Very low-loss Y-junction power divider

March 1, 1989 / Vol. 14, No. 5 / OPTICS LETTERS

293

Very low-loss Y-junction power divider Z. Weissman, E. Marom, and A. Hardy Faculty of Engineering, Tel-Aviv University, Ramat-Aviv 69978,Israel Received August 23, 1988; accepted December 20, 1988

The design of an efficient wide-angle dielectric optical waveguide Y-junction power divider is outlined. The method has several degrees of freedom that can be used to optimize the device's performance to achieve minimization of the radiation loss for a specified mode at the input and equalization of the modal losses in a dual-mode device.

Symmetric dielectric Y-junctions are widely used as power dividers in interferometers

(e.g., Sagnac, Mach-

Zehnder),1 switching arrays,2 and Yjunction laser arrays.3 One problem of such structures is radiation loss at and near the junction, which can be significant when the separation angle between the two branches is greater than approximately 1 deg. In an ordinary (linear) Y-junction power divider (YPD) the loss in-

creases slowly for small branching angles and then rapidly for larger angles.

To maintain low loss one

should thus use small angles, say 1 deg. Such small branching angles dictate relatively long structures, which are generally undesirable. Furthermore for small branching angles any unintentional asymmetry (e.g., unequal branch widths) may prevent even power splitting between the two branches.4 An additional problem is caused by the dependence of the radiation loss on the mode number.5 Thus unequal loss of the two modes in a switch configuration

can give rise to

cross talk, an effect that usually increases with the branching angle. The purpose of this Letter is to propose a new design that has a loss minimum for branching angles of several degrees.

The loss is significantly lower than that

obtained for a comparable ordinary YPD with the same branching angle, thus allowing for shorter structures and a lower sensitivity to unintended fabrication asymmetries. Furthermore the loss minima are mode dependent, and by a proper choice of the YPD parameters one can minimize loss differences between the modes and consequently reduce cross talk in a dualmode YPD switch. Previous proposals for low-loss YPD's have been published.6'7 However, although the suggested structures were more efficient than comparable ordinary YPD's, they have inherent limitations. In the curved-branch YPD suggested by Baets and Lagasse6 the final branching angle (considered where the branches are practically uncoupled) is relatively large, and the retilting of the branches (to the original signal flow direction) causes an additional radiation loss. In the three-refractive-index YPD's suggested by Hanizumi et al., 7 the fabrication process is inherently a two-step process, which is more complicated and more sensitive to errors than a single-step process. In the design suggested below the branches are linear and the YPD is based on a two-refractiveindex structure that can be fabricated in a single-step process. 0146-9592/89/050293-03$2.00/0

- Here several design ideas are combined, and their effects are analyzed. As a result a very low-loss YPD (VLLYPD) is proposed that can be optimized for various applications. The numerical loss calculations are carried out using the beam-propagation method.8 The structures analyzed are all planar, but an extension to two-dimensional waveguides is straightforward by applying the effective-index method.9 Thus the basic principles and conclusions should apply to channel waveguides as well.

Let us consider an ordinary dual-mode YPD, as shown in Fig. 1(a).

An analysis of this structure re-

veals that the radiation loss in the vicinity of the junction may be attributed to two basic mechanisms5' 10: wave-front mismatch due to the sudden tilt and the change of the modal field distributions along the separating branches. The first mechanism dominates at small branching angles and depends on the guiding strength. The weaker the guidance the more significant this loss mechanism is, owing to the longer exponential mode tails. Based on this qualitative analysis several design ideas are incorporated to create a VLLYPD [Fig. 1(b)]. To reduce the tilt effect on the modal tails the junction region is tapered and, furthermore, the two branches run parallel to each other along some distance (with a length Lp that can be optimized) before being tilted at

2a

(Ca)

(b)

Fig. 1. (a) Ordinary dual-mode YPD and (b) the proposed VLLYPD. In the designs discussed here and in Figs. 2-4, wo = 6 /Am,wl = 3 Am, no = 2.2, An = n, - no = 5.1 X 10-3, and X = 0.9 ,um (the V number in the input waveguide is 2ir). © 1989 Optical Society of America

294

OPTICS LETTERS / Vol. 14, No. 5 / March 1, 1989

Ii~

_

_

_

where the distance z is given in micrometers, wo(-c) = 6 gm, wl(o) = 3 Am, X = 0.9 Am, no = 2.2, and An = n, - no = 5.1 X 10-3. Thus the input branch supports

1

two guided modes, whereas the output branches support one guided mode each. The length of the parallel region Lp is such that the internal boundaries of the two tilted branches meet at the junction [i.e., it is a

4

dependent in this example, as shown in Fig. 1(b)].

The effects of the above-mentioned design improvements on a propagating mode's transmission are illustrated in Fig. 2. The odd-mode propagation is shown in the VLLYPD described above [Fig. 2(b)] and in a ½

______________

7 /

,'

____

comparable ordinary YPD (i.e., with the same basic parameters) [Fig. 2(a)], both with 2a = 100 mrad. The smoother transition in the VLLYPD and consequently its much lower loss is evident. The power transmission curves for the ordinary YPD and for the

__________

4

VLLYPD are shown in Figs. 3(a) and 3(b), respective-

ly, as a function of 2 a. Note that the transmission of the ordinary YPD decreases monotonically with a and

(a)

is lower for the symmetrical mode for any branching

angle. On the other hand, the transmission curve of either mode in a VLLYPD has a maximum at some -K

ZZ- __

1.0

=

~

-_____

____________

•-= I E ½i½~_ ''½

NN N

\/i/

0.81

Ii

z0 C)

0.61

Cn

z

'1-

0.4 F 0.2F

o

I

I

I

20 40

60

80

I

100 120

2a (mrad)

(b'

(a)

Fig. 2. Propagation of the antisymmetric mode in (a) an ordinary YPD and (b) a VLLYPD with do = 5 gim. The basic parameters are as specified in Fig. 1, with 2a = 100

1.o0_

mrad and the propagation step equal to 1.5 ,4m.

an angle ±a with respect to the structure's axis of symmetry. Thus better modal confinement (and con-

z0

sequently lower device loss) is achieved in each of the

C',

two branches before tilting takes place. The separation dobetween the two parallel branches is optimized, considering the location of the peak (or peaks) of the input-mode distribution. The branching angle 2a should be optimized as well, so that maximal transmis-

/

0.81_

/

N

/

N

/ 0.6_

C)

z

itar

0.4_0.2 _

sion (minimal radiation loss) for a specific mode is

obtained.

I

As an example consider a VLLYPD with do = 5 gm

0

and a taper function given by

20

I

40

I

I

I

I

_

60 80 100 120 140 2a (mrcad) (b)

T(z) = 1 + 0.5[cosh (z)

]2

where [see Fig. 1(b)]

(1)

Fig. 3. Curves describing the power transmission versus the branching angle for (a) an ordinary YPD and (b) a

VLLYPD that is optimized for the antisymmetric mode (do

wo(Z)= wo(-o)T(z)

for z < 0,

= 5 Am). The basic parameters are as specified as Fig. 1.

wl(z) = w 1 (o)T(z)

for z > 0,

symmetric mode.

The solid curve, symmetric mode; the dashed curve, anti-

4

March 1, 1989 / Vol. 14, No. 5 / OPTICS LETTERS

mission -r and the ratio between the transmissions of

4

two unequal branches (2.9 gm:3.1 Am) with a spread of 2a = 65 mrad, do = 2.5 Am, and even-mode excitation.

1.0

a""\

Z 0.81

0

W 0.6k_ W 0.4k 0.2-

0

20 40

60

80

100 120 140-

2a (mrad) Fig. 4.

Power transmission versus the branching angle for

the VLLYPD of Fig. 1(b) optimized for equal and minimal losses for both modes (do = 2.5 Am). The solid curve, sym-

metric mode; the dashed curve, antisymmetric mode.

finite value of a. At 2 apeak - 100 mrad (-5.7O) the antisymmetric mode has a transmission maximum of greater than 97%. The symmetric mode has a maximum at 2 apeak - 65 mrad (-3.9O). At this angle the transmissions of the symmetric and antisymmetric modes are 76%and 73%,respectively. The peak angle at which radiation loss attains its minimum is close to the angle at which the two plane waves that make up each input mode (in the geometrical optics approximation) refract into the two tilted branches. In mathematical terms, apeak- 90° - 01- sin-{°

cos sini,(/n sin 00)]}

where 00and 01are the geometrical angles of propagation in the input and output branches, respectively. A similar observation was made by Hanizumi et al.7 Since the transmission maximum of the antisymmetric mode is higher and obtained at a significantly larger angle than for the symmetric mode, it would be useful for many applications to excite the antisymmetric mode only. This can be accomplished in various ways.1"'" 2

295

If, however, a dual-mode operation is re-

quired with equal radiation loss for the two modes, one should design the VLLYPD with 2a - 40 or 70 mrad, which are the two a values for which the two curves intersect [as can be seen in Fig. 3(b)].

Alternatively, one can optimize the design and bring the maxima of the two modes close to each other. As an example, the transmission curves for a VLLYPD with do = 2.5 Mmare given in Fig. 4. All other parame-

ters are similar to those used in deriving Fig. 3(a). Note that a transmission of greater than 92% is obtained for either mode at 2a - 65 mrad and that the two peaks are close to each other.

The fact that the VLLYPD has more design parameters than the ordinary YPD may make it more sensitive to fabrication tolerances. However, this is not necessarily the case. To demonstrate this we consider one possible example of the effects of such tolerances, that of unequal branch widths. Instead of equal (3 Am:3 ,m) branches we calculated the full power trans-

The full transmissions remain approximately the same as for the symmetric junctions [seeFigs. 3(a) and 4]. On the other hand, in both devices the branch transmissions become unequal, to different extents. In the ordinary YPD structure r2.9/T3.1 = 0.92,whereas in the VLLYPD the ratio is 0.97. Moreover since for such a large angle the ordinary YPD's full transmission is much lower than that of the VLLYPD (0.69 versus 0.92), it is more appropriate to compare the transmission's asymmetry in a VLLYPD at 2a = 65 mrad with that of an ordinary YPD at 2a = 20 mrad (for which the full transmission is -0.92). For the ordinary YPD we get T2 .9 /T3 .1 = 0.89. Thus the VLLYPD is less sensitive to unequal branch widths than an ordinary YPD is. This difference is related to the fact that the impinging mode is diffused at the VLLYPD's junction and thus senses the asymmetry much further (along the device) than in the ordinary YPD. In conclusion, a novel YLD geometry has been proposed that exhibits improved features such as lower loss at larger branching angles compared with that of ordinary YPD's. The transmission curve peaks at some angle owingto a resonant behavior of the refracted field. Thus the structure's parameters could be optimized to tailor YPD's for various applications. In addition, the VLLYPD seems less susceptible to fabrication errors than an ordinary YPD. In the examples given above only dual-mode VLLYPD's were consid-

ered, but the same ideas apply to single-mode YPD's as well.

The research of Z. Weissman was supported by a stipend from the Manuel Klachky Fund, which is gratefully acknowledged. The research of the other authors has been partially supported by a grant from the Israel National Council for Research and Development.

References 1. For example, W. K. Burns and A. F. Milton, IEEE J. Quantum Electron. QE-18, 1790 (1982). 2. R. Forber and E. Marom, IEEE J. Quantum Electron. QE-22,911 (1986). 3. D. F. Welch, W. Streifer, P. S. Cross, and D. R. Scifres,

IEEE J. Quantum Electron. QE-23, 752 (1987). 4. W. K. Burns and A. F. Milton, IEEE J. Quantum Electron. QE-lI, 32 (1975).

5. Z. Weissman, A. Hardy, and E. Marom, "Mode-dependent radiation loss in Y junctions and directional couplers," IEEE J. Quantum Electron. (to be published). 6. R. Baets and P. E. Lagasse, Appl. Opt. 21, 1972 (1982). 7. 0. Hanizumi, M. Miyagi, and S. Kawakami, Opt. Commun. 51, 236 (1984).

8. For example, J. Saijonmaa and D. Yevick, J. Opt. Soc. Am. 73, 1785 (1983). 9. G. B. Hocker and W. K. Burns, Appl. Opt. 16,113 (1977).

10. M. Kuznetsov, IEEE J. Lightwave Technol. LT-3, 674 (1985).

11. R. N. Thurston, E. Kapon, and Y. Silberberg, IEEE J. Quantum Electron. QE-23, 1245(1987). 12. A. Hardy, E. Marom, and J. Shama, Appl. Opt. 27, 447 (1988).