CROSS-REFERENCES TO RELATED APPLICATIONS 0001 This application is related to copending, commonly assigned U.S. patent application Ser. No. 09/442,061 (the '061 application), entitled Wavelength Router, filed Nov. 16, 1999 by Robert T. Weverka et al., which is herein incorporated by reference in its entirety, including the Appendix, for all purposes.

BACKGROUND OF THE INVENTION 0002 This application relates generally to fiber-optic communications and more specifically to techniques and devices for routing different spectral bands of an optical beam to different output ports (or conversely, routing different spectral bands at the output ports to the input port). 0003 The Internet and data communications are causing an explosion in the global demand for bandwidth. Fiber optic telecommunications systems are currently deploying a relatively new technology called dense wavelength division multiplexing (DWDM) to expand the capacity of new and existing optical fiber systems to help satisfy this demand. In DWDM, multiple wavelengths of light simultaneously transport information through a single optical fiber. Each wavelength operates as an individual channel carrying a stream of data. The carrying capacity of a fiber is multiplied by the number of DWDM channels used. Today DWDM systems employing up to 80 channels are available from multiple manufacturers, with more promised in the future. 0004 In all telecommunication networks, there is the need to connect individual channels (or circuits) to individual destination points, such as an end customer or to another network. Systems that perform these functions are called cross-connects. Additionally, there is the need to add or drop particular channels at an intermediate point. Systems that perform these functions are called add-drop multiplexers (ADMs). All of these networking functions are currently performed by electronicstypically an electronic SONET/SDH system. However SONET/SDH systems are designed to process only a single optical channel. Multi-wavelength systems would require multiple SONET/SDH systems operating in parallel to process the many optical channels. This makes it difficult and expensive to scale DWDM networks using SONET/SDH technology. 0005 The alternative is an all-optical network. Optical networks designed to operate at the wavelength level are commonly called wavelength routing networks or optical transport networks (OTN). In a wavelength routing network, the individual wavelengths in a DWDM fiber must be manageable. New types of photonic network elements operating at the wavelength level are required to perform the cross-connect, ADM and other network switching functions. Two of the primary functions are optical add-drop multiplexers (OADM) and wavelength-selective cross-connects (WSXC). 0006 In order to perform wavelength routing functions optically today, the light stream must first be de-multiplexed or filtered into its many individual wavelengths, each on an individual optical fiber. Then each individual wavelength must be directed toward its target fiber using a large array of optical switches commonly called as optical cross-connect (OXC). Finally, all of the wavelengths must be re-multiplexed before continuing on through the destination fiber. This compound process is complex, very expensive, decreases system reliability and complicates system management. The OXC in particular is a technical challenge. A typical 40-80 channel DWDM system will require thousands of switches to fully cross-connect all the wavelengths. Opto-mechanical switches, which offer acceptable optical specifications are too big, expensive and unreliable for widespread deployment. New integrated solid-state technologies based on new materials are being researched, but are still far from commercial application. 0007 Consequently, the industry is aggressively searching for an all-optical-wavelength routing solution which enables cost-effective and reliable implementation of high-wavelength-count systems.

BRIEF SUMMARY OF THE INVENTION 0008 The present invention provides a wavelength router that allows flexible and effective routing of spectral bands between an input port and a set of output ports (reversibly, also between the output ports and the input port). 0009 An embodiment of the invention includes a free-space optical train disposed between the input port and the output ports. The free-space optical train may include air-spaced elements or may be of generally monolithic construction. The optical train includes a transmissive dispersive element, such as a transmissive diffraction grating, disposed so that light is intercepted from the input port and encounters the transmissive dispersive element at least four times before reaching any of the output ports. Certain embodiments also include a routing mechanism having at least one dynamically configurable routing element, which cooperates with elements in the optical train to provide optical paths that couple desired subsets of the spectral bands to desired output ports. The routing elements are disposed to intercept the different spectral bands after they have been spatially separated by the transmissive dispersive element. 0010 In certain embodiments, the transmissive dispersive element is encountered by light in pairs, with a reflective surface being disposed to reflect light immediately back towards the transmissive dispersive element after it has propagated through the transmissive dispersive element. The reflective surface and the transmissive dispersive element may be oriented with respect to an optical axis of the wavelength router so that each encounter with the transmissive dispersive element is near the Littrow condition. The reflective surface may be flat, although in other embodiments it comprises optical power. In a specific embodiment, the transmissive dispersive element and the reflective surface are comprised by an integrated element. 0011 The invention includes dynamic switching embodiments and static embodiments. In dynamic embodiments, the routing mechanism includes one or more routing elements whose state may be dynamically changed in the field to effect switching. In static embodiments, the routing elements are configured at the time of manufacture or under circumstances where the configuration is intended to remain unchanged during prolonged periods of normal operation. 0012 In the most general case, any subset of the spectral bands, including the subset that consists of no spectral bands and including the subset that consists of the whole set of spectral bands, can be directed to any of the output ports. However, there is no requirement that the invention be able to provide every possible routing. Further, in general, there is no constraint on whether the number of spectral bands is greater or less than the number of output ports. 0013 In some embodiments, the routing mechanism includes one or more retroreflectors, each disposed to intercept a respective one of the spectral bands after twice encountering the transmissive dispersive element, and direct the light in the opposite direction with a controllable transverse offset. In other embodiments, the routing mechanism includes one or more tiltable micromirrors, each of which can redirect one of the spectral bands with a controllable angular offset. There are a number of ways to implement the retroreflectors. 0014 In some embodiments, the beam is collimated before encountering the transmissive dispersive element, so as to result in each spectral band leaving after twice encountering the dispersive element as a collimated beam traveling at an angle that varies with its wavelength. The dispersed beams are then refocused onto respective routing elements and directed back so as to encounter the same elements in the optical train and to encounter the transmissive dispersive element twice before exiting the output ports as determined by the disposition of the respective routing elements. Some embodiments of the invention use cylindrical lenses while others use spherical lenses.

BRIEF DESCRIPTION OF THE DRAWINGS 0015 A further understanding of the nature and advantages of the present invention may be realized by reference to the remaining portions of the specification and the drawings wherein like reference numerals are used throughout the several drawings to refer to similar components. In some instances, a sublabel is associated with a reference numeral and follows a hyphen to denote one of multiple similar components. When reference is made to a reference numeral without specification to an existing sublabel, it is intended to refer to all such multiple similar components. 0016 FIG. 1A provides a schematic illustration of the operation of a reflective diffraction grating; 0017 FIG. 1B provides a schematic illustration of the combined operation of a transmissive diffraction grating and reflective surface; 0018 FIGS. 2A, 2B, and 2C provide schematic top, side, and end views, respectively, of a wavelength router according to an embodiment of the invention that uses spherical focusing elements; 0019 FIG. 3 provides an example of a structure in which a transmissive diffraction grating and reflective surface form an integrated structure; 0020 FIG. 4 provides a schematic top view of a wavelength router according to another embodiment of the invention that uses spherical focusing elements; 0021 FIGS. 5A and 5B provide schematic top and side views, respectively, of a wavelength router according to another embodiment of the invention that uses cylindrical focusing elements; and 0022 FIGS. 6A and 6B provide schematic top and side views, respectively, of a wavelength router according to another embodiment of the invention in which an integrated element provides both dispersion and optical power.

DETAILED DESCRIPTION OF THE INVENTION 0023 1. Introduction 0024 The following description sets forth embodiments of an all-optical wavelength router according to the invention. Embodiments of the invention can be applied to network elements such as optical add-drop multiplexers (OADMs) and wavelength-selective cross-connects (WSXCs) to achieve the goals of optical networking systems. 0025 The general functionality of the wavelength router is to accept light having a plurality of (say N) spectral bands at an input port, and selectively direct subsets of the spectral bands to desired ones of a plurality of (say M) output ports. Most of the discussion will be with reference to dynamic (switching) embodiments where the routing mechanism includes one or more routing elements whose state can be dynamically changed in the field to effect switching. The invention also includes static embodiments in which the routing elements are configured at the time of manufacture or under circumstances where the configuration is intended to remain unchanged during prolonged periods of normal operation. 0026 The embodiments of the invention include a dispersive element, such as a diffraction grating or a prism, which operates to deflect incoming light by a wavelength-dependent amount. Different portions of the deflected light are intercepted by different routing elements. Although the incoming light could have a continuous spectrum, adjacent segments of which could be considered different spectral bands, it is generally contemplated that the spectrum of the incoming light will have a plurality of spaced bands. 0027 The terms input port and output port are intended to have broad meanings. At the broadest, a port is defined by a point where light enters or leaves the system. For example, the input (or output) port could be the location of a light source (or detector) or the location of the downstream end of an input fiber (or the upstream end of an output fiber). In specific embodiments, the structure at the port location could include a fiber connector to receive the fiber, or could include the end of a fiber pigtail, the other end of which is connected to outside components. Most of the embodiments contemplate that light will diverge as it enters the wavelength router after passing through the input port, and will be converging within the wavelength router as it approaches the output port. However, this is not necessary. 0028 The International Telecommunications Union (ITU) has defined a standard wavelength grid having a frequency band centered at 193,100 GHz, and another band at every 100 GHz interval around 193,100 GHz. This corresponds to a wavelength spacing of approximately 0.8 nm around a center wavelength of approximately 1550 nm, it being understood that the grid is uniform in frequency and only approximately uniform in wavelength. Embodiments of the invention are preferably designed for the ITU grid, but finer frequency intervals of 25 GHz and 50 GHz (corresponding to wavelength spacings of approximately 0.2 nm and 0.4 nm) are also of interest. 0029 2. Diffraction of Optical Signals 0030 The size of a wavelength router that meets the ITU standards is constrained physically by two principal considerationsthe rate at which a beam may be dispersed when propagated longitudinally within the wavelength router and the transverse separation that may be achieved with elements disposed to intercept a portion of the beam. The size of the wavelength router may generally be decreased either by increasing the rate at which the beam disperses during longitudinal propagation or by decreasing the transverse separation of the intercepting elements. Embodiments of the invention permit such a decrease in size by providing an increased dispersion rate for the beam. 0031 The dispersive element acts to demultiplex an optical signal that contains a plurality of signals at different wavelengths. The operation of a dispersive element is illustrated in FIG. 1A with the example of a reflective diffraction grating 104. When illuminated at an angle from its normal, the reflective diffraction grating 104 directs light with wavelength towards angle also with respect to the normal, in accordance with the grating equation,

md(sinsin),

0032 where m is an integral order of interference and d is the grating period. FIG. 1A shows schematically the result when a multiplexed signal comprising wavelengths 1, and 2 is incident on the reflective diffraction grating 104 at angle . Signals corresponding to the independent wavelengths are reflected respectively at different angles 1 and 2 from the grating 104. The dispersion between the two reflected signals is defined by the angular separation 21 between them. 0033 The geometry of the reflective diffraction grating 104 imposes a physical limitation on the dispersion. According to the grating equation, the diffraction angle is approximately inversely related to the grating period d so that, in general, the dispersion increases with the line density of the grating. The line density, however, may not be increased so as to be arbitrarily large and still maintain certain desirable functional qualities of the diffraction. The upper limit on line density may be understood by considering the diffraction equation near the Littrow condition, in which incident and diffracted rays are autocollimated so that . Under these circumstances, the diffraction equation takes the simple form 1

\sin = \frac{m}{2 d} .

0034 Since the sine function is a bounded function, the line density is constrained in first order m1 so that 2

\frac{1}{d} \frac{2}{},

0035 providing a maximum line density at 1550 nm in of about 1290 lines/mm. 0036 Embodiments of the invention thus use a combination of a transmissive dispersive element and a reflective surface to avoid the physical constraint on dispersion provided by a reflective dispersive element. This is exemplified in FIG. 1B, in which a transmissive diffraction grating 108 is disposed at an angle with respect to a flat reflective surface 112. A multiplexed signal comprising wavelengths 1 and 2 is transmissively diffracted with a dispersion that separates the signals by angle , provided the grating 108 has the same grating period as the reflective grating 104 in FIG. 1A and the multiplexed signal is incident at the same angle. With the arrangement shown in FIG. 1B, however, the dispersed signals are reflected from the reflective surface 112 and diffracted again through the transmissive diffraction grating 108, causing an increase in dispersion. After passing through the transmissive diffraction grating 108 twice, the 1 and X2 signals are dispersed by separation angle . The relationship between and depends, in general, on the properties of the transmissive diffraction grating 108 and the orientation of the reflective surface 112, but generally > so that as the signals propagate within a wavelength router their dispersion is increased relative to that provided by the arrangement of FIG. 1A. For the specific orientations discussed in more detail below, 2. It is noted that reflective surface 112, while shown as a flat surface, may alternatively be curved. 0037 3. Embodiments Using Spherical Focusing Elements 0038 FIGS. 2A, 2B, and 2C are schematic top, side, and end views, respectively, of a wavelength router 200 according to an embodiment of the invention. The general functionality of the wavelength router 200 is to accept light having a plurality of (say N) spectral bands at an input port 204, and selectively to direct subsets of the spectral bands to desired ones of a plurality of (say M) output ports 240. The output ports 240 are shown in the end view of FIG. 2C as disposed along a line 236 that extends generally perpendicular to the top view of FIG. 2A. The input port 204 and the output ports 240 are shown as communicating with respective input and output optical fibers, but it should be understood that the input port 204 could also receive light directly from a light source, and the output ports 240 could be coupled directly to optical detectors. The drawings are not to scale, and in some instances the diffraction by certain optical elements is exaggerated for illustrative purposes; generally, beams will propagate approximately parallel to the optical axis of the wavelength router 200. 0039 Light entering the wavelength router 200 from the input port 204 forms a diverging beam 228, which includes the different spectral bands. The beam 228 encounters a lens 208, which collimates the light and directs it to a transmissive diffraction grating 212. The transmissive diffraction grating 212 diffracts the light so that it is reflected from a reflective surface 216 back through the grating 212, where it is further dispersed as described above. 0040 In one embodiment, the grating 212 and the reflective surface 216 are oriented with respect to each other at an angle that is approximately 45 and the system is configured for near-Littrow behavior. Under the Littrow condition in first order with 45, the line density of the grating is given by 3

\frac{1}{d} = \frac{\sqrt{2}}{},

0041 so that at 1550 nm, the line density of the grating 212 is of the order of 900 lines/mm. In this configuration, then, when the beam 228 is incident near the Littrow angle 45, it is diffracted substantially normal to the reflective surface 216 so that it is also incident near the Littrow angle 45 when it encounters the grating 212 for the second time. After the two encounters with the grating, the effective dispersion achieved by this arrangement is approximately 2.4 radians/m. This dispersion is approximately twice as large as the corresponding dispersion provided by a reflective grating having a line density 1/d of 900 lines/mm at 1550 nm of 1.25 radians/m. 0042 After dispersion by the combination of the transmissive diffraction grating 212 and reflective surface 216, collimated beams at different wavelengths are directed at different angles back towards the lens 208. Two such beams are shown explicitly and denoted 232 and 232, the latter shown with dashed lines. Since these collimated beams encounter the lens 208 at different angles, they are focused at different points along a line 236 in a transverse focal plane. Line 236 extends in the plane of the top view of FIG. 2A. 0043 The focused beams encounter respective ones of a plurality of retroreflectors 220 located near the focal plane. Each retroreflector 220 sends its intercepted beam along a reverse path that may be displaced in a direction perpendicular to line 224. More specifically, the beams are displaced along respective lines 244 that extend generally parallel to line 236 in the plane of the side view of FIG. 2B and the end view of FIG. 2C. Any suitable retroreflector may be used, some examples of which are described in the '061 application, which has been incorporated by reference. In some embodiments, the displacement of each beam is effected by moving the position of the retroreflector 220 along its respective line 244. In other embodiments, the beam displacement is effected by a reconfiguration of the retroreflector 220. It is noted that the retroreflectors 220 are shown below the output ports 240 in the plane of FIG. 2C, but this is not necessary; other relative positions may occur for different orientations of the grating 212 or other elements. 0044 The beams returning from the retroreflectors 220 are collimated by the lens 208 and directed once more to the transmissive diffraction grating 212. The beams are diffracted by the grating 212, reflected by the reflective surface 216, and diffracted again by the grating 212, in a fashion similar to that described above. These third and fourth encounters with the grating 212 remove the angular separation between the different beams, and direct the collimated beams back to the lens 208, which focuses the beams. As a result of the possible displacement of each beam by its respective retroreflector 220, the beams will be focused at possibly different points along line 236. Thus, depending on the positions of the retroreflectors 220, each beam is directed to one or another of the output ports 240. 0045 In this embodiment, the light traverses the region between the ports and the grating four times, twice in each direction, and encounters the transmissive grating 212 four times. This is to be compared with a similar arrangement in which a reflective grating is substituted for the transmissive grating 212/reflective surface 216 combination, in which the reflective grating would be encountered only twice for a similar fourfold traversal of the arrangement. As a result of the increased dispersion from encountering the transmissive grating 212 four times, various improvements in the design are possible, including shortening the overall length of the wavelength router element 200, increasing the center-center distance required for adjacent channels, and decreasing the clear apertures needed for the lens 208 and the grating 212. Table I provides a comparison of three embodiments, one using a reflective grating and two using a combined transmissive grating and reflective surface in accordance with embodiments of the invention. 1TABLE ITransmissiveTransmissiveGrating Grating ReflectiveReflectiveReflectiveGratingSurfaceSurfaceLine density900 lines/mm900 lines/mm900 lines/mmLens focal length100 mm50 mm100 mmWavelength router200 mm100 mm200 mmLengthCenter-center50 m50 m100 mDistance ofAdjacent ChannelsLens and Grating32 mm18 mm34 mmClear Apertures

0046 In each case, the center-center distance for adjacent channels has been provided for channel separations of about 50 GHz (corresponding to wavelength spacings of about 0.4 nm). The first column shows that with a reflective grating, the overall length of the wavelength router is relatively large and the channel spacing is relatively small. The second column shows an embodiment with a transmissive gratingreflective surface combination in which, for the same channel spacing as the reflective-grating embodiment, the overall length of the wavelength router is decreased by about a factor of two. This embodiment also permits the use of a lens having a smaller clear aperture. The third column shows an embodiment with a transmissive grating reflective surface combination in which, instead of decreasing the overall length of the wavelength router permits increasing the channel spacing by about a factor of two. 0047 The embodiment shown in FIGS. 2A-2C is an airspace implementation of a more generic class of what are referred to as free-space embodiments. In some other free-space embodiments, the various beams are all within a body of glass. The term free-space refers to the fact that the light within the body is not confined in the dimensions transverse to propagation, but rather can be regarded as diffracting in those transverse dimensions. Since the third and fourth encounters with the dispersive element effectively undo the dispersion induced by the first and second encounters, each spectral band exits the wavelength router with substantially no dispersion. 0048 In other embodiments, various alternatives and/or equivalents to specific elements described in connection with FIGS. 2A-2C may be substituted. For example, the transmissive diffraction grating 212 may be substituted with an alternative transmissive dispersive element, such as a prism. FIG. 3 illustrates the structure of an integrated element 300 that may be substituted for the combination of the transmissive diffraction grating 212 and reflective surface 216. The integrated element 300 retains a similar structure, but uses a prism 308 formed of a material such as glass, to combine a transmissive diffractive element 304 with a solid reflector 312. The integrated element 300 functions in a similar fashion when used in the wavelength router 200 shown in FIGS. 2A-2C, so that the transmissive diffractive element 304 is still encountered four times when a signal is routed. 0049 The integrated element is also suitable for use in other embodiments, such as the solid-glass wavelength router 400 shown schematically in a top view in FIG. 4. This embodiment uses a concave reflector 404 in the place of the lens 208 of FIGS. 2A-2C, and can be considered a folded version of the embodiment of FIGS. 2A-2C. Light entering the wavelength router 400 from the input port 204 forms a diverging beam 228, which includes the different spectral bands. The beam 228 encounters the concave reflector 404, which collimates the light and directs it to the integrated element 410 comprised as part of the wavelength router 400. The transmissive grating 408 formed as part of the integrated element 410 is encountered twice by the light, before and after it reflects from the reflective surface 412. After encountering the transmissive grating 408 twice, the light is dispersed so that collimated beams at different wavelengths are directed back at different angles towards the concave reflector 404. Two such beams are shown explicitly, one in solid lines and one in dashed lines. Since these collimated beams encounter the concave reflector 404 at different angles, they are focused at different points in a transverse focal plane. 0050 The focused beams encounter retroreflectors 220 located near the focal plane. The operation in the reverse direction is similar to that described with respect to FIGS. 2A-2C. The beams follow reverse paths displaced in a direction orthogonal to the plane of FIG. 4, and are therefore not visible in the figure since they underlie the forward paths. On the return paths, the beams encounter, in order, the concave reflector 404, the transmissive grating 408, the reflective surface 412, the transmissive grating 408, and the concave reflector 404. The two encounters with the transmissive grating 408 remove the dispersion in the beams and the final encounter with the concave reflector 404 focuses the beams to the desired output ports 240 (also not shown in FIG. 4 since they underlie the input port 204). 0051 4. Embodiments Using Cylindrical Focusing Elements 0052 FIGS. 5A and 5B are schematic top and side views, respectively, of a wavelength router 500 according to an embodiment of the invention. This embodiment uses cylindrical lenses rather than spherical lenses, uses tiltable mirrors rather than retroreflectors, and uses an integrated element 524 that includes a transmissive diffraction grating 516 and a reflective surface 520. The general functionality of wavelength router 500 is the same as the wavelength router 200 shown in and described with respect to FIGS. 2A-2C, namely to accept light having a plurality of spectral bands at the input port 204, and selectively to direct subsets of the spectral bands to desired ones of the plurality of output ports 240. 0053 A first cylindrical lens 508 has refractive power only in the plane of the top view (FIG. 5A), and a second cylindrical lens 512 has refractive power only in the plane of the side view (FIG. 5B). As such, the first lens 508 is drawn as a rectangle in the plane of FIG. 5B and the second lens 512 is drawn as a rectangle in the plane of FIG. 5A. Light entering the wavelength router 500 from the input port 204 forms a diverging beam 228, which includes the different spectral bands. The beam 228 encounters the first cylindrical lens 508, which collimates the light in one transverse dimension, but not the other, so that the beam has a transverse cross section that changes from circular to elliptical, i.e. the beam 228 continues to expand in the plane of FIG. 5B but not in the plane of FIG. 5A. 0054 The beam 228 then encounters, in order, the second cylindrical lens 512, the integrated element 524, and the second cylindrical lens 512 again. The two encounters with the second cylindrical lens 512 collimate the light that is diverging in the plane of FIG. 5B so that the beam propagates with a constant elliptical cross section. The integrated element 524 uses the principles discussed above, using the combination of transmissive diffraction grating 516 and reflective surface 520 comprised by the integrated element 524, to disperse the light in the plane of FIG. 5A. Accordingly, beams at different wavelengths are transmitted at different angles in the plane of FIG. 5A, but not in the plane of FIG. 5B. 0055 The collimated beams encounter the first cylindrical lens 508 and are focused to respective lines. The focused beams encounter respective ones of a plurality of tiltable micromirrors 504 located near the focal plane. Various examples of micromirror configurations that may be used, among others, are described in the following copending, commonly assigned applications, each of which is herein incorporated by reference in its entirety for all purposes: U.S. patent application Ser. No. 09/898,988, entitled SYSTEMS AND METHODS FOR OVERCOMING STICTION USING A LEVER, filed Jul. 3, 2001 by Bevan Staple et al.; U.S. patent application Ser. No. 09/899,000, entitled FREE-SPACE OPTICAL WAVELENGTH ROUTER BASED ON STEPWISE CONTROLLED TILTING MIRRORS, filed Jul. 3, 2001 by Victor Buzzetta et al.; U.S. patent application Ser. No. 09/899,001, entitled TWO-DIMENSIONAL FREE-SPACE OPTICAL WAVELENGTH ROUTER BASED ON STEPWISE CONTROLLED TILTING MIRRORS, filed Jul. 3, 2001 by Victor Buzzetta; U.S. patent application Ser. No. 09/899,002, entitled MEMS-BASED, NONCONTACTING, FREE-SPACE OPTICAL SWITCH, filed Jul. 3, 2001 by Bevan Staple and Richard Roth; U.S. patent application Ser. No. 09/899,004, entitled BISTABLE MICROMIRROR WITH CONTACTLESS STOPS, filed Jul. 3, 2001 by Lilac Muller; U.S. patent application Ser. No. 09/899,014, entitled METHODS AND APPARATUS FOR PROVIDING A MULTI-STOP MICROMIRROR, filed Jul. 3, 2001 by David Paul Anderson; and U.S. patent application Ser. No. 09/941,998, entitled MULTIMIRROR STACK FOR VERTICAL INTEGRATION OF MEMS DEVICES IN TWO-POSITION RETROREFLECTORS, filed Aug. 28, 2001 by Frederick Kent Copeland (Attorney Docket No. 019930-004400US). 0056 After encountering the tiltable micromirrors 504, the beams are directed back to the first cylindrical lens 508, diverging only in the plane of FIG. 5A. Depending on the tilt angles of the respective micromirrors 504, the beams are angularly displaced in the plane of FIG. 5B. The return beams undergo different transformations in the planes of FIGS. 5A and 5B. 0057 In the plane of 5A, the beams are collimated by the first cylindrical lens 508, and directed again to the integrated element 524. In this plane, encounters with the second cylindrical lens 512 do not change the collimated character of the beams. The integrated element 524 removes the angular separation between the different beams as a result of two encounters with the transmissive diffraction grating 516 and a reflection from the reflective surface 520. The collimated beams are thus directed back to the first cylindrical lens 508, which focuses the beams in the plane of FIG. 5A at the output ports 240. In FIG. 5A, the return beams are not shown separately, but rather have projections in the plane that coincide with the projection of the forward beam. 0058 In the plane of FIG. 5B, the return beams are focused by the two encounters with the second cylindrical lens 512 onto the output ports 240. Because of possible angular displacement of each beam by its respective micromirror 504, the beams are directed to one or another of the output ports 240. In FIG. 5B, neither the first cylindrical lens 508 nor the integrated element 524 affects whether the beams are diverging, collimated, or converging. The second cylindrical lens 512 provides a Fourier relation in the plane of the side view that maps tilted wave fronts at the micromirrors 504 to displaced positions at the output ports 240. 0059 5. Embodiments with Combined Focusing and Dispersion 0060 In alternative embodiments, the integrated element combines dispersion and optical power. For example, FIGS. 6A and 6B illustrate a wavelength router 600 according to an embodiment of the invention in which the integrated element 604 comprises a curved reflective surface 612 instead of a flat reflective surface. Within the integrated element, dispersion is provided by a transmissive diffraction grating 608 while optical power is provided by the curvature of the reflective surface 612. The wavelength router 600 otherwise functions in a manner similar to that described with respect to FIGS. 2A-2C, with the transmissive dispersive element being encounter four times in a given pass through the router 600. While the figures illustrate an embodiment with an integrated element 604, it will be understood that the integrated element 604 may be substituted by a discrete transmissive diffractive element and curved reflective surface. 0061 6. Efficiency Considerations 0062 The efficiency and polarization-dependent loss (PDL) of the transmissive dispersive elements used in various embodiments of the wavelength router affect optical signals with each encounter of the grating. The PDL accumulates additively so that four encounters results in a total PDL due to the dispersive element equal to 4PDL(0). The efficiency accumulates multiplicatively so that four encounters result in efficiencies of P4 and S4 respectively in the orthogonal polarization states P and S. Transmission gratings having an efficiency exceeding 95% in both P and S polarizations at wavelengths of 1530-1565 nm have been reported in Dense wavelength division multiplexing (DWDM) and the Dickson grating by R. D. Rallison, January 2001, the entire disclosure of which is herein incorporated by reference for all purposes. Accordingly, use of a transmission grating having such an efficiency limits the grating losses of the wavelength router to less than 20% and a PDL less than 0.5 dB. 0063 Having described several embodiments, it will be recognized by those of skill in the art that various modifications, alternative constructions, and equivalents may be used without departing from the spirit of the invention. Accordingly, the above description should not be taken as limiting the scope of the invention, which is defined in the following claims.