JOURNAL OF LIGHTWAVE TECHNOLOGY,VOL.13.NO.4.APRIL 1995 615 Optical Multi-Mode Interference Devices Based on Self-Imaging:Principles and Applications Lucas B.Soldano and Erik C.M.Pennings,Member,/EEE Invited Paper Abstract-This paper presents an overview of integrated optics outline of the modal propagation analysis (MPA),which routing and coupling devices based on multimode interference. will be used later to describe image formation by general The underlying self-imaging principle in multimode waveguides and restricted multimode interference (Sections IV and V. is described using a guided mode propagation analysis.Special issues concerning the design and operation of multimode inter- respectively).Special design and behavior issues concerning ference devices are discussed,followed by a survey of reported MMI devices are discussed in Section VI.Performances and applications.It is shown that multimode interference couplers compatibility with other components are presented through offer superior performance,excellent tolerance to polarization examples of fabricated MMI couplers and their applications and wavelength variations,and relaxed fabrication requirements in more elaborate optical circuits (Section VII).We conclude when compared to alternatives such as directional couplers adiabatic X-or Y-junctions,and diffractive star couplers. by comparing the properties of MMI devices with those of more conventional routing and coupling devices. I.INTRODUCTION II.THE SELF-IMAGING PRINCIPLE ODAY'S evolving telecommunication networks are in- creasingly focusing on flexibility and reconfigurability Self-imaging of periodic objects illuminated by coherent which requires enhanced functionality of photonic integrated light was first described more than 150 years ago [7].Self- circuits (PICs)for optical communications.In addition,mod- focusing(graded index)waveguides can also produce periodic ern wavelength demultiplexing (WDM)systems will require real images of an object [8].However,the possibility of signal routing and coupling devices to have large optical achieving self-imaging in uniform index slab waveguides was bandwidth and to be polarization insensitive.Also small device first suggested by Bryngdahl [9]and explained in more detail dimensions and improved fabrication tolerances are required by Ulrich [10],[111. in order to reduce process costs and contribute to large-scale The principle can be stated as follows:Self-imaging is a PIC production. property of multimode waveguides by which an input field In recent years,there has been a growing interest in the ap- profile is reproduced in single or multiple images at periodic plication of multimode interference (MMI)effects in integrated intervals along the propagation direction of the guide. optics.Optical devices based on MMI effects fulfil all of the above requirements,and their excellent properties and ease of fabrication have led to their rapid incorporation in more III.MULTIMODED WAVEGUIDES complex PICs such as phase diversity networks [1].Mach- The central structure of an MMI device is a waveguide Zehnder switches [2]and modulators [3].balanced coherent designed to support a large number of modes (typically receivers [4],and ring lasers [5],[6]. 3).In order to launch light into and recover light from that This paper reviews the principles and properties of MMI multimode waveguide,a number of access (usually single- devices and their applications.The operation of optical MMI moded)waveguides are placed at its beginning and at its devices is based on the self-imaging principle,presented end.Such devices are generally referred to as N x M MMI in Section II.Basic properties of multimode waveguides couplers,where N and M are the number of input and output are introduced early in Section III,followed by a short waveguides respectively. A full-modal propagation analysis is probably the most Manuscript received August 8,1994;revised December 19.1994.This comprehensive theoretical tool to describe self-imaging phe- work was supported in part by the Netherlands Technology Foundation (STW) nomena in multimode waveguides.It not only supplies the as part of the programme of the Foundation for Fundamental Research on basis for numerical modelling and design,but it also provides Matter (FOM). L.B.Soldano is with Delft University of Technology.Department of insight into the mechanism of multimode interference.Other Electrical Engineering.Laboratory of Teecommunication and Remote Sensing approaches make use of ray optics [121.hybrid methods [13], Technology,2628 CD Delft,The Netherlands. E.C.M.Pennings is with Philips Research Laboratories.Wideband or BPM type simulations.We follow here the guided-mode Communication Systems.5656AA Eindhoven.The Netherlands. propagation analysis (MPA),proposed first in [11]for the IEEE Log Number 9409613. formulation of the periodic imaging. 0733-8724/95$04.00@1995EEE
I I1 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO. 4, APRIL 1995 615 Optical Multi-Mode Interference Devices Based on Self-Imaging : Principles and Applications Lucas B. Soldano and Erik C. M. Pennings, Member, IEEE Invited Paper Abstract-This paper presents an overview of integrated optics outline of the modal propagation analysis (MPA), which will be used later to describe image formation by general and restricted multimode interference (Sections IV and V, MMI devices are discussed in Section VI. Performances and compatibility with other components are presented through examDles of fabricated MMI CouDlers and their aDDlications routing and coupling devices based on multimode interference. The underlying self-imaging principle in multimode waveguides is described using a guided mode propagation analysis. Special ference devices are discussed, followed by a survey of reported applications. It is shown that multimode interference couplers Offer Superior performance, excellent tolerance to polarization issues concerning the design and operation of multimode inter- design and behavior issues concerning I. and wavelength variations, and relaxed fabrication requirements when compared to alternatives such as directional couplers, adiabatic X- or Y-junctions, and diffractive star couplers. in elaborate optical circuits ;Section ~11). we conclude by comparing the properties of MMI devices with those of more conventional routing and coupling devices. I. INTRODUCTION ODAY’S evolving telecommunication networks are in- T creasingly focusing on flexibility and reconfigurability, which requires enhanced functionality of photonic integrated circuits (PICs) for optical communications. In addition, modem wavelength demultiplexing (WDM) systems will require signal routing and coupling devices to have large optical bandwidth and to be polarization insensitive. Also small device dimensions and improved fabrication tolerances are required in order to reduce process costs and contribute to large-scale PIC production. In recent years, there has been a growing interest in the application of multimode interference (MMI) effects in integrated optics. Optical devices based on MMI effects fulfil all of the above requirements, and their excellent properties and ease of fabrication have led to their rapid incorporation in more complex PICs such as phase diversity networks [l], MachZehnder switches [2] and modulators [3], balanced coherent receivers [4], and ring lasers [5], [6]. This paper reviews the principles and properties of MMI devices and their applications. The operation of optical MMI devices is based on the self-imaging principle, presented in Section 11. Basic properties of multimode waveguides are introduced early in Section 111, followed by a short Manuscript received August 8, 1994; revised December 19, 1994. This work was supported in part by the Netherlands Technology Foundation (STW) as part of the programme of the Foundation for Fundamental Research on Matter (FOM). L. B. Soldano is with Delft University of Technology, Department of Electrical Engineering, Laboratory of Telecommunication and Remote Sensing Technology, 2628 CD Delft, The Netherlands. E. C. M. Pennings is with Philips Research Laboratories, Wideband Communication Systems, 5656 AA Eindhoven, The Netherlands. IEEE Log Number 9409613. 11. THE SELF-IMAGING PRINCIPLE Self-imaging of periodic objects illuminated by coherent light was first described more than 150 years ago [7]. Selffocusing (graded index) waveguides can also produce periodic real images of an object [8]. However, the possibility of achieving self-imaging in uniform index slab waveguides was first suggested by Bryngdahl [9] and explained in more detail by Ulrich [lo], [lll. The principle can be stated as follows: Self-imaging is a property of multimode waveguides by which an input field profile is reproduced in single or multiple images at periodic intervals along the propagation direction of the guide. 111. MULTIMODED WAVEGUIDES The central structure of an MMI device is a waveguide designed to support a large number of modes (typically _> 3). In order to launch light into and recover light from that multimode waveguide, a number of access (usually singlemoded) waveguides are placed at its beginning and at its end. Such devices are generally referred to as N x M MMI couplers, where N and M are the number of input and output waveguides respectively. A full-modal propagation analysis is probably the most comprehensive theoretical tool to describe self-imaging phenomena in multimode waveguides. It not only supplies the basis for numerical modelling and design, but it also provides insight into the mechanism of multimode interference. Other approaches make use of ray optics [12], hybrid methods [13], or BPM type simulations. We follow here the guided-mode propagation analysis (MPA), proposed first in [ll] for the formulation of the periodic imaging. 0733-8724/95$04.00 0 1995 IEEE I -.‘
616 JOURNAL OF LIGHTWAVE TECHNOLOGY.VOL.13.NO.4.APRIL 1995 Self-imaging may exist in three-dimensional multimode nr structures,for which MPA combined with two-dimensional (finite-element or finite-difference methods)cross-section cal- culations can provide a useful simulation tool [14].How- ever,the current trend of etch-patterning produces step-index waveguides,which are,in general,single-moded in the trans verse direction.As the lateral dimensions are much larger than the transverse dimensions,it is justified to assume that the modes have the same transverse behavior everywhere in the waveguide.The problem can thus be analyzed using a two-dimensional (lateral and longitudinal)structure,such as the one depicted in Fig.1,without losing generality.The y analysis hereafter is based on such a 2-D representation of the multimode waveguide,which can be obtained from the actual Fig.I.Two-dimensional representation of a step-index multimode wave. 3-D physical multimode waveguide by several techniques, guide:(effective)index lateral profile (left),and top view of ridge boundaries and coordinate system (right). such as the effective index method (EIM)[15]or the spectral index method (SIM)[16]. A.Propagation Constants Fig.I shows a step-index multimode waveguide of width We Wv.ridge (effective)refractive index n and cladding (effec- tive)refractive index ne.The waveguide supports m lateral modes (as shown in Fig.2)with mode numbers=0. We 1...(m -1)at a free-space wavelength Ao.The lateral +6 wavenumber and the propagation constant B are related to the ridge index n by the dispersion equation +院=品m2 (1) u=0 with Fig.2.Example of amplitude-normalized lateral field profiles (y).cor- responding to the first 9 guided modes in a step-index multimode waveguide. k0= (2) 入0 (w+1)m (3) the propagation constants spacing can be written as Wey where the "effective"width Wer takes into account the (%-)≈+2)m (7) (polarization-dependent)lateral penetration depth of each 3Lz mode field,associated with the Goos-Hahnchen shifts at the ridge boundaries.For high-contrast waveguides,the B.Guided-Mode Propagation Analysis penetration depth is very small so that We WM.In An input field profile (y,0)imposed at z 0 and totally general,the effective widths W can be approximated by the contained within We (Fig.3),will be decomposed into the effective width Weo corresponding to the fundamental mode modal field distributions(y)of all modes: [17].(which shall be noted W for simplicity): o 亚(y,0)=∑c4() (8) Wev≈W.=WM+ (n2-n3)-1/2)(4) where o =0 for TE and o 1 for TM.By using the binomial where the summation should be understood as including expansion withnthe propagation constantsBcan guided as well as radiative modes.The field excitation co- be deduced from (1)-(3) efficients c can be estimated using overlap integrals B≈konm,- (v+1)2TA0 AnrW? (5) 业(y,0)p(y)dy Therefore,the propagation constants in a step-index mul- (9) timode waveguide show a nearly quadratic dependance with 2(）dg respect to the mode number v. By defining L as the beat length of the two lowest-order based on the field-orthogonality relations modes 4n,W2 If the"spatial spectrum"of the input field0)is narrow Lm兰 (6)enough not to excite unguided modes.(a condition satisfied 3入0 for all practical applications),it may be decomposed into the
616 JOURNAL OF LIGHTWAVE TECHNOLOGY. VOL. 13, NO. 4, APRIL 1995 Self-imaging may exist in three-dimensional multimode structures, for which MPA combined with two-dimensional (finite-element or finite-difference methods) cross-section calculations can provide a useful simulation tool [14]. However, the current trend of etch-patterning produces step-index waveguides, which are, in general, single-moded in the transverse direction. As the lateral dimensions are much larger than the transverse dimensions, it is justified to assume that the modes have the same transverse behavior everywhere in the waveguide. The problem can thus be analyzed using a two-dimensional (lateral and longitudinal) structure, such as the one depicted in Fig. 1, without losing generality. The analysis hereafter is based on such a 2-D representation of the multimode waveguide, which can be obtained from the actual 3-D physical multimode waveguide by several techniques, such as the effective index method (EIM) [15] or the spectral index method (SIM) [16]. A. Propagation Constants Fig. 1 shows a step-index multimode waveguide of width Whl. ridge (effective) refractive index nr and cladding (effective) refractive index nc. The waveguide supports m lateral modes (as shown in Fig. 2) with mode numbers v = 0, 1, ... (m - 1) at a free-space wavelength Xo. The lateral wavenumber k,, and the propagation constant 8, are related to the ridge index n, by the dispersion equation kp, + P; = IC&? (1) with 27r k” = - XO (U + 1)7r k,, = ___ WW where the “effective” width We, takes into account the (polarization-dependent) lateral penetration depth of each mode field, associated with the Goos-Hahnchen shifts at the ridge boundaries. For high-contrast waveguides, the penetration depth is very small so that We, N WM. In general, the effective widths W,, can be approximated by the effective width We, corresponding to the fundamental mode [17], (which shall be noted We for simplicity): where o = 0 for TE and o = 1 for TM. By using the binomial expansion with k& << kgn:, the propagation constants 8, can be deduced from (1)-(3) (5) Therefore, the propagation constants in a step-index multimode waveguide show a nearly quadratic respect to the mode number v. By defining L, as the beat length of the modes 7r 4n, W,“ L ,- 2-w- - PO -PI 3x0 dependance with two lowest-order ItC nr ID I i II 2 D Fig. 1. Two-dimensional representation of a step-index multimode waveguide; (effective) index lateral profile (left), and top view of ridge boundaries and coordinate system (right). v=O 1 2 3 4 5 6 7 8... Fig. 2. Example of amplitude-normalized lateral field profiles I.’~ ( y). corresponding to the first 9 guided modes in a step-Index multimode waveguide the propagation constants spacing can be written as Y(Y + 2)7r 3L, (Po - Pu) = (7) B. Guided-Mode Propagation Analysis An input field profile Q(y, 0) imposed at z = 0 and totally contained within We (Fig. 3), will be decomposed into the modal field distributions ?I,,(y) of all modes: where the summation should be understood as including guided as well as radiative modes. The field excitation coefficients c, can be estimated using overlap integrals e, = /m (9) based on the field-orthogonality relations. If the “spatial spectrum” of the input field q(y, 0) is narrow enough not to excite unguided modes, (a condition satisfied for all practical applications), it may be decomposed into the 1-- -- I
SOLDANO AND PENNINGS:OPTICAL MULTI-MODE INTERFERENCE DEVICES BASED ON SELF-IMAGING 617 the latter being a consequence of the structural symmetry with respect to the plane y=0. IV.GENERAL INTERFERENCE y=0 This section investigates the interference mechanisms which 平y,0)5 are independent of the modal excitation,that is,we pose no restriction on the coefficients c and explore the periodicity z-02(3Lx) (BLg)(L)2(3L) of(14). y7 A.Single Images Fig.3.Multimode waveguide showing the input field (y,0),a mirrored By inspecting (13).it can be seen that L)will be an single image at (3Lx).a direct single image at 2(3L).and two-fold images image of乎(y,0)if at(3)and(3). [.v(v+2)π exp 3Ln =1or(-1). (17) guided modes alone The first condition means that the phase changes of all the (,0)= cuv(y) (10) modes along L must differ by integer multiples of 2.In this =0 case,all guided modes interfere with the same relative phases The field profile at a distance z can then be written as a as in0:the image is thus a direct replica of the input field. superposition of all the guided mode field distributions The second condition means that the phase changes must be m-1 alternatively even and odd multiples of In this case,the (,2)=】 ,cv吨w()exp[j(ut-Bz (11) even modes will be in phase and the odd modes in antiphase. =0 Because of the odd symmetry stated in (16),the interference Taking the phase of the fundamental mode as a common produces an image mirrored with respect to the plane y=0. factor out of the sum,dropping it and assuming the time de- Taking into account (15),it is evident that the first and pendence exp(jwt)implicit hereafter,the field profile) second condition of(17)will be fulfilled at becomes L=p(3Lx)with p=0,1,2,·… (18) m-1 Ψ(，z)=∑c()cxpi(-B) (12) for p even and p odd,respectively.The factor p denotes =0 the periodic nature of the imaging along the multimode A useful expression for the field at a distance z=L is then waveguide.Direct and mirrored single images of the input found by substituting (7)into (12) fieldy,0)will therefore be formed by general interference m-1 at distances z that are,respectively,even and odd multiples (y,L)=>cv(y)exp w(w+2)π (13) of the length(3L),as shown in Fig.3.It should be clear at =0 3Lx this point that the direct and mirrored single images can be The shape of (y,L),and consequently the types of images exploited in bar-and cross-couplers,respectively. formed,will be determined by the modal excitation c,and Next,we investigate multiple imaging phenomena,which provide the basis for a broader range of MMI couplers. the properties of the mode phase factor 「.(w+2)π exp 3Ls (14) B.Multiple Images In addition to the single images at distances given by (18). It will be seen that,under certain circumstances,the field multiple images can be found as well.Let us first consider (y,L)will be a reproduction (self-imaging)of the input the images obtained half-way between the direct and mirrored field (y,0).We call General Interference to the self-imaging image positions,i.e.,at distances mechanisms which are independent of the modal excitation: and Restricted Interference to those which are obtained by L=3L）wi曲p=135, (19) exciting certain modes alone. The following properties will prove useful in later deriva- The total field at these lengths is found by substituting (19) tions: into (13) w(w+2)= ∫even for v even (15) Lodd for v odd (,号3L)=cw()exp [fju(v+2p()】 (20) and, (-）= (y) for v even with p an odd integer.Taking into account the property of (15) -(y)for v odd (16) and the mode field symmetry conditions of (16),(20)can be
I I1 SOLDANO AND PENNINGS: OPTICAL MULTI-MODE INTERFERENCE DEVICES BASED ON SELF-IMAGING 617 the latter being a consequence of the structural symmetry with respect to the plane y = 0. IV. GENERAL INTERFERENCE This section investigates the interference mechanisms which are independent of the modal excitation, that is, we pose no I restriction on the coefficients c, and explore the periodicity A. Single Images Fig. 3. Multimode waveguide showing the input field *(y,o), a mirrored single image at (3L,), a direct single image at 2(3L,). and two-fold images at ;(3L,) and %(3L,). By inspecting (13), it can be seen that 6(y, L) will be an image of 6(y, 0) if guided modes alone m-1 @(Y,O) = CV+U(Y). (10) u=o The field profile at a distance z can then be written as a superposition of all the guided mode field distributions m-1 Q(Y, .) = CU+U(Y) exp[j(wt - PU.)]. (11) u=o Taking the phase of the fundamental mode as a common factor out of the sum, dropping it and assuming the time dependence exp(jwt) implicit hereafter, the field profile 6(y, z) becomes m-1 The first condition means that the phase changes of all the modes along L must differ by integer multiples of 27r. In this case, all guided modes interfere with the same relative phases as in z = 0; the image is thus a direct replica of the input field. The second condition means that the phase changes must be alternatively even and odd multiples of 7r. In this case, the even modes will be in phase and the odd modes in antiphase. Because of the odd symmetry stated in (1 6), the interference produces an image mirrored with respect to the plane y = 0. Taking into account (15), it is evident that the first and second condition of (17) will be fulfilled at L = p(3L,) with p = 0,1,2,. . . (18) q(Y, 2) = c~?l~(Y)exP[j(Po - b).]. (12) A useful expression for the field at a distance 2 = L is then for p even and p odd, respectively. The factor p denotes the periodic nature of the imaging along the multimode waveguide. Direct and mirrored single images of the input field 6(y, 0) will therefore be formed by general interference at distances z that are, respectively, even and odd multiples of the length (3L,), as shown in Fig. 3. It should be clear at this point that the direct and mirrored single images can be exploited in bar- and cross-couplers, respectively. u=o found by substituting (7) into (12) m-1 (13) u=o The Of '(Y, L), and the Of images and Next, we investigate multiple imaging phenomena, which be determined by the excitation provide the basis for a broader range of MMI couplers. the properties of the mode phase factor (14) exp [j v(v + 3LiT It will be seen that, under certain circumstances, the field @(y,L) will be a reproduction (self-imaging) of the input field 6 (y , 0). We call General Interference to the self-imaging mechanisms which are independent of the modal excitation; and Restricted Interference to those which are obtained by exciting certain modes alone. The following properties will prove useful in later derivations: B. Multiple Images In addition to the single images at distances given by (18), multiple images can be found as well. Let us first consider the images obtained half-way between the direct and mirrored image positions, i.e., at distances P 2 L= -(3L,) with p= 1,3,5,... . (19) The total field at these lengths is found by substituting (19) into (13) even for v even odd for U odd v(v + 2) = { and, +,,(y) for v even (16) with p an odd integer. Taking into account the property of (15) = { and the mode field symmetry conditions of (16), (20) can be -?,hu(y) for v odd
618 JOURNAL OF LIGHTWAVE TECHNOLOGY.VOL.13,NO.4.APRIL 1995 304m boundary),and with periodicity 2W 业n()三∑[(y-2w,0)-(-y+v2W,0明 =-00 (22) 122μm 2.4μm and to approximate the mode field amplitudes by sine-like functions 8.0m p(）≈sin(kv) (23) Based on these considerations,(10)can be interpreted as R±300um a(spatial)Fourier expansion,and it is shown [22]that,at distances L=3u) (24) Fig.4.Schematic layout of a 2 x 2 MMI coupler based on the where p 0 and N 1 are integers with no common divisor, general interference mechanism [19].The multimode waveguide length is the field will be of the form LMMI250 um.Offsets are used to minimize losses at the transitions between waveguides of different curvature.Note the widely spaced access N-1 branches.which decrease coupling between access waveguides and obviates (y,L)= (25) blunting duc to poor photolithography resolution. 90 with written as a=p(2q-N)N (26) (u,3L.)=∑cw()+∑(-Pc() even 9g=p(W-9g) W (27) =1+Yu,0+1--Y(-,0 2 2 where C is a complex normalization constant with C= (21) VN,p indicates the imaging periodicity along z,and g refers to each of the N images along y. The last equation represents a pair of images of (y,0), The above equations show that,at distances z=L,N in quadrature and with amplitudes 1/v2,at distances= images are formed of the extended field in(y),located at the (3Lx),L),..as shown in Fig.3.This two-fold imaging positions each with amplitude 1/N and phaseThis can be used to realize 2 x 2 3-dB couplers. leads to N images (generally not equally spaced)of the inpur Optical 2 x 2 MMI couplers based on the single and two- field (y,0)being formed inside the physical guide (within the fold imaging by general interference have been realized in guide's lateral boundaries),as shown in Fig.5.The multiple III-V semiconductor waveguides [18],[19],in silica-based self-imaging mechanism allows for the realization of N x N dielectric waveguides [201,and in non-lattice matched III-V or N x M optical couplers.Shortest devices are obtained for quantum wells [21],[3]. p=1.In this case,the optical phases of the signals in a NxN Fig.4 shows the schematic layout of the InGaAsP 2 x 2 MMI coupler are,(apart from a constant phase),given by multimode interference coupler reported in [181.[19).The 8- um wide multimode section supports 4 guided modes.Excess 4N(s-1)(2N +r-s)+7 for r+s even (28) losses of 0.4-0.7 dB,with extinction ratios of-28 dB at the and cross state (3=500 um)and imbalances well below 0.1 dB for the 3-dB state (3=250 um)were measured for Prs= 4N(r+8-1)(2N-r-s+1)forr+sodd TE and TM polarizations at Xo=1.52 um.The imbalance of (29) an N x M coupler is defined as the maximum to minimum output power ratio for all M outputs,expressed in dB.This where r 1,2,...N is the (bottom-up)numbering of definition will be used throughout the paper. the input waveguides and s=1.2...N is the (top-down) In general,multi-fold images are formed at intermediate z- numbering of the output waveguides. positions [12].Analytical expressions for the positions and It is important to note that the phase relationships given phases of the N-fold images have been obtained [22]by by (28)and (29)are inherent to the imaging properties of using Fourier analysis and properties of generalized Gaussian multimode waveguides.It appears that the output phases of the sums.A very brief summary of the bases and results of that 4 x 4 coupler satisfy the phase quadrature relationship,and derivation is given here.The starting point is to introduce a that this MMI device can be used as a 90-hybrid which is a field in()as the periodic extension of the input field,0):key component in phase-diversity or image rejection receivers antisymmetric with respect to the plane y=0(which,for and which can be used to avoid the quadrature problem in this analysis,is chosen to coincide with one guide's lateral interferometric sensors
618 122 prn offset Fig. 4. Schematic layout of a 2 x 2 MMI coupler based on the general interference mechanism [19]. The multimode waveguide length is LMMI cz 250 pm. Offsets are used to minimize losses at the transitions between waveguides of different curvature. Note the widely spaced access branches, which decrease coupling between access waveguides and obviates blunting due to poor photolithography resolution. written as U even uodd The last equation represents a pair of images of Q(y, 0), in quadrature and with amplitudes 1/ a, at distances z = (3L,), ;(3L,), . . . as shown in Fig. 3. This two-fold imaging can be used to realize 2 x 2 3-dB couplers. Optical 2 x 2 MMI couplers based on the single and twofold imaging by general interference have been realized in 111-V semiconductor waveguides [ 181, [ 191, in silica-based dielectric waveguides [20], and in non-lattice matched 111-V quantum wells [21], 131. Fig. 4 shows the schematic layout of the InGaAsP 2 x 2 multimode interference coupler reported in [18], [19]. The 8- pm wide multimode section supports 4 guided modes. Excess losses of 0.4-0.7 dB, with extinction ratios of -28 dB at the cross state (3L, = 500 pm) and imbalances well below 0.1 dB for the 3-dB state ($3L, = 250 pm) were measured for TE and TM polarizations at A0 = 1.52 pm. The imbalance of an N x M coupler is defined as the maximum to minimum output power ratio for all M outputs, expressed in dB. This definition will be used throughout the paper. In general, multi-fold images are formed at intermediate zpositions [ 121. Analytical expressions for the positions and phases of the N-fold images have been obtained 1221 by using Fourier analysis and properties of generalized Gaussian sums. A very brief summary of the bases and results of that derivation is given here. The starting point is to introduce a field Qin(y) as the periodic extension of the input field q(y, 0); antisymmetric with respect to the plane y = 0 (which, for this analysis, is chosen to coincide with one guide’s lateral JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO. 4, APRIL 1995 boundary), and with periodicity 2W, 03 Si,(Y) [*(y- W2We,0) - *(-y+v2We;0)] 1)=--03 (22) and to approximate the mode field amplitudes by sine-like functions $Ju(Y) 2 sin(k,vy). (23) Based on these considerations, (10) can be interpreted as a (spatial) Fourier expansion, and it is shown 1221 that, at distances P N L = -(3L,) where p 2 0 and N 2 1 are integers with no common divisor, the field will be of the form with where C is a complex normalization constant with IC1 = fi,p indicates the imaging periodicity along z, and q refers to each of the N images along y. The above equations show that, at distances z = L, N images are formed of the extended field qin(y), located at the positions yn, each with amplitude 1/m and phase pn. This leads to N images (generally not equally spaced) of the input field Q(y, 0) being formed inside the physical guide (within the guide’s lateral boundaries), as shown in Fig. 5. The multiple self-imaging mechanism allows for the realization of N x N or N x M optical couplers. Shortest devices are obtained for p = 1. In this case, the optical phases of the signals in a N x N MMI coupler are, (apart from a constant phase), given by r prs = -(s - l)(2N + T - s) + 7r for T + s even (28) 4N and 7l cprS = -(r + s - l)(2N - T - s + 1) for T + s odd 4N (29) where T = 1, 2, ... N is the (bottom-up) numbering of the input waveguides and s = 1, 2,...N is the (top-down) numbering of the output waveguides. It is important to note that the phase relationships given by (28) and (29) are inherent to the imaging properties of multimode waveguides. It appears that the output phases of the 4 x 4 coupler satisfy the phase quadrature relationship, and that this MMI device can be used as a 90O-hybrid which is a key component in phase-diversity or image rejection receivers and which can be used to avoid the quadrature problem in interferometric sensors. 7- r
SOLDANO AND PENNINGS:OPTICAL MULTI-MODE INTERFERENCE DEVICES BASED ON SELF-IMAGING 619 的W X中 504m R=300um 200m 50μm ☑2书 400um Lmm=34 400μm Fig.6.Schematic layout of the 4x490-hybrid and modal propagation analysis within the multimode waveguide [27].The length and the width of the multimode waveguide are Lmmi945 um and Wmmi 21.6 um. respectively. N-fold images will be formed at distances (cf.(24)) (b) (33) Fig.5.Theoretical light intensity patterns corresponding to general or paired interference mechanisms in two multimode waveguides,leading to a mirrored single image (a).and a 4-fold image (b).Note also the multi-fold images at where p≥0andN≥1 are integers having no common intermediate distances.non-equally spaced along the lateral axis.Reproduced by kind permission of J.M.Heaton,British Crown Copyright DRA 1992. divisor. One possible way of attaining the selective excitation of (31)is by launching an even symmetric input field (y,0)(for Several 4 x 4 MMI optical hybrids have been demonstrated example,a Gaussian beam)at y=+We/6.At these positions, in different technologies and sizes,such as 10-25 mm long the modes y=2,5,8,...present a zero with odd symmetry. semi-bulk constructions of sandwiched glass sheets [23],and as shown in Fig.2.The overlap integrals of(9)between the ion-exchanged waveguides on glass substrates [24],[25]. (symmetric)input field and the (antisymmetric)mode fields Recently,ultra-compact (sub-millimeter length)4 x 4 will vanish and therefore c=0 for v=2,5,8,...Obviously deeply etched waveguide couplers were fabricated by reactive- the number of input waveguides is in this case limited to two. ion etching in III-V semiconductor material [26],[27].These When the selective excitation of (31)is fulfilled,the modes devices (shown in Fig.6)attained excess losses below I dB. contributing to the imaging are paired,i.e.the mode pairs 0-1. imbalances from 0.3-0.9 dB and phase deviations of the order 3-4,6-7,...have similar relative properties.(For example of 5, each even mode leads its odd partner by a phase difference of 7/2 at z=L/2-the 3-dB length-,by a phase difference V.RESTRICTED INTERFERENCE of at=L-the cross-coupler length-,etc).This Thus far,no restrictions have been placed on the modal mechanism will be therefore called paired interference.Two- excitation.This section investigates the possibilities and real- mode interference (TMI)can be regarded in this context as a izations of MMI couplers in which only some of the guided particular case of paired interference. modes in the multimode waveguide are excited by the input 2 x 2 MMI couplers based on the paired interference field(s).This selective excitation reveals interesting multiplic- mechanism have been demonstrated in silica-based dielectric ities of v(+2),which allow new interference mechanisms rib-type waveguides with multimode section lengths of 240 through shorter periodicities of the mode phase factor of(14). um (cross state)and 150 um (3-dB state)[30],[31].Insertion loss lower than 0.4 dB,imbalance below 0.2 dB,extinction ratio of-18 dB,and polarization-sensitivity loss penalty of A.Paired Interference 0.2 dB were reported for structures supporting 7-9 modes. By noting that Calculations predict that power excitation coefficients as low as-40 dB for the modes v=2.5,8 can be achieved through a mod3[w(w+2)=0forw≠2,5,8，· (30) correct positioning of the access waveguides,remaining below -30 dB for a 0.1-um misalignment [29]. it is clear that the length periodicity of the mode phase factor of (14)will be reduced three times if Recently,extremely small paired-interference MMI devices were reported [32].The 3-dB (cross)couplers,realized in a cw=0forv=2,5,8., (31) raised-strip InP-based waveguide,are 107-um(216-um)long, and show 0.9-dB(2-dB)excess loss and-28 dB crosstalk. Therefore,as shown in [28],[29].single (direct and inverted) images of the input field (y,0)are now obtained at (cf.(18)) B.Symmetric Interference L=p(L=)with p=0,1,2,... (32) Optical N-way splitters can in principle be realized on the basis of the general N-fold imaging at lengths given by(24). provided that the modes =2,5.8,...are not excited in the However,by exciting only the even symmetric modes,I-to- multimode waveguide.By the same token,two-fold images are N beam splitters can be realized with multimode waveguides found at(p/2)L with p odd.Based on numerical simulations,four times shorter [33]
I SOLDANO AND PENNINGS: OPTICAL MULTI-MODE INTERFERENCE DEVICES BASED ON SELF-IMAGING (b) Fig 5 Theoretical light intensity patterns corresponding to general or pared interference mechanisms in two multimode waveguides, leading to a mrrored single image (a), and a 4-fold image (b) Note also the multi-fold images at intermediate distances, non-equally spaced along the lateral axis Reproduced by kind pernussion of J M Heaton, @British Crown Copynght DRA 1992 Several 4 x 4 MMI optical hybrids have been demonstrated in different technologies and sizes, such as 10-25 mm long semi-bulk constructions of sandwiched glass sheets [23], and ion-exchanged waveguides on glass substrates [24], [25]. Recently, ultra-compact (sub-millimeter length) 4 x 4 deeply etched waveguide couplers were fabricated by reactiveion etching in 111-V semiconductor material [26], [27]. These devices (shown in Fig. 6) attained excess losses below 1 dB, imbalances from 0.3-0.9 dB and phase deviations of the order of 5". V. RESTRICTED INTERFERENCE Thus far, no restrictions have been placed on the modal excitation. This section investigates the possibilities and realizations of MMI couplers in which only some of the guided modes in the multimode waveguide are excited by the input field(s). This selective excitation reveals interesting multiplicities of v(v+ 2), which allow new interference mechanisms through shorter periodicities of the mode phase factor of (14). A. Paired Integerence By noting that mods[v(v + 2)] = 0 for v # 2,5,8,. . . (30) it is clear that the length periodicity of the mode phase factor of (14) will be reduced three times if Therefore, as shown in [28], [29], single (direct and inverted) images of the input field q(y, 0) are now obtained at (cf. (18)) L = p(L,) with p = 0,1,2,. . . (32) provided that the modes v = 2, 5, 8, . . . are not excited in the multimode waveguide. By the same token, two-fold images are found at (p/2)L, with p odd. Based on numerical simulations, 619 400pm , Lm,,=3Lrd4 , 400pm Fig. 6. Schematic layout of the 4 x 4 90O-hybrid and modal propagation analysis within the multimode waveguide [27]. The length and the width of the multimode waveguide are L,,, N 945 pm and W,,, N 21.6 pm, respectively. N-fold images will be formed at distances (cf. (24)) P N L = -(Lr) (33) where p 2 0 and N 2 1 are integers having no common divisor. One possible way of attaining the selective excitation of (31) is by launching an even symmetric input field @(y, 0) (for example, a Gaussian beam) at y = kWe/6. At these positions, the modes v = 2, 5, 8, . . . present a zero with odd symmetry, as shown in Fig. 2. The overlap integrals of (9) between the (symmetric) input field and the (antisymmetric) mode fields will vanish and therefore c, = 0 for v = 2,5,8, . . . Obviously, the number of input waveguides is in this case limited to two. When the selective excitation of (31) is fulfilled, the modes contributing to the imaging are paired, i.e. the mode pairs 0- 1, 3-4, 6-7, . . . have similar relative properties. (For example, each even mode leads its odd partner by a phase difference of 7r/2 at z = L,/2-the 3-dB length-, by a phase difference of 7r at z = L,-the cross-coupler length-, etc). This mechanism will be therefore called paired interference. Twomode interference (TMI) can be regarded in this context as a particular case of paired interference. 2 x 2 MMI couplers based on the paired interference mechanism have been demonstrated in silica-based dielectric rib-type waveguides with multimode section lengths of 240 pm (cross state) and 150 pm (3-dB state) [30], [31]. Insertion loss lower than 0.4 dB, imbalance below 0.2 dB, extinction ratio of - 18 dB, and polarization-sensitivity loss penalty of 0.2 dB were reported for structures supporting 7-9 modes. Calculations predict that power excitation coefficients as low as -40 dB for the modes v = 2,5,8 can be achieved through a correct positioning of the access waveguides, remaining below -30 dB for a 0.1-pm misalignment [29]. Recently, extremely small paired-interference MMI devices were reported [32]. The 3-dB (cross) couplers, realized in a raised-strip InP-based waveguide, are 107-pm (216-pm) long, and show 0.9-dB (2-dB) excess loss and -28 dB crosstalk. B. Symmetric Inte$erence Optical N-way splitters can in principle be realized on the basis of the general N-fold imaging at lengths given by (24). However, by exciting only the even symmetric modes, l-toN beam splitters can be realized with multimode waveguides four times shorter [33]
620 JOURNAL OF LIGHTWAVE TECHNOLOGY,VOL.13.NO.4,APRIL 1995 TABLE L SUMMARY OF CHARACTERISTICS OF THE GENERAL, PAIRED.AND SYMMETRIC INTERFERENCE MECHANSIMS Interference mechanism Symmetric Inputs x Outputs NXN 2xN First single image distance 3L (Lr) (3,/4 First N-fold image distance (3LO/N Le】/N 3L.)74N (a Excitation none c=0 c=0 requirements for=2,5,8 fory=1,3,5 Input(s)location(s) any y=土W6 y=0 and 50-70 um for InP-based waveguides)have been fabricated with excess losses of around I dB and imbalances below 0.15 dB [361,in agreement with numerical predictions [37],[38]. A number of 1 x N waveguide splitters/combiners covering (b) a wide range of different multimode guide widths(12-48 um) Fig.7.Theoretical light intensity patters corresponding to (single-input) and lengths(250-3800 um)have been demonstrated in GaAs- symmetric interference mechanisms in a 20-gm-wide multimode waveguide showing "I x I"imaging (a);and in a 40-gm-wide multimode waveguide and InP-based rib waveguides which divide power with <0.4- showing 1-to-4 way splitting (b).Note also the multi-fold images at inter- dB imbalances between N output guides,for values of N mediate distances,equally spaced along the lateral axis.Reproduced by kind permission of J.M.Heaton etal 34].British Crown Copyright DRA1992. between 2 and 20 [34],[39],[40]. These experiments permit to conclude that,setting 1 um as an achievable lithographic limit to the open gap,and 2 um as In effect,by noting that a workable width of the access waveguides.InP-based 1-to-N mod4v(v+2)=0 for v even (34) way splitters at Ao =1.55 um could be as short as Nx 20 um. it is clear that the length periodicity of the mode phase of(14) VI.DISCUSSION will be reduced four times if MMI devices differ from other routing and coupling devices cw=0forw=1,3,5,… (35) in a number of aspects.This section discusses how self- Therefore,single images of the input field (y,0)will now imaging determines design and behavior characteristics of MMI devices in comparison to alternative devices. be obtained at (cf.(18)) Table I summarizes some characteristics of the general, L=p( 4 with p=0,1.2.... (36) paired and symmetric interference mechanisms. if the odd modes are not excited in the multimode wave- A.Properties and Requirements guide.This condition can be achieved by centre-feeding the The general interference mechanism is in principle in- multimode waveguide with a symmetric field profile.The dependent of the position and shape of the input fields imaging is obtained by linear combinations of the (even) However,MPA calculations and experiments for strongly symmetric modes,and the mechanism will be called symmetric guiding structures [261,and full 3-D calculations for weakly- interference. as well as strongly-guiding structures [14],have shown that In general,N-fold images are obtained [331,[34]at dis- the performance of MMI devices based on general interference tances (cf.(24)) can be further optimized by careful positioning of the access =() waveguides. (37) Restricted (paired and symmetric)interference mechanisms must have well-located and reasonably symmetric input with N images of the input field(y,0),symmetrically field(s)in order to comply with the selective modal excitation located along the y-axis with equal spacings We/N. requirements of (31)and (35).respectively Fig.7 shows the calculated intensity patterns inside the For the case of 2 x 2 couplers,paired interference actually multimode waveguide of single-input,symmetrically excited leads to longer devices than those based on the general interfer- MMI couplers [34].At mid-way from the self-imaging length, ence mechanism.The selective excitation requirement dictates a two-fold image is formed.The number of images increases an increase in the multimode waveguide width-and there- at even shorter distances,according to (37),until they are no fore in its length (see (6))-which cancels out the potential longer resolvable.A good rule of thumb is that in order to length reduction.However,general interference mechanisms obtain low-loss well-balanced 1-to-N splitting of a Gaussian in weakly guiding structures may suffer from higher losses field,the multimode waveguide is required to support at least than paired interference,due to decreased image resolution m N+1 modes [35]. (Section 6.2).The access waveguides positioned at the corners The I x 2 waveguide splitter/combiner is perhaps the sim-of the multimode waveguide(Fig.4)cause the image to be plest MMI structure ever realized,needing just two symmetric reconstructed mainly by the (wider)outer lobes of the high- modes.Extremely short splitters (20-30 um for silica-based order modes (see [141)
620 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO. 4, APRIL 1995 TABLE I SUMMARY OFCHARAC~ERISTICS OF THE GENERAL, PAIRED, AND SYMMETRICNTERFERENCE MECHANSIMS 11 Interference mechanism 11 General I Parred I Symmetric U (bj Fig. 7. Theoretical light intensity patterns corresponding to (single-input) symmetric interference mechanisms in a 20-~1 m-wide multimode waveguide, showing “1 x 1” imaging (a); and in a 40-pm-wide multimode waveguide, showing ]-to-4 way splitting (bj. Note also the multi-fold images at intermediate distances, equally spaced along the lateral axis. Reproduced by kind permission of J. M. Heaton et al. [34]. OBritish Crown Copyright DRA 1992. In effect, by noting that mod4[v(v + a)] = 0 for v even (34) it is clear that the length periodicity of the mode phase of (14) will be reduced four times if c, = 0 for v = 1,3,5,... (35) Therefore, single images of the input field 9(y, 0) will now be obtained at (cf. (18)) if the odd modes are not excited in the multimode waveguide. This condition can be achieved by centre-feeding the multimode waveguide with a symmetric field profile. The imaging is obtained by linear combinations of the (even) symmetric modes, and the mechanism will be called symmetric interference. In general, N-fold images are obtained 1331, [34] at distances (cf. (24)) (37) with N images of the input field Q(y,O)! symmetrically located along the y-axis with equal spacings WJN. Fig. 7 shows the calculated intensity patterns inside the multimode waveguide of single-input, symmetrically excited MMI couplers 1341. At mid-way from the self-imaging length, a two-fold image is formed. The number of images increases at even shorter distances, according to (37), until they are no longer resolvable. A good rule of thumb is that in order to obtain low-loss well-balanced 1 -to-N splitting of a Gaussian field, the multimode waveguide is required to support at least m = N+ 1 modes 13.51. The 1 x 2 waveguide splitterkombiner is perhaps the simplest MMI structure ever realized, needing just two symmetric modes. Extremely short splitters (20-30 pm for silica-based and 50-70 pm for InP-based waveguides) have been fabricated with excess losses of around 1 dB and imbalances below 0.15 dB [36], in agreement with numerical predictions [37], 1381. A number of 1 x N waveguide splitterskombiners covering a wide range of different multimode guide widths (12-48 pm) and lengths (250-3800 pm) have been demonstrated in GaAsand InP-based rib waveguides which divide power with <0.4- dB imbalances between N output guides, for values of N between 2 and 20 [34], [39], [40]. These experiments permit to conclude that, setting 1 pm as an achievable lithographic limit to the open gap, and 2 pm as a workable width of the access waveguides, InP-based 1-to-N way splitters at X0 = 1.55 pm could be as short as N x 20 pm. VI. DISCUSSION MMI devices differ from other routing and coupling devices in a number of aspects. This section discusses how selfimaging determines design and behavior characteristics of MMI devices in comparison to alternative devices. Table I summarizes some characteristics of the general, paired and symmetric interference mechanisms. A. Properties and Requirements The general interference mechanism is in principle independent of the position and shape of the input fields. However, MPA calculations and experiments for stronglyguiding structures [26], and full 3-D calculations for weaklyas well as strongly-guiding structures [14], have shown that the performance of MMI devices based on general interference can be further optimized by careful positioning of the access waveguides. Restricted (paired and symmetric) interference mechanisms must have well-located and reasonably symmetric input field(s) in order to comply with the selective modal excitation requirements of (31) and (35), respectively. For the case of 2 x 2 couplers, paired interference actually leads to longer devices than those based on the general interference mechanism. The selective excitation requirement dictates an increase in the multimode waveguide width-and therefore in its length (see (6))-which cancels out the potential length reduction. However, general interference mechanisms in weakly guiding structures may suffer from higher losses than paired interference, due to decreased image resolution (Section 6.2). The access waveguides positioned at the comers of the multimode waveguide (Fig. 4) cause the image to be reconstructed mainly by the (wider) outer lobes of the highorder modes (see [ 141)
SOLDANO AND PENNINGS:OPTICAL MULTI-MODE INTERFERENCE DEVICES BASED ON SELF-IMAGING 621 B.Imaging Quality coupling between the access guides and leads to a sharp onset Imaging quality refers to how accurately the input field is of coupling in the MMI section.This prevents additional. reproduced at the end of the multimode waveguide. difficult to control,power exchange in the access guides and The quadratic dependence of the propagation constants with associated radiation losses,a problem commonly found in the mode number,found in (5),is an approximation.This directional couplers. means that the guided modes will actually accumulate small For many applications,balancing is even more important deviations from the calculated phases at the imaging distances than the insertion loss.In coherent detection techniques for which tend to blur the reconstructed image field.This situation example,the balancing of the output powers of the 3-dB is analogous to the focal shift from paraxial rays prediction due coupler determines the suppression of the RIN noise of the to aberration in optical systems of finite aperture.However, local oscillator laser.And when 3-dB couplers are used in some balancing of the phase errors-and thus an improvement Mach-Zehnder modulators or switches,the balancing directly of the imaging quality-is possible by a slight correction of translates into extinction ratio and crosstalk.With respect the imaging lengths predicted by (24).(33).and (37).135] to balancing.MMI devices operate fundamentally different The imaging quality of a multimode waveguide can be from directional couplers.The output powers of a directional formally evaluated with its line-spread function (LSF)[35]. coupler are proportional to cos2()and sin2(/L). The LSF represents the complex image field of an infinitely meaning that the sensitivity of the transmission to length narrow input field.An imaging system of high resolution and variations is maximum at the 3-dB point and of opposite sign good contrast is characterized by a narrow-peak and low-ripple for each output.MMI-devices function differently as can be LSF. seen in Fig.8 which shows the simulated behavior of the 4 In device terms,a narrow-peak and low-ripple LSF means x 4 90-hybrid reported in [271.Each single image of the 4- low insertion loss and low crosstalk,respectively.The charac. fold image is a local maximum,implying that the sensitivity teristics of the LSF are given by the discrete modal amplitude is minimum at the optimum length of L 978 um and that spectrum c from(9).A flat mode amplitude spectrum (i.e..all all output powers decrease similarly for deviations from the guided modes equally excited)with a sharp cut-off will pro- optimum length.As a consequence,balancing remains better duce a maximally narrow but heavily rippled LSF.Conversely than 0.3 dB for a total range of L =978+25 um,leading a ripple-free but broader LSF can be obtained by a smooth roll- to common mode rejection ratios in excess of 30 dB for the off in the mode spectrum (i.e..gradually decreasing excitation entire 50 um range. coefficients for the higher-order modes). Since the output phases of the 90-hybrid (see (27))are A simple way of estimating the imaging resolution of a inherently linked to the 4-fold image,the output phases remain multimode waveguide is as follows.As the image field is a within a margin of+5from the phase quadrature relationship linear combination of the guided mode fields,the narrowest for the same 50 um range.The excellent balancing and the obtainable image in a multimode waveguide,and thus its stable phase relationships,in turn lead to a total 40 um range resolution p,will be roughly equal to the cosine-like lobe width where the simulated image rejection ratio is better than 30 dB of the highest supported mode (i.e.,its spatial half-period,see This analysis is not specific for the 4 x 4 hybrid,but holds for Fig.2) MMI devices in general which has been confirmed by several experimental observations [19].[271.[41]. W p (38) D.Reflections Properties A much more elaborate analysis,involving the calculation of the LSF [351.predicts a resolution ranging from 0.89 W./m Several applications such as lasers and coherent detection (for a flat mode spectrum)to approximately 1.50 W/m (for techniques are very sensitive to reflections.Reflections in a Gaussian mode spectrum).Practical MMI devices usually MMI devices may originate at the end of the MMI-section have smoothly decaying mode spectra. in between the output guides.Nonnegligible reflections may The imaging resolution is a useful parameter in designing occur when large refractive index differences are encoun- an MMI coupler.The multimode waveguide must be able tered such as the semiconductor-air interface in deeply etched to provide an image field as narrow as the input field(s) waveguides.For nonoptimum lengths,some light may be launched from the access waveguide(s).For a given width of reflected off the end of the MMI section and may eventually the multimode waveguide,the resolution p is determined by reach the input guides.However,even for optimum lengths, the number of guided modes m.The number of guided modes reflections in MMI devices can be surprisingly effective, in turn.is determined by the lateral refractive index contrast because the reflection mechanisms involve the very same in ridge (rib)waveguides.whereas it is determined by the imaging property of multimode waveguides.Two different transversal contrast in deeply etched(raised-strip)waveguides. reflection mechanisms have been identified [44]: 1)An "internal resonance"mechanism,which is caused by C.Loss.Balance,and Phases the presence of several simultaneously occurring self-images. For example,the MMI 3-dB coupler shown in Fig.4 is based Employing MMI effects can produce low-loss devices,due on the two-fold image occurring at a length of L =3L/2 to the efficient imaging of the input of the MMI section onto as given by (19).This length equals precisely twice the self- the output.In addition,an increased guide-separation prevents imaging length for symmetric excitation L 3L/4 as given
I I1 SOLDANO AND PENNINGS: OPTICAL MULTI-MODE INTERFERENCE DEVICES BASED ON SELF-IMAGING 62 1 B. Imaging Quality Imaging quality refers to how accurately the input field is reproduced at the end of the multimode waveguide. The quadratic dependence of the propagation constants with the mode number, found in (5), is an approximation. This means that the guided modes will actually accumulate small deviations from the calculated phases at the imaging distances, which tend to blur the reconstructed image field. This situation is analogous to the focal shift from paraxial rays prediction due to aberration in optical systems of finite aperture. However, some balancing of the phase errors-and thus an improvement of the imaging quality-is possible by a slight correction of the imaging lengths predicted by (24), (33), and (37), 1351. The imaging quality of a multimode waveguide can be formally evaluated with its line-spread function (LSF) [35]. The LSF represents the complex image field of an infinitely narrow input field. An imaging system of high resolution and good contrast is characterized by a narrow-peak and low-ripple LSF. In device terms, a narrow-peak and low-ripple LSF means low insertion loss and low crosstalk, respectively. The characteristics of the LSF are given by the discrete modal amplitude spectrum c, from (9). A flat mode amplitude spectrum (i.e., all guided modes equally excited) with a sharp cut-off will produce a maximally narrow but heavily rippled LSF. Conversely, a ripple-free but broader LSF can be obtained by a smooth rolloff in the mode spectrum (i.e., gradually decreasing excitation coefficients for the higher-order modes). A simple way of estimating the imaging resolution of a multimode waveguide is as follows. As the image field is a linear combination of the guided mode fields, the narrowest obtainable image in a multimode waveguide, and thus its resolution p, will be roughly equal to the cosine-like lobe width of the highest supported mode (i.e., its spatial half-period, see Fig. 2) we pp-. rn A much more elaborate analysis, involving the calculation of the LSF [35], predicts a resolution ranging from 0.89 We/m (for a flat mode spectrum) to approximately 1.50 We/m (for a Gaussian mode spectrum). Practical MMI devices usually have smoothly decaying mode spectra. The imaging resolution is a useful parameter in designing an MMI coupler. The multimode waveguide must be able to provide an image field as narrow as the input field(s) launched from the access waveguide(s). For a given width of the multimode waveguide, the resolution p is determined by the number of guided modes vi. The number of guided modes, in turn, is determined by the lateral refractive index contrast in ridge (rib) waveguides, whereas it is determined by the transversal contrast in deeply etched (raised-strip) waveguides. C. Loss, Balance, and Phases Employing MMI effects can produce low-loss devices, due to the efficient imaging of the input of the MMI section onto the output. In addition, an increased guide-separation prevents coupling between the access guides and leads to a sharp onset of coupling in the MMI section. This prevents additional, difficult to control, power exchange in the access guides and associated radiation losses, a problem commonly found in directional couplers. For many applications, balancing is even more important than the insertion loss. In coherent detection techniques for example, the balancing of the output powers of the 3-dB coupler determines the suppression of the RIN noise of the local oscillator laser. And when 3-dB couplers are used in Mach-Zehnder modulators or switches, the balancing directly translates into extinction ratio and crosstalk. With respect to balancing, MMI devices operate fundamentally different from directional couplers. The output powers of a directional coupler are proportional to cos2(7rz/2L,) and sin2(7rz/2L,), meaning that the sensitivity of the transmission to length variations is maximum at the 3-dB point and of opposite sign for each output. MMI-devices function differently as can be seen in Fig. 8 which shows the simulated behavior of the 4 x 4 90”-hybrid reported in [27]. Each single image of the 4- fold image is a local maximum, implying that the sensitivity is minimum at the optimum length of L = 978 pm and that all output powers decrease similarly for deviations from the optimum length. As a consequence, balancing remains better than 0.3 dB for a total range of L = 978 4 25 pm, leading to common mode rejection ratios in excess of 30 dB for the entire 50 pm range. Since the output phases of the 90”-hybrid (see (27)) are inherently linked to the 4-fold image, the output phases remain within a margin of f 5”from the phase quadrature relationship for the same 50 pm range. The excellent balancing and the stable phase relationships, in turn lead to a total 40 pm range where the simulated image rejection ratio is better than 30 dB. This analysis is not specific for the 4 x 4 hybrid, but holds for MMI devices in general which has been confirmed by several experimental observations [ 191, [27], [41]. D. ReJections Properties Several applications such as lasers and coherent detection techniques are very sensitive to reflections. Reflections in MMI devices may originate at the end of the MMI-section in between the output guides. Nonnegligible reflections may occur when large refractive index differences are encountered such as the semiconductor-air interface in deeply etched waveguides. For nonoptimum lengths, some light may be reflected off the end of the MMI section and may eventually reach the input guides. However, even for optimum lengths, reflections in MMI devices can be surprisingly effective, because the reflection mechanisms involve the very same imaging property of multimode waveguides. Two different reflection mechanisms have been identified [44]: 1) An “internal resonance” mechanism, which is caused by the presence of several simultaneously occurring self-images. For example, the MMI 3-dB coupler shown in Fig. 4 is based on the two-fold image occurring at a length of L = 3LJ2 as given by (19). This length equals precisely twice the selfimaging length for symmetric excitation L = 3L,/4 as given
622 JOURNAL OF LIGHTWAVE TECHNOLOGY.VOL.13,NO.4.APRIL 1995 是 10 (a) 978μm 5 940 96098010001020 LMMIμm) (a) 20 (b) 10 Fig.9.MPA-simulated field contour plots in a general-interference 2x 2 0 3-dB MMI coupler:(a)transmission and (b)intemal resonance. 身 -10 4 2 vary from a minimum for in-phase excitation to a maximum 3 for out-of-phase excitation for a single MMI combiner op -40 94096098010001020 timized for maximum transmission.Note that this reflection LMMI(um) mechanism can cause increased back reflection during the off-state of a Mach-Zehnder modulator using a 2 x 1 MMI (b) combining element.This potential type of reflection can be avoided by using a Mach-Zehnder switch incorporating a 2 x 60 2 3-dB coupler rather than a combiner. For reflection-sensitive applications,several means can be used to achieve an effective reduction of reflections,such as using low-contrast waveguides or tapering the ends of the MMI section [44]. 94096098010001020 LMM(μm) E.Tolerances (c) Relaxed tolerances are important for fabrication as well as for operating conditions.Fabrication tolerances refer to 40 the control of the geometrical dimensions during processing 00 and its subsequent impact on device performance.Operation tolerances relate to the device behavior for changes in the wavelength,polarization,temperature,input field distribution, 10 and refractive index. 0 A tolerance analysis can be performed [46]in which each 94096098010001020 image is considered as a Gaussian beam focused at a self. LMMI(Hm) image distance 2 =L.Then,the loss penalty produced (d) by a(small)finite shift 6L in the a-position of the output Fig.8.Simulated performance for 4 x 4 900-hybrid:(a)relative output waveguides can be evaluated by overlapping the defocused power.(b)phase deviation from the phase quadrature condition,(c)common mode rejection ratio,and (d)image rejection ratio. beam with the output waveguide mode field.It is found that the length shift which produces a 0.5-dB loss penalty is approximately equal to the so-called Rayleigh range: by (36).This symmetric self-imaging mechanism ensures efficient imaging of both reflecting ends onto each other as 6L≥Tn,0哈 (39) illustrated in Fig.9.In lasers employing such an MMI 3-dB 4λ0 coupler,this "internal resonance"may show up as a separate where wo is defined here as the Gaussian beam waist,and contribution in the laser spectrum [45].Simultaneously oc- equals the full 1/e amplitude width of the input field (y0). curring general and symmetric self-imaging mechanisms can Equation (39)can be interpreted as an absolute length tol- possibly be prevented by employing couplers based on the erance,which does not depend on the dimensions of the paired interference mechanism. multimode waveguide.An important conclusion is that,for 2)A second type of reflection is encountered when an MMI a given wavelength and technology,all tolerances can be power splitter is used in reverse as a power combiner.Efficient relaxed by using wider access waveguides.Tapered access combining operation requires inputs of equal amplitude and waveguides have been successfully experimented in deeply- phase.If,however,the two inputs are 180 out of phase,power etched InP-based MMI couplers,resulting in a tolerant process is minimum in the output guide but maximum at the reflecting and low-loss operation [42]. end of the MMI section.This leads to perfect imaging of the The tolerances corresponding to other fabrication or oper- input guides back onto themselves.Back reflection can thus ation parameters can now be related to L from (18),using
622 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO. 4, APRIL 1995 I oL---LILI-LLL-IJ 940 960 980 1000 1020 - LMMI(P~) (a) 20" 10" 0" ,4-100 -20" 1 -30" -40" 940 960 980 1000 1020 - LMMI(P~) (b) - 80 m 60 U 5 40 t 2: 940 960 980 1000 1020 - LMMI(P~) (C) 4 940 960 980 1000 1020 --m LMMI(P~) (d) Fig. 8. Simulated performance for 4 x 4 90O-hybnd: (a) relative output power, (b) phase deviation from the phase quadrature condition, (c) common mode rejection ratio, and (d) image rejection ratio. by (36). This symmetric self-imaging mechanism ensures efficient imaging of both reflecting ends onto each other as illustrated in Fig. 9. In lasers employing such an MMI 3-dB coupler, this "internal resonance" may show up as a separate contribution in the laser spectrum [45]. Simultaneously occurring general and symmetric self-imaging mechanisms can possibly be prevented by employing couplers based on the paired interference mechanism. 2) A second type of reflection is encountered when an MMI power splitter is used in reverse as a power combiner. Efficient combining operation requires inputs of equal amplitude and phase. If, however, the two inputs are 180" out of phase, power is minimum in the output guide but maximum at the reflecting end of the MMI section. This leads to perfect imaging of the input guides back onto themselves. Back reflection can thus J (b) Fig. 9. 3-dB MMI coupler: (a) transmission and (b) internal resonance. MPA-simulated field contour plots in a general-interference 2 x 2 vary from a minimum for in-phase excitation to a maximum for out-of-phase excitation for a single MMI combiner optimized for maximum transmission. Note that this reflection mechanism can cause increased back reflection during the off-state of a Mach-Zehnder modulator using a 2 x 1 MMI combining element. This potential type of reflection can be avoided by using a Mach-Zehnder switch incorporating a 2 x 2 3-dB coupler rather than a combiner. For reflection-sensitive applications, several means can be used to achieve an effective reduction of reflections, such as using low-contrast waveguides or tapering the ends of the MMI section [44]. E. Tolerances Relaxed tolerances are important for fabrication as well as for operating conditions. Fabrication tolerances refer to the control of the geometrical dimensions during processing and its subsequent impact on device performance. Operation tolerances relate to the device behavior for changes in the wavelength, polarization, temperature, input field distribution, and refractive index. A tolerance analysis can be performed [46] in which each image is considered as a Gaussian beam focused at a selfimage distance z = L. Then, the loss penalty produced by a (small) finite shift SL in the z-position of the output waveguides can be evaluated by overlapping the defocused beam with the output waveguide mode field. It is found that the length shift which produces a 0.5-dB loss penalty is approximately equal to the so-called Rayleigh range: (39) mi,wi SL N - where WO is defined here as the Gaussian beam waist, and equals the full l/e amplitude width of the input field e(y, 0). Equation (39) can be interpreted as an absolute length tolerance, which does not depend on the dimensions of the multimode waveguide. An important conclusion is that, for a given wavelength and technology, all tolerances can be relaxed by using wider access waveguides. Tapered access waveguides have been successfully experimented in deeplyetched InP-based MMI couplers, resulting in a tolerant process and low-loss operation [42]. The tolerances corresponding to other fabrication or operation parameters can now be related to SL from (18), using 4x0
SOLDANO AND PENNINGS:OPTICAL MULTI-MODE INTERFERENCE DEVICES BASED ON SELF-IMAGING 623 TABLE II DESIGN PARAMETERS OF MMI DEVICES FABRICATED IN III-V SEMICONDUCTOR MATERIALS,AND EXPERIMENTALLY MEASURED TOLERANCE FIGURES FOR A GIVEN LOSS PENALTY.PARENTHESIZED NUMBERS ARE RESULTS OF NUMERICAL SIMULATIONS BY MPA OR BPM Ref. Loss penalty mbdlance 2610 mechanism um]ium][] (dB] [dB] [m] [nm General 2×2 19 3.241.523.08.0240 0.8) 0.17 (0.20)100 2×2 4 3.28 250 0.5 0.1 0.20 4×4■■27 3.24 152 3.0 21.6945 2.0 10.20】 Paired 2×2413.291.533.018.0530 0.5 0.20 0.30 100 2×2 ■433.301.512.216.0425 0.5 020 0.25 Symmetric 1×4 343.471.062.6 400.1300 0.25 1×4 40 3.30 1.55 2.5 24.0 300 0.4 0.20 0.30 60 the definition of (6) 6L E 26w≈l60l≈6m = (40) W。 λ0 nr Hence,it is apparent that the multimode waveguide length L must be made as short as possible in order to allow for relaxed tolerances to the other parameters As an example,let us consider the 2 x 2 MMI coupler of Fig.4 [19],comprising a multimode waveguide with We8 um,L =240 um and n =3.24,fed by access waveguides with wo3 um,and operated at 1.52-m wavelength.From (39).L 15 um;which substituted into (40)yields 6W 0.25 um,A95 nm,and on,0.20.Thus,the multimode section width is by far the most critical parameter to control Fig.10.Schematic of polarization-diversity balanced coherent receiver during fabrication.In a development stage,small variations front-end OEIC [4]. in the width can be compensated for by varying lengths in steps of 6L.In our example,five lengths L =220,235. A.Coherent Receiver Front-End 250,265,and 280 um are sufficient to obtain at least a pair Possibly the earliest reported application using an MMI of devices performing very close to design values.Table II device in a complex photonic integrated circuit is the coherent summarizes reported tolerance figures of MMI devices,for receiver front-end [4],[49],[50]shown in Fig.10.This chip specified penalty losses and imbalances. contains an MMI 3-dB coupler to combine the optical powers The dependence on polarization changes,which may be from the photosignal and the local oscillator laser.In addition, investigated through the term(nW2)in (6),results in slightly two pairs of polarization-sensitive photodetectors generate a different optimum imaging lengths for both polarizations. Polarization-independent operation is then possible by design- polarization-insensitive IF signal using diversity architectures. Several key features of MMI devices enhanced the overall ing at an intermediate length,at the price of a small loss performance of the chip. increase.Polarization-change induced penalty losses below 0.30 dB have been calculated and experimentally verified in 2 The ultracompact size of the MMI 3-dB coupler(298 um) and its compatibility with deeply etched waveguides allowing x 2 strip-loaded waveguide MMI couplers [41]. for monomode ultracompact bends (R=250 um),led to a total chip size of merely 1.3 mm. VII.APPLICATIONS Balanced operation is important to fully use the available In addition to their use as single routers or couplers,MMI optical powers of the photosignal and the LO laser and to min- devices have been applied to perform a number of more imize common mode noise due to LO intensity fluctuations. complex functions.Soon after the theory of the self-imaging Typical measured balance of both coupler outputs was within principle in multimode waveguides was established [10],[35] +0.1I dB for both polarizations leading to measured common an MMI modulator or switch in LiNbOs was demonstrated, mode rejection ratios of 32 dB and better [4]. which achieved 0.5-dB loss and 13-20 dB extinction ratios by The polarization insensitive behavior of the MMI 3-dB cou- a nonuniform electro-optical modulation of the refractive index pler is crucial since polarization splitting is achieved after the profile in the multimode waveguide [47],[47],thus effectively 3-dB coupler by means of polarization selective photodetector combining the coupling and the phase shift functions in one pairs.This configuration has the advantage,that in addition single device. to being suitable for polarization-diversity reception,it is also Further applications concentrated more on making use of suitable for phase-diversity detection,which has been tested in MMI couplers as constituents of larger passive and/or active a 2.5 Gbit/s phase-diversity homodyne detection experiment structures.The following examples illustrate their compatibil-[50],[51]. ity to many types of materials and technologies,and highlight The wavelength insensitive behavior of the 3-dB coupler how their performances are used to an advantage in OEICs. in combination with the compact design of the photodetectors
SOLDANO AND PENNINGS: OPTICAL MULTI-MODE INTERFERENCE DEVICES BASED ON SELF-IMAGING 623 ~ Interference NxM Ref. n, A0 WO WM L Loss penaliy mechanism [Pml [Pml bl [Pml (dB1 2x2 [42] 3.28 1.51 3.0 7.5 250 0.5 4x4 [27] 3.24 1.52 3.0 21.6 945 (2.0) General 2x2 [19] 3.24 1.52 3.0 8.0 240 (0.8) Paired 2x2 [41] 3.29 1.53 3.0 18.0 530 0.5 2x2 [43] 3.30 1.51 2.2 16.0 425 0.5 Symmetric 1x4 [34] 3.47 1.06 2.6 40.0 1300 1x4 [40] 3.30 1.55 2.5 24.0 300 0.4 TABLE I1 DESIGN PARAMETERS OF MMI DEVICES FABRICATED IN 111-V SEMICONDUCTOR MATERIALS, AND EXPERIMENTALLY MEASURED TOLERANCE FIGURES FOR A GIVEN Loss PENALTY. PARENTHESIZED NUMBERS ARE RESULTS OF NUMERICAL SIMULATIONS BY MPA OR BPM Imbalance 6w~ 26X0 (0.17) (0.20) (100) [dBl [Pml [nml (0.20) 0.1 0.20 0.20 0.30 100 0.20 0.25 0.20 0.30 (60) (0.25) the definition of (6) Hence, it is apparent that the multimode waveguide length L must be made as short as possible in order to allow for relaxed tolerances to the other parameters. As an example, let us consider the 2 x 2 MMT coupler of Fig. 4 [19], comprising a multimode waveguide with W, N 8 pm, L = 240 pm and n, = 3.24, fed by access waveguides with WO 21 3 pm, and operated at 1.52-pm wavelength. From (39), SL N 15 pm; which substituted into (40) yields SW, N 0.25 bm, SA 21 95 nm, and Sn, 21 0.20. Thus, the multimode aAsP:Fe Waveguide aAsP:Fe Waveguide Local Oscill section width is by far the most critical parameter to control during fabrication. In a development stage, small variations in the width can be compensated for by varying lengths in steps of SL. In our example, five lengths L = 220, 235, 250, 265, and 280 pm are sufficient to obtain at least a pair Fig. 10. Schematic of polarization-diversity balanced coherent receiver front-end OEIC L41. A. Coherent Receiver Front-End possibly the reported application using an MMI Of devices performing summarizes 'lose to design 'I figures Of MM1 devices, for device in a complex photonic integrated circuit is the coherent receiver front-end [4], [49], [5O] shown in Fig. 10. This chip contains an MMI 3-dB coupler to combine the optical powers from the photosignal and the local oscillator laser. In addition, polarization-insensitive IF signal using diversity architectures. Several key features of MMI devices enhanced the overall performance of the chip. The ultracompact size of the MMI 3-dB coupler (298 pm) and its compatibility with deeply etched waveguides allowing for monomode ultracompact bends (R = 250 pm), led to a specified penalty losses and imbalances. The dependence On which may be different optimum imaging lengths for both polarizations. Polarization-independent operation is then possible by designing at an intermediate length, at the price of a small loss increase. Polarization-change induced penalty losses below 0.30 dB have been calculated and experimentally verified in 2 x 2 strip-loaded waveguide MMI couplers [41]. investigated through the term (nTWz) in (6), in two pairs of polarization-sensitive photodetectors generate a VII. APPLICATIONS In addition to their use as single routers or couplers, MMI devices have been applied to perform a number of more complex functions. Soon after the theory of the self-imaging principle in multimode waveguides was established [lo], [35], an MMI modulator or switch in LiNbOs was demonstrated, which achieved 0.5-dB loss and 13-20 dB extinction ratios by a nonuniform electro-optical modulation of the refractive index profile in the multimode waveguide [47], [47], thus effectively combining the coupling and the phase shift functions in one single device. Further applications concentrated more on making use of MMI couplers as constituents of larger passive and/or active structures. The following examples illustrate their compatibility to many types of materials and technologies, and highlight how their performances are used to an advantage in OEICs. total chip size of merely 1.3 mm. Balanced operation is important to fully use the available optical powers of the photosignal and the LO laser and to minimize common mode noise due to LO intensity fluctuations. Typical measured balance of both coupler outputs was within fO. 1 1 dB for both polarizations leading to measured common mode rejection ratios of 32 dB and better [4]. The polarization insensitive behavior of the MMI 3-dB coupler is crucial since polarization splitting is achieved after the 3-dB coupler by means of polarization selective photodetector pairs. This configuration has the advantage, that in addition to being suitable for polarization-diversity reception, it is also suitable for phase-diversity detection, which has been tested in a 2.5 Gbit/s phase-diversity homodyne detection experiment The wavelength insensitive behavior of the 3-dB coupler in combination with the compact design of the photodetectors [501, [511
® JOURNAL OF LIGHTWAVE TECHNOLOGY.VOL.13.NO.4.APRIL 1995 should result in a broad spectral operating range (70 nm) [191,[521 B.Mach-Zehnder Structures Mach-Zehnder interferometers have been extensively used IxN or in practical realizations of optical processing because of their NxN MMI splitter Phase shifters NxN MMI combiner natural physical separation between the splitting/recombining functions and the phase-shifting function. The extinction ratio in a Mach-Zehnder interferometer is directly limited by the imbalance of the input splitter and the output combiner.For example,a 0.2-dB power imbalance would limit the extinction ratio to -33 dB.In addition,an output phase deviation of the splitting/combining elements will Fig.11.Schematic layouts of a 1 x N and an N x N general- further worsen the extinction ratio in passive interferometers ized Mach-Zehnder interferometers,comprising MMI couplers as split. or(in the case of an active device)will have to be compensated ting/combining elements,and waveguide phase shifters. for by forcing a biasing phase-shift driving voltage. The good balancing and stable relative phases shown by influence on the performance of the ring laser,since the MMI couplers around their optimum operating point (see outcoupler forms an integral part of the ring resonator [58]. Section VI-C),together with their polarization insensitivity The most commonly used outcoupling element is the Y- make these devices ideal candidates for integration into Mach- junction,which offers ease of design,but can only couple one Zehnder structures. of the counter-propagating beams out of the ring.Directional A passive polarization splitter comprising a pair of 3- couplers have not proven to be a successful outcoupler,partly dB MMI couplers in a Mach-Zehnder structure provided TE due to their incompatibility with high-contrast waveguides (TM)extinction ratios better than -16 dB (-13 dB)over which are required to create low-loss small-radii bends.MMI a 60-nm wavelength range [43].Electro-optic Mach-Zehnder devices on the other hand provide symmetric outcoupling interferometer switches including 3-dB MMI couplers have relaxed fabrication tolerances,ease of design and compatibility been demonstrated in double-heterostructure (DH)[2]as well with high-contrast waveguides. as multi-quantum wells (MQW)[3],[53]III-V materials. The first ring lasers using MMI 3-dB outcouplers (L 233 featuring extinction ratios ranging from -10 dB to -19 um)were reported for Ao 1.6 um in GalnAsP/InP using dB.Mach-Zehnder interferometers with MMI splitters and deeply etched waveguides thereby enabling low-loss R recombiners have also been experimented in hollow dielectric 150 um bends [5],[6].A differential quantum efficiency of waveguides operated at 10.6-um wavelength [54]. next =3.9%was reported with almost kink-free LI curves at In all these designs,MMI couplers played a crucial role CW operation and at 20C [6].An additional MMI combiner in attaining large bandwidth and polarization independent has been used to combine both counter-propagating beams in operation. a single output waveguide,thereby increasing the efficiency The possibility of achieving 1 xN and N x N split- to next =5.2%[6].Stable single-mode operation has been ter/combiners with MMI devices allows the realization of very observed with a sidemode suppression of 35 dB.Occasional compact integrated multiway optical switches.Such a function mode-hopping and stable single mode operation have been is performed in a so-called multi-arm or generalized Mach- explained as being due to coupled cavity behavior caused by Zehnder interferometers [55](shown in Fig.11).where the reflections in the output path and in the MMI devices (see input signal is split by a 1 x N (or N x N)MMI splitter, Section 6.4 and [44]). fed into individually addressable waveguide phase shifters. MMI 3-dB couplers have also been incorporated in and recombined in an N x N MMI coupler.By controlling GaAs/AlGaAs ring lasers using low-contrast waveguides(R= N phase shifters,the input signal(s)can be made to switch 400 jm),with a reported differential quantum efficiency of to any one (or certain sets)of the N output waveguides, next =7%at Ao0.87 um and for CW operation [59].In though not independently [55],[56].Multiway switches have these experiments,the compatibility of MMI couplers with been demonstrated in generalized Mach-Zehnder structures low-contrast waveguides was successfully demonstrated. incorporating MMI splitters and combiners.The 1 x 10 Comparing the performance of ring lasers employing MMI (10.6-mm long)and 10 x 10 (13.1-mm long)switches in couplers to those using Y-junctions 61,60]or directional GaAs/AIGaAs [56]showed +9%switching uniformity,-10 couplers [60],the stability of the splitting ratio of the out- dB maximum crosstalk,and around 6-dB excess loss.A 1 coupler is found to be the key factor.Lasers are subject x 4 switch in InGaAsP/InP achieved-13 dB crosstalk and to varying operating conditions;changes in current affect polarization insensitivity [57]. the gain spectrum,change the temperature and cause carrier induced refractive index changes.If the splitting ratio of the outcoupler,in turn,depends on wavelength,refractive index or C.Ring Lasers excitation conditions,unstable lasing operation results,since MMI devices have also proven to be successful outcoupling laser performance is determined by the interplay of all these elements in ring lasers.The outcoupling element has a crucial parameters.It is therefore the extreme stability of the splitting
624 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO. 4, APRIL 1995 should result in a broad spectral operating range (~70 nm) [191, [521. B. Mach-Zehnder Structures Mach-Zehnder interferometers have been extensively used in practical realizations of optical processing because of their natural physical separation between the splitting/recombining functions and the phase-shifting function. The extinction ratio in a Mach-Zehnder interferometer is directly limited by the imbalance of the input splitter and the output combiner. For example, a 0.2-dB power imbalance would limit the extinction ratio to -33 dB. In addition, an 1xN or NxN MMI splitter Phase shifters NxN MMI combiner output phase deviation of the splittingkombining elements will further the extinction ratio in passive interferometers or (in the case of an active device) will have to be compensated Fig. 11. Schematic layouts of a 1 x S and an S x -V generalized Mach-Zehnder interferometers, comprising MMI couplers as splittingkombining elements, and waveguide phase shifters. for by forcing a biasing phase-shift driving voltage. The good balancing and stable relative phases shown by MMI couplers around their optimum operating point (see Section VI-C), together with their polarization insensitivity make these devices ideal candidates for integration into MachZehnder structures. A passive polarization splitter comprising a pair of 3- dB MMI couplers in a Mach-Zehnder structure provided TE (TM) extinction ratios better than -16 dB (-13 dB) over a 60-nm wavelength range [43]. Electro-optic Mach-Zehnder interferometer switches including 3-dB MMI couplers have been demonstrated in double-heterostructure (DH) [2] as well as multi-quantum wells (MQW) [3], [53] 111-V materials, featuring extinction ratios ranging from -10 dB to -19 dB. Mach-Zehnder interferometers with MMI splitters and recombiners have also been experimented in hollow dielectric waveguides operated at 10.6-pm wavelength [54]. In all these designs, MMI couplers played a crucial role in attaining large bandwidth and polarization independent operation. The possibility of achieving 1 xN and N x N splitterkombiners with MMI devices allows the realization of very compact integrated multiway optical switches. Such a function is performed in a so-called multi-arm or generalized MachZehnder interferometers [55] (shown in Fig. 11), where the input signal is split by a 1 x N (or N x N) MMI splitter, fed into individually addressable waveguide phase shifters, and recombined in an N x N MMI coupler. By controlling N phase shifters, the input signal(s) can be made to switch to any one (or certain sets) of the N output waveguides, though not independently [55], [56]. Multiway switches have been demonstrated in generalized Mach-Zehnder structures incorporating MMI splitters and combiners. The 1 x 10 (10.6-mm long) and 10 x 10 (13.1-mm long) switches in GaAsIAlGaAs [56] showed &9% switching uniformity, - 10 dB maximum crosstalk, and around 6-dB excess loss. A 1 x 4 switch in InGaAsPhnP achieved -13 dB crosstalk and polarization insensitivity [57]. C. Ring Lasers MMI devices have also proven to be successful outcoupling elements in ring lasers. The outcoupling element has a crucial influence on the performance of the ring laser, since the outcoupler forms an integral part of the ring resonator [58]. The most commonly used outcoupling element is the Yjunction, which offers ease of design, but can only couple one of the counter-propagating beams out of the ring. Directional couplers have not proven to be a successful outcoupler, partly due to their incompatibility with high-contrast waveguides which are required to create low-loss small-radii bends. MMI devices on the other hand provide symmetric outcoupling, relaxed fabrication tolerances, ease of design and compatibility with high-contrast waveguides. The first ring lasers using MMI 3-dB outcouplers (L = 233 pm) were reported for Xo z 1.6 pm in GaInAsP/InP using deeply etched waveguides thereby enabling low-loss R = 150 pm bends [5], [6]. A differential quantum efficiency of qext = 3.9% was reported with almost kink-free LI curves at CW operation and at 20°C [6]. An additional MMI combiner has been used to combine both counter-propagating beams in a single output waveguide, thereby increasing the efficiency to vext = 5.2% [6]. Stable single-mode operation has been observed with a sidemode suppression of 35 dB. Occasional mode-hopping and stable single mode operation have been explained as being due to coupled cavity behavior caused by reflections in the output path and in the MMI devices (see Section 6.4 and [44]). MMI 3-dB couplers have also been incorporated in GaAsIAlGaAs ring lasers using low-contrast waveguides (R = 400 pm), with a reported differential quantum efficiency of qext = 7% at Xo z 0.87 pm and for CW operation [59]. In these experiments, the compatibility of MMI couplers with low-contrast waveguides was successfully demonstrated. Comparing the performance of ring lasers employing MMI couplers to those using Y-junctions [6], [60] or directional couplers [60], the stability of the splitting ratio of the outcoupler is found to be the key factor. Lasers are subject to varying operating conditions; changes in current affect the gain spectrum, change the temperature and cause carrier induced refractive index changes. If the splitting ratio of the outcoupler, in turn, depends on wavelength, refractive index or excitation conditions, unstable lasing operation results, since laser performance is determined by the interplay of all these parameters. It is therefore the extreme stability of the splitting