Abstract:
A passband-flattened phasar including two free space regions coupled by a plurality of waveguides having predetermined differences between their lengths so as to act as an arrayed waveguide grating. The phasar is particularly useful in a wavelength-division multiplexed (WDM) optical communication system transmitting multiple wavelength systems arranged in a wavelength comb with a constant wavelength channel spacing. The input waveguide is coupled to the first free space region through a Mach-Zehnder interferometer (MZI) having two waveguide arms of differing lengths receiving approximately equal amounts of the input signal. The arms differ in lengths so as to produce a phase difference between them. In a WDM network, the waveguide arm produce a phase difference such that the free spectral range of the MZI equals the wavelength channel spacing, such that the wavelength response of the MZI is the same for each of the WDM wavelengths. The two outputs of the MZI are coupled into the input end of a multi-mode interferometer (MMI) with a lateral separation which provides a lateral spatial dispersion in the MMI equaling the lateral spatial dispersion of the conventional phasar. Thereby, a larger portion of the passband is equally passed through the phasar.

Description:
FIELD OF THE INVENTION 
     The invention relates optical communications networks. In particular, the invention relates to an arrayed waveguide demultiplexing/switching element. 
     BACKGROUND ART 
     Optical wavelength-division multiplexing (WDM) elements are becoming increasingly important in advanced optical communications networks incorporating optical fiber transmission paths. Silica optical fiber has a transmission bandwidth of over 300 terahertz per second. Such an extremely large bandwidth is, however, limited by the electronics on the transmitting and receiving ends. Such electronic transmitters and receivers, typically bases on silicon electronics, are limited commercially at the present time to 2 to 10 gigabits/s (Gbs). Further increases to 40 Gbs are contemplated, but further increases will be difficult to achieved. 
     For these reasons, WDM has been proposed in which multiple (N) electronic data channels, as illustrated in FIG. 1, enter a transmitter  10  and modulate separate optical emitters such as lasers  12  having N respective output carrier wavelengths λ 1 , λ 2 , . . . λ N . Conveniently, these wavelengths are arranged in a WDM wavelength comb having the neighboring wavelengths λ 1 , λ 2 , . . . λ N  separated by a substantially constant inter-channel spacing given by 
     
       
         Δλ S =λ i+1 −λ i .  (1) 
       
     
     An optical wavelength-division multiplexer  14  combines the optical signals of different wavelengths and outputs the combined signal on a single optical fiber  16 . An optical receiver  20  includes a wavelength-division demultiplexer  22  which divides its received signals according to their optical wavelength to N optical detectors  24  according to the same wavelength allocation λ 1 , λ 2 , . . . λ N . In view of usually experienced reciprocity in passive systems, a wavelength-division demultiplexer is usually substantially identical to a wavelength-division multiplexer with a reversal of their inputs and outputs. 
     Additionally, an optical add/drop multiplexer (ADM)  30  may be interposed on the optical path  16  between the transmitter and the receiver  20 . The optical add/drop circuit  30  removes from the optical channel on the fiber  16  one or more wavelength channels at wavelength λ AD  and inserts back onto the fiber  16  an optical data signal perhaps containing different information but at the same optical carrier wavelength λ AD . The ADM  30  is typically implemented with technology closely resembling the WDMs  14 ,  22 . All-optical networks have been proposed in which a distributed networks having many nodes each including a transmitter  10  and receiver  20  are linked by a functionally passive network which routes the signals between the nodes according to their wavelengths. The routing elements in such an all-optical network require switching elements similar to the ADM  30 . 
     In order to maximize the transmission capacity of the optical fiber  16 , the wavelength channels λ 1 , λ 2 , . . . λ N  should be placed as closely together as possible with a minimum channel spacing Δλ S . In advanced systems, this inter-channel spacing Δλ S  is 1 nm or less for a signal centered around 1300 or 1550 nm, the preferred bands for silica fiber. Such closely spaced WDM networks are referred to as dense WDM networks (DWDM). 
     The network design described above may be subject to a problem arising from the fact that the operation of the transmitter  10 , receiver  20  and intermediate node  30  are all referenced to the same set of WDM wavelengths λ 1 , λ 2 , . . . λ N . However each of the distributed elements must provide its own wavelength calibration. Due to environmental and aging effects, the wavelength calibration settings at one element are likely to differ from those at another element. In view of the close spacing of the optical channels, any miscalibration between network elements is likely to produce inter-channel interference. 
     For an optimized optical system, the fiber  16 , the WDMs  14 ,  22 , and the ADM  30  are typically designed to be single-mode at least at their ports for the optical wavelengths being used. Although each of the lasers  12  is likely emitting light across an exceedingly narrow bandwidth, the single-mode response of the frequency sensitive elements  14 ,  22 ,  30  usually has a wavelength (frequency) characteristic that approximates a gaussian distribution about the center wavelength λ 0  of the channel F(λ)=exp(−(λ−λ o   2 )/Δλ G   2 ). The value of the gaussian passband Δλ G  can be fairly freely chosen for present day fabrication techniques. However, the value of the passband is subject to countervailing restraints. For dense WDM systems, the inter-channel spacing Δλ S  is made as small as possible. The gaussian passband Δλ G  must be substantially smaller than the inter-channel spacing Δλ S  to avoid interference between channels. On the other hand, the frequency characteristics of the lasers  12  and other frequency-sensitive elements are subject to permanent or temporary variations. If the passband Δλ G  is made too small, the peak is very narrow and small variations in wavelength away from the peak&#39;s wavelength λ 0  causes operation to shift to the sides of the peak, thereby degrading the signal strength. That is, for a strong signal the passband Δλ G  should be made as large as possible to provide a broad top of the peak. 
     Amersfoort et al. have already recognized these problems, as disclosed in U.S. Pat. No. 5,629,992. These patents describe arrayed waveguide gratings, also called phasars, of the sort described by Hunsperger et al. in U.S. Pat. No. 4,773,063, and by Dragone in U.S. Pat. Nos. 5,412,744 and 5,488,680. In particular Amersfoort et al. describe a WDM phasar  40  exemplified in the schematic illustration of FIG. 2. A single-mode waveguide  42  is coupled to one end of a multi-mode waveguide  44  of length chosen to produce a doubled image of the radiation from the single-mode waveguide  42  at a port  46  on one side wall  47  of a first free space region  48 . The multi-mode waveguide  44  acts as a multi-mode interferometer (MMI). Multiple single-mode array waveguides  50  are coupled to ports on the other side of the first free space region  48  in the form of a star coupler. The array waveguides  50  are coupled on the other end to one side of a second free space region  52 . The array waveguides  50  have lengths with predetermined length differences between them to act as an arrayed waveguide grating (AWG), operating similarly to a planar diffraction grating. Single-mode output waveguides  54  are coupled to the other side of the second free space region  50  along an output wall  56 . The AWG causes the multi-wavelength signal from the input waveguide  42  to be wavelength demultiplexed on the respective output waveguides  54 . Because of the reciprocal nature of the device, the roles of input and output can be reversed so that the same structure can be used as a wavelength multiplexer and as a wavelength demultiplexer. The placement and number of waveguides contemplated by Amersfoort et al. are wider than the example of a single input presented below. 
     The gaussian wavelength distribution described above for single-mode elements is related to the gaussian spatial distribution of intensity experienced at the outputs of single-mode fibers. However, the multi-mode waveguide  44 , because it typically contains two closely spaced peaks at the port  46 , produces a spatial output pattern into the first free space region  48  that is not gaussian but is much flatter at its peak than a corresponding gaussian distribution of the same passband. The wavelength characteristic of the free space between the multi-mode waveguide  44  and the rest of the phasar  40  is therefore also flattened. As a result, with the use of the multi-mode interference filter  44 , it is possible to obtain a narrow wavelength response for the phasar but with smaller variations in response for small wavelength variations about the central values. However, the MMI solution of Amersfoort et al. suffers a power penalty of 2 to 3 dB as the single-mode power is spread out over a wider area. Chen discloses a somewhat similar approach in U.S. Pat. No. 5,889,906, wherein he uses multi-mode sections, not in order to flatten the bandpass of the individual channels as Amersfoort et al. did, but in order to obtain better uniformity for the different individual channels. 
     Dragone in U.S. Pat. No. 5,412,744 broadens the passband of a standard phasar by having a Y-coupler interposed between the single-mode input waveguide  42  and two single-mode waveguides separately coupled into the free space region  48 . The result is to spread the intensity for one mode across a larger area on the input wall of the free space region  48 . This approach suffers a similar power penalty of 2 to 3 dB. 
     Dragone in U.S. Pat. No. 5,488,680 suggests the advantage of cascading wavelength routing devices such as phasars. One configuration he develops includes a Mach-Zehnder interferometer (MZI), a 3 dB cross coupler between the two output waveguides of the MZI, and a standard phasar having a first free space region receiving the two waveguides from the MZI on its input wall. The geometry is such that one output waveguide focuses radiation of one wavelength at the output of the phasar and the other output waveguide radiation of another wavelength there with about 0.9 dB ripple for wavelengths in between. Thereby, the passband of the combination of the Mach-Zehnder and the phasar is flattened. 
     Thompson et al. disclose an alternative technique for passband flattening of a phasar in “An original low-loss and pass-band flattened SiO 2  on Si planar wavelength demultiplexer,” OFC &#39;98  Technical Digest, Optical Fiber Conference , Feb. 22-27, 1988, San Jose, Calif., p. 77. Two phasars are arranged in series. The first phasar has a free spectral range equal to the channel spacing. The free spectral range is the frequency range over which the frequency characteristics are repeated. In most one-stage phasar designs, all N channel spacings fit within one free spectral range. While the Thompson design theoretically offers a lossless broadening, in practice phasars are difficult to build to achieve optimum performance. 
     Accordingly, it is desired to provide a phasar design which offers passband flattening with low loss in a simple design. 
     SUMMARY OF THE INVENTION 
     The invention involves a phasar which is an optical coupler, such as a wavelength multiplexer or demultiplexer, which includes an arrayed waveguide grating between two free space regions, particularly applicable to a wavelength-division multiplexing (WDM) communication system transmitting a plurality of wavelength-differentiated signals separated by a wavelength channel spacing. A Mach-Zehnder interferometer (MZI) receives an optical input signal, divides it into two parts, and passes the parts through waveguides of differing lengths, thereby introducing a phase difference between the two parts dependent upon the wavelength. The MZI is designed with a spectral free range equal to the channel spacing so that the MZI presents the same optical characteristics for each of the WDM signals. The two parts of the MZI signal are input to a multi-mode interferometer (MMI) outputting to a first free space region. The MMI preferably has a length which is a half integral of the beat length of the two lowest order modes such that the lateral position of maximum intensity at the interface between the MMI and the free space region depends upon the phase difference of the signals from the MZI. The MZI inputs are laterally spaced on one side of the MMI so that the signal output from the MMI to the free space region has a lateral spatial optical dispersion matching the wall optical dispersion of the phasar. Thereby, the transmission characteristics of the phasar are flattened for each of the passbands of the phasar. Alternatively, such an arrangement can be disposed on the output side. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic diagram of a wavelength-division multiplexing (WDM) optical fiber communication system. 
     FIG. 2 is a schematic illustration of a prior art design for broadening the passband in a phasar by the use of a multi-mode interference filter. 
     FIG. 3 is a schematic illustration of an embodiment of a passband-broadened phasar of the present invention. 
     FIG. 4 is an exploded view of a portion of FIG.  3 . 
     FIGS. 5A through 5H are graphs showing the lateral displacement of an intensity peak at the output plane of the multi-mode interferometer as a function of the phase difference of the signals input to the multi-mode interferometer. 
     FIGS. 6 and 7 contain graphs illustrating the passband flattening achievable with the invention and compared to the prior art. 
     FIGS. 8 through 13 are schematic illustrations of alternative embodiments of the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     One embodiment of the invention is schematically illustrated in the optical circuit of FIG.  3 . The portion of the optical circuit close to the multi-mode interferometer  44  is shown in more detail in the exploded view of FIG.  4 . The optical circuit includes a Mach-Zehnder interferometer (MZI)  60  which produces a linear dispersion of a distributed wavelength signal that balances the dispersion of the phasar  40  around the wavelength of the center channel of the multi-wavelength signal λ 1 , λ 2 , . . . λ N . The Mach-Zehnder interferometer  60  receives the multi-wavelength signal on a single-mode fiber  62  or other optical waveguide. A Y-coupler  64  or other type of 50:50 optical power splitter divides the signal to two single-mode waveguide arms  66 ,  68  of the MZI  60 , preferably with equal intensities. The two arms  66 ,  68  have different physical lengths differing by ΔL so that a phase difference Δφ arises between signals of equal wavelength λ i  as they traverse the MZI  60 . However, the phase difference depends upon the value of the wavelength, as given by Equation (1)                Δ                 φ     =     2      π                 Δ                 L                                    n   eff          (     λ   i     )           λ   i                 (   2   )                                
     where n ff (λ c ) is the effective optical index of the two waveguides  66 ,  68  at the central wavelength λ c  of the WDM comb. It is assumed that the waveguides are of similar construction. However, an inspection of Equation (2) shows that the more relevant length is the optical length including the refractive index rather than the physical length. Techniques are well know for dynamically varying the refractive index in a waveguide by an electronic signal, for example, by a thermo-optic, electro-optic or piezo-electric effect, as described by Nishihara et al. in  Optical Integrated Circuits , (McGraw-Hill, 1985, ISBN 0-07-046092-2). The MZI may be designed to operate in a higher order mode in which there are extra multiples of 2π in the phase difference. The order is given by              m   =     Δ                 L                       n   eff          (     λ   C     )         λ   C            (     1   -         λ   C         n   eff          (     λ   C     )                                  n   eff          (     λ   C     )                         λ                       (   3   )                                
     The free spectral range Δλ FSR  of an optical device is the wavelength difference over which the spectral characteristics repeat, generally corresponding to the next higher multiple of the optical wavelength. At higher orders, the free spectral range becomes increasingly narrow. For the MZI  60  operating in a high-order mode, the free spectral range is given by                Δ                   λ   FSR       =         λ   C     m     .             (   4   )                                
     According to one aspect of the invention, the free spectral range Δλ FSR  is made approximately equal to the inter-channel spacing Δλ S  with the result that the MZI  60  is designed to operate in the high order mode given by 
     The equality need not be exact but Δλ FSR  should be accurate within 0.25/N of the channel spacing Δλ S , where N is the number of output channels For a channel spacing below 1 nm for infrared radiation of 1300 to 1550 nm, the order m is above 1000. The result of such a design is that the spectral response of the MZI  60  is the same for each of the WDM wavelengths λ 1 , λ 2 , . . . λ N  although there may be significant variations for small wavelength variations about the central values of the WDM wavelengths. The waveguide arms  64 ,  68  operating with the free spectral range equal to the channel spacing are preferably designed such that signals precisely calibrated to each of the N WDM wavelengths λ 1 , λ 2 , . . . λ N  traverse the MZI  60  with zero phase difference Δφ. When the number N of output-channels of the phasar is even, the design may be such that a 180° phase difference between the two arms  64 ,  68  is required 
     The MZI waveguides  64 ,  64  have ends that approach each other as they near the MMI  44 . However, their close approach does not extend over an appreciable distance, and the free space interaction length is much less the 3 dB coupling length promoted by Dragone. As a result, the wavelength components enter the MMI  44  with equal intensity but with a phase difference varying with wavelength. Any unintended coupling during close approach can be partly eliminated by a slight reduction of the length of the MMI section  44 . 
     As shown best in FIG. 4, the two waveguide arms  66 , 68  are separately coupled into the multi-mode interference interferometer (MMI)  44  with a gap between them on one longitudinal end of the MMI  44 . The gap is preferably measured by a separation G between the centers of the MZI waveguide  66 ,  68  as they enter the MMI  44 . The MZI waveguides  66 ,  68  have ends that approach each other as they near the MMI  44 . However, their close approach does not extend over an appreciable distance, and the interaction length is much less the 3 dB coupling length promoted by Dragone. Although the MZI  60  and MMI  44  are closely coupled without a clear interface between them, it can be considered that the signals at a given wavelength propagating on the two MZI waveguides  66 ,  68  enter the MMI  44  with equal intensity but with a phase difference varying with wavelength of the two signals. 
     The length L MMI  of the MMI  44  is chosen to be approximately half the beat length L π  between the two lowest order modes, that is,                  L   MMI     =       L   π     2       ,           (   6   )                                
     where the beat length is represented by                  L   π     =         λ   C       2        (       n   0     -     n   1       )         ≈       4        n   C        W       3        λ   C             ,           (   7   )                                
     where n 0  and n 1  are the effective optical indices for the fundamental and next higher-order modes supported in the MMI  44 . The 2-D engineering approximation for the beat length on the right side of Equation (7) depends upon W, which is the width of the MMI-section, and n C , which is the effective index of the core region of the waveguide. It is assumed that only two non-degenerate modes are supported, but the invention is not so limited. A wide MMI supports many modes and results in nearly perfect imaging using either paired or general interference, as is described by Soldano et al. in “Optical multi-mode interference devices based on self-imaging principles and applications”,  IEEE Journal Lightwave Technology,  vol . 13, no. 4, pp. 615-627, 1995. However perfect imaging is not particularly desired in the present invention. Instead, it is desired to achieve linear dispersion of a gaussian peak and low crosstalk, which is better realized with smaller MMI sections supporting only two lateral modes, and consequently introducing some excess loss of approximately 0.3 dB. 
     For the preferred technology of silica on silicon, with Ge-doped silica waveguides with core-to-cladding index-difference of 0.0075 and 7 μm×7 μm cores, the beat length L π  equals approximately 750 μm and thus L MMI  approximately equals 350 μm including some reduction approximately accounting for the waveguide cross coupling, where the MMI width is taken to be approximately 20 μm. It is possible that the MMI length be increased by multiples of the beat length so that acceptable lengths are approximately {fraction ( 1 / 2 ,  3 / 2 ,  5 / 2 )}, etc. of the beat length, but it must be remembered that the addition of a beat length to the length of the MMI changes the sign of the dispersion. 
     The optical signals from the two inputs to the MMI  44  can be considered to propagate independently. However, the two radiation signals interfere according to the phase difference between them. At half the beat length, the intensity distribution at the port  46  between the MMI  44  and the first free space region  48  has a spatial dispersion across the port  46  that varies almost linearly with the phase difference Δφ for a restricted range of phase differences, for example, between −90° and 90°. 
     A calculation has been performed based upon an MMI having a width W MMI  of 20 μm and a half-beat length of 350 μm compared to a single-mode waveguide width of 7 μm and where the separation G between the input waveguides is 10 μm. The optical intensity I measured in dB was calculated over a width of ±60 μm from the center of the MMI for phase differences Δφ over the range of −180° to +135°. The results are graphed in FIGS. 5A through 5H. Considering only FIGS. 5C through 5G, the position of the intensity peak varied over about 10 μm as the phase difference Δφ varied between −90° and 90°. Furthermore, the peak position varies approximately linearly with the phase difference. Because the phase difference varies with the wavelength, as is evident from Equation (2), the variation in peak position may be represented by a lateral MMI dispersion dλ/dy) MMI , the sign of which depends on whether the upper or lower branch  66 ,  68  of the MZI  60  is longer, resulting in a positive or negative sign respectively. 
     In very general terms for a simple embodiment of the invention, the MMI  44  supports a fundamental mode with one lateral peak in the center of the MMI output plane  46  and a first harmonic mode that has two lateral peaks at that position. The two MZI waveguides  66 ,  68  are approximately aligned with respective ones of the two hannonic peaks. At the half-beat length, a zero phase difference produces a strong fundamental peak with small harmonic peaks; at positive or negative phase differences, one or the other of the harmonic peaks dominate more, and the center of the peak has a lateral displacement with respect to the center. 
     For phase differences of magnitude greater than approximately 90°, the linear relation between lateral position and wavelength breaks down. These large phase differences correspond to wavelengths between the WDM comb. The precise value of the onset of the non-correspondence between position and wavelength is not crucial to the operation of the invention. 
     As shown in the exploded schematic view of FIG. 3, the phasar  40  is designed so that the first free space region  48  has a spatial dispersion dλ/dy) WALL  along the wall including the port  46  between the MMI  44  and the first free space region  48 . If hypothetical waveguides carrying signals of distinctive wavelengths were coupled into the first free space region  48  at locations corresponding to wavelengths calculated to include the spatial dispersion dλ/dy) WALL , all the different wavelengths would be focused at a single spot on the output wall  56  of the second free space region  52  of FIG.  3 . Another way of viewing the optical dispersion is to consider a multi-wavelength signal entering the first free space region at a fixed position on its wall  47  and determining the wavelength dispersion of that signal on the output wall  56  of the second free space region  52 . The lateral dispersion of the MMI  44  is designed to compensate for the wavelength dispersion on the output wall  56  so that a broadened passband is presented to a single point on the output wall  56 . Assuming that the phasar  40  is designed to have generally symmetric input and output geometries, the spatial dispersion is what enables a multi-wavelength signal input on the waveguide  42  to be wavelength demultiplexed into the output waveguides  54 , and similarly for multiplexing in the opposite direction, but this separation is between different wavelengths of the WDM comb. The compensation of the invention is useful when limited to a limited passband of the separate wavelengths. 
     According to the invention, the phasar and MMI are designed such that the phasar spatial dispersion and the MMI lateral dispersion are equal                  (           (            λ          y       )     )     MMI     =          λ          y         )     )     WALL     .           (   7   )                                
     Of course, it is important that the sign of the dispersion of the MMI and the phasar are the same at the wall  46 . The sign of the dispersion of the phasar dλ/dy) WALL  depends on whether the length increments of the branches  50  is positive or negative. An implementation where the dispersion is of correct sign is shown in FIG.  3 . It is further appreciated that the equality need not be exact and a 25% variation between the two would still produce an advantageous result. Because of the equality of the inter-channel spacing and the spectral free range, the MMI lateral dispersion can be represented by                        Δ                   λ   S         2      G       =          λ          y         )     WALL     .           (   8   )                                
     That is, half a channel spacing is spread across the separation between the MZI waveguides at their interface to the MMI. In the usual symmetric phasar design, the spatial dispersion is equal on the input and output walls. If the waveguide spacing on the output wall is d, then the input waveguide separation G should be approximately half this value. For a more conservative design utilizing less than half of the inter-channel phase spacing, G may be somewhat less than half of d, for example, 0.4, while still maintaining equality of the two spatial dispersions. 
     As mentioned above, each of the precise WDM wavelengths λ 1 , λ 2 , . . . λ N  should enter the MMI  44  with zero phase difference Δφ (or 180° for even values of N), and thus each will have a peak laterally positioned in the middle of port  56  between the free space region  48  and the MMI  44  of half beat length. All these precisely registered signals will be demultiplexed according to wavelength to the corresponding output waveguide  54  of FIG.  3 . Furthermore, because of the matching of dispersion, signals entering the MMI  44  from the MZI  60  with phase differences Δφ between ±90° will also be accurately conveyed across the phasar to be demultiplexed on the proper output waveguide  54 . This phase window of 180° corresponds to half the channel spacing Δλ S . The result is a spectral response that is approximately flat for half the channel spacing and thus much flatter than the typical gaussian response exhibited by phasars. 
     An example of the passband flattening achievable with the invention is presented in the graphs of FIG. 6, which are based upon calculations. When the MMI is designed with a large width of  30 tm and the waveguide separations G is 10 μm, the spectral response of the phasar is represented by the double-peaked curve  70  of FIG. 6. A far better spectral response is obtained when the MMI is designed with a width of 18.5 μm with the same gap G of 10 μm so that the MMI supports only two modes. The resulting spectral response is represented by the flattened curve  72 . This response should be compared to the response represented by a double-peak curve  74 , shown in FIG. 7, for the Dragone phasar using a 3 dB coupler between the MZI outputs rather than an MMI. Each of the two peaks corresponds to the generally gaussian response of the Dragone phasar. The peaks of Dragone are doubled because the MZI introduces the signals at two different spots along phasar wall. If the MZI were not used, the spectral response would correspond to one of the peaks. 
     The phasar represented in FIG. 3 is a linear, reciprocal device. Accordingly, it can be operated either as a demultiplexer as described or a multiplexer in which different wavelength signals are separately input on the respective corresponding waveguides  54  and a single wavelength multiplexed signal is output on the waveguide  62 . By a similar extension, respective MZIs and MMIs can be placed on each of the N output waveguides rather than a single pair on the one input waveguide. Also, it is well known that a demultiplexer such as that illustrated in FIG. 3 can be generalized to an optical splitter having more than one input waveguide  62 . In this case, each of the input waveguides has its own MZI and MMI, with the MMIs positioned at precisely chosen locations on the input wall of the first free space region. 
     The geometry of the interface between the MZI  60  and MMI  44  illustrated in FIG. 3 is intended to be only suggestive. It is preferred that adjacent the MMI  44 , the two MZI waveguides  66 ,  68  symmetrically approach the MMI  44  from different lateral sides with equally curving paths. 
     The designs and calculations presented above have assumed a simple geometry of a rectangular MMI joined directly to symmetrically placed MZI waveguides. Other designs are represented in FIG. 8 through 13. An FIG. 8, the MZI waveguides  66 ,  68  are asymmetrically placed on the input side of the MMI  44 . In FIG. 9, the MMI  44  is tapered. As a result, the radiation field input from the MZI waveguides  66 ,  68  is compressed to the output side. The MMI lateral dispersion then needs to be determined at the output side, not the input side. The outward tapering allows a relaxed design for the interface between the MZI and MMI. In FIG. 10, the MMI  44  is both tapered and angled. Different configurations of multi-mode sections with comparable perfonnances, for example, butterfly and angled MMI&#39;s, are described by Besse et al. in “New 1×2 multi-mode interference couplers with free selection of power splitting ratios,” ECOC 94 and by Besse in Swiss Patent Application No. 03 310/93-3, 4. November 1993. Similar multi-mode sections are also shown in FIGS. 2B to  2 H of U.S. Pat. No. 5,889,906 to Chen et al. where multi-mode sections are used for different purposes. 
     In FIG. 11, taper sections  80  couple the MZI waveguides  66 , 68  to the MMI  44 . The taper sections  80  taper from single mode on the MZI side to double mode on the MMI side. This allows a more efficient coupling of the single-mode field distribution from the MZI branches into the MMI. 
     In FIG. 12, the taper sections  80  couple directly into the first free space region  48  of FIG.  3 . Each tapered section itself acts as the required multi-mode section. 
     The embodiment of FIG. 13 is close to that of FIGS. 2 and 3 except that the waveguides  66 ,  68  have slightly tapered sections  82  that are adiabatically changed in width at the entrance of the MMI section  44 . 
     The invention thus provides a flattened passband in a phasar, thus enabling a multi-wavelength communication system to be more tolerant of wavelength drift and other forms of miscalibration between different nodes in a network. The flattening is obtained by a slight increase in the complexity of the waveguide structure of the phasar, without the need for additional materials or controls.