics and Acoust. 2
0 --,2
0
z+ 8 12 2e . d e g r e e s
Fig. 4. Relative index difference An3/n I ~ (n I - n3)/nl as functions of 20 determined by eq. (4). Parameters corresponding to solid and dashed lines are the same with those
238
4. Conclusion
i
r-
in fig. 3.
angles 20 o f the conventional and proposed Y-junctions are 4 ° and 11 o, respectively. The refractive index difference An3/n 1 = (n 1 - n3)/n 1 near the branching regions calculated b y eq. (4) are shown in fig. 4. To help understanding why the junction losses are so reduced b y decreasing the refractive indices near the branching region, power distributions far from the braching point are shown in fig. 5 for the conventional and proposed Y-junctions. Numerical calculations have been also carried out to minimize junction losses b y decreasing or increasing refractive indices near the branching regions. We have found that a similar structure has been obtained and the minimum attainable losses are not appreciably different from those obtained in the proposed Y-junctions when the branching angle is large.
,z
.4
<
and
conventional (---) Y-junctions at z.= 500 #m for 20 = 6", where nl = 1.5, h= 1 #m, 2T = 2T = 5 #m, and o = o = 1.57 are assumed.
8
(1978) 7. [2] H. Sasaki and I. Anderson, IEEE J. Quantum Electron QE-14 (1978) 883. [3] G. Stewart and P.J.R. Laybourn, IEEE J. Quantum Electron. QE-14 (1978) 930. [4] S. Kawakami and J. Nishizawa, Proc. IEEE 53 (1965) 2148. [5] J.A. Fleck, J.R. Morris and M.D. Felt, Appl. Phys. 10 (1976) 129.
OPTICS COMMUNICATIONS
15 September 1984
LOW RADIATION LOSS Y-JUNCTIONS IN PLANAR DIELECTRIC OPTICAL WAVEGUIDES Osamu HANAIZUMI, Mitsunobu MIYAGI and Shojiro KAWAKAMI Research Institute o f Electrical Communication, Tohoku University, Sendai, 980 Japan Received 15 June 1984
A simple structure is proposed to reduce radiation losses of Y-junctions in planar optical waveguidesby decreasingrefractive indices near the branchingregions. The losses of the properly designed Y-junctions can be reduced by around an order of magnitude compared with those of conventional ones when the branching angles are large.
1. Introduction Branching waveguides are important structures in planar optical waveguides as power dividers and switches [1,2]. One of the most important problems in the branching waveguides is the radiation loss at the junctions. When the refractive index difference between the core and the cladding is large, power of the guided mode is divided into the branches with relatively small losses. However, in some situations, the refractive index difference cannot be made large [3], because it is necessary to match the spot size in the planar waveguides with that in fibers, and one wants to realize waveguides with large branching angles in order to avoide long waveguide sections for the separation of the waveguides. In this paper, we propose a simple structure to reduce radiation losses of Y-junctions in planar optical waveguides by decreasing refractive indices near the branching regions. A principle to reduce radiation losses is presented and the junction losses are calculated by means of the propagating beam method (PBM) [4,5]. It is theoretically possible to realize the Y-junctions with large branching angles with small junction losses.
2. Principle to reduce radiation losses Fig. 1 shows a basic structure for reducing radia236
x
n 2T
J
n2 ~3~
~Z
T n
z=O
TcosecO (2TsecO -T)cot 0
Fig. 1. Symmetricplanar optical waveguide with a Y-junction with decreased index distributions, where the refractive index in region A and B is n3. tion losses which we propose. For simplicity, a twodimensional symmetric slab geometry is assumed. The regions (A and B) near the branching point are assumed to have lower refractive indices than that of the cladding. A principle to reduce the junction loss is to match the direction of each elementary wave of the guided mode to that in the branches to introducing regions with lower refractive indices. We assume that a waveguide with a refractive index n 2 of the core and core width 2T is followed by branches with a refractive index h 2 of the core and core width 21r, which are embedded in the cladding with a refractive index n 1 and a total branching angle 0 030-4018/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 51, number 4
OPTICS COMMUNICATIONS
o,
I
15 September 1984
n,
Fig. 2. Ray trajactory in the proposed Y-junction. 20. Let the angles between the elementary waves of the guided modes and the propagation a~xesbe ~0and ~b, and the refraction angles at the media with refractive indices n 3 and h 2 be 01 and 02, respectively, as shown in fig. 2. By Snell's law, one has
n 2 sin ~0=n 3 sin01
,
n 3 cos 01 = h 2 cos 0 2 .
(1) (2)
By using the relation 0
+ ~ =
02,
(3)
3. Analysis and numerical results In order to evaluate the branching loss, the propagating beam method (PBM) [4,5] is employed. To show the effectiveness of decreasing the refractive indices near the branching region described above, we only show the case of the TE 0 mode incident to the single-mode waveguide, i.e., the normalized frequency o defined by [2(n2/n 1 - 1)] 1/2nlkoTis less than ,r/2. Let the field distributions obtained by the PBM be E(x, z), which is symmetric around x = 0, and the dominant modal field be Co(X):
we can express n 3 as n 3 = [n22sin2t.0 + n22cos2(O + ~b)]1/2 .
(4)
~oand ~ are determined from the corresponding char. acteristic equations of the guided modes. One might think that the above discussion can only be applied to over.moded waveguides, i.e., waveguides with a large normalized frequency. However, as shown later, this can suecessfuUy apply to single-mode waveguides and the radiation losses of Y-junctions designed by use of eq. (4) can be reduced drastically A simple discussion shows that eq. (4) can only be applied to the waveguide structure 0> ~
(5)
for reducing radiation losses, because the ray refracted to the branches should not appear in the central region at all.
60(x)-- [ ~ 1 + =
I[W)I-1/2COS(UX/:/);
IX[< :/,
[:/(I+ 11g,)]-l[2costJ
Ixl> :/, (6)
X e x p [ - ~ ( [ x L / : / - 1)] ;
where t~/:/and jff/:/are the transverse phase constants in the core and the cladding, respectively. Then the power transmission coefficient n is expressed by
~=41!E(x,z)~O(X-x X exp(jk0h2x sin 0) dx
c) ,
(7)
where x c is the x coordinate corresponding to the center of the upper branch. The power transmission coefficient is numerically evaluated at some distance 237
Volume 51, number 4 15
'
OPTICS COMMUNICATIONS Power
'
/
conventional
ca
•o
15 September 1984
/
/
10
-5'0
ii
Ao.it_ii
~core -
o
X
~core -
~o
, ~iTI
th
o
Fig. 5. Power distributions of the proposed ( - - )
u_.
//
//
z/~ 2
4 2e
proposed 6
8
10
12
4
, degrees
Fig. 3. Junction losses of the proposed and conventional Y-
junctions as functions of 20 for nl = 1.5, h = 1 #m, and 2T = 2T = 5 #m. Solid and dashed lines correspond to o = o = 1.57 and o = 1.4, o = 1.2, respectively. Arrows indicate the angle of 20 = 2~ showing lower limits of the angle predicted by eq. (5). where the coupling between the branches is negligible. Fig. 3 shows the junction losses - 1 0 log r / o f the proposed Y-junction as well as those o f the conventional one where the refractive index is h 2 in region A and n 1 in region B as functions of the total branching angle 20 for two cases o f o = b= 1.57 and o = 1.4, b= 1.2, where n 1 = 1.5, k = 1 grn, and 2 T = 2 J ' = 5 p m are assumed. One can see that the junction losses can be drastieaUy reduced in the proposed structure when the branching angle is large. This fact shows that the junction with large angles can be realized in planar optical waveguides. In this particular examples, if the allowed junction loss is 1 dB, maximum branching
.8
.
.6
.
.
.
.
,/
.2
A simple structure has been proposed to reduce radiation losses o f Y-junctions in planar optical waveguides. The principle described in this paper can be applied to some other similar derivatives and threedimensional waveguides with branches in i n t e g r a t e d optical circuits.
References [ 1] I. Anderson, IEE J. Microwaves, Optics and Acoust. 2
0 --,2
0
z+ 8 12 2e . d e g r e e s
Fig. 4. Relative index difference An3/n I ~ (n I - n3)/nl as functions of 20 determined by eq. (4). Parameters corresponding to solid and dashed lines are the same with those
238
4. Conclusion
i
r-
in fig. 3.
angles 20 o f the conventional and proposed Y-junctions are 4 ° and 11 o, respectively. The refractive index difference An3/n 1 = (n 1 - n3)/n 1 near the branching regions calculated b y eq. (4) are shown in fig. 4. To help understanding why the junction losses are so reduced b y decreasing the refractive indices near the branching region, power distributions far from the braching point are shown in fig. 5 for the conventional and proposed Y-junctions. Numerical calculations have been also carried out to minimize junction losses b y decreasing or increasing refractive indices near the branching regions. We have found that a similar structure has been obtained and the minimum attainable losses are not appreciably different from those obtained in the proposed Y-junctions when the branching angle is large.
,z
.4
<
and
conventional (---) Y-junctions at z.= 500 #m for 20 = 6", where nl = 1.5, h= 1 #m, 2T = 2T = 5 #m, and o = o = 1.57 are assumed.
8
(1978) 7. [2] H. Sasaki and I. Anderson, IEEE J. Quantum Electron QE-14 (1978) 883. [3] G. Stewart and P.J.R. Laybourn, IEEE J. Quantum Electron. QE-14 (1978) 930. [4] S. Kawakami and J. Nishizawa, Proc. IEEE 53 (1965) 2148. [5] J.A. Fleck, J.R. Morris and M.D. Felt, Appl. Phys. 10 (1976) 129.