Multimode Interference Couplers for the Conversion and Combining of ...

IEEE Journal of Lightwave Technology

July 1998 VOLUME 16

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NUMBER 7

JLTEDG

(ISSN 0733-8724)

PAPER

Copyright © 1998 IEEE.

Reprinted from Journal of Lightwave Technology, vol. 16, no. 7, pp. 1228-1239, July 1998 Multimode Interference Couplers for the Conversion and Combining of Zero- and First-Order Modes, Dual Order Mode (DOMO) MMIs J. Leuthold, J. Eckner, E. Gamper, P.A. Besse, H. Melchior

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Multimode Interference Couplers for the Conversion and Combining of Zero- and First-Order Modes Juerg Leuthold, Juerg Eckner, Emil Gamper, Pierre A. Besse, and Hans Melchior

Abstract—Optical waveguide mode-combiners for fundamental and first-order modes, based on multimode interference (MMI) couplers are presented. These devices convert a fundamental mode into a transversal first-order mode and combine it in lossless fashion with a second fundamental mode. They can separate zero- and first-order modes in a common waveguide and allow the splitting and combining of zero- and first-order modes with nonuniform power splitting ratios. Realizations in InGaAsP/InP are demonstrated. These new components have successfully been integrated into all-optical switches and were found to have advantageous characteristics in all-optical devices. Index Terms—Mode converters, mode filters, multimode interference couplers, multimode waveguides.

I. INTRODUCTION

I

NTEGRATED waveguide couplers, that generate first-order modes and that allow to combine them with zero-order modes have attractive applications in photonic integrated circuits. They are already used as adiabatic asymmetrical 2 digital optical (DOS)-switches [2] junctions [1] in 2 and in Mach–Zehnder interferometer (MZI) switches [1]. A TE/TM-mode splitter has been reported, which transforms the TM-mode selectively into a first-order mode and then extracts it using an asymmetrical -junction [3]. Although these junctions work well, they have considerable lengths and sharp intersection angels, which poses a technological challenge. Pedersen et al. [4] recently described -junctions of good quality in InGaAsP/InP. Their couplers’ -junctions can be used as mode converters and mode combiners but they are longer than 1.5 mm. Multimode interference (MMI) couplers [5]–[8] on the other hand, have found a considerable interest in the last few years. They feature compactness, high design tolerances, a large optical bandwidth and polarization insensitivity when strongly guided structures are used [9], [10]. Currently, MMI’s are used as 3 dB power splitters and combiners [11], as power splitters with free selection of power splitting ratio (so called butterfly , MMI’s) [12], as multileg-splitters, that can act as 1

Manuscript received December 1, 1997; revised March 6, 1998. This work was supported in part by the Swiss Research Programme in Optics. J. Leuthold, J. Eckner, E. Gamper, and M. Melchior are with the Institute of Quantum Electronics, Swiss Federal Institute of Technology (ETH), CH-8093 Z¨urich, Switzerland. P. A. Besse was with the Institute of Quantum Electronics, Swiss Federal Institute of Technology (ETH), CH-8093 Z¨urich, Switzerland. He is now with the Institute of Microengineering, Swiss Federal Institute of Technology, Lausanne, Switzerland. Publisher Item Identifier S 0733-8724(98)04092-4.

2 , or [13]–[15] splitters and they have recently been used for wavelength-multiplexing [16]. In this paper, we introduce new types of short MMIconverter-combiners, that convert a fundamental mode into a transversal first-order mode and that allow to combine the firstorder mode with a second fundamental mode. The ease with which the couplers can be integrated and the high coupling efficiencies make these couplers attractive for applications in all-optical devices, that use optical signals to control an optical data-signal [17]–[21]. The new couplers have successfully been used to introduce the control-signal as a first-order mode into all-optical switches and to modulate the zero-order mode data-signal [22], [23]. Due to the difference in the mode’s symmetry, the control-signal can easily be separated from the data-signal after signal-processing even if the two signals copropagate and have the same wavelength. After a short introduction on multimode interference in Section II, we explain the principle for mode-conversion in Section II-A and we also propose three different kinds of converters, which should be chosen depending on the applications. In Section II-B, we show how these MMI’s can be used as mode combiners for a zero-order mode in combination with a second input guide. The opposite process—the separation of modes of different orders into different waveguides—is discussed in a last section. The manifold possibilities of zero-order mode MMI’s, like splitting and combining, are guaranteed for a first-order mode also. They are discussed in Section III. Experimental results are given in Section IV. The experiments are in good agreement with the theoretical predictions.

II. PRINCIPLES OF MMI-CONVERTER-COMBINERS MMI-converter-combiners are waveguide couplers, that convert a fundamental-order mode into a first-order mode and that allow to couple a second fundamental mode into the same output waveguide. A demonstration of the converter-combiner principle for a simple structure is given in Fig. 1. The mode conversion principle can be derived from the presently known MMI’s. We, therefore, start by classifying them and introduce the notation used throughout in this paper. Multimode interference couplers base on self-imaging [5]–[7], which goes back to the Talbot effect, discovered in 1836 [8]. In multimode waveguides, self-imaging is the property to reproduce an input field profile in single or multiple images at periodic intervals along the propagation direction of the guide.

0733–8724/98$10.00  1998 IEEE

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If the input guide position, described by the parameter lies we obtain a general-MMI. In a general between: MMI, the -fold images have the same shape and intensity as the input mode and only differ in the phase-relations between each other. New and simple equations describing the phase relation between an output arm and an input arm have recently been derived [25]. We repeat these phase relations in Appendix I-A as we are going to use them in this paper. The positions of the in- and output guides is shown in Fig. 9(a) for odd. The case of even can be treated analogously. On the other hand we obtain overlap-MMI’s if takes the or They are derived by letting value: or in the MMI in Fig. 9(a). By doing that, one observes that usually two in- and output guides of Fig. 9(a) overlap. The constructive and destructive interference of the two overlapping output arms lead to new intensity distributions at the MMI-output. The resulting new MMI consists of possible in- and output guides in the middle and two half guides at the MMI-edges. We will use the notation given in Fig. 9(b) for overlap-MMI’s. The phase relations of the overlap-MMI’s are given in Appendix I-B. -overlap-MMI’s are Important special cases of the the “symmetric” and “restricted interference MMI’s.” They and splitters, have found applications as respectively. We are going to use these MMI’s and refer the reader to Appendix I-A, where they are briefly discussed and and is given. where also the relation between A. Mode Conversion Based on Multimode Interference Fig. 1. Beam propagation simulation (BPM) of a ridge MMI waveguide structure demonstrating the MMI-converter-combiner principle. (A) shows how a fundamental mode introduced at the wider input guide is completely mapped onto the wider output guide. (B) shows how a second fundamental mode is converted with a 66% efficiency into a first-order mode and mapped into the same wider output waveguide. The remaining 33% of the light are decoupled through the thinner output on the left side of the MMI.

We consider MMI-structures of length [24] with

(1)

and are positive integers without any common where denotes the effective refractive index, the divisor the equivalent MMI width, wavelength in vacuum and which is the geometric width of the MMI including the penetration into the neighbor material of the waveguide. Then gives the number of in- and in the most general case, gives other lengths of output arms of the MMI, whereas output arms. The position of the in- and MMI’s having output waveguides is determined by the unique parameter [see Fig. 9(a) of Appendix I]. Since MMI’s are supposed to and use be short, we restrict ourselves to cases with . throughout the text the notation We classify a MMI as general-MMI if the light from either possible input guides is equally distributed onto the of the possible output guides and we classify MMI’s as overlapMMI if the input guide position is chosen such that the output images overlap and unequally distributed output ratios arise.

The principle for the conversion of a fundamental mode into a first-order mode by use of MMI’s is discussed first. We use general MMI’s to explain the basic mode conversion mechanism and then improve the conversion efficiency of these MMI’s. The method of multimode interference allows to convert a fundamental mode into a first-order mode. A first-order TE01 or TM01 -mode is characterized by its intensity profile and by the phase relation within the mode. Two steps lead to the desired mode characteristics. 1) The intensity profile of the first-order mode is realized by positioning an input arm of the MMI such, that the output guides of the MMI touch each other to form a wider waveguide that transmits two beams in the form of a first-order mode. Referring to Fig. 9(a) this implies the parameter to take the value of approximately one half of the rib width. of the fundamental In a first approach the rib width of the first-order mode input guide and the rib width mode output guide are for strongly guided structures with sufficient accuracy related by (2) A careful analysis reveals that the Gaussian beam waist of the zero-order mode guided in the waveguide with and the beam waist of the first-order rib-width are related by [27] mode guided in a rib of width (3)

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TABLE I PHASE-RELATIONS OF THE GENERAL 4

Fig. 2. Multimode-interference (MMI) couplers to convert a zero-order mode into a first-order mode. (a) MMI-converter with a 50% conversion efficiency of a fundamental mode into a first-order mode. Each of the two outer waveguides contain 25% of the intensity. (b) A 66%-MMI-converter that converts a fundamental mode with a 66% efficiency into a first-order mode. The remaining 33% of the light intensity is mapped into a zero-order mode. (c) MMI-converter realized with a 1 2-MMI, a phase-shifter and the 50%-MMI-converter of Fig. 2(a) with two inputs. A zero-order mode is completely converted into a first-order mode.

2

(The beam waist is the width of the mode, where the of the maximum value. amplitude has decayed on Due to the definition of first-order Gaussian modes, is the span of the mode where its amplitude has decayed on a value of 0.86 of the peak maximums.) 2) The phase distribution within a first-order mode varies by from one intensity peak to the other. This phaseprofile is automatically obtained when using an MMIinput guide at the MMI edge. With the phase relations given in (A1) and (A2) we derive for adjacent output -MMI that uses the inputport guides of a general for

and for (4)

Thus, the phases at the adjacent output guides and for are always automatically phase-shifted with between each other, is used. The same applies for the opposite if input for reasons of symmetry. input guide and Mode-combiners that use general-MMI’s with are shown in Fig. 2(a) and (b). The first one couples 25% of the power of the fundamental input mode into the fundamental modes of the outer outputs and 50% into the firstorder mode of the central output. In the following lines we

2 4 MMI

refer to this MMI as 50%-MMI-converter. The mode converter MMI, or 66%-MMI-converter, couples 33% of the power of the fundamental input mode into the fundamental and a fraction of mode of the output waveguide output 66% to the first-order mode of the wider waveguide. The conversion efficiency can be improved to 100% by modifying the 50%-MMI-converter. Consider the phase relations of the 50%-MMI-converter respectively it’s primal 4-MMI in Table I. If we introduce version, the general 4 and with a phase two coherent signals at input arms retardation of between each other, then the phases of the and the phases of the two two signals in the output interfere constructively and they signals in the output and interfere destructively in the output arms Therefore the signal in the output of the first-order are mode superpose and the zero-order mode outputs deleted. That’s exactly what we are looking for. A possible realization of such a device is given in Fig. 2(c). It consists of an 1 2-MMI for splitting the input mode into two equal parts, followed by a phase-shifter region to adapt the phases The two signals in the two to the required phase shift of 4-MMI, whose input branches are then guided into the 4 arms are positioned to form a 50%-MMI-converter. B. MMI-Converter-Combiners The above MMI-converters that couple light from one input to a first-order output are of interest since, with a second input they allow a zero-order mode to be exited into the same output waveguide. We call these new couplers MMI-convertercombiners. The MMI-converter-combiners of Fig. 3(a)–(d) and Fig. 10 combine three operations in a single device: 1) The complete projection of a fundamental mode A into a common output, 2) the conversion of a zero-order mode B into a first-order mode, which is mapped into the common output guide, and 3) when going to the generalization, the splitting of the zero-order output waveguides. as well as the first-order mode onto The generalization is discussed in Appendix I. The different structures are compared in Table II. 1) 50%-MMI-Converter-Combiner: A MMI-convertercombiner with high technological tolerances is obtained by modifying the 50%-MMI-converter. The new MMI has a 100% coupling efficiency for the fundamental mode A into the wider output guide and a 50% first-order mode conversion efficiency of a fundamental mode B into the same output waveguide.

LEUTHOLD et al.: MULTIMODE INTERFERENCE COUPLERS

Fig. 3. MMI converter-combiner structures coupling a zero-order mode A completely into the wider output arm and mapping mode B as a first-order mode into the same output waveguide. The different structures have a (a) 50%, (b) 66%, and (c) and (d) 100% conversion efficiency for the mode B to be converted from a zero into a first-order mode. The MMI-converter-combiners include the 1 1 overlap-MMI characteristics for mode A with the conversion capabilities proposed in Fig. 2 for mode B.

2

TABLE II COMPARISON BETWEEN THE DIFFERENT MMI-CONVERTER-COMBINER STRUCTURES

Fig. 3(a) illustrates how the mapping characteristics of two different MMI’s have been combined to form the new 50%-MMI-converter combiner. The new MMI includes the -MMI-splitter with mentioned in Appendix IA, and the 50%-MMI-converter of Fig. 2(a). For these two MMI’s have the same geometry (the same length

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for the same width ). The resulting 50%-MMI-converter-combiner possess the in- and outputs of both MMI’s. We state that the inputs of the two MMI’s are at different positions, however the outputs of the MMIsplitter and the output of the MMI-converter for the first-order mode merge. A zero-order mode A introduced at the center is completely mapped into the waveguide-output at the center. The zero-order mode B launched into the MMI at the edge is converted into two zero-order modes and a single first-order mode. The first-order mode is imaged into the output port, that already guides the image of the zero-order mode A. The 50%-MMI-converter-combiner of Fig. 3 is of special interest, since it has got in- and output guides that are positioned either at the center or the edge of the MMI, so that a technological deviation in the rib widths of the MMI’s can not shift the waveguide arms out of their relative correct position. For this reason that sort of MMI should be preferred when high technological tolerances are desired. 2) 66%-MMI-Converter-Combiner: The 66%-MMI-converter allows to introduce an MMI-converter-combiner with good broadband-characteristics, a complete coupling of the fundamental mode A into the wider output waveguide, a 66% first-order mode conversion efficiency of the fundamental mode B and the superposition of the former with the latter into the wider output waveguide. The 66%-MMI-converter-combiner is derived in analogy to the previous coupler by combining the 66%-MMI-converter -MMI-splitter with given in Fig. 2(b) and the which has the input at as described in Appendix I-A. These MMI’s have got the same length for the same MMIIn Fig. 3(b) we have laid the former MMI into width the latter. Again we can state, that the inputs are at different positions, but the outputs of the waveguides guiding the firstorder mode and the output guiding the zero-order mode of the MMI-splitter join. A beam propagation (BPM) simulation is given in Fig. 1. It shows the intensity evolution, when introducing a fundamental mode once at the MMI-splitter input port and once at the MMI-converter input port. The 66%-MMI-converter-combiners have small device sizes in comparison to the access waveguide widths and therefore have a large optical bandwidth [27]. They are preferentially used, when good broadband-characteristics are required. 3) 100%-MMI-Converter-Combiner: Two versions of MMI-converter-combiners delivering a superposition of the fundamental mode A with the fundamental mode B that is completely converted into a first-order mode are demonstrated subsequently. These MMI’s base on the MMI-converter with 100% conversion efficiency presented in Fig. 2(c). A realization of such a 100%-MMI-converter-combiner is given in Fig. 3(c). It shows how a zero-order mode A is 1-MMI for guided to the second-MMI, that acts as a 1 the fundamental mode when the central input of the MMIconverter is used. (For an explanation refer to the description of the 50%-MMI-converter-combiner.) The zero-order mode B is only effected by the structure of the 100%-converter as outlined in Fig. 2(d), so that it is completely converted into a first-order mode. By using the symmetric interference 1 2-MMI-splitter from Appendix I-A, we use a short MMI

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In principle, the bent waveguide connecting the 2 2MMI and the 50%-MMI-converter in the MMI-convertercombiner of Fig. 3(d) can be omitted. The phase shift of which is necessary for a complete conversion can as well be obtained by twisting the MMI’s against each other, see Fig. 10(b). However, structure (c) and (d) were superior—both in simulation as well as in experiment. C. Decoupling of Modes of Different Order

Fig. 4. MMI-filter and short MMI-splitter can be identified with this simulation for the symmetric (zero-order) mode and the antisymmetric (first-order) mode introduced at the central input guide. MMI-filters, that project the symmetric and the antisymmetric modes onto different output guides, have lengths L =3 Lc =4; 3Lc =8; 3Lc =12: Short MMI-splitters have MMI-lengths L = 3LC =2; 3Lc =6; 3Lc =10: The formation of 1, 3, and 5 images of a zero and a first-order mode, respectively, at identical output positions are clearly visible.

with the corresponding good broadband-characteristics. The Thus, this variant length of the 1 2-MMI is of a 100% MMI-converter-combiner is recommended when the spectral bandwidth is of relevance. However this structure contains waveguides that cross each other, which might require increased technological efforts. The crossing waveguides can be circumvented by using an other MMI-splitter, which introduces the two signals A and B at different input guides and couples them out such, that they are correctly positioned for the 100%-MMI-converter. 2-MMI offers these possibilities. Fig. 3(d) The general 2 illustrates this MMI in combination with the MMI-converter. 2-MMI, the When using the central input port of the 2 input mode is mapped onto itself at the center. We refer to the simulation depicted in Fig. 4(a), which shows how the zero-order mode introduced at the central input of the MMI is mapped onto the central output after the distance which is exactly the length of the general 2 2MMI. However when coupling the mode B at the edge into 2-MMI, the mode B coupled in through this input the 2 arm is split into two branches. The phase-shifters are used again to adapt the phases of the two modes in the outer branches. In contrast to the MMI-converter-combiner, that is 2-MMI, only a phase-shift adaptation of built with the 1 is needed between the splitter and converter-MMI, since 2-MMI already delivers a phase-shift difference of the 2 between the two output arms, as one can derive from the phase relations given in Appendix I-A. As there are no crossing waveguides, this structure should show improved technological tolerances.

A decoupler, that allows to separate modes of different order is useful, for applications in all-optical devices, where first-order mode control-signals are used for signal processing but have to be extracted afterwards [22], [23]. In comparison with the wavelength demultiplexing in integrated optics, the demultiplexing of modes of different order or more precise of different symmetry is simple. The 100%-MMI-converter-combiners of Fig. 3(c) and (d) can be used as decouplers when operated reversely. This is a direct consequence of the reciprocity theorem in optics. These decouplers guide the light depending on the symmetry of the mode onto separate waveguides. Noteworthy are the short and highly efficient MMI-filters, that have been discussed elsewhere [26]. They are useful, if the first-order modes are not any more used afterwards. In contrast to the MMI-converter-combiners with 100%-conversion efficiency the first-order mode is not mapped into a single waveguide but split off and mapped onto several different waveguides. The devices rely on the different mapping characteristics -MMI of symmetric and antisymmetric modes in 1 splitters. Fig. 4 displays the mode evolution of a symmetric zero order and an antisymmetric first-order mode introduced at the center of the MMI. At MMI lengths with the zero-order mode is clearly mapped to output positions different from those of the first-order mode. are useful if the fundamental mode MMI-filters with branches and has to be freed from has to be split into antisymmetrical modes. III. POWER-SPLITTER FOR ZERO- AND FIRST-ORDER MODES In this paragraph we discuss MMI splitters, that can be used to handle zero- and first-order modes. Such devices are useful in integrated optics to allow for the simultaneous signal processing of zero- and first-order modes. Although there exist already a wide variety of devices for zero-order modes, their behavior in combination with a first-order mode has not yet been studied. A. MMI-Couplers with Uniform Power-Splitting Ratios -MMI’s of Appendix IThe theory of the general B1). is valid for light with an arbitrary mode profile. Therefore it remains valid for zero-order modes as well as for firstorder modes. Thus, the structure given in Fig. 9 allows to split optical modes of any order onto output guides and it allows to combine modes of any order into a common output guide. -MMI’s, there exist short Besides these known devices, that split the fundamental and the first-order modes common outputs. They exist as 1 1, 1 3, into

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1 5, , etc., splitters. These devices correspond to overlap. With MMI’s with lengths with other words, they have lengths according to (1). They have an input guide at the center and Fig. 4 the output guides at equidistant positions of gives the light distribution in an MMI for a fundamental and a first-order mode respectively. For MMI-lengths the formation of 1, 3, and 5 images of a zero and a first-order mode respectively at identical output positions is clearly visible. B. MMI-Couplers with Nonuniform Power-Splitting Ratios Subsequently, we discuss the existence of nonuniform firstorder mode power-splitting ratios for MMI’s of the general and MMI’s of the overlap type. Recently, MMI’s with free selection of splitting and combining ratios for zero-order modes have found attention [12]. We pick up this idea to vary the first-order mode output intensity ratios. As an interesting result we find, that the symmetric and antisymmetric modes split up nonuniformly jointly when general-MMI’s are used and they split up nonuniformly in an opposite way if overlapMMI’s are used. We start discussing nonuniform but fix power splitting ratios of first-order modes in overlap-MMI’s and then turn to the effect of the butterfly modification in the general- and overlapMMI’s. 1) MMI’s with Fix, Nonuniform Power-Splitting, and Combining Ratios: We derive MMI’s with fix, nonuniform powersplitting and combining ratios from the overlap-MMI [see Fig. . Their length is given A1(b)] with with (1) (5) with For waveguide-input positions and waveguide output positions at with and even numbers and measured from the bottom MMI-edge, one obtains with (A3) and (A4) in the overlap-notation the following output intensity distributions: for symmetric modes

(6)

for antisymmetric modes (7) The following conclusions can be stated from (6) and (7). If one chooses the same input guide for a normalized symmetric and a normalized antisymmetric mode, the sum of the intensity of the symmetric and antisymmetric mode at remains constant. In Fig. 5(a), we have the output guides . Because has to be even, we exemplarily chosen with only find output guides at Likewise, one obtains a constant intensity distribution at the and output guides (for this case the outputs have to be considered also, and give together a full output), if one chooses for the normalized symmetric mode an input and for the normalized antisymmetric mode guide at

Fig. 5. MMI-splitters with fix, nonuniform power-splitting ratios for two modes of different symmetry. (a) Case where the two modes use the same input guide. The intensity distribution in the output guides depends on the symmetry of the input mode. (b) Case where the antisymmetric mode uses input i0 = 1 and the symmetric mode uses input guide i0 = 2K 1:

0

an input guide at

with

a number between

However, if one chooses for the symmetric mode the input and for the antisymmetric mode the input guide then both modes show at the output guide at the same nonuniform intensity distribution Fig. 5(b) 2) MMI’s with Free Selection of Power Splitting and Combining Ratios: The output intensity distribution of the different output guides can be changed by applying the so called butterfly MMI concept. Butterfly MMI’s are obtained by dividing a rectangular MMI-box into two sections and downand uptapering the two sections. With the extent of the taper the output intensity ratio varies. This effect has been discussed in [12] for zero-order modes. Butterfly-MMI’s can be derived from general-MMI’s. Since the general-MMI theory remains valid independent of the mode form, the nonuniform power-splitting ratios are for a zero as well as a first-order mode identical. The deviation from the uniform power-splitting ratio only depends on the taper. The butterfly MMI concept can similarly be applied to the overlap-MMI’s. We discuss the just mentioned overlap-type for the case [Fig. 6(a)]. This MMI is of interest since it allows with a free choice of the splitting ratios the nonuniform distribution of a zero or/and a first-order mode into the two output waveguides. To give the splitting ratio as a function of the taper, we have identified the taper by the where is the MMI-width at the begin ratio the MMI-width in the middle of the MMI. and end and The total length of the butterfly-MMI has then to be adapted and to depending on the widths with

(8)

In Fig. 6(b), we have depicted the splitting ratio for a symmetric and antisymmetric input mode using input port

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Fig. 7. Mask layout of the 100%-MMI-converter-combiner from Fig. 3(c). The 1 2-MMI is as small as 12 150 m and the 50%-MMI-converter is 12 340 m. Curve radii of the waveguides are 1000 m. The inset shows the cross section through the InP/InGaAsP/InP waveguide-structure.

2

Fig. 6. MMI splitter of Fig. 5(a) with K = 2 and butterfly geometry. The butterfly geometry allows to deviate from the fix splitting ratios given by the rectangular MMI-geometry. Depending on whether one down- or uptapers the middle MMI-width W1 in relation to the MMI-width W0 at the front and back of the MMI, the splitting ratio varies. The Graph shows the variation of the intensities in the output guides j 0 = 1 and j 0 = 3 as a function of the taper-ratio for the symmetric (solid line) and the antisymmetric mode (dotted line).

as a function of ratio at the output

and

The variation in the splitting are clearly visible.

IV. EXPERIMENT For experimental demonstration of the mode conversion and mode combining efficiency we have realized the 50%, the 66% and both types of the 100%-MMI-converter-combiners. We demonstrate how the 50%-MMI-converter-combiner of Fig. 3(a) couples a zero-order mode A introduced from the wider input waveguide with a 100% coupling efficiency into the central output guide and how the zero-order mode B from the lower left input guide is coupled with a 50 and 25% efficiency as a first-order mode into the central output guide and as zero-order mode into the two outer output guides, respectively. Analogously, we demonstrate, that the 66%converter-combiner of Fig. 3(b) couples the fundamental mode A completely into the wider output guide and it converts the zero-order mode B with a 66% efficiency into a first-order mode, which is mapped into the wider output waveguide also. The remaining 33% of the light are coupled as a zero-order mode into the thinner output guide. The 100%-MMI-convertercombiners of Fig. 3(c) and (d) couple the mode A and B with a 100% efficiency as a zero and a first-order mode into the same output waveguide. A. Structure The 50%, the 66% and the 100% -MMI-converter-combiner of Fig. 3(a)–(d) were produced as ridge waveguide structures on a double-heterostructure InP/InGaAsP/InP wafer, optimized for light at a wavelength around 1.5 m (inset of Fig. 7). The

2

2

epitaxial layers were grown by low-pressure metal organic chemical vapor deposition (LP-MOVPE) on (100) Indium Phosphide. The structure of the wafer has an InP buffer layer, a 250-nm waveguiding quaternary layer (InGaAsP with corresponding material gap wavelength of 1.19 m) and a 1590 nm InP upper cladding layer. Dry and wet etching 1500 nm into the InP cladding layer formed the ridge. After cleaving, a broad-band antireflection coating was applied. Measurements of the optical properties were then performed on an optical bench. The 50%-MMI-converter-combiner has a dimension of 12.0 m 340 m and the 66%-MMI-converter-combiner has a 270 m. The mask layout of the dimension of 9.0 m MMI-converter-combiner with 100% efficiency of Fig. 3(c) is depict in Fig. 7. It consists of a 1 2-MMI which is designed as small as 12.0 m 150 m and a 100%-MMI-converter, 340 m. The 1 2which has a geometry of 12.0 m MMI splits the signal B into two identical branches of light 2-MMI. The signals that have equal phases behind the 1 are then guided into two slightly different bent curves with m and m to induce the radiuses of required phase shift of as mentioned in paragraph II. Finally the two signals are completely converted into a first-order mode signal in the 100%-MMI-converter. To guide the signal A to the center of the 100%-MMI-converter we have to cross waveguides. We have bent the input waveguides to obtain an intersection angle of 18 . The widths of the in- and output guides before and behind the MMI-converter-combiners are 1.8 and 3.8 m for the zero and first-order mode waveguides, respectively [27]. Behind the MMI’s we uptapered the thinner waveguides to 2.5 m and the wider waveguide to 4.5 m to avoid for unnecessary high waveguide losses. The MMIconverter-combiner with 100% efficiency of Fig. 3(d) is built 2-MMI of 13.0 m 780 m and a 100%up of a 2 390 m. The total angle of MMI-converter of 13.0 m the bent curves between the two MMI’s is 0.6 for a curve phaseradius of 995, 1000, and 1005 m. This induces a shift between the two outer bent waveguides. The input and output waveguides are designed with rib-widths of 1.7 and 4.3 m, respectively. Again the waveguides were uptapered behind the MMI’s. B. Experimental Results The functioning of the 50%-MMI-converter-combiner, Fig. 3(a), the 66%-MMI-converter-combiner, Fig. 3(b), and

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Fig. 8. Video camera images of the output intensity distribution of the MMI-converter-combiner shown in Fig. 3. (a) A 50%-MMI-converter-combiner, (b) a 66%-MMI-converter-combiner, and (c) a 100%-MMI-converter-combiner Type 1. The left sides show the image generated by the zero-order mode A, which is completely mapped onto itself. In (a) and (b), small crosstalks into the adjacent outputs are visible on the left photos. The right sides show the first-order modes, which are generated with 50, 66, and 100% when the second input guide is used. The predicted output distributions of 25 : 50 : 25 and 33 : 66 in (a) and (b), respectively, for the zero- and first-order modes are found with good accuracy.

the 100%-MMI-converter of Fig. 3(c) are demonstrated in Fig. 8(a)–(c). In Table II we have summarized the excess loss of all four devices under investigation in comparison to straight 3 m waveguides. The output intensity distribution of the 50%-MMIconverter-combiner is depicted in Fig. 8(a). The left photo shows how TE-light of wavelength 1.5 m from the input mode A is completely mapped as a fundamental mode onto the wider waveguide. This output shows a 0.1-dB excess loss in comparison to a straight 3- m rib waveguide of the same length. At the position of the two outer output ports, only a slight crosstalk is visible. The crosstalk is asymmetric due to technological inhomogeneities. The right picture of Fig. 8(a) shows the output guides of the MMI of the mode B, which is mapped onto two fundamental modes, which are visible at the outer sides and onto a first-order mode in the center. 54% of the light is coupled into the first-order mode. The fundamental modes on the left and right side of the wider waveguide contains 46% of the light. The outer outputs guide less light than the expected 50% because of the weak guiding in the sharp S bends of the outer waveguides

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behind the MMI, which were designed to avoid crosstalk with the central waveguide. The total excess loss of the first-order mode in comparison to a 3- m straight waveguide of equal length is 0.3 dB. The losses were measured by projecting the output beams through a lens onto a photodiode. Although an estimate of the conversion efficiencies can be obtained from the figures, by taking the integral over the light shape, we used the values measured with the photodiodes because the signal shape from the camera does only approximately linearly correspond with the signal intensity. The TM-mode showed an analogous behavior, tough slightly worse, because the structures were not designed to be polarization insensitive. For the 66%-MMI-converter-combiner we measured a 0.0 dB excess loss for the mode A that was projected into the wider waveguide and for the fundamental mode B, which is converted into a first-order mode we found a 0.3 dB excess loss in comparison to the 3 m waveguide. The output intensity distributions of mode A and B behind the MMI are given on the photos of Fig. 8(b). The left photo shows how 99% of the light is coupled into the wider output. The photo on the right displays the zero and the first-order modes containing 32 and 68% of the light. The peak of the zero-order mode is smaller in comparison to the first-order mode peak. On the one hand, this is due to the higher propagation losses in the S-bend of the zero-order mode waveguide behind the MMI and on the other hand, it is an effect of the unequal rib-widths of the output waveguides at the cleave position. The area in the integral over the zero-order mode shape corresponds quite exactly to half of the area of the integral over the first-order mode shape as one expects from theory. To proof the predicted good broad-band characteristics of this device we measured the 1 dB optical bandwidth. It was found to be as large as 160 nm for the first-order mode. The zero-order mode bandwidth is even better. The measured excess losses of the MMI-converter-combiner with 100% conversion efficiency of Fig. 3(c) were similar to those of the above devices. The mode B, that was converted into a first-order mode showed a 0.7 dB excess loss and the mode A that kept its zero-order mode geometry gave a 0.2 dB excess gain in comparison with the 3 m waveguide. A 0.2 dB excess gain lies within the design and measurement tolerances but might also be due to the lower waveguide losses in the MMI’s, which have a considerable wider rib width in comparison to the 3 m rib widths of the straight waveguides. The output intensity distributions of the device are presented on Fig. 8(c). To avoid high excess losses with this structure three design parameters have to be optimized carefully. First of all, the phase shifter introduced between the two MMI’s A deviation of from the required has to be adjusted to phase shift leads to an excess loss of dB. Second the intersection angle of the waveguides has to be maximized and third, a possible cross-talk between the three waveguides that are leaded to the 50%-MMI-convertercombiner has to be suppressed by choosing strongly guided waveguide structures with small curvature radii. The last two problems can be circumvented by using the structure of Fig. 3(d) instead. However the MMI-converter-combiner of Fig. 3(d) has a worse spectral bandwidth. For this structure

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we found a 0.1 dB excess gain for the zero-order mode and a 0.6 dB excess loss for the mode that was converted into a first-order mode. V. CONCLUSIONS We have proposed and realized new types of short and low-loss MMI-couplers that allow to combine a fundamental mode with a second mode, that is converted into a first-order mode. The performances of the 50 and 66%-MMI-convertercombiners realized in InGaAsP/InP have excess losses below 0.3 dB. The 100%-MMI-converter-combiners with conversion efficiencies of theoretically 100% show excess losses below 0.7 dB. The 100%-MMI-converter-combiners can also be used to decouple modes of different symmetry. Additionally we have proposed new possibilities to split zero and first-order modes uniformly and nonuniformly. The new MMI’s have found applications in all-optical switches and wavelengthconverters where they can be used to introduce a first-order mode optical signal to control the data-signal processing. They are of interest because of the simple and efficient coupling scheme. Moreover first-order mode optically controlled devices allow copropagating data and control signals even at the same wavelength, since the different symmetry of the signals always guarantees an easy separation of the two signals, so that external wavelength filters for the extraction of control signals are unnecessary with these devices. APPENDIX I In this Appendix, we summarize the basic mathematical description of the general and overlap-MMI’s [25], [28], [13], [14] used in this paper. In Appendix II, we will outline the generalization of the conversion principle.

2

Fig. 9. (a) General N N -MMI coupler with N odd in- and output guides. The positions of the N in- and output waveguides are defined by the parameter a and the MMI width Weq1 : (b) N N -overlap-MMI with N 1 access-waveguides within the MMI and two half access-waveguides at the MMI-edge. All waveguide positions are solely defined through the MMI-width Weq and N [28].

2

0

A. Basic MMI’s Used in the Paper -MMI’s: The phase relations at the out1) General put arms in relation to the input arms are given for the , for a wave general MMI of Fig. 9(a) with a length by [25] propagating as

For a symmetrical input image at input arm with even, one gets port

and output

even: (A1) odd:

for

(A3)

and for an antisymmetrical input image (A2)

is a constant phase shift depending on the MMI-length. for the important We have calculated the phases 4-MMI in Table I. 4 2) Overlap MMI’s: As these MMI’s [see Fig. 9(b)] can be considered as a special case of two overlapping input arms -MMI the resulting phase relations at of a general the corresponding output arms are given as a superposition of the phase relations given in (A1) and (A2). If one additionally studies the mirror characteristics, the following phase relations can be written down for inputs and outputs when the MMI[28]. lenght is

for (A4) is a number greater or equal one. We only use MMI’s with Now that we have an overlapping image the signals at the output guides do not have any more equal intensities. For a symmetrical input image at input arm the amplitudes

LEUTHOLD et al.: MULTIMODE INTERFERENCE COUPLERS

at the output arms

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are given according to (A5)

at the output of an antisymmetrical The amplitudes input image from input arm are given as (A6) -MMI’s [13] are a special case of overlap The 1 MMI’s, that have one input guide at the center. The are derived and an input guide at the center, of MMI’s with uniform images. This which splits the input mode onto result follows directly when calculating the output intensities and of an MMI in the overlap-picture with These 1 -MMI’s are often called “symmetric interference MMI’s.” -MMI’s [14] are another special case Analogously, 2 of overlap-MMI’s. They have the input guide at or and are often referred as “restricted interference a length after (1) and an input guide at MMI’s.” With the input mode is split onto images. This result can be verified with the theory of the overlap-MMI’s, when using with For even the input an input guide at and lead to identical output distributions. at

(a)

APPENDIX II A. Generalization of the Concept to Converter-Combiner Outputs MMI’s with In this Appendix, we demonstrate, how the convertercombiners can be generalized to allow for the splitting up common output guides for both the zero-order and the into first-order modes. 1) Generalized Mode Conversion: We first mention, that -MMI’s can for the generation of first-order modes, any and MMI’s with be used in full analogy to the the 66 and 50% conversion efficiencies presented in Fig. 2. Because of (4), which guarantees the first-order mode phase-MMI, first-order modes are relations for any general generated whenever the input guide is positioned at or near the MMI-edge. Such MMI’s allow for odd to generate one zerofirst-order modes and for even, order mode and first-order they generate 2 zero-order modes and modes. first-order modes can be A complete conversion into obtained by modifying the 100%-converter of Fig. 2(c). We only have to replace the 50%-MMI-converter of Fig. 2(c), 4-MMI by a general which is derived of a general 4 -MMI. The new MMI is shown in Fig. 10(a). As in the 100%-MMI-converter a signal is first launched into the 2-MMI and split into two parts. The phases of the two 1 signals have to be properly adjusted before introduced through the inputs and The required phase shift amounts odd and to 0 for even. Due to constructive and to for destructive interferences of the two signals from input and in the general -MMI, only output

(b) Fig. 10. (a) Generalized MMI-converter that converts a fundamental mode with 100% efficiency into first-order modes. (b) MMI-converter-combiner with outputs and a 100% coupling efficiency for the mode A onto zero-order modes and for the mode B onto K first-order modes. The structures are obtained by adding the central waveguide to the generalized 100%-MMI-converter of (a).

K

K

K

ports guide light. We have given the output guides that guide light, in the general-MMI notation. As we have more than one signal at the output, it is of interest to know the phase relations of the first-order modes. For simplicity, we introduce the knotation as given on Fig. 10(a). The phases of the first-order modes at the output of the converter can then be calculated with (A1)–(A4) to be (A7) 2) Generalized MMI-Converter-Combiner: We now derive two versions of MMI-converter-combiners with a 100% coupling efficiency for both modes that additionally split the outputs. All we have to do is modes completely into to append a central input guide on the second MMI of the

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100%-MMI-converter given in Fig. 10(a). Fig. 10(b) shows realizations of generalized 100%-MMI-converter-combiners outputs. They have the geometry of the generalized with first-order mode output guides. 100%-MMI-converter with Moreover the second MMI has the same geometry as the -MMI. With the central-input symmetric interference 1 -splitter for the zeroguide the MMI can be used as 1 order mode A. Fortunately the outputs of the generalized -MMI splitter have the same MMI-converter and the 1 positions. The intensities of the zero-order mode image A and first-order mode image B are uniformly split onto the output waveguides. Last, we mention that both the MMI-converter-combiner with 50 and 66%-efficiencies can be generalized analogously, so that they combine the conversion, combining and splitting outputs. of zero, and first-order modes into

[17]

[18] [19]

[20]

[21]

[22]

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N 2N

Juerg Leuthold was born in St. Gallen, Switzerland, on July 11, 1966. He received the diploma in physics from the Swiss Federal Institute of Technology, Z¨urich, Switzerland, in 1991. Since 1992, he has been pursuing the Ph.D degree in the area of all-optical switching, multimode interference and material studies at the Institute of Quantum Electronics of the Swiss Federal Institute of Technology in Z¨urich, Switzerland.

N

Juerg Eckner was born in Z¨urich, Switzerland, on October 23, 1965. He studied at the Swiss Federal Institute of Technology, Z¨urich, Switzerland, and received the diploma in experimental physics in 1990. He has been working towards the Ph.D. degree at the Swiss Federal Institute of Technology in the field of integrated optics. His research interests are semiconductor optical amplifier technology, mainly for the 1.55 mm range, and their integration into larger switching matrices and all optical switches.

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Emil Gamper was born in Z¨urich, Switzerland, on May 12, 1968. He received the diploma in physics from the Swiss Federal Institute of Technology, Z¨urich, Switzerland, in 1994. Besides a part time job in industry, he has been pursuing the Ph.D degree in the area of semiconductor optical amplifier technology since 1996.

Pierre A. Besse was born in Sion, Switzerland, in 1961. He received the diploma in physics and the Ph.D. degree on semiconductor optical amplifiers from the Swiss Federal Institute of Technology, ETH Z¨urich, Switzerland, in 1986 and 1992, respectively. In 1986, he joined the group of Micro- and Optoelectronics of the Institute of Quantum Electronics at ETH Z¨urich, where he was engaged in research of optical telecommunication. In August 1994, he joined the Institute of Microsystems of the Swiss Federal Institute of Technology at Lausanne (EPFL) as Senior Assistant where he has been working on sensors and actuators microsystems.

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Hans Melchior was born in Pontresina, Switzerland, on February 23, 1935. He received the Diploma in electrical engineering and Dr.Sci.Technol. from the Swiss Federal Institute of Technology, Z¨urich, Switzerland, in 1959 and 1965, respectively. From 1965 to 1976, he joined at Bell Telephone Laboratories, NJ, in the fields of high-speed photodetectors, avalanche photodiodes and fiber-optical communications. In addition, he was active in early liquid-crystal and ferroelectric-ceramic projection display work. Since 1976, he is Professor for Electronics of the Swiss Federal Institute of Technology in Z¨urich, Switzerland. He leads a group in the physics department, that is active in compound semiconductor optoelectronics and high-speed electronics devices and technology. His group is, besides basic technology and device developments, also involved in Swiss and European Union industry oriented work in the fields of fiber optical communication, optoelectronic waveguide devices and optical and electronic interconnects and packaging.