Abstract:
In communications where synchronization of optical signals containing data is required, a multi-channel optical arrayed time buffer may be used. The time buffer includes multiple delay paths comprising delay elements, some of which can be shared to dispense different delays. In an embodiment, an arrayed waveguide grating (AWG) is illustratively used to route an optical signal to a first delay path, which is returnable to the AWG through the first delay path to be rerouted to a second delay path. The total delay affordable to the optical signal is a function of at least a first delay afforded by a delay element in the first delay path, and a second delay afforded by a delay element in the second delay path. In addition, without returning to the AWG, another optical signal may be routed through the second delay path alone to be afforded the second delay only.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is related to commonly assigned, copending U.S. patent application Ser. No. 11/941,191 (“the &#39;191 application”), filed on Nov. 16, 2007, and published on May 21, 2009 as Pub. No. 2009/0129779; and also related to commonly assigned, copending U.S. patent application Ser. No. 11/941,201 (“the &#39;201 application”), filed on Nov. 16, 2007, and published on May 21, 2009 as Pub. No. 2009/0129780, both of which are incorporated herein by reference in their entirety. 
     
    
       [0002]    The present invention was made with the U.S. Government support under Contract No. FA 8750-04-C-0013 awarded by the Microsystems Technology Office (MTO) of Defense Advanced Research Projects Agency (DARPA). The U.S. Government has certain rights in the invention. 
     
    
     FIELD OF THE INVENTION 
       [0003]    The invention relates to a technique for optical communications and, more particularly, to a technique for time-buffering optical signals. 
       BACKGROUND OF THE INVENTION 
       [0004]    This section introduces aspects that may help facilitate a better understanding of the invention. Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is prior art or what is not prior art. 
         [0005]    An optical packet router is an important component of an optical communication network. An efficient optical packet router is based on a synchronous optical switch fabric, which enables substantial enhancement of bandwidth and reduction in network latency. Proper operation of a synchronous optical switch fabric is achieved when all incoming data packets are appropriately synchronized to a reference clock. However, if the synchronization is not sufficiently accurate and/or stable, the resulting skew and/or jitter in incoming data packets may cause transmission errors or other deleterious effects on the network traffic. For example, one deleterious effect of poor alignment is that it might force the use of a relatively large guard time between packets, bits, cells, and/or envelopes, which appreciably reduces the throughput of the switch or router. 
         [0006]    The aforementioned &#39;191 and &#39;201 applications disclose channel synchronizers for synchronizing data packets from different channels heading to an optical router. Different channel synchronizers are described in such applications, some of which incorporate a multi-channel optical arrayed time buffer, having an array of delay lines (e.g., optical fibers) of different lengths coupled between two arrayed waveguide gratings (AWGs). 
       BRIEF SUMMARY 
       [0007]    While the aforementioned multi-channel optical arrayed time buffer may be desirable in that it can be implemented as an integrated waveguide circuit, an aspect of this time buffer has been recognized to be disadvantageous in certain applications. In particular, in an application where longer delays are required of the time buffer, the optical lengths of the individual delay lines in the time buffer may need to increase dramatically to accommodate such delays. Accordingly, the time buffer may become so bulky that it can no longer be efficiently integrated into a compact circuit. 
         [0008]    The invention overcomes the above-identified size limitation by sharing some of the delay lines in a time buffer to dispense different delays. In accordance with an embodiment of the invention, a time buffer includes multiple delay paths which comprise delay elements for imparting delays to optical signals traversing therethrough, respectively. A passive optical device (e.g., an AWG) is used in the time buffer for routing an optical signal input thereto to a first delay path. The optical signal is returnable to the passive optical device through the first delay path to be rerouted by the passive optical device to a second delay path. As a result, the total delay affordable to the optical signal is a function of at least a first delay afforded by a delay element in the first delay path, and a second delay afforded by a delay element in the second delay path. In addition, without returning to the AWG, another optical signal may be routed through the second delay path alone to be afforded the second delay only. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]      FIG. 1  shows a portion of an optical communication system according to an illustrative embodiment of the invention; 
           [0010]      FIG. 2  is a block diagram of a channel synchronizer which may be used in the system of  FIG. 1 ; 
           [0011]      FIG. 3  is a block diagram of a multi-channel optical arrayed time buffer which may be used in the channel synchronizer of  FIG. 2  according to an illustrative embodiment of the invention; 
           [0012]      FIGS. 4A-C  are tables showing input/output relations between respective pairs of arrayed waveguide gratings (AWGs) used in the time buffer of  FIG. 3 ; 
           [0013]      FIG. 4D  illustrates a generic AWG which can be used in the time buffer of  FIG. 3 ; 
           [0014]      FIG. 4E  is a table depicting input/output port mapping of the AWG of  FIG. 4D ; 
           [0015]      FIG. 5  is a table for use with the time buffer of  FIG. 3 , which shows, among other things, the wavelength requirements of input optical signals to the time buffer for them to attain various delays; 
           [0016]      FIG. 6  is a block diagram of a multi-channel optical arrayed time buffer which may be used in the channel synchronizer of  FIG. 2  according to another illustrative embodiment of the invention; 
           [0017]      FIGS. 7A-C  are tables showing input/output relations between respective pairs of arrayed waveguide gratings (AWGs) used in the time buffer of  FIG. 6 ; 
           [0018]      FIG. 8  is a table for use with the time buffer of  FIG. 6 , which shows, among other things, the wavelength requirements of input optical signals to the time buffer for them to attain various delays; 
           [0019]      FIG. 9  is a block diagram of a multiplex synchronizer that may be used in the system of  FIG. 1 ; 
           [0020]      FIG. 10  is a block diagram of an optical tunable delay circuit that may be used in the multiplex synchronizer of  FIG. 9  according to an illustrative embodiment of the invention; 
           [0021]      FIGS. 11A  and B show top views of an optical tunable delay circuit that may be used in the multiplex synchronizer of  FIG. 9  according to another illustrative embodiment of the invention; and 
           [0022]      FIG. 12  is a graph illustrating a group delay generated by an optical all-pass filter used in the optical tunable delay circuit of  FIGS. 11A  and B. 
       
    
    
     DETAILED DESCRIPTION 
       [0023]      FIG. 1  shows a portion of an optical communication system  100  according to an embodiment of the invention. System  100  receives a plurality of wavelength division multiplexing (WDM) signals  102   1 - 102   M  from external network components (not shown). Each of signals  102   1 - 102   M  has N carrier wavelengths (λ 1 -λ N ), each modulated to carry data packets. 
         [0024]    An optical communication system similar to system  100  is usually designed so that each of its optical elements has appropriate spectral characteristics that enable proper handling of the WDM signals that populate the system. The number of and spectral separation between the WDM components of a WDM signal are usually set based on a convention or standard. For example, the most common frequency (wavelength) grid is that used for dense WDM (WDM) and defined by a standard promulgated by the International Telecommunication Union (see ITU-T G.694.1). This grid is defined relative to 193.1 THz and extends from about 191.7 THz to about 196.1 THz, with 100-GHz spacing. While defined in frequency, the grid is also often expressed in terms of wavelength, in which case its wavelength range is from about 1528 nm to about 1564 nm, with about 0.8-nm channel spacing. For practical purposes the grid is often extended to cover the range from about 186 THz to about 201 THz and subdivided to provide 50-GHz and 25-GHz spaced grids. 
         [0025]    At a transmitter (not shown) of system  100 , different WDM components are generated, e.g., using lasers and optical modulators, and applied to a multiplexer, where they are multiplexed to form a corresponding WDM signal. En route to a receiver (not completely shown in  FIG. 1 ) of system  100 , the WDM signal may pass through one or more optical add-drop multiplexers, optical filters, and optical routers (e.g., similar to router  130 ), wherein the original WDM signal might be altered in terms of its wavelength composition and/or data content. At the receiver, the WDM signal is applied to a de-multiplexer, which splits it into individual WDM components for detection. The hardware of the optical signal generators, multiplexers, filters, routers, and de-multiplexers employed in the system ultimately defines the spectral characteristics of the WDM signals transported therein. 
         [0026]    For a given WDM signal  102 , data packets corresponding to different wavelengths may or may not be synchronized with one another. As used herein, the term “synchronized” refers to temporal alignment of data packets at respective selected locations. For example, two data packets of different wavelengths in a single WDM signal  102  are considered to be synchronized at an input port of system  100  if their leading edges arrive at that input port substantially simultaneously, i.e., the difference between the times of arrival is smaller than a designated relatively small tolerance. Two data packets of the same wavelength or different wavelengths in two different WDM signals  102  are considered to be synchronized at two different respective input ports of system  100  if their leading edges arrive at those respective input ports substantially simultaneously. Furthermore, two data packets of the same or different wavelengths in the same or different WDM signals  102  are considered to be synchronized if their leading edges arrive at respective same or different locations with a predetermined relative time delay, i.e., the difference between the times of arrival deviates from the predetermined time delay by no more than a designated tolerance. 
         [0027]    System  100  has a synchronous optical router  130  having M input ports and M output ports and capable of directing a data packet received at any of its input ports to any of its output ports. For example, data packets of wavelengths λ a  and λ b  (1≦a, b≦N) applied at times to an input port can be routed to any selected output ports p and q (1≦p, q≦M), respectively. Router  130  incorporates an appropriate controller that prevents packet collisions at the output ports. More specifically, the controller configures router  130  so that, in any given time slot, an output port does not receive from the input ports more than one packet of each wavelength. More details on synchronous optical routers similar to router  130  can be found, e.g., in an article by J. Gripp, et al., entitled “Optical Switch Fabrics for Ultra-High Capacity IP Routers,” published in Journal of Lightwave Technology, 2003, v. 21, no. 11, pp. 2839-2850, which is incorporated herein by reference in its entirety. 
         [0028]    Router  130  operates properly if WDM signals  128   1 - 128   M  applied to input ports  1 -M, respectively, are appropriately synchronized to one another and to a reference clock that controls the synchronous switching function of the router. To have signals  128   1 - 128   M  synchronized, system  100  incorporates an optical signal synchronizer  110 . Synchronizer  110  receives WDM signals  102   1 - 102   M , which may or may not be synchronized, and processes them to produce synchronized WDM signals  128   1 - 128   M , respectively. The following synchronizations might be lacking in WDM signals  102   1 - 102   M : (1) between two or more different WDM components of a single WDM signal  102  and (2) between two or more different WDM signals  102 . In contrast, WDM signals  128   1 - 128   M  are appropriately synchronized to one another and to a reference clock signal  132  supplied by router  130 . More specifically, different WDM signals  128  are synchronized to one another and to reference clock signal  132 . In addition, different WDM components of each WDM signal  128  are synchronized to one another and to reference clock signal  132 . As used herein, the term “WDM component” means a component of the WDM signal that can carry data, e.g., a data packet. Spectrally, a WDM component comprises a carrier wavelength and one or more modulation sidebands corresponding to that carrier wavelength. Different WDM components of the same WDM signal have different carrier wavelengths and generally carry independent sets of data. 
         [0029]    Synchronizer  110  has a plurality of channel synchronizers  112   1 - 112   M . Each channel synchronizer  112  is dedicated to processing a respective WDM signal  102  and operates to synchronize packets of different wavelengths (channels) in that signal to each other. A WDM signal  116   m  produced by channel synchronizer  112   m  carries the same data packets as WDM signal  102   m  (1≦m≦M). However, those data packets are synchronized to one another even if such synchronization was not present in the original WDM signal. 
         [0030]    WDM signals  116   1 - 116   M  produced by channel synchronizers  112   1 - 112   M , respectively, are applied to a multiplex synchronizer  120 , which operates to synchronize different WDM signals to one another and to reference clock signal  132 . The resulting synchronized WDM signals  128   1 - 128   M  are suitable for synchronous switching in router  130 . Synchronizer  120  is termed a “multiplex synchronizer” because it synchronizes a plurality of multiplexes, i.e., WDM signals  116   1 - 116   M . In one embodiment, multiplex synchronizer  120  is a waveguide circuit designed to synchronize WDM signals  116   1 - 116   M  without demultiplexing any of them into individual WDM components. 
         [0031]      FIG. 2  shows a block diagram of an all-optical channel synchronizer  300  that can be used as each instance of channel synchronizer  112  of  FIG. 1  according to one embodiment of the invention. Channel synchronizer  300  has a demultiplexer (DEMUX)  210  that separates WDM signal  102  into its N individual WDM components and applies each WDM component to a respective tunable wavelength converter (TWC)  220 . Each TWC  220  is designed to convert its input wavelength into a selected one of K output wavelengths, which K output wavelengths may or may not include some or all of wavelengths λ 1 -λ N . The output of each TWC  220  feeds a respective channel of multi-channel optical arrayed time buffer  230 . In this instance, time buffer  230  includes an array of delay lines  234   1 - 234   K  (e.g., optical fibers) coupled between arrayed waveguide gratings (AWGs)  360   a  and  360   b . Each of AWGs  360   a  and  360   b  has (i) a first side having N ports and (ii) a second side having K ports. Each AWG  360  is designed to operate using the K possible output wavelengths of TWCs  220 . Delay lines  234   1 - 234   K  have different optical lengths, e.g., incrementally increasing from a relatively short length of delay line  234   1  to a relatively long length of delay line  234   K . In one embodiment, signal-propagation times for any two adjacent delay lines  234  differ by the same time increment Δt, which time increment determines the time resolution of time buffer  230 . 
         [0032]    Time buffer  230  relies upon delay lines  234   1 - 234   K  which, as fully described below, are individually addressable via wavelength switching in AWG  360   a , to impart different delays to a signal  228  traversing time buffer  230 . The wavelength conversion imposed by TWC  220  determines to which one of delay lines  234   1 - 234   K  a signal  228  is switched by AWG  360   a . By appropriately selecting the output wavelengths for different TWCs  220 , one can therefore delay signals  228   1 - 228   N  by respective appropriate delay times to produce at the output ports of AWG  360   b  synchronized optical signals  238   1 - 238   N . Note that signals  238   1 - 238   N  are synchronized to within about one half of or less the time resolution (Δt) of time buffer  230 . In one embodiment, delay unit  230  has a Δt value of about 1/10 of the optical-packet length. If the temporal alignment of one or more components of WDM signal  102  changes over time, the wavelength conversion selection for TWCs  220   1 - 220   N  can be adjusted accordingly to maintain synchronization of signals  238   1 - 238   N . 
         [0033]    In this instance, each AWG  360  in time buffer  230  is a cyclical AWG. More specifically, each of the N ports located at the first side of AWG  360  is optically coupled to each of the K ports located at the second side of the AWG using K wavelengths. Mathematically, optical coupling of any port located at the first side of AWG  360  to the K optical ports located at the second side of that AWG can be described by a K-dimensional vector (hereinafter the “coupling vector”) having, as its components, the K wavelengths arranged in an appropriate order. For an N×K cyclical AWG, if one of such coupling vectors is known, then the remaining N−1 coupling vectors can be obtained by cyclically shifting the wavelength components of the known coupling vector. 
         [0034]    AWGs  360  in time buffer  230  are arranged symmetrically, and provisioned in such a well known manner that an optical signal  228 , regardless of its wavelength, entering input port i (1≦i≦N) of AWG  360   a  emerges from a respective output port o (1≦o≦N) of AWG  360   b  as the corresponding signal  238 , thereby achieving a fixed connectivity between an input port i of AWG  360   a  and an output port o of AWG  360   b . For the sake of convenience, in this instance, AWGs  360  are provisioned in such a way that optical signal  228   i , regardless its wavelength, entering input port i of AWG  360   a  emerges from output port i (i.e., o=i) of AWG  360   b  as signal  328   i . 
         [0035]    By exploiting the above-described cyclical property of AWG  360   a , the N coupling vectors associated with the respective input ports of AWG  360   a  can be easily defined. Where K≧N which is the case here, these coupling vectors vary from one another and each have a different k th  wavelength component (1≦k≦K). That is, any input optical signals  280  having the same wavelength but applied to different input ports of AWG  360   a  are always routed to its different output ports, and thus different delay lines connected thereto, in accordance with the different coupling vectors associated with the input ports. Alternately stated, if any one of delay lines  234   1 - 234   K  receives two or more optical signals at the same time, those optical signals would have different respective wavelengths and would not collide with one another. Advantageously, with no signal collisions, only one array of delay lines  234   1 - 234   K , as opposed to multiple arrays, for all input optical signals  280  is needed in channel synchronizer  300 . 
         [0036]    As previously mentioned, the wavelength conversion imposed by each particular TWC  220  in channel synchronizer  300  determines through which one of delay lines  234   1 - 234   K  the corresponding optical signal  228  propagates before it emerges as optical signal  238  at the back side of AWG  360   b . By appropriately selecting the output wavelengths for different TWCs  220  in channel synchronizer  300 , one can therefore synchronize optical signals  238   1 - 238   N  to one another. 
         [0037]    A limitation of the design of time buffer  230  stems from the fact that where longer delays are required of the time buffer, the optical lengths of the individual delay lines in the array may need to increase dramatically to accommodate such delays. Accordingly, time buffer  230  may become so bulky that it can no longer be efficiently integrated into a compact circuit. To overcome this limitation, in accordance with an embodiment of the invention, time buffer  230  may be replaced by multi-channel optical arrayed time buffer  330 , as illustrated in  FIG. 3 . Without loss of generality, time buffer  330  has N=8 input optical ports at which the respective optical signals  228   1 - 228   8  enter, each of which is afforded one of K=24 different delays. Unlike an equivalent time buffer  230  with N=8 and K=24, time buffer  330  may re-circulate an input optical signal in a manner to be described to extend a delay thereto through a shared delay line, thereby reducing the lengths of some of the delay lines, and thus the size, of the equivalent time buffer  230 . To that end, time buffer  330  in this instance employs a 24×24 AWG, denoted  310 , and three 8×8 AWGs, denoted  312 ,  314  and  316 , respectively. Optical signals  228   1 - 228   8  enter time buffer  330  at respective input ports  1 - 8  of AWG  310  and emerge from time buffer  330  at respective output ports  1 - 8  of AWG  316  as  238   1 - 238   8 . For ease of following, some of the port numbers are indicated in  FIG. 3 . Like time buffer  230 , time buffer  330  is provisioned to maintain a fixed connectivity between its input ports (same as input ports  1 - 8  of AWG  310 ) and its output ports (same as output ports  1 - 8  of AWG  316 ). For the sake of convenience and without loss of generality, in this embodiment such a fixed input/output (I/O) port connectivity is implemented as depicted in  FIG. 4A , whereby optical signal  228   i  (1≦i≦8) entering input port i of AWG  310  always emerges from output port i of AWG  316  as signal  238   i , regardless of the actual wavelength of signal  228   i . 
         [0038]    Similarly, in this embodiment a fixed (I/O) port connectivity between the AWG  312  and  310  pair is maintained as depicted in  FIG. 4B , whereby an optical entering input port i (1≦i≦8) of AWG  312  always emerges from output port i of AWG  310 , regardless of the actual wavelength of the entering optical signal. In addition, in this embodiment a fixed (I/O) port connectivity between the AWG  314  and  310  pair is maintained as depicted in  FIG. 4C , whereby an optical signal entering input port i (1≦i≦8) of AWG  314  always emerges from output port i of AWG  310 , regardless of the actual wavelength of the entering optical signal. Again, it should be noted that the above I/O port connectivity between the various AWG pairs are for illustrative purposes only. It will be appreciated that a person skilled in the art may implement other I/O port permutations to suit his/her particular needs. 
         [0039]    Referring back to  FIG. 3 , in this embodiment AWG  310  has 24 input ports, which is a multiple of the number of input signals to time buffer  330 , i.e., three times the number of input signals (8). The 24 output ports of AWG  310  are divided into groups of eight. The first group consists of output ports  1 - 8 , which are connected to input ports  1 - 8  of AWG  316  through an array of eight delay lines (denoted  321 ), affording Δt, 2Δt . . . and 8Δt delays, respectively, which arrangement is analogous to that of time buffer  230  of  FIG. 2 . The second group of output ports  9 - 16  of AWG  310  are connected to input ports  1 - 8  of AWG  312 , and reconnected to AWG  310  through a second array of eight delay lines, denoted  323 , which uniformly afford an 8Δt delay. The third group of output ports  17 - 24  of AWG  310  are connected to input ports  1 - 8  of AWG  314  through a third array of eight delay lines, denoted  326 , which uniformly afford a 16Δt delay. The output ports of AWG  314  are connected to respective input ports of AWG  310 . 
         [0040]    In accordance with an embodiment of the invention, each AWG in time buffer  330  in this instance is a cyclical AWG, and has a free spectral range equal to the number of input ports times the channel spacing (Δλ) of input wavelengths λ k  (k=1 . . . 24), where λ k =λ 1 +kΔλ, and λ 1  is a predetermined wavelength. Depending on the actual wavelength λ k  of signal  228   i , it may circulate through AWG  312  to gain an extended delay of 8Δt, or through AWG  314  to gain an extended delay of 16Δt, before reentering AWG  310  to be routed to one of delay lines in array  321 . In fact, by adjusting TWC  220   i  to provide a selected one of λ k  for signal  228   i , the above-described arrangement of time buffer  330  can impart any of Δt, 2Δt . . . up to 24Δt to signal  228   i .  FIG. 5  is a table  500  defining the relation between input signal  228   i  of varying wavelengths λ k  and the 24 different time delays which can be imparted to the signal by routing it to the corresponding output port j (=1 . . . 24) of AWG  310  in time buffer  330 . In general, for input optical signal  228   i  of wavelength λ k , time buffer  330  imparts a delay DΔt to the input signal, where D=8(p DIV 8)+(k+i−1) MOD 8, p=(k+i−1) MOD 24, and DIV represents the standard integer division operator, and MOD represents the standard modulo operator. 
         [0041]    In table  500 , columns  501 ,  503 ,  505 ,  507 ,  509 ,  511 ,  513  and  515  represent the coupling vectors associated with input ports  1 - 8  (CV 1 -CV 8 ) of AWG  310 , respectively, each having 24 wavelength components. For example, by referring to column  501 , the coupling vector associated with input port  1  (CV 1 ) of AWG  310  is (λ 1  λ 2  . . . λ 24 ). Because of the cyclical nature of all AWGs including AWG  310  in time buffer  330  in this instance, other coupling vectors, CV 2  through CV 8 , can easily be obtained by cyclically shifting the components of CV 1  one position at a time. 
         [0042]    It should be noted at this point that because in this embodiment, each of 8×8 AWGs  312 ,  314  and  316  is also a cyclical AWG, it exhibits the cyclic properties similar to those of AWG  310 .  FIG. 4D  shows an 8×8 AWG  412 , without loss of generality, representing any one of AWGs  312 ,  314  and  316  here. The input/output port mapping of AWG  412  with respect to different wavelength inputs is shown using table  425  in  FIG. 4E . For example, referring to row  431 , inputs signals having wavelengths λ 1  λ 2  . . . λ 8  entering input port  1  are routed by AWG  412  to its output ports  1 - 8 , respectively. Thus, the coupling vector associated with input port  1  (CV 1 ) of AWG  412  is (λ 1  λ 2  . . . λ 8 ). Similarly, CV 2  through CV 8  of AWG  412  are defined by the other rows of table  425 . In fact, because of the cyclical nature of AWG  412 , CV 2  through CV 8 , can easily be derived from CV 1  by cyclically shifting the components of CV 1  one position at a time. It should also be noted that each column of table  425  has different wavelength entries, signifying the fact that no wavelength (signal) collision is possible at each output port of AWG  412 . 
         [0043]    Referring back to  FIG. 5 , each row of table  500  is associated with a particular one of the 24 delays, which specifies the required wavelengths of individual signals  228   i  to be afforded the particular delay, and the output port j of AWG  310  from which a delay path emanates through which the required wavelengths travel in time buffer  330 . For example, referring to row  521  and  FIG. 3 , any of optical signal  228   1  entering input port  1  of AWG  310  having a wavelength of λ 1 , optical signal  228   2  entering input port  2  of AWG  310  having a wavelength of λ 2  . . . , and optical signal  228   8  entering input port  8  of AWG  310  having a wavelength of λ 8  would all converge onto output port j=1 of AWG  310 , and thence traverse the same Δt delay line  321 - 1  to AWG  316 . According to the connectivity table of  FIG. 4A , any such signal  228   i  from input port i of AWG  310 , after being delayed by Δt, would emerge from output port i of AWG  316  as the corresponding  238   i . 
         [0044]    Referring now to row  523  and  FIG. 3 , any of optical signal  228 , entering input port  1  of AWG  310  having a wavelength of λ 9 , optical signal  228   2  entering input port  2  of AWG  310  having a wavelength of λ 10  . . . , and optical signal  228   8  entering input port  8  of AWG  310  having a wavelength of λ 16  would all converge onto output port j=9 of AWG  310 . The converged signals  228   i  thence travel to input port  1  of AWG  312  and reenter AWG  310  through one of the 8Δt delay line in array  323 . According to the connectivity table of  FIG. 4B , the converged signals  228   i  from input port  1  of AWG  312 , after being delayed by 8Δt, would emerge from output port  1  of AWG  310 . The respective 8Δt-delayed versions of signals  228   i  thence traverse the same Δt delay line  321 - 1  to AWG  316 , thereby gaining an additional Δt delay. According to the connectivity table of  FIG. 4A , any such signals  228   i  originally from input port i of AWG  310 , after being delayed by 9Δt, would emerge from output port i of AWG  316  as the corresponding signals  238   i . 
         [0045]    Referring now to row  525  and  FIG. 3 , any of optical signal  228 , entering input port  1  of AWG  310  having a wavelength of λ 24 , optical signal  228   2  entering input port  2  of AWG  310  having a wavelength of λ 1  . . . , and optical signal  228   8  entering input port  8  of AWG  310  having a wavelength of λ 7  would all converge onto output port j=24 of AWG  310 . The converged signals  228   i  thence travel to input port  8  of AWG  314  and reenter AWG  310  through one of the 16Δt delay line in array  326 . According to the connectivity table of  FIG. 4C , the converged signals  228   i  from input port  8  of AWG  314 , after being delayed by 16Δt, would emerge from output port  8  of AWG  310 . The respective 16Δt-delayed versions of signals  228   i  thence traverse the same 8Δt delay line  321 - 8  to AWG  316 , thereby gaining an additional 8Δt delay. According to the connectivity table of  FIG. 4A , any such signals  228   i  originally from input port i of AWG  310 , after being delayed by 24Δt, would emerge from output port i of AWG  316  as the corresponding signals  238   i . 
         [0046]    It should be noted at this point that no wavelength (or signal) collision is possible when some or all of signals  228   i  traverse the same delay line in time buffer  330 . This is evident by the fact that the rows of table  500  (e.g., rows  521 ,  523  and  527 ) corresponding to each trio of delays (e.g., Δt, 9Δt and 17Δt) afforded by sharing the same delay line (e.g.,  321 - 1 ) all have different wavelengths required of signals  228   i . 
         [0047]    It should also be noted that the size of a time buffer is determined primarily by the cumulative length of the delay lines in the buffer. For comparison of the size of time buffer  330  with that of the equivalent time buffer  230  with N=8 and K=24, let&#39;s assume each unit length of a delay line contributes to a Δt delay. Thus, time buffer  330  has array  321  including 8 delay lines ranging from 1 unit to 8 units in length, array  323  including 8 delay lines each of which is 8 units in length, and array  326  including 8 delay lines each of which is 16 units in length. As a result, the cumulative length of the delay lines in buffer  330  is 8×8+8×16+1+2+3+4+5+6+7+8=224 units. In contrast, the equivalent time buffer  230  includes 24 delay lines ranging from 1 unit to 24 units in length, resulting in a cumulative length of 1+2 . . . +24=300 units. Advantageously, the size of time buffer  330  is significantly smaller than that of the equivalent time buffer  230 . 
         [0048]    In accordance with another embodiment of the invention, time buffer  230  in  FIG. 3  may be replaced by multi-channel optical arrayed time buffer  630 , as illustrated in  FIG. 6 . Without loss of generality, time buffer  630  has N=8 input optical ports at which the respective optical signals  228   1 - 228   8  enter, each of which is afforded one of K=24 different delays. Like time buffer  330 , time buffer  630  may re-circulate an input optical signal in a manner to be described to extend a delay thereto through a shared delay line, thereby reducing the lengths of some of the delay lines, and thus the size, of the equivalent time buffer  230 . To that end, time buffer  630  in this instance also employs a 24×24 AWG, denoted  610 , and three 8×8 AWGs, denoted  612 ,  614  and  616 , respectively. Where AWGs  612 ,  614  and  616  are cyclical in an embodiment, each of the AWGs may be provisioned similarly to AWG  412  of  FIG. 4D  and may have the same input/output port mapping depicted in  FIG. 4E . Optical signals  228   1 - 228   8  enter time buffer  630  at respective input ports  1 - 8  of AWG  610  and emerge from time buffer  630  at respective output ports  1 - 8  of AWG  616  as  238   1 - 238   8 . For ease of following, some of the port numbers are indicated in  FIG. 6 . Like time buffer  330 , time buffer  630  is provisioned to maintain a fixed connectivity between its input ports (same as input ports  1 - 8  of AWG  610 ) and its output ports (same as output ports  1 - 8  of AWG  616 ). For the sake of convenience and without loss of generality, in this embodiment such a fixed input/output (I/O) port connectivity is implemented as depicted in  FIG. 7A , whereby optical signal  228   i  (1≦i≦8) entering input port i of AWG  610  always emerges from output port i of AWG  616  as signal  238   i , regardless of the actual wavelength of signal  228   i . 
         [0049]    Similarly, in this embodiment a fixed (I/O) port connectivity between the AWG  612  and  610  pair is maintained as depicted in  FIG. 7B , whereby an optical entering input port i (1≦i≦8) of AWG  612  always emerges from output port i of AWG  610 , regardless of the actual wavelength of the entering optical signal. In addition, in this embodiment a fixed (I/O) port connectivity between the AWG  614  and  610  pair is maintained as depicted in  FIG. 7C , whereby an optical signal entering input port i (1≦i≦8) of AWG  614  always emerges from output port i of AWG  610 , regardless of the actual wavelength of the entering optical signal. Again, it should be noted that the above I/O port connectivity between the various AWG pairs are for illustrative purposes only. It will be appreciated that a person skilled in the art may implement other I/O port permutations to suit his/her particular needs. 
         [0050]    Referring back to  FIG. 6 , in this embodiment AWG  610  has 24 input ports, which is a multiple of the number of input signals to time buffer  630 , i.e., three times the number of input signals (8). The 24 output ports of AWG  610  are divided into groups of eight. The first group consists of output ports  1 - 8 , which are connected to input ports  1 - 8  of AWG  616  through an array of eight delay lines (denoted  621 ). Unlike the delay lines in array  321  in time buffer  330 , the delay lines in array  621  here afford delays in an increment of 3Δt. In this instance, these delays are Δt, 4Δt . . . and 22Δt, respectively. The second group of output ports  9 - 16  of AWG  610  are connected to input ports  1 - 8  of AWG  612 , and reconnected to AWG  610  through a second array of eight delay lines, denoted  623 , which uniformly afford a Δt delay, as opposed to an 8Δt delay afforded by the delay lines in array  323  of  FIG. 3 . The third group of output ports  17 - 24  of AWG  610  are connected to input ports  1 - 8  of AWG  614  through a third array of eight delay lines, denoted  626 , which uniformly afford a 2Δt delay, as opposed to a 16Δt delay afforded by the delay lines in array  326  of  FIG. 3 . The output ports of AWG  614  are connected to respective input ports of AWG  610 . 
         [0051]    In this instance, each AWG in time buffer  630  is a cyclical AWG, and has a free spectral range equal to the number of input ports times the channel spacing (Δλ) of input wavelengths λ k  (k=1 . . . 24), where λ k =λ 1 +kΔλ, and λ 1  is a predetermined wavelength. Depending on the actual wavelength λ k  of signal  228   i , it may circulate through AWG  612  to gain an extended delay of Δt, or through AWG  614  to gain an extended delay of 2Δt, before reentering AWG  610  to be routed to one of delay lines in array  621 . In fact, by adjusting TWC  220   i  to provide a selected one of λ k  for signal  228   i , the above-described arrangement of time buffer  330  can impart any of Δt, 2Δt . . . up to 24Δt to signal  228   i .  FIG. 8  is a table  800  defining the relation between input signal  228   i  of varying wavelengths λ k  and the 24 different time delays which can be imparted to the signal by routing it to the corresponding output port j (j=1 . . . 24) of AWG  610  in time buffer  630 . In general, for input optical signal  228   i  of wavelength λ k , time buffer  630  imparts a delay DΔt to the input signal, where D=(p−1) DIV 8+3[(k+i−2) MOD 8]+1, p=(k+i−1) MOD 24, and DIV represents the standard integer division operator, and MOD represents the standard modulo operator. 
         [0052]    By sorting the rows of table  800  on the j index of AWG  610  output port numerically, the coupling vectors CV 1  through CV 8  associated with the input ports of AWG  610  can readily be read from the resulting columns of table  800 , respectively. Thus, based on column  801  in table  800 , it can be shown that the coupling vector associated with input port  1  (CV 1 ) of AWG  610  in this instance is (λ 1  λ 2  . . . λ 24 ). Because of the cyclical nature of all AWGs including AWG  610  in time buffer  630  in this embodiment, other coupling vectors of AWG  610 , CV 2  through CV 8 , can easily be obtained by cyclically shifting the components of CV 1  one position at a time. That is, CV 2 =(λ 24  λ 1  . . . λ 23 ), CV 3 =(λ 23  λ 24  . . . λ 22 ), and CV 8 =(λ 18  λ 19  . . . λ 17 ) in this embodiment. 
         [0053]    Each row of table  800  is associated with a particular one of the 24 delays, which specifies the required wavelengths of individual signals  228   i  to be afforded the particular delay, and the output port j of AWG  610  from which a delay path emanates through which the required wavelengths travel in time buffer  630 . For example, referring to row  821  and  FIG. 6 , any of optical signal  228   1  entering input port  1  of AWG  610  having a wavelength of λ 1 , optical signal  228   2  entering input port  2  of AWG  610  having a wavelength of λ 24  . . . , and optical signal  228   8  entering input port  8  of AWG  610  having a wavelength of λ 18  would all converge onto output port j=1 of AWG  610 , and thence traverse the same Δt delay line  621 - 1  to AWG  616 . According to the connectivity table of  FIG. 7A , any such signal  228   i  from input port i of AWG  610 , after being delayed by Δt, would emerge from output port i of AWG  616  as the corresponding  238   i . 
         [0054]    Referring now to row  823  and  FIG. 6 , any of optical signal  228   1  entering input port  1  of AWG  610  having a wavelength of λ 10 , optical signal  228   2  entering input port  2  of AWG  610  having a wavelength of λ 9  . . . , and optical signal  228   8  entering input port  8  of AWG  610  having a wavelength of λ 3  would all converge onto output port j=10 of AWG  310 . The converged signals  228   i  thence travel to input port  2  of AWG  612  and reenter AWG  610  through one of the Δt delay line in array  623 . According to the connectivity table of  FIG. 7B , the converged signals  228   i  from input port  2  of AWG  612 , after being delayed by Δt, would emerge from output port  2  of AWG  610 . The respective Δt-delayed versions of signals  228   i  thence traverse the same 4Δt delay line  621 - 2  to AWG  616 , thereby gaining an additional 4Δt delay. According to the connectivity table of  FIG. 7A , any such signals  228   i  originally from input port i of AWG  610 , after being delayed by 5Δt, would emerge from output port i of AWG  616  as the corresponding signals  238   i . 
         [0055]    Referring now to row  825  and  FIG. 6 , any of optical signal  228   1  entering input port  1  of AWG  610  having a wavelength of λ 24 , optical signal  228   2  entering input port  2  of AWG  610  having a wavelength of λ 23  . . . , and optical signal  228   8  entering input port  8  of AWG  610  having a wavelength of λ 17  would all converge onto output port j=24 of AWG  610 . The converged signals  228   i  thence travel to input port  8  of AWG  614  and reenter AWG  610  through one of the 2Δt delay line in array  626 . According to the connectivity table of  FIG. 7C , the converged signals  228   i  from input port  8  of AWG  614 , after being delayed by 2Δt, would emerge from output port  8  of AWG  610 . The respective 2Δt-delayed versions of signals  228   i  thence traverse the same 22Δt delay line  621 - 8  to AWG  616 , thereby gaining an additional 22Δt delay. According to the connectivity table of  FIG. 7A , any such signals  228   i  originally from input port i of AWG  610 , after being delayed by 24Δt, would emerge from output port of AWG  616  as the corresponding signals  238   i . 
         [0056]    It should be noted at this point that no wavelength (or signal) collision is possible when some or all of signals  228   i  traverse the same delay line in time buffer  630 . This is evident by the fact that the rows of table  800  (e.g., rows  821 ,  827  and  829 ) corresponding to each trio of delays (e.g., Δt, 2Δt and 3Δt) afforded by sharing the same delay line (e.g.,  621 - 1 ) all have different wavelengths required of signals  228   i . 
         [0057]    Again, it should be noted that the size of a time buffer is determined primarily by the cumulative length of the delay lines in the buffer. Let&#39;s assume each unit length of a delay line contributes to a Δt delay. Thus, time buffer  630  has array  621  including 8 delay lines having 1, 4, 7, 10, 13, 16, 19 and 22 units in length, respectively; array  623  including 8 delay lines each of which is 1 unit in length; and array  626  including 8 delay lines each of which is 2 units in length. As a result, the cumulative length of the delay lines in buffer  630  is 8×1+8×2+1+4+7+10+13+16+19+22=116 units. Advantageously, the size of time buffer  330  is significantly smaller than that of the equivalent time buffer  230  (cumulative length of 300 units) and time buffer  330  (cumulative length of 224 units). 
         [0058]    Based on the disclosure of various embodiments of the invention heretofore, a person skilled in the art will readily be able to further reduce the total length of delay lines in a time buffer by allowing an optical signal to re-circulate through an AWG multiple times. Moreover, a person skilled in the art will readily be able to use an appropriate combination of few AWGs to significantly increase the longest affordable delay in a time buffer without an appreciable increase in its footprint. In addition, proper use of AWGs in the time buffer allows sharing the entire arrangement among multiple optical channels without additional hardware. The full arrangement may be integrated on a planar lightwave circuit (PLC) in a compact form, on a single chip in semiconductor substrate, or on a Si-based platform. To compensate for any propagation losses which may limit the length of the longest affordable delay, in some embodiments, semiconductor optical amplifiers on a semiconductor substrate or Erbium-doped waveguide amplifiers on a silica based platform are used for monolithic or hybrid integration. Further reduction of propagation losses may be achieved by use of simple, low cost, low loss fiber ribbons as some of the delay-line arrays in the embodiments. The architecture of the time buffers, as described, is conducive to effective scalability. For example, in some embodiments, the depth of the time buffers is increased by employing AWGs with more ports and/or increasing the number of wavelengths used. In other embodiments, it is increased by increasing the number of arrays of delay lines sharing the input/output ports of the same AWG (e.g.,  310 ,  610 ) in the time buffers. 
         [0059]    Referring back to  FIG. 2 , each optical signal  238  is applied to a respective “fixed” wavelength converter (WC)  240 , where it undergoes a wavelength conversion process that is reverse to that imposed by the preceding TWC  220 . More specifically, WC  240 , converts the wavelength of signal  238   1  back into λ 1 . WC  240   i  (not explicitly shown in  FIG. 2 , 1≦i≦N) converts the wavelength of signal  238   i  back into λ i . Finally, WC  240   N  converts the wavelength of signal  238   N  back into λ N . WC  240  is termed “fixed” because it essentially converts any input wavelength into a prescribed (“fixed”) wavelength. In one embodiment, TWC  220  and WC  240  can be implemented using different instances of the same physical wavelength-conversion device. To implement TWC  220 , an instance of that device is configured, using appropriate control signals, to convert a predetermined input wavelength into a desired (tunable) output wavelength. Similarly, to implement WC  240 , an instance of that device is configured, using appropriate control signals, to convert any (tunable) input wavelength into a predetermined output wavelength. 
         [0060]    MUX  250  multiplexes the optical signals produced by WCs  240   1 - 240   N  into WDM signal  116 . Note that the latter signal has the same wavelength and data packet composition as WDM signal  102 . However, unlike the packets carried by the WDM components of WDM signal  102 , the packets carried by the WDM components of WDM signal  116  are synchronized to one another. 
         [0061]      FIG. 9  shows a block diagram of a multiplex synchronizer  900  that can be used as multiplex synchronizer  120  in  FIG. 1  according to one embodiment of the invention. Multiplex synchronizer  900  has an array of optical tunable delays  908   1 - 908   M , each receiving a respective one of WDM signals  116   1 - 116   M . Tunable delay  908  is a continuously tunable optical delay circuit controlled by a control signal  972  generated by a delay controller  970 . Delay controller  970  receives reference clock signal  132  of  FIG. 1  and M monitor signals  968   1 - 968   M . Each monitor signal  968  is generated by (i) tapping the respective WDM signal  116  using an optical tap  902  and (ii) converting the output of the tap into an electrical signal using an optical-to-electrical converter (e.g., a photodiode)  904 . Delay controller  970  processes monitor signals  968   1 - 968   M  to determine temporal alignment of WDM signals  116   1 - 116   M  with one another and with reference clock signal  132 . Based on the processing results, delay controller  970  generates control signals  972   1 - 972   M  that configure tunable delays  908   1 - 908   M , respectively, to delay each of WDM signals  116   1 - 116   M  by a respective appropriate amount so that the resulting delayed signals, i.e., WDM signals  128   1 - 128   M , are synchronized to one another and to reference clock signal  132 . Continuous monitoring of WDM signals  116   1 - 116   M  via monitor signals  968   1 - 968   M  enables delay controller  970  to appropriately adjust, if necessary, the settings of tunable delays  908   1 - 908   M  to maintain said synchronization of WDM signals  128   1 - 128   M . In an alternative embodiment, multiplex synchronizer  900  may tap WDM signals  128   1 - 128   M  instead of or in addition to WDM signals  116   1 - 116   M . The tap signals can similarly be converted into electrical signals and supplied to delay controller  970  for generating control signals  972   1 - 972   M . 
         [0062]      FIG. 10  is a block diagram of an optical tunable delay circuit  1008  that can be used as each instance of optical tunable delay  908  according to one embodiment of the invention. Circuit  1008  has a plurality of optical delay elements  1018  and  1022  connected between five 2×2 switches SW 1 -SW 5 . Each of optical delay elements  1018   a - b  is a continuously tunable delay element that can be configured to introduce any selected signal-propagation delay between 0 and τ. Optical delay elements  1022   a - d  are fixed delay elements that introduce signal-propagation delays τ, 2τ, 4τ, and 8τ, respectively. In other words, optical delay elements  1022   a - d  form a binary set of fixed delay elements. 
         [0063]    By engaging or disengaging various delay elements, delay circuit  1008  can access a continuous delay range between 0 and 16τ. More specifically, switch SW 1  can direct the optical signal (e.g., WDM signal  116 ) applied to the input port of delay circuit  1008  to a delay arm having serially connected delay elements  1018   a  and  1022   a  or to a delay arm having delay element  1018   b . Then, switch SW 2  can direct the optical signal received from switch SW 1  to a delay arm having delay element  1022   b  or to a delay arm that bypasses that delay element. Switch SW 3  can direct the optical signal received from switch SW 2  to a delay arm having delay element  1022   c  (not explicitly shown in  FIG. 10 ) or to a delay arm that bypasses that delay element. Switch SW 4  (not explicitly shown in  FIG. 10 ) can direct the optical signal received from switch SW 3  to a delay arm having delay element  1022   d  or to a delay arm that bypasses that delay element. Finally, switch SW 5  directs the optical signal received from switch SW 4  to the output port of delay circuit  1008 , e.g., to produce WDM signal  128 . 
         [0064]    To produce a delay value between 0 and τ, switches SW 1 -SW 5  of delay circuit  1008  are configured to direct WDM signal  116  through delay element  1018   b  and bypass all other delay elements. To produce a delay value between τ and 2τ, switches SW 1 -SW 5  are configured to direct WDM signal  116  through delay elements  1018   a  and  1022   a  and bypass all other delay elements. To produce a delay value between 2τ and 3τ, switches SW 1 -SW 5  are configured to direct WDM signal  116  through delay elements  1018   b  and  1022   b  and bypass all other delay elements, etc. A detailed description of the design and operation of optical tunable delay circuits that, similar to circuit  1008 , can provide a relatively large continuously tunable delay range can be found, e.g., in commonly owned U.S. Pat. Nos. 6,956,991 and 7,212,695, both of which are incorporated herein by reference. 
         [0065]      FIGS. 11A  and B show an optical tunable delay circuit  1108  that can be used as each instance of optical tunable delay  908  of  FIG. 9  according to another embodiment of the invention. Circuit  1108  is generally analogous to circuit  1008 , and analogous elements of the two circuits are designated with labels having the same last two or three digits/letters. However, circuit  1108  is specifically designed as an integrated waveguide circuit, whereas circuit  1008  is generic and not limited to any particular implementation technology. Circuit  1108  can be viewed as one possible implementation of circuit  1008 . 
         [0066]    Referring to  FIG. 11A , each of fixed delay elements  1122   a - d  has a bi-spiral waveguide loop. The first spiral of the loop spirals inward until it connects with the second spiral, which then spirals outward. The length of the waveguide loop and therefore the signal-propagation delay time accrued therein is determined by the number of spiral turns. Therefore, delay element  1122   a  has fewer spiral turns than delay element  1122   b , which has fewer spiral turns than delay element  1122   c , etc. The bi-spiral layout of delay elements  1122   a - d  is advantageous in that it efficiently packs into a relatively small area a substantial length of waveguide, which helps to reduce the surface area occupied by circuit  1108 . 
         [0067]    Each of tunable delay elements  1118   a - b  is a tunable four-stage optical all-pass filter (OAPF). All-pass filters are known in the electrical and optical arts and have an advantageous property of affecting only the phase of a signal, rather than its amplitude. As explained in the above-cited U.S. Pat. No. 6,956,991, this OAPF property can be used to create a continuously tunable optical delay element that is relatively compact and does not have any mechanically movable parts. A tunable delay element based on an OAPF can contain one, two, or more OAPF stages. Various suitable single-stage and multi-stage OAPFs are disclosed, e.g., in commonly owned U.S. Pat. Nos. 6,289,151 and 7,016,615, both of which are incorporated herein by reference. 
         [0068]      FIG. 11B  shows an OAPF  1124  that is used as a stage in OAPF  1118 . OAPF  1124  has a Mach-Zehnder interferometer (MZI)  1126  and a feedback path  1128 . The internal arms of MZI  1126  are coupled to one another via two tunable optical couplers, each illustratively shown as having optical coupling strength κ. One of the MZI arms incorporates a tunable phase shifter  1130   a , and feedback path  1128  incorporates a tunable phase shifter  1130   b . In the frequency domain, the group delay generated by OAPF  1124  is represented by a periodic sequence of resonance-like peaks, with the shape and amplitude of the peaks and their periodicity (also referred to as the free spectral range (FSR) of the OAPF) determined by the lengths of the feedback loop and MZI arms, the coupling strengths, and phase shifts Φ a  and Φ b  introduced by phase shifters  1130   a - b , respectively. Using appropriate control signals, e.g., applied to tunable phase shifters  1130   a - b  and/or the tunable optical couplers (KP), one can change the shapes of the group delay curves generated by individual OAPFs  1124  to produce a desired group delay curve for OAPF  1118 . Representative examples of group delay curves generated by OAPF  1124  are disclosed, e.g., in the above-cited U.S. Pat. No. 6,289,151. Other OAPFs suitable for use as individual stages in other embodiments of OAPF  1118  are also disclosed therein. 
         [0069]      FIG. 12  graphically illustrates the group delay generated by OAPF  1118 . As already mentioned above, the group delay generated by an OAPF is periodic in the frequency domain.  FIG. 12  shows two such periods for OAPF  1118 . One skilled in the art will appreciate that each of the group delay curves shown in  FIG. 12  has additional periods extending out in wavelength (frequency) at both sides of the shown curve. 
         [0070]    Each of the group delay curves shown in  FIG. 12  corresponds to a particular configuration of OAPF  1118 . For example, a curve  1202  corresponds to a configuration, in which four OAPFs  1124  of OAPF  1118  are configured, e.g., by selecting the MZI coupling strengths and the phase shifts, to stagger their respective resonance-like peaks so that the resulting cumulative group delay curve has a periodic sequence of relatively flat portions, each having a delay value of about 180 ps. The four ripples within each “flat” portion is a manifestation of the four staggered peaks, each representing a different one of OAPFs  1124 . One skilled in the art will appreciate that the amplitude of the ripples and/or the spectral width of the “flat” portion can be controlled, e.g., by changing the number of stages in OAPF  1118 . Other (unlabeled) group delay curves shown in  FIG. 12  are analogous to curve  1202  and are produced by tuning OAPFs  1124 , primarily by changing their respective MZI coupling strengths, to change the delay value corresponding to the “flat” portions. Generally, the spectral width of a “flat” portion decreases as the delay value corresponding to the “flat” portion increases. 
         [0071]    In one embodiment, OAPF  1118  is designed and configured so that the periodicity of its group delay curve (or its FSR) matches the spectral separation between the carrier wavelengths (frequencies) of WDM signal  116 . As used herein the term “matches” means that the difference Δf (expressed in Hz) between the spectral separation and the FSR is sufficiently small so that the cumulative frequency mismatch NΔf across the wavelength multiplex (λ 1 -λ N ) of WDM signal  116  does not exceed the spectral width of one “flat” portion. Although, in the above description, the term “flat portion” was explained in reference to a multi-stage OAPF, this term is similarly applicable to a single stage OAPF. More specifically, a spectral region near the maximum of a resonance-like group-delay peak of a single-stage OAPF, e.g., the spectral region encompassing delay values that do not deviate from the maximum delay value by more than 5%, can be considered as such “flat portion.” 
         [0072]    Furthermore, the “flat” portions of the group delay curves are spectrally aligned with the carrier wavelengths, e.g., as shown in  FIG. 12 . More specifically,  FIG. 12  shows carrier wavelengths λ i  and λ i+1  of wavelength multiplex λ 1 -λ N . Note that the “flat” portions of the various group delay curves are aligned with carrier wavelengths λ i  and λ i+1  so that the respective modulation sidebands (see, e.g., modulation sidebands λ s1i  and λ s2i  of carrier wavelength λ i ) can substantially fit within the “flat” portions of the group delay curves for a desired range of delay values, e.g., those between about 180 and 320 ps. All these properties of OAPF  1118  enable optical tunable delay circuit  608  to controllably delay all WDM components of WDM signal  116  by substantially the same delay time without demultiplexing that WDM signal. Using a plurality of tunable delay circuits  1108 , multiplex synchronizer  900  ( FIG. 9 ) can advantageously be implemented as a waveguide circuit that has a relatively small size, does not have movable parts, has relatively low power consumption, and is able to efficiently maintain synchronization of a relatively large number of independent WDM signals. 
         [0073]    The foregoing merely illustrates the principles of the invention. It will thus be appreciated that those skilled in the art will be able to devise numerous arrangements which embody the principles of the invention and are thus within its spirit and scope. 
         [0074]    For example, although in some of the disclosed embodiments, the multi-channel optical arrayed time buffer employs cyclical AWGs for the sake of convenience, it will be appreciated that a person skilled in the art may use some or no cyclical AWGs to implement such a time buffer. In that case, some or all cyclic properties of the time buffer may disappear, e.g., the set of coupling vectors associated with the input ports of the time buffer not being readily obtainable by cyclically shifting wavelength components of one of the vectors. In addition, without the cyclic properties, the same set of wavelengths may not be used for each input of the time buffer to avoid signal collision. 
         [0075]    In addition, in some of the disclosed embodiments, the time buffer employs, by way of example, but not limitation, AWGs having an equal number of input and output ports. It will be appreciated that a person skilled in the art to implement the time buffer may use AWGs having an unequal number of input and output ports, instead. 
         [0076]    Finally, although communication system  100  and it various components, as disclosed, are embodied in the form of various discrete functional blocks, such a system and components could equally well be embodied in an arrangement in which the functions of any one or more of those blocks or indeed, all of the functions thereof, are realized, for example, by one or more appropriately programmed processors or devices.