IEEE Journal of Lightwave Technology

May 2001 VOLUME 19

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NUMBER 5

JLTEDG

(ISSN 0733-8724)

PAPER

Copyright © 2001 IEEE.

Reprinted from Journal of Lightwave Technology, vol. 19, no. 5, pp. 700-707, May 2001 Multimode Enterference Couplers with Tunable Power Splitting Ratios J. Leuthold, C.H. Joyner

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Multimode Interference Couplers with Tunable Power Splitting Ratios Juerg Leuthold, Member, IEEE, and Charles H. Joyner

Abstract—New, compact multimode interference couplers with tunable power splitting ratios have been realized. Experiments show large tuning ranges. Such couplers are needed to optimize ON–OFF ratios in interferometric devices and may find applications as extremely compact switches. Index Terms—Integrated optics, multimode interference (MMI), optical coupler, optoelectronic devices, semiconductor devices.

I. INTRODUCTION

T

UNABLE mode couplers are of high interest in integrated optics. They can be used to increase design and fabrication tolerances of devices that need accurately defined coupler splitting ratios [1]–[3]. For instance, interferometric-type electrooptic and all-optical devices need well-defined coupler relations in order to provide high extinction ratios [3]. Recently, a fully integrated 100-Gb/s wavelength converter has been demonstrated [4]. The device has two interferometer arms of different length that consequently have different fabrication-related waveguide losses. Nevertheless, extinction ratios exceeding 14 dB were achieved with this interferometer-based switch. Such a result can only be reproducibly achieved by use of integrable, tunable power splitters that allow adaptation of the splitting ratio to the actual propagation losses. Thus, tunable power splitters are key elements for performance improvement of integrated optic devices and may lead to new integrated optics circuits and eventually to ultracompact integrable switches. Standard couplers that allow for tuning of the splitting ratios include digital-optical switches like - and -junctions [5] or directional couplers [6]. But digital-optical switches are large and require precise lithography at waveguide intersections. Directional couplers on the other hand need tight ( 0.1 m) control of the waveguide dimensions since they exploit mode coupling between two waveguides that are close to each other. In the past couple of years, multimode interference (MMI) couplers [7], [8] have attracted considerable interest due to advantageous characteristics such as compactness, relaxed fabrication tolerance, and large optical bandwidths, as well as polarization insensitivity, when strongly guided structures are used [9]. Meanwhile, they have found applications as splitters and combiners [8], mode converters [10], and power splitters with arbitrary splitting ratios [11], [12]. Attempts to tune MMIs have been made with two-mode-interference waveguides [13]and 1 1 MMI couplers [14]having partially

Manuscript received June 30, 2000; revised February 5, 2001. The authors are with Bell Labs, Lucent Technologies, Holmdel, NJ 07733 USA (e-mail: [email protected]). Publisher Item Identifier S 0733-8724(01)03626-X.

metallized surfaces to current-bias the material beneath the metal layer in order to provide switching. Unfortunately, the demonstrated performance was limited, and tuning around the important 50 : 50 splitting ratio was not demonstrated. Recently, a versatile tunable 3 3 coupler was proposed [15]. 1 MMI with an intricate metallization It is based on a 1 pattern for current biasing. The presumed length of this MMI was 1300 m, while the width was as thin as 12 m. We believe that such tunable MMI concepts are of considerable theoretical interest, but based on our experience we think that it is unlikely that such long MMI structures can be realized with current technology and satisfactory performance. The authors also assume that they can change the refractive index by as much as 1% by current injection without changing the absorption or gain characteristics of the device. It is unclear how this can be realized, since most of the strong refractive index changes are usually accompanied by considerable absorption or gain changes. Here we propose and demonstrate tunable MMIs that have both a short length and a wide width and that have been realized with current standard technology. Using MMI theory, we locate new spots to tune the refractive index around well-determined locations within the MMIs. Refractive-index-related absorption or gain effects are considered within the framework of the theory. It is shown that significant tuning of the splitting ratios can be achieved by only slightly biasing the refractive index and with little degradation from absorption effects when using the suggested spots for tuning. If properly designed, the new MMIs might even be used as compact switches. In Section II, we introduce the operation principle of the tunable MMIs. Section III presents the theoretical model that allows quick investigation of the tuning performance of an MMI. Comparison of theory with beam-propagation simulation (BPM) and experiment is performed in Section IV. There we 2 MMI splitter. Secalso discuss tuning of a symmetric 2 tion V is devoted to 2 2 MMIs that allow for tuning around some given asymmetric splitting ratios. In the last section, we describe other interesting tunable MMIs in order to show that the theory and ideas are more generally applicable. The results are summarized in the conclusions. II. PRINCIPLE FOR TUNING SPLITTING RATIOS IN MMIS The idea for tuning the splitting ratios of MMIs exploits the fact that within an MMI, the input field is reproduced in single or multiple images at certain periodic intervals along the propagation direction of the light. The interference patterns of the self-images at one interval lead to the formation of new self-images at the next interval and finally to the output images. Con-

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1 = 00 005

Fig. 1. Tuning the output power from one output into the other in a 2 2 MMI by biasing the refractive index by as little as 0.15% (or n : ) in the black shaded areas within the MMI. The figures show the result of a BPM simulation for (a) an edge-biased, (b) a nonbiased, and (c) a center-biased MMI.

sequently, the output images can be changed by modifying the refractive index around some selected spots within one interval of the MMI where such self-images occur. This will lead to new phase relations between the self-images at the next interval and with that to a modified output image [8], [10], [11], [15]. The simplest approach to build MMIs with tunable splitting ratios is to modify the material properties around spots within the MMI, where the most dominant self-images appear. Usually, self-image pattern formation is most dominant and simple halfway along the propagation direction of an MMI. For instance, in a 2 2 MMI, only four self-images can be identified halfway along the MMI coupler, whereas the situation is more difficult anywhere else within the MMI. The BPM simulation of the overlap 2 2 MMI, as depicted in Fig. 1(b), visualizes these self-images found around the center. In our simulation, they appear as spots with higher field intensities (darker color) and are marked with black and white circles. In the case of the 2 2 MMI, the splitting ratios can then be tuned by changing the refractive index around the two self-images at the edge of the MMI with respect to the self-images at the center of the MMI. For example, by inducing a negative refractive index change of as little as 0.15% at the edges halfway along the MMI, the splitting ratios of the bar to cross output ports turns from a 50 : 50 into a 20 : 80 ratio, as visualized in Fig. 1(a), where we have changed the refractive index in the black shaded area of the MMI. By inducing the same negative refractive index change at the center halfway along the MMI, the splitting ratio turns into an 80 : 20 ratio [see Fig. 1(c)]. A detailed discussion of the geometry and structure of the MMI for which we have performed the simulation will be given below. Proper choice of the MMI type is a prerequisite in order to obtain significant tuning of the splitting ratios. For example, 2 2

MMIs can be designed in the geometry of the general-MMI type as well as in the geometry of the overlap-MMI type [10]. Overlap MMIs are a special case of the general MMIs, where the input and output ports have been chosen at a very specific location within the MMI input side. The special choice of the input and output positions leads to very simple interference patterns for wider MMIs that would normally have much more complicated patterns. Although these two types have almost the same performance, their geometry is quite different. For example, for a general 2 2 and overlap 2 2 MMI of the same length, the overlap type MMI (with its input ports at 1/3 of the MMI times wider MMI width than width) can be designed with a 2 MMI. This is important, since one is usuthe general 2 ally interested in designing the MMIs as wide and as short as possible. The reason for this is that short MMIs provide larger optical wavelength bandwidths while wider MMI widths lead to relaxed fabrication tolerances. (The relative error for a given technological width deviation is less severe for a wide MMI in comparison to an MMI with small width.) In addition, in our case, we would like to modify the refractive index around certain spots within an MMI. This, of course, is much simpler the larger the spots around which we may modify the refractive index. For this reason, we subsequently restrict our discussion to tunable MMI splitting ratios of the overlap type. Tuning of the splitting ratios of the general MMIs can be performed with the same technique and in most cases even by tuning the refractive index at the same spots as described for the overlap MMIs. III. THEORY OF MMIS WITH TUNABLE SPLITTING RATIOS This section describes a theory that gives a correct description of all overlap-type MMIs that tune the splitting ratios by

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where and are 1-dimensional vectors, and the maand are 1 1 matrices. and trices describe the field amplitudes at the 1 input and output ports, describes the mapping of the fields respectively. The matrix from the input to the center of the MMI and again from the center to the output guides. The matrix describes the intensity and phase modulations induced at the middle part onto the 1 self-images. A convenient description of the matrix has been given by Heaton and Jenkins [18], which we would like to use in a slightly modified form to express the elements of the matrix

N0

Fig. 2. Generic overlap MMI with 1 possible access waveguides. The positions of the waveguides are determined by the MMI width and the integer number . The tuning section comprises several shaded areas that indicate the locations where self-images appear. The output splitting ratios are tuned by biasing the refractive index in one or simultaneously in several of these areas.

N

W

varying the refractive index at certain spots halfway in the light propagation direction of the MMI. The theory can easily be extended to other overlap MMIs where the material parameter has to be tuned at other spots. As mentioned above, we can restrict the discussion to overlap-type MMIs that have wider geometrical widths and therefore are simpler to tune than the thinner general-type MMIs. The geometry of a generic overlap-type MMI with at 1 possible input and 1 output guides is depicted most in Fig. 2. Allowed input and output guide locations are at of the total MMI width . integer multiples of is the equivalent MMI width, which is the geometric width of the MMI including the penetration into the neighbor material of the waveguide. The length of such an MMI has been given by the relation [16], [17] with

(1)

where possible MMI lengths of overlap MMIs with 1 possible input and output guides; effective refractive index; wavelength in vacuum. To describe the tunable MMI from Fig. 2, we split the MMI into three sections. The first section describes the mapping of 1 possible input fields up to halfway along the field propagation direction of the MMI. The second section must describe the tuning of the fields at the middle of the MMI, and the last section again describes the mapping of the modified fields halfway 1 output guides. This leads us to a along the MMI to the description in terms of a matrix equation of the form (2)

with

(3)

. The diagonal matrix then has the form as and shown in (4) at the bottom of the page, where , with the phase shift induced by along the tunable the change of the effective refractive index for a signal with a vacuum wavelength section of length . Refractive-index changes in a material are associated with absorption changes as implied by the Kramers–Krönig relations. considers these refractiveThe intensity absorption term index change losses. These losses may be negligible or stronger or even might be turned into gain, depending on the underlying process that has been chosen to change the refractive index. IV. COMPARISON OF THEORY WITH EXPERIMENT, TUNABLE 2 2 MMI WITH SYMMETRIC SPLITTING RATIO In this section, we first compare the analytical model with BPM simulations and then with experiments performed on overlap 2 2 MMIs with symmetric splitting ratios. A. Device Geometry and Structure 2 MMI as used for comparison The geometry of the 2 of theory with experiment is shown in Fig. 3(a). To find the and . width-to-length ratio, we used (1) with has five possible input and output guides, An MMI with . However, when light is only injected each displaced by or , the MMI maps all the light with a 50 : 50 into input and and thus acts as splitting ratio onto the outputs a 2 2 splitter [8]. The 2 2 MMI has been realized as buried heterostructure waveguide in the InGaAsP/InP material system. The guiding 1.3- m quaternary layer is 260 nm thick and completely surrounded by InP. The top InP cladding layer is 1.5 m thick. A cross-section of the structure is depicted in the inset of Fig. 3(a). The dimensions of the MMI are 200 m for the length and 11.3 m for the width.

(4)

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exceeding 14 dB in all-optical devices operated at bit rates up to 100 Gb/s [4]. Unfortunately, the plasma effect is accompanied by free-carrier absorption, which leads to increased propagation losses with increasing refractive-index changes. These losses have to be considered in any model that aims to make accurate predictions. The actual amount of the free-carrier absorption and the amount of the refractive index changes used in our model were derived from the experiment below. We first determined the free-carrier absorption losses with increasing current bias. The theory of the carrier absorption implies that for not too high currents, the losses are approximately linear to the current density such that we can write with reasonable accuracy with

mA cm

(5)

where losses in units of cm ; applied current bias in units of mA; experimentally determined loss constant. Comparison of simulation with experiment also allowed us to approximate the refractive index change as a function of the applied current. We found with

2

Fig. 3. (a) Geometry of a symmetric 2 2 MMI with locations of the pads where we induce a negative refractive index change in order to tune the splitting ratios. The inset shows the structure of the waveguide. (b) Simultaneously biasing the edge pads decreases the bar intensity P in favor of the cross port P , whereas biasing the center pad leads to the opposite effect. Both the theoretical model (solid and dashed lines) used in this paper as well as a BPM simulation (box and cross symbols) lead to the same results. (c) Experimental verification of the tuning characteristics by applying a forward current at the edge pads and alternatively at the center pad.

B. Method for Tuning the Refractive Index In order to tune the refractive index within the different tuning sections of the MMI, we applied gold contacts on top of the waveguides where tuning was desired. This allowed us to individually current bias the different sections, exploiting the carrier-related plasma effect. The plasma effect leads to a negative refractive index change. Good metal contacts are advantageous in order to avoid heating of the MMI sections, which otherwise would lead to a temperature-related refractive index change with an opposite sign. In the simulation, the dimensions of the gold contacts, where the refractive indices were tuned, were 2 50 m for the edge pads and 6 50 m for the center pad. Yet, in the experiment, we have used MMIs with shorter MMI pads. The pad length was kept as small as 25 m. In the experiment, we used tunable MMIs with shorter pads, because we only needed a small tuning range to optimize the ON–OFF ratios in our all-optical wavelength converter [4], [19], rather than a large one as needed for full switching. These tunable MMIs actually enabled us to demonstrated ON–OFF ratio improvement

mA

(6)

where is the constant relating the applied current with the refractive index change. The constant and may vary depending on the device implementation. Both in experiment and in our model, we need and measure the effective refractive index changes and effective absorption changes rather than the real changes in the guiding layer. However, these are approximately interrelated by the confinement factor via and

(7)

where the confinement factor has been determined with the effective index method along the vertical and horizontal direction. . We found Finally, this allows us to express the losses as a function of the refractive-index changes by the relation (8) where the parameters

and have been given above.

C. Comparison of Theory with BPM Simulation and Experiment We have calculated the tuning of the splitting ratios as induced by a negative refractive-index change from the plasma effect for the 2 2 MMI of Fig. 3(a). The results are shown in Fig. 3(b). The effect from edge biasing the device are shown toward the left side of the figure, whereas the right-hand side shows the effect from a center-biased negative refractive-index change. It can be seen that edge biasing changes the power in , whereas center biasing favors the favor of the cross port output. The dashed and solid lines show the bar port

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and output powers obtained by applying the theory of Section III under consideration of absorptions according to (8). The and output cross and box symbols show, respectively, the powers obtained with the help of a two-dimensional BPM simulation for different discrete points along the refractive index change axis. Overall agreement between the analytical method and the BPM simulation is good. Deviations in the output port that guides more light is attributed to the finite dimensions of the pads. The finite dimensions of the pads where the refractive-index change is applied lead to phase changes in self-images that are not mapped into the corresponding pad sections. Fortunately, this only leads to increased overall losses, but not to a degradation in the quality of the switched off port. Minimum off ratios as low as 18 and 20 dB are obtained in the and output independent of the model that is used. Finally, we should mention that the two-dimensional BPM simulation needed the slab refractive index changes and absorption parameters rather than the effective refractive index changes and absorptions. We obtained the actual values by applying the reand . However, lations the axis in the figure is always given in terms of the effective refractive index changes. The measured splitting ratio changes as a function of the applied current bias are shown in Fig. 3(c) for both the edgeand center-biased case of the 2 2 MMI. Calculated (dashed and solid lines) and measured splitting ratio tuning (cross and box symbols) are in good agreement. The edge-biased MMI showed a considerably better—although less efficient—tuning characteristic than the center-biased MMI. We attribute this to leakage currents, which in the edge-biased case flow through the cladding InP materials and thus lead to less efficient tuning. In the center-biased case, they flow through the MMI edges, where they cancel the effective refractive index changes at higher currents, leading to the observed saturation effect. In the case of the center-biased MMI, temperature effects of the inefficiently used current might also have led to a performance degradation. In this first design, we have made no effort to effectively confine the current flow onto the MMI and its pad sections. By better control of the current flows within the MMI layers, the tuning characteristics will considerably improve. The MMI losses were measured to be 0.2 dB in comparison with straight waveguides of the same length.

V. TUNABLE 2

2 MMIS WITH ASYMMETRIC SPLITTING RATIOS

A variety of 2 2 MMIs with asymmetric splitting ratios have already been discussed in the literature. The simplest and most compact are based on overlap MMIs and have asymmetric splitting ratios of 28 : 72, 15 : 85, and 0 : 100 [8], [20]. While asymmetric couplers with fixed splitting ratios such as 90 : 10 are already commercially used, asymmetric splitters with tunable splitting ratios are hardly available. They will not only allow coupling out a small amount of power into a given output (e.g., for control purposes), but will also allow adjustment of the power coupled into the main output and thus can act as power equalizers such as used in multiwavelength systems.

(a)

(b)

2

Fig. 4. (a) Geometry of a 2 2 MMI with a 28 : 72 splitting ratio when not tuned. (b) Negative refractive index biasing of the edge pads increases the intensity in the cross ports, whereas center biasing favors the intensity in the bar output ports. The plasma-effect-related carrier absorption effect, which was considered in this calculation, leads to different output power patterns depending on whether the signal is introduced into input port P or P .

A. Tunable 28 : 72 Splitter 2

2 MMI

2 MMI with a 28 : 72 splitting ratio is depicted in A2 and , so that the Fig. 4(a). We have chosen width-to-length ratio for the structure given in the previous section is completely determined by (1). As mentioned above, we get four possible input guide positions for an overlap MMI with . All possible input guides are lying equidistantly dis. A signal introduced into input port will be placed by mapped onto the two output ports and . No light is mapped onto the other output ports. Without tuning the MMI, we will find a 28 : 72 splitting ratio into the output guides at ports and , respectively. This can be tested with (2). When introducing a signal into input port , the light is mapped with a and . 72 : 28 splitting ratio onto the two output ports at Current biasing and thus inducing a negative refractive index change at the pads depicted in Fig. 4(a) will tune the splitting ratios as plotted in Fig. 4(b). Edge biasing will tune the MMI into a symmetric splitting ratio MMI, whereas center biasing increases the asymmetry in the splitting ratios. It is actually interesting to see that for the output that guides more light, it makes a differor port . ence whether the light is introduced from port This can be explained as follows. When the light is introduced into port , the larger amount of light is located at the edge pads halfway in the propagation direction of the MMI, whereas when the light is introduced into port , more light is located around the center pad, where absorption increases when biasing. Thus, when current biasing the edge pads, we will find higher losses port, whereas higher losses occur in the case of the for the light when center biasing the pads. The splitting ratios of

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(a) (a)

(b) (b)

2

Fig. 5. (a) Geometry of a 2 2 MMI with a 15 : 85 splitting ratio when not biased. (b) Small negative refractive index baising of the edge pads increases the intensity in the cross ports, whereas center biasing favors the intensity in the bar output port.

the output that guides less light is hardly affected by this asymmetry. B. Tunable 15 : 85 Splitter 2

2 MMI

A 15 : 85 splitting ratio was found for a signal guided into an MMI with the geometry shown in Fig. 5(a) [20]. For with , the width-to-length ratio is again given by (1), and 4. We consider possible inputs and outputs are spaced by the splitting ratios for light injected into waveguides 1 and 3. Calculation performed with (2) under consideration of the losses given by (8), leads to the splitting ratios shown in Fig. 5(b). Without biasing, we find that 15% of the light is coupled into the bar and 85% of the light is coupled into the cross port. However, when tuning the refractive index of the two pads at the MMI edge, we change the splitting ratios toward a symmetric MMI. When tuning the refractive index of the center pad, the bar port switches off and all the light will be mapped into the cross port. C. Tunable 0 : 100 Splitter MMI A very special MMI that has only a left and a right refractive index tuning pad (in the propagation direction of the light) is drawn in Fig. 6(a) [8]. The MMI is derived from an overlap MMI and . It has two possible input and output with . When not tuned, this overlap guides that are spaced by MMI can be considered as an overlap 1 1 MMI. It maps all the light from either of the two input guides into the corresponding cross port at the output. Due to its simplicity, we can increase the dimension of the pads considerably. A BPM simulation has m, good tuning shown that for a device of length performances can be achieved for pads up to a length of

Fig. 6. (a) Geometry of an MMI that acts in its unbiased operation state as a 1 1 MMI. For example, it maps the signal from an input port completely into its corresponding cross output port. (b) The simulations reveal that left or right biasing the refractive index couples light from the cross into the bar port, the stronger the refractive index change.

2

m. Thus we choose the pad length twice as large as for the previous devices. In comparison with the device introduced in [14], our device has the same width but only half the length. It works with only one metallization pad instead of four pads. Tuning of the refractive index at either pad will decrease the port and increase the power in favor power coupled into the port. If the refractive index change is strong enough, of the the device can actually be used as a novel compact switch. This new kind of switch combines the compactness of directional coupler switches with the design tolerances of MMIs. So far, MMIs could only be used within a Mach–Zehnder interferometer configuration for switching. VI. OTHER TUNABLE MMIS The concept for turning MMI output ratios is more generally applicable. Almost any of the published MMIs can be tuned to a certain extent when both the location of the pad and its dimension are properly chosen. An example of a tunable 1 3 splitter is shown in Fig. 7(a). 2 splitter with The device has the same geometry as the 2 discussed in Fig. 5. However, in contrast to the device in Fig. 5, we have chosen the central input port to introduce the signal. The device behaves as follows. Without any biasing at the edge pads, all the light from the central input guide will be mapped onto the central output guide . Consequently, this is another version of an overlap 1 1 MMI [21]. When tuning the edge pads, light will be redirected to the two outer output guides with increasing refractive index change. The light coupled out into the two outer ports might be used for detection purposes or any other operation. The MMI might be used instead of the device shown in Fig. 6. The advantage of this tunable MMI over

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(a)

(b) Fig. 7. The concept of tuning the output powers in the output guides of MMIs is more generally applicable. For example, in (a), we show the power distribution for a 1 3 MMI when left or right biasing one of the pads. (b) shows the output-power tuning of a butterfly shaped MMI under edge biasing.

2

the one proposed in Fig. 6 is its complete symmetric geometry, which makes it more tolerant of fabrication inhomogenities. It also has a large dynamic range when used as a power equalizer. MMIs that do not have a rectangular shape can be tuned as well. Recently parabolically tapered MMIs have been introduced in order to reduce the MMI size [22]. Earlier butterfly shaped MMIs have been proposed [22] and applied [3] to build MMIs with asymmetric fixed splitting ratios. Our tuning concept can be applied onto all of these MMIs. In Fig. 7(b), we demonstrate how the splitting ratio of a butterfly MMI with a wider width at the center is tuned under a negative refractive index change applied at the two pads at the edge. Such MMIs might indeed be very interesting to optimize extinction ratios of electrooptic switches. The butterfly asymmetry provides a small asymmetry, which by edge-biasing, can be easily tuned toward the ideal 50 : 50 splitting ratio. In the device of Fig. 7(b), only the edge bias will be needed to make the MMI symmetric. In addition, by using the MMI of Fig. 7(b), we can exploit the edge-biasing technique, which in our experiment was more efficient than center-biasing and moreover benefit from a wider MMI section allowing for larger pads. VII. CONCLUSION We have successfully demonstrated new tunable MMI splitters by changing the refractive index around some determined spots within the MMI. Tunability around 20% was obtained for the splitting ratios of a symmetric 2 2 MMI. We have introduced a general theoretical model to predict the splitting ratio tuning for various kinds of MMIs. Comparison of the theory, BPM simulation, and experiment show good agreement. Based on these theories, we can optimize the present configurations and even predict novel, ultracompact switches based on single MMIs.

ACKNOWLEDGMENT The authors would like to thank Dr. T. L. Koch for support of this work. REFERENCES [1] H. Lü, B. Luo, W. Pan, and J. Chen, “Tunable output power varying with the splitting ratio of a coupler from a fiber ring semiconductor laser,” Appl. Opt., vol. 38, no. 9, pp. 1764–1766, Mar. 1999. [2] C. R. Doerr, C. H. Joyner, and L. W. Stulz, “Integrated WDM dynamic power equalizer with potentially low insertion loss,” IEEE Photon. Technol. Lett., vol. 10, pp. 1443–1445, Oct. 1998. [3] J. Leuthold, P. A. Besse, J. Eckner, E. Gamper, M. Dük, and H. Melchior, “All-optical space switches with gain and principally ideal extinction ratios,” IEEE J. Quantum Electron., vol. 34, pp. 622–633, Apr. 1998. [4] J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, “100 Gbit/s all-optical wavelength conversion with an integrated SOA delayed-interference configuration,” in Proc. Optical Amplifier and Application Conf. (OAA’2000), Quebec, Canada, July 2000. [5] G. Müller, L. Stoll, G. Schulte-Roth, and U. Wolff, “Low current plasma effect optical switch on InP,” Electron. Lett., vol. 26, no. 2, pp. 115–116, 1990. [6] Y. Silberberg, P. Perlmutter, and J. E. Baran, “Digital optical switch,” Appl. Phys. Lett., vol. 51, no. 16, pp. 1230–1232, Oct. 1987. [7] O. Bryngdahl, “Image formation using self-imaging techniques,” J. Opt. Soc. Amer., vol. 63, pp. 416–419, Apr. 1973. [8] L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, and E. C. M. Pennings, “Planar monomode optical couplers based on multimode interference effects,” J. Lightwave Technol., vol. 10, pp. 1843–1845, Dec. 1992. [9] P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol., vol. 12, pp. 1004–1009, June 1994. [10] J. Leuthold, J. Eckner, E. Gamper, P. A. Besse, and H. Melchior, “Multimode interference couplers for the conversion and combining of zeroand first-order modes,” J. Lightwave Technol., vol. 16, pp. 1228–1239, July 1998. [11] P. A. Besse, E. Gini, M. Bachmann, and H. Melchior, “New 1 2 multimode interference couplers with free selection of power splitting ratios,” in Proc. ECOC’94, Firenze, Italy, Sept. 1994, pp. 669–672.

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LEUTHOLD AND JOYNER: MMI COUPLERS WITH TUNABLE POWER SPLITTING RATIOS

[12] Q. Lai, M. Bachmann, W. Hunziker, P. A. Besse, and H. Melchior, “Arbitrary ratio power splitters using angled silica on silicon multimode interference couplers,” Electron. Lett., vol. 32, no. 17, pp. 1576–1577, Aug. 1996. [13] G. A. Fish, L. A. Coldren, and S. P. DenBaars, “Compact InGaAsP/InP 1 2 optical switch based on carrier induced suppression of modal interference,” Electron. Lett., vol. 33, no. 22, pp. 1898–1900, Oct. 1997. [14] S. Nagai, G. Morishima, M. Yagi, and K. Utaka, “InGaAsP/InP multimode inteterference photonic switches for monolithic photonic integrated circuits,” Jpn. J. Appl. Phys., vol. 38, no. 2B, pp. 1269–1272, Feb. 1999. [15] M. Yagi, S. Nagai, H. Inayoshi, and K. Utaka, “Versatile multimode interfernece photonic switches with partial index-modulation regions,” Electron. Lett., vol. 36, no. 6, pp. 533–534, Mar. 2000. [16] R. M. Jenkins, R. W. J. Devereux, and J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett., vol. 17, no. 14, pp. 991–993, July 1992. [17] M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging multimode interference couplers including phase properties in relations,” Appl. Opt., vol. 33, pp. 3905–3911, July 1994. [18] J. M. Heaton and R. M. Jenkins, “General matrix theory of self-imaging in multimode interference (MMI) couplers,” IEEE Photon. Technol. Lett., vol. 11, pp. 212–214, Feb. 1999. [19] J. Leuthold, C. H. Joyner, B. Mikkelsen, G. Raybon, J. L. Pleumeekers, B. I. Miller, K. Dreyer, and C. A. Burrus, “Compact and fully packaged wavelength converter with integrated delay loop for 40 Gbit-s RZ Signals,” in Proc. Optical Fiber Communication Conf. (OFC’2000), Baltimore, MD, Mar. 2000, postdeadline paper 17. [20] M. Bachmann, P. A. Besse, and H. Melchior, “Overlapping-image multimode interference couplers with reduced number of self-images for uniform and nonuniform power splitting,” Appl. Opt., vol. 34, no. 30, pp. 6898–6910, Oct. 1995.

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[21] J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, “Novel 1-to- way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides,” Appl. Phys. Lett., vol. 61, pp. 1754–1756, Oct. 1992. [22] D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and St. Forrest, “Fabrication of ultracompact 3-dB 2 2 MMI power splitters,” IEEE Photon. Technol. Lett., vol. 11, pp. 1009–1011, Aug. 1999.

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Juerg Leuthold (S’95–A’98–M’99) was born in St. Gallen, Switzerland, on July 11, 1966. He received the Diploma degree in physics and the Ph.D. degree from the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, in 1991 and 1998, respectively. In 1992, he joined the Institute of Quantum Electronics of the Swiss Federal Institute of Technology, where he worked in the field of integrated optics. His doctoral work was in the field of all-optical switching and other integrated optoelectronic components. In 1999, he first was with the Integrated Photonics Laboratory, Tokyo University, before joining Bell Labs, Lucent Technologies, Holmdel, NJ.

Charles H. Joyner was born in Decatur, GA, in 1953. He received the bachelor’s degree in chemistry from Furman University, Greenville, SC, in 1975 and the master’s and Ph.D. degrees in physical chemical engineering from Harvard University, Cambridge, MA, in 1978 and 1981, respectively. In 1981, he joined AT&T Bell Laboratories as a Member of Technical Staff. He currently works on design and fabrication of InP-based integrated photonic devices.