Abstract:
The abstract is amended to read, “An inventive method and apparatus is provided by a bidirectional optical 1×2 device formed by a cascade of three optical 2×2 devices. Each 2×2 device is bidirectional where optical signals propagate through the 2×2 device in the forward and backward directions simultaneously. The demultiplexing and multiplexing occur simultaneously to thereby perform bidirectional 1×2 optical demultiplexing and 2×1 optical multiplexing in the 1×2 device.”

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to optical communication systems, and more particularly, to a bidirectional optical interleaver. 
     Demand for voice and data bandwidth in telecommunications networks continues to increase as population grows, work habits evolve (for example, the increased reliance on telecommuting and video/teleconferencing) and business and personal usage of internet-based telecommunications accelerates. Network operators and telecommunications service providers face an increasingly competitive environment that demands low operating and infrastructure costs, and fast supply of new capacity. Operators and service providers are thus motivated to deploy optical telecommunications equipment that maximizes feature and function density within their facilities. 
     The telecommunications industry has been actively working to develop new technologies to increase network capacity while continuing to meet the financial expectations experienced in today&#39;s less regulated telecommunication landscape. Of particular importance has been the emergence of wavelength division multiplexing (“WDM”), which supports the transmission of multiple optical channels (each channel having a different wavelength) on a single fiber. Each channel is modulated with a different information signal to thus provide a substantial increase in data and voice carrying capacity without requiring the installation of new transport media, such as optical cables, in the network. 
     Dense wavelength division multiplexing (“DWDM”) technology is developing as an approach to scale up network capacity even further. In DWDM technology, the optical channels are packed more tightly within the available transmission spectrum. Individual optical channels thus become more closely spaced. Recently, 400 and 200 GHz spacings were common for optical channels. As the state of the art improved, 100 GHz and then 50 GHz channel spacing has become more common. Optical interleaving products have been introduced to address capacity needs by interleaving multiple sets of optical channels into a more densely packed stream. In its simplest form, with 2×1 interleaving, two subsets of optical channels are multiplexed into a single set with half the channel spacing of the subsets. A 1×2 deinterleaver operates in a complementary manner to demultiplex a set of optical channels into two subsets of optical channels where each subset has twice the channel spacing of the input set. The single term “interleaver” is typically used to refer to both multiplexing and demultiplexing functions. Currently, interleavers may be used to support either multiplexing or demultiplexing, but not both functions simultaneously. 
     Interleavers are utilized in transmission applications include multiplexing (and demultiplexing) in DWDM networks. Optical Add/Drop Multiplexing (“OADM”) is another common application. In addition, interleavers may be deployed as an interface among transmission streams having unequal channel spacings to allow existing networks to be gracefully scaled upwards to meet future capacity demands. While current interleaver technology is entirely satisfactory in many applications, some classes of interleavers are physically large while others may be complex to manufacture and thus have high costs. Accordingly, it would be very desirable to reduce size and costs while increasing the feature set and functionalities provided in today&#39;s optical networking infrastructure. 
     SUMMARY OF THE INVENTION 
     An inventive method and apparatus is provided by a bidirectional optical 1×2 device formed by a cascade of three optical 2×2 devices. The first of two distal end ports of a first 2×2 device in the first tier of the cascade is optically coupled via a first bidirectional optical path to a proximal end port of a second 2×2 device (one of two 2×2 devices in the second tier of the cascade). The second distal end port of the first 2×2 device is optically coupled via a second bidirectional optical path to a proximal end port FL of the third 2×2 device (the other of the two 2×2 devices in the second tier of the cascade). 
     Each 2×2 device is bidirectional where optical signals propagate through the 2×2 device in the forward and backward directions simultaneously. An input WDM signal is received at a first proximal end port of the first 2×2 device. As the input WDM signal forward propagates through the first 2×2 device (from proximal end to distal end), it is demultiplexed into first and second subsets of optical channels. In some applications of the invention, the channel spacing in each of the first and second subsets may be approximately double that of the input WDM signal. 
     Third and fourth subsets of optical channels are received, respectively, at a distal end port of the second 2×2 device and a distal end port of the third 2×2 device. As the third and fourth subsets of optical channels backward propagate through the first 2×2 device (from distal end to proximal end), they are multiplexed into an output WDM signal that is output at the second proximal end port of the first 2×2 device. In some applications of the invention, the output WDM signal may have a channel spacing that is approximately half that of the third and fourth subsets. The demultiplexing in the forward direction and multiplexing in the backward direction occur simultaneously to thereby perform bidirectional 1×2 optical demultiplexing and 2×1 optical multiplexing in the 1×2 device. 
     In illustrative embodiments of the invention, a bidirectional 1×4 demultiplexer, 4×1 multiplexer is disclosed for demultiplexing an input WDM signal propagating in the forward direction into four discrete output channels while simultaneously multiplexing four discrete input channels propagating in the backward direction into an output WDM signal. The bidirectional 1×4 demultiplexer, 4×1 multiplexer is arranged from a two-tiered cascade of three 1×2 devices. The input WDM signal is received at the proximal end of the cascade and the four discrete input channels are received at the distal end. A bidirectional 1×8 demultiplexer, 8×1 multiplexer is also disclosed for demultiplexing an input WDM signal propagating in the forward direction into a eight discrete output channels while simultaneously multiplexing eight discrete input channels propagating in the backward direction into an output WDM signal. The bidirectional 1×8 demultiplexer, 8×1 multiplexer is arranged from a three-tiered cascade of seven 1×2 devices. Optical isolators are disposed at each input of the cascade in both the four and eight channel embodiments (i.e., at the proximal end input for the WDM signal and at each of the distal end inputs for the discrete input channels) to prevent feedback to the signal sources. 
     In another illustrative embodiment of the invention, an input WDM signal having N channels is received at a first proximal end port of a 1×2 device disposed in a first tier of a cascade of (N−1) 1×2 devices having m tiers where 2 m =N. As the input WDM signal forward propagates through the cascade, 1×N demultiplexing thereby occurs to generate a set of N discrete output channels that are output at respective first distal end ports of the 2×2 devices in the last tier (i.e., the m th  tier) of the cascade. 
     A set of N discrete input channels is received at second distal end ports of the 2×2 devices in the m th  tier of the cascade. As the set of N input channels backward propagates through the cascaded array, N×1 optical multiplexing thereby occurs to generate an output WDM signal that is output at a second proximal end port of the 1×2 optical device in the  1   st  tier of the cascade. Optical isolators are disposed at the inputs of the cascade (i.e., at the proximal end input for the WDM signal and at each of the N distal end inputs) to prevent feedback to the signal sources. 
     Advantageously, the invention provides simultaneous multiplexing and demultiplexing through a single optical cascade. By functioning bidirectionally, the invention doubles the feature set while maintaining the same footprint as single function A equipment. In addition, the doubled functionality does not come at twice the cost of single function equipment as only incremental costs are incurred to implement the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 depicts a bidirectional 1×2 device comprising three cascaded 2×2 devices arranged in accordance with the invention; 
     FIG. 2 depicts a bidirectional 1×4 demultiplexer, 4×1 multiplexer that is arranged from three cascaded bidirectional 1×2 devices, in accordance with the invention; and 
     FIG. 3 depicts a bidirectional 1×8 demultiplexer, 8×1 multiplexer that is arranged from a plurality of cascaded bidirectional 1×2 devices, in accordance with the invention. 
    
    
     DETAILED DESCRIPTION 
     Referring now to FIG. 1, a bidirectional 1×2 optical device  100  is depicted. As used here, the nomenclature “1×2” is used to indicate that an input signal is demultiplexed into two signals in the forward direction, and two input signals are multiplexed into a single output signal in the backward direction. As indicated in FIG. 1, the forward direction of signal propagation is oriented from left to right on the page, while the backward direction is oriented from right to left. 
     The bidirectional 1×2 devices is comprised of three 2×2 devices  110   1 ,  110   2 , and  110   3 . As used here, “2×2” device means a device having four optical ports where two optical ports are located at the proximal end of the device, and the remaining two optical ports are located at the distal end of the device. In all the figures accompanying this description, the proximal end of a device is located on its left side, while the distal end is located on its right. Signals propagate in the forward direction in devices from proximal end to distal end, and backward propagate from distal end to proximal end. It is noted that the term “signal” is used generally to refer to an information stream propagated within an optical medium (including optical paths and devices) and may include one or more optical channels. 
     Each 2×2 device  110  may be selected from a variety of optical devices including couplers, narrow band couplers, Mach-Zehnder interferometers, interleavers, and Fourier filters. As shown in FIG. 1, the 2×2 devices  110  are arranged in cascade having two tiers. The 2×2 device  110   1  is located in the first tier of the cascade and 2×2 optical devices  110   2  and  110   3  are located in the second tier. The 2×2 device  110   1  in the first tier of the cascade is optically coupled to both 2×2 devices  110   2  and  110   3  in the second tier. As shown, bidirectional optical path  155 , which may comprise an optical fiber, optically couples one of the two distal end ports of 2×2 device  110   1  to one of the proximal end ports of 2×2 device  110   2 . Similarly, bidirectional optical path  165 , which may comprise an optical fiber, optically couples the other distal end port of 2×2 device  110   1  to one of the proximal end ports of 2×2 device  110   3 . 
     Unidirectional optical path  142  is coupled to one of the proximal end ports of 2×2 device  101   1 . Unidirectional optical path  147  is coupled to the other proximal end port of 2×2 device  110   1 . Unidirectional optical path  142  is configured to carry an input WDM signal as an input to the 2×2 device  110   1  (and accordingly, to the 1×2 device  100 ). Unidirectional optical path  147  is configured to carry an output WDM signal as an output from the 2×2 device  110   1  (and accordingly, from the 1×2 device  100 ). 
     At the distal ends of 2×2 devices  110   2  and  110   3 , unidirectional optical fibers  170 ,  173 ,  182  and  185  are coupled to the four respective distal end ports, as shown in FIG.  1 . Unidirectional optical fibers  170 ,  173 ,  182  and  185  may comprise optical fibers. Unidirectional optical path  170  is configured to carry an optical signal as an output from the first distal end ports of 2×2 device  110   2 . Unidirectional path  173  is configured to carry an optical signal as an input to the second distal end port of 2×2 device  110   2 . Unidirectional optical path  182  is configured to carry an optical signal as an input from the first distal end ports of 2×2 device  110   3 . Unidirectional path  185  is configured to carry an optical signal as an output from the second distal end port of 2×2 device  110   3 . 
     The arrangement of the optical paths  142 ,  147 ,  170 ,  173 ,  182  and  185  thus configures 1×2 device  100  so that an input WDM signal received at the proximal end of the cascade (at optical path  142 ) is demultiplexed (via forward propagation through the device as indicated by arrow  112  in FIG. 1) into two output signals at the distal end of the cascade (at optical paths  170  and  185 ). In addition, two signals input at the distal end of the cascade (at optical paths  173  and  182 ) are multiplexed (as indicated by the arrow  114  in FIG. 1) into a single output WDM signal that is output at the proximal end of 1×2 device  100  (at optical path  147 ). In accordance with the invention, 1×2 device  100  thus simultaneously operates as a 1×2 demultiplexer in the forward direction and a 2×1 multiplexer in the backward direction by using bidirectional signal propagation. 
     In the illustrative embodiment shown in FIG. 1, an input WDM signal having four optical channels—λ 1 F, λ 2 F, λ 3 F, and λ 4 F—is received on optical path  142  at the first proximal end port of 2×2 device  110   1  in the first tier of the cascade. The designation “F” indicates that these optical channels forward propagate through the cascade forming the 1×2 device  100 . The four channels of the input WDM signal in this embodiment is merely illustrative as other channel counts may also be utilized in the invention. For example, in the case of an eight channel input WDM signal, in the forward direction, the 1×2 device  100  demultiplexes the input WDM signal into two output signals having four channels each. 
     As the input WDM signal forward propagates through 2×2 device  110   1 , it is demultiplexed into first and second subsets of optical channels. The first subset of optical channels, including λ 1 F and λ 3 F, is output at the first distal end port of 2×2 device  110   1 , and is carried in the forward direction by bidirectional optical path  155  to a proximal end port of 2×2 device  110   2 . The second subset, including λ 2 F and λ 4 F, is output at the second distal end port of 2×2 device  110   1 , and is carried in the forward direction by bidirectional optical path  165  to a proximal end port of 2×2 device  110   3 . The first subset, including λ 1 F and λ 3 F, forward propagates through 2×2 device  110   2 , and is output on the first distal end port of device  110   2  on unidirectional optical path  170  at the distal end of the cascade, as shown in FIG.  1 . Similarly, the second subset, including λ 2 F and λ 4 F, forward propagates through 2×2 device  110   3 , and is output on the second distal end port of 2×2 device  110   3  on unidirectional optical path  185  at the distal end of the cascade. 
     As depicted in FIG. 1, the even-numbered channels of the input WDM signal are output on one optical path exiting the 1×2 device  100  (path  170 ) and the odd channels are output on another optical path exiting the 1×2 device  100  (path  185 ). In some applications of the invention, the channel spacing of the output signal may be arranged to be approximately twice the channel spacing of the input WDM signal. In accordance with the invention, therefore, the separation of the channels making up the input WDM signal into odd and even subsets each having increased channel spacing may be advantageously used to deinterleave the input WDM signal. 
     At the distal end of the 1×2 device  100 , input signals are received at one of the two distal end ports of each 2×2 devices  110   2  and  110   3  in the second tier of the cascade. As shown in FIG. 1, a third subset of optical channels, including λ 2 B and λ 4 B, is received at the second distal end port of 2×2 device  110   2  on unidirectional optical path  173 . Similarly a fourth subset of optical channels, including λ 1 B and λ 3 B, is received at the first distal end port of 2×2 device  110   3  on unidirectional optical path  182 . The designation “B” indicates that these optical channels backward propagate through the cascade forming the 1×2 device  100 . 
     In accordance with the invention, λ 1 F, λ 2 F, λ 3 F and λ 4 F may be substantially equal in wavelength to λ 1 F, λ 2 B, λ 3 B, and λ 4 B, respectively, and vary only in terms of direction of propagation through the 1×2 device  100 . However, such substantial equality is not a requirement imposed by the invention. The two channels in each of the third and fourth subsets in this embodiment are merely illustrative as other channels counts may be utilized in the invention. For example, in the case of the third and fourth subsets having four channels each, in the backward direction, the 1×2 device  100  multiplexes the third and fourth subsets into an output WDM signal having eight channels. 
     The third subset of optical channels received on unidirectional optical path  173  backward propagates through 2×2 device  110   2 , is output on the proximal end port, and is carried by the bidirectional optical path  155  to the first distal end port of 2×2 device  110   1 . Similarly, the fourth subset of optical channels received on optical path  182  backward propagates through 2×2 device  110   3 , is output on the proximal end port, and is carried by the bidirectional optical path  165  to the second distal end port of 2×2 device  110   1 . In accordance with the invention, bidirectional optical path  155  is configured so that it may simultaneously carry the forward propagating optical channels λ 1 F and λ 3 F, and backward propagating channels λ 2 B and λ 4 B. Similarly, bidirectional optical path  165  is configured so that it may simultaneously carry the forward propagating optical channels λ 2 F and λ 4 F, and backward propagating channels λ 1 B and λ 3 B. 
     The third and fourth subsets of optical channels are multiplexed as they backward propagate through 2×2 device  110   1 . The multiplexed optical channels are output as an output WDM signal on the second proximal end port of 2×2 device  110   1  on unidirectional optical path  147 . As depicted in FIG. 1, the output WDM signal comprises λ 1 B, λ 2 B, λ 3 B and λ 4 B. In some applications of the invention, the channel spacing of the output WDM signal may be arranged to be approximately half that of the first and second subsets of optical channels. In accordance with the invention, therefore, the 1×2 device  100  shown in FIG. 1 may be advantageously used as an interleaver. Such interleaving may be performed simultaneously with the deinterleaving function described above. 
     Referring now to FIG. 2, an illustrative bidirectional 1×4 demultiplexer, 4×1 multiplexer  200  is depicted that is arranged from three cascaded 1×2 devices, in accordance with the invention. The nomenclature “1×4” and “4×1” is used to indicate, respectively, the demultiplexing of an input WDM signal into four discrete output signals in the forward direction, and the multiplexing of four discrete input signals into a single output WDM signal in the backward direction. 
     In accordance with the invention, the bidirectional 1×4 demultiplexer, 4×1 multiplexer  200  demultiplexes an input WDM signal received at the proximal end of the cascade into four discrete optical channels at the distal end. As indicated by the arrow  212  in FIG. 2, the demultiplexing occurs as the input WDM signal forward propagates through the two tiered cascade forming the bidirectional 1×4 demultiplexer, 4×1 multiplexer  200 . In addition, as indicated by the arrow  214  in FIG. 2, four discrete channels received at the distal end of the cascade are multiplexed as the channels backward propagate through the two tiered cascade forming the bidirectional 1×4 demultiplexer, 4×1 multiplexer  200 . In accordance with the invention, the demultiplexing and multiplexing functions is performed simultaneously using bidirectional optical signal propagation. 
     The 1×2 devices, identified by reference numerals  202   1,2,3  in FIG. 2, are each similar in form and operation to the 1×2 device  100  shown in FIG.  1  and described in the accompanying text. The cascade is arranged in two tiers where the first tier (designated as m=1 in FIG. 2) comprises a 1×2 device  202 , that is optically coupled to both the 1×2 device  202   2  and the 1×2 device  202   3  that are each disposed in the second tier (designated as m=2 in FIG.  2 ). 
     As shown in FIG. 2, 2×2 device  210   2  in 1×2 device  202   1  is coupled at the first distal end port via unidirectional optical path  221  to a first proximal end port of 2×2 device  224 , in 1×2 device  202   2 . The second proximal end port of 2×2 device  224   1  is coupled via unidirectional optical path  219  to the first distal end port of 2×2 device  210   3  in 1×2 device  2021 . The second distal end port of 2×2 device  2103  is coupled via unidirectional optical path  231  to the second proximal end port of 2×2 device  235   1  in 1×2 device  202   3 . The first proximal end port of 2×2 device  235   1  is coupled via unidirectional optical path  217  to the second distal end port of 2×2 device  210   2  in 1×2 device  202   1 . Optical paths  221 ,  219 ,  231 , and  217  may comprise optical fibers. 
     In the illustrative embodiment shown in FIG. 2, an input WDM signal having four optical channels—λ 1 F, λ 2 F, λ 3 F, and λ 4 F—is received on unidirectional optical path  201  at the first proximal end port of2×2 device  2101  in the 1×2 device  202   1  in the first tier of the cascade. An optical isolator  205 , is disposed along the optical path  201  to prevent feedback to the WDM signal source (not shown in FIG.  2 ). 
     As the input WDM signal forward propagates through 2×2 device  2101 , it is demultiplexed into first and second subsets of optical channels. The first subset of optical channels, λ 1 F and λ 3 F, is carried in the forward direction by bidirectional optical path  212 . The second subset, including λ 2 F and λ 4 F, is carried in the forward direction by bidirectional optical path  214 . The first subset, including λ 1 F and λ 3 F, forward propagates through 2×2 device  210   2 , and is output on the first distal end port of device  210   2  on unidirectional optical path  221  in the forward direction to the first proximal end port of 2×2 device  224   1  in the 1×2 device  202   2 . Similarly, the second subset, including λ 2 F and λ 4 F, forward propagates through 2×2 device  210   3 , and is output on the first distal end port of 2×2 device  210   3  on unidirectional optical path  231  in the forward direction to the second proximal end port of 2×2 device  235   1  in 1×2 device  202   3 . In accordance with the invention, the even-numbered channels of the input WDM signal are output on unidirectional optical path  231  and the odd channels are output on unidirectional optical path  221 . In some applications of the invention, the channel spacing of the signals output on unidirectional optical paths  231  and  221  may be arranged to be approximately twice the channel spacing of the input WDM signal received on unidirectional optical path  201 . 
     The first subset of optical channels, including λ 1 F and λ 3 F, forward propagates through 2×2 device  224   1  where it is demultiplexed so that a single optical channel λ 1 F is carried in the forward direction by bidirectional optical path  223  to a proximal end port of 2×2 device  224   2 , and a single optical channel λ 3 F is carried in the forward direction by bidirectional optical path  222  to a proximal end port of 2×2 device  224   3 . The optical channel λ 1 F forward propagates through 2×2 device  224   2  and is output on the first distal end port to unidirectional optical path  226 . The optical channel λ 3 F forward propagates through 2×2 device  224   3  and is output at the first distal end port to unidirectional optical path  228 . 
     The second subset of optical channels, including λ 2 F and λ 4 F, forward propagates through 2×2 device  235   1  where it is demultiplexed so that a single optical channel λ 2 F is carried in the forward direction by bidirectional optical path  233  to a proximal end port of 2×2 device  235   2  and a single optical channel λ 4 F is carried in the forward direction by bidirectional optical path  232  to a proximal end port of 2×2 device  235   3 . The optical channel λ 2 F forward propagates through 2×2 device  235   2  and is output on the first distal end port on unidirectional optical path  236 . The optical channel λ 4 F forward propagates through 2×2 device  235   3  and is output at the first distal end port on unidirectional optical path  238 . 
     Therefore in the forward direction, in accordance with the invention, as the input WDM signal having four channels (λ 1 F, λ 2 F, λ 3 F, and λ 4 F) forward propagates through the bidirectional 1×4 demultiplexer, 4×1 multiplexer  200 , it is demultiplexed and the four optical channels emerge as discrete channels on respective optical paths  226 ,  228 ,  236 , and  238  at the distal end. In the first tier of the cascade (i.e., 1×2 device  202   1 ), the input WDM signal is demultiplexed into separate odd and even optical channel subsets. In this illustrative example, each subset contains two optical channels. The odd and even optical channels subsets are demultiplexed in respective 1×2 devices in the second tier of the cascade to further demultiplex each optical channel subset by half again and output each subset half at the distal end of the second tier. Of course in this illustrative example, by splitting each subset of two members in half, the second tier operates to create discrete optical output channels. In some applications of the invention, the channel spacing may thus be approximately doubled as the input WDM signal is demultiplexed as it forward propagates from the first tier to the second tier in the cascade forming the bidirectional 1×4 demultiplexer, 4×1 multiplexer  200 . 
     In the illustrative embodiment shown in FIG. 2, four discrete optical channels—λ 3 B, λ 1 B, λ 4 B, and λ 2 B—are received on respective unidirectional optical paths  227 ,  229 ,  237  and  239  at respective second distal end ports of 2×2 devices  224   2 ,  224   3 ,  235   2  and  225   3 . Optical isolators  205   2 ,  205   3 ,  205   4  and  205   5  are disposed along the optical paths, as shown, to prevent feedback to the optical channel sources (not shown in FIG.  2 ). In accordance with the invention, λ 1 F, λ 2 F, λ 3 F and λ 4 F may be substantially equal in wavelength to λ 1 B, λ 2 B, λ 3 B, and λ 4 B, respectively, and vary only in terms of direction of propagation through the bidirectional 1×4 demultiplexer, 4×1 multiplexer  200 . However, such substantial equality is not a requirement imposed by the invention. 
     At 1×2 device  202   2 , λ 3 B and λ 1 B are received at respective second distal end ports of 2×2 device  224   2  and  224   3 . λ 3 B backward propagates through 2×2 device  224   2 , is output on a proximal end port of device  224   2 , and is carried by optical path  223  in the backward direction to the first distal end port of 2×2 device  224   1 . Similarly, optical channel λ 1 B backward propagates through 2×2 device  224   3 , is output on a proximal end port of 2×2 device  224   3 , and is carried by optical path  222  in the backward direction to the second distal end port of 2×2 device  224   1 . As they backward propagate, 2×2 device  224   1  multiplexes λ 3 B and λ 1 B into a third subset of optical channels that is output on the second proximal end port of 2×2 device  224   1  and carried by optical path  219  in the backward direction to the first distal end port of 2×2 device  210   3  in the 1×2 optical device  202   1 . 
     At 1×2 device  202   3 , λ 4 B and λ 2 B are received at respective second distal end ports of 2×2 device  225   2  and  225   3 . λ 4 B backward propagates through 2×2 device  225   2 , is output on a proximal end port of device  235   2 , and is carried by optical path  217  in the backward direction to the first distal end port of 2×2 device  235   1 . Similarly, optical channel λ 2 B backward propagates through 2×2 device  235   3 , is output on a proximal end port of 2×2 device  235   3 , and is carried by optical path  232  in the backward direction to the second distal end port of 2×2 device  235   1 . As they backward propagate, 2×2 device  235   1  multiplexes λ 2 B and λBB into a fourth subset of optical signals that is output on the first proximal end port of 2×2 device  225   1  and carried by optical path  217  in the backward direction to the second distal end port of 2×2 device  210   2  in the 1×2 optical device  202   1 . 
     At 1×2 device  202   1 , the fourth subset, including λ 2 B and λ 4 B, received at the second distal end port of 2×2 device  210   2  backward propagates through 2×2 device  210   2 . The fourth subset, including λ 2 B and λ 4 B, is output on a proximal end port of device  210   2 , and is carried by optical path  212  in the backward direction to the first distal end port of 2×2 device  210   1 . Similarly, the third subset, including λ 1 B and λ 3 B, received at the first distal end port of 2×2 device  210   3  backward propagates through 2×2 device  210   3 . The third subset, including λ 1 B and λ 3 B, is output on a proximal end port of device  210   3 , and is carried by optical path  214  in the backward direction to the second distal end port of 2×2 device  210   1 . The 2×2 device  235 , multiplexes the third and fourth subsets into an output WDM signal that is output on the second proximal end port of 2×2 device  225   1  on optical path  207  in the backward direction. The output WDM signal has four channels—λ 1 B, λ 2 B, λ 2 B and λ 4 B—as shown in FIG.  2 . 
     Therefore in the backward direction, in accordance with the invention, an output WDM signal is multiplexed from four optical channels (λ 1 B, λ 2 B, λ 3 B, and λ 4 B that are received a the distal end of the second tier as discrete optical channels on respective unidirectional optical paths  227 ,  229 ,  237 , and  239 ) as the optical channels backward propagate through the bidirectional 1×4 demultiplexer, 4×1 multiplexer  200 . In the second tier of the cascade (i.e., 1×2 devices  202   2,3 ), the received optical channels are multiplexed into separate odd and even optical channel subsets in the respective 1×2 devices  202   2  and  202   3 . In this illustrative example, each subset contains two optical channels. Thus, the second tier of the cascade operates in the backward direction to output, at the proximal end of the second tier, a pair of optical subsets each having double the channel count of each of the discrete input signals received at the distal end of the cascade&#39;s second tier. The odd and even optical channels subsets are each multiplexed in the 1×2 device  202   1  in the first tier of the cascade to double channel count again and generate the output WDM signal that is output at the proximal end of the cascade&#39;s first tier on optical path  207 . In some applications of the invention, the channel spacing may thus be approximately halved (i.e., the optical channels are closer together) as the optical subsets backward propagate from the second tier to the first tier of the cascade forming the bidirectional 1×4 demultiplexer, 4×1 multiplexer  200 . 
     Referring now to FIG. 3, an illustrative bidirectional 1×8 demultiplexer, 8×1 multiplexer  300  is depicted that is arranged from seven cascaded 1×2 devices, in accordance with the invention. The nomenclature “1×8” and “8×1” is used to indicate, respectively, the demultiplexing of an input WDM signal into eight discrete signals in the forward direction, and the multiplexing of eight discrete signals into a single output WDM signal in the backward direction. 
     In accordance with the invention, the bidirectional 1×8 demultiplexer, 8×1 rat multiplexer  300  demultiplexes an input WDM signal received at the proximal end of the cascade into eight discrete optical channels at the distal end. As indicated by the arrow  312 , the demultiplexing occurs as the input WDM signal forward propagates through the three tiered cascade forming the bidirectional 1×8 demultiplexer, 8×1 multiplexer  300 . In addition, as indicated by the arrow  314 , eight discrete channels received at the distal end of the cascade are multiplexed as the channels backward propagate through the three tiered cascade forming the bidirectional 1×8 demultiplexer, 8×1 multiplexer  300 . In accordance with the invention, the demultiplexing and multiplexing functions is performed simultaneously using bidirectional optical signal propagation. 
     The 1×2 devices, identified by reference numerals  302   1-7  in FIG. 3, are each similar in form and operation to the 1×2 device  100  shown in FIG.  1  and described in the accompanying text. The cascade forming the bidirectional 1×8 demultiplexer, 8×1 multiplexer  300  is arranged in three tiers where the first tier (designated as m=1 in FIG. 3) comprises a 1×2 device  302   1  that is optically coupled to both the 1×2 device  302   2  and the 1×2 device  302   3  that are each disposed in the second tier (designated as m=2 in FIG.  3 ). The 1×2 device  302   2  in the second tier of the cascade is optically coupled to both the 1×2 device  302   4  and the 1×2 device  302   5  that are each disposed in the third tier (designated as m=3 in FIG.  3 ). The 1×2 device  302   3  in the second tier of the cascade is optically coupled to both the 1×2 device  302   6  and the 1×2 device  302   7  that are each disposed in the third tier. 
     The structure of bidirectional 1×8 demultiplexer, 8×1 multiplexer  300  is similar in form to bidirectional 1×4 demultiplexer, 4×1 multiplexer  200  shown in FIG.  2  and described in the accompanying text. However, in order to provide the additional multiplexing and demultiplexing function for the additional optical channels, a third tier of 1×2 devices is added. It may also be recognized that the 1×8, 8×1 structure may be considered as a bidirectional 1×4 demultiplexer, 4×1 demultiplexer (formed from 1×2 devices  302   1 ,  302   2  and  302   3 ) that is coupled to the four 1×2 devices  302   4 ,  302   5 ,  302   6  and  302   7 . Alternatively, the 1×8, 8×1 structure may be considered as two 1×4 demultiplexer, 4×1 demultiplexers (the first being forming 1×2 devices  302   2 ,  302   5  and  302   5  and the second being formed from 1×2 devices  302   3 ,  302   6  and  302   7 ) that are both coupled to the single 1×2 device  302 , and operated in parallel. 
     The signal flow through the arrangement shown in FIG. 3 is similar to that shown in FIG. 2 with the fundamental difference being that eight channels propagate in each direction rather than the four in the previous illustrative example. Accordingly, an input WDM signal having eight optical channels—λ 1 F to λ 8 F—is received on the unidirectional optical path  307  at the first proximal end port of 2×2 device  315 , in the 1×2 device  302 , in the first tier of the cascade. An optical isolator  305   1  is disposed along the optical path  307  to prevent feedback to the WDM signal source (not shown in FIG.  3 ). 
     As the input WDM signal forward propagates through 2×2 device  315   1 , it is demultiplexed into a first subset of four optical channels, λ 1 F, λ 3 F, λ 5 F and λ 7 F, and a second subset of the other four optical channels, λ 2 F, λ 4 F, λ 6 F and λ 8 F. The first subset is carried in the forward direction by bidirectional optical path  311  to a proximal end port of 2×2 device  315   2 . The second subset is carried in the forward direction by bidirectional optical path  313  to a proximal end port of 2×2 device  315   3 . 
     The first subset of optical channels, including λ 1 F, λ 3 F, λ 5 F and λ 7 F, forward propagates through 2×2 device  315   2 , is output on the first distal end port of device  315   2 , and is carried by optical path  316  in the forward direction to the first proximal end port of 2×2 device  324   1  in the 1×2 device  302   2 . Similarly, the second subset of optical channels, including λ 2 F, λ 4 F, λ 6 F and λ 8 F, forward propagates through 2×2 device  315   3 , is output on the second distal end port of 2×2 device  315   3 , and is carried by optical path  319  in the forward direction to the second proximal end port of 2×2 device  331   1  in 1×2 device  302   3 . Thus, the even-numbered channels of the input WDM signal are output on optical path  319  and the odd channels are output on optical path  316 . In some applications of the invention, the channel spacing of the signals output on paths  319  and  316  may be arranged to be approximately twice the channel spacing of the input WDM signal received on unidirectional optical path  307 . 
     As indicated in FIG. 3, as the first subset of optical channels, including λ 1 F, λ 3 F, λ 5 F and λ 7 F, forward propagates through 2×2 device  324   1 , it is demultiplexed into a third subset of optical channels, including λ 1 F and λ 5 F, and a fourth subset of optical channels, including λ 3 F and λ 7 F. The third subset of optical channels, including λ 1 F and λ 5 F, is carried in the forward direction by bidirectional optical path  323 , forward propagates through 2×2 device  324   2  and is output from the first distal end port to the first proximal end port of 2×2 device  342   1  in 1×2 device  302   4  via unidirectional optical path  327 . The fourth subset of optical channels, including λ 3 F and λ 7 F, is carried in the forward direction by bidirectional optical path  325 , forward propagates through 2×2 device  324   3  and is output at the first distal end port to the second proximal end port of 2×2 device  351   1  in 1×2 device  302   5  via unidirectional optical path  329 . 
     The third subset of optical channels, including λ 1 F and λ 5 F, forward propagates through 2×2 device  324   1 , where it is demultiplexed so that a single optical channel λ 1 F is carried in the forward direction by bidirectional optical path  343  to a proximal end port of 2×2 device  342   2  and a single optical channel λ 5 F is carried in the forward direction by bidirectional optical path  344  to a proximal end port of 2×2 device  342   3 . The optical channel λ 1 F forward propagates through 2×2 device  342   2  and is output on the first distal end port on unidirectional optical path  346 . The optical channel λ 5 F forward propagates through 2×2 device  342   3  and is output at the first distal end port on unidirectional optical path  348 . 
     The fourth subset of optical channels, including λ 3 F and λ 7 F, forward propagates through 2×2 device  351   1  where it is demultiplexed so that a single optical channel λ 3 F is carried in the forward direction by bidirectional optical path  352  to a proximal end port of 2×2 device  351   2  and a single optical channel λ 7 F is carried in the forward direction by bidirectional optical path  353  to a proximal end port of 2×2 device  351   3 . The optical channel λ 3 F forward propagates through 2×2 device  351   2  and is output on the first distal end port on unidirectional optical path  356 . The optical channel λ 7 F forward propagates through 2×2 device  351   3  and is output at the first distal end port on unidirectional optical path  358 . 
     As indicated in FIG. 3, as the second subset of optical channels, including λ 2 F, λ 4 F, λ 6 F and λ 8 F, forward propagates through 2×2 device  331   1 , it is demultiplexed into a fifth subset of optical channels, including λ 2 F and λ 6 F, and a sixth subset of optical channels, including λ 4 F and λ 8 F. The fifth subset of optical channels, including λ 2 F and λ 6 F, is carried in the forward direction by bidirectional optical path  333  to a proximal end port of 2×2 device  331   2 , forward propagates through 2×2 device  331   2  and is output from the first distal end port to the first proximal end port of 2×2 device  364   1  in 1×2 device  302   6  via unidirectional optical path  337 . The sixth subset of optical channels including λ 4 F and λ 8 F is carried in the forward direction by bidirectional optical path  335  to a proximal end port of 2×2 device  331   3 , forward propagates through 2×2 device  331   3  and is output at the second distal end port to the second proximal end port of 2×2 device  375   1  via unidirectional optical path  339 . 
     The fifth subset of optical channels, including λ 2 F and λ 6 F, forward propagates through 2×2 device  364   1  where it is demultiplexed so that a single optical channel λ 2 F is carried in the forward direction by bidirectional optical path  361  to a proximal end port of 2×2 device  364   2  and a single optical channel λ 6 F is carried in the forward direction by bidirectional optical path  363  to a proximal end port of 2×2 device  364   3 . The optical channel λ 2 F forward propagates through 2×2 device  364   2  and is output on the first distal end port on unidirectional optical path  366 . The optical channel λ 6 F forward propagates through 2×2 device  364   3  and is output at the first distal end port on unidirectional optical path  368 . 
     The sixth subset of optical channels, including λ 4 F and λ 8 F, forward propagates through 2×2 device  375   1  where it is demultiplexed so that a single optical channel λ 4 F is carried in the forward direction by bidirectional optical path  372  to a proximal end port of 2×2 device  375   2  and a single optical channel λ 8 F is carried in the forward direction by bidirectional optical path  373  to a proximal end port of 2×2 device  375   3 . The optical channel λ 4 F forward propagates through 2×2 device  375   2  and is output on the first distal end port on unidirectional optical path  376 . The optical channel λ 8 F forward propagates through 2×2 device  375   3  and is output at the first distal end port on unidirectional optical path  378 . 
     Therefore in the forward direction, in accordance with the invention, as the input WDM signal having eight channels (λ 1 F through λ 8 F) forward propagates through the bidirectional 1×8 demultiplexer, 8×1 multiplexer  300 , it is demultiplexed and the eight optical channels emerge as discrete channels on respective optical paths  346 ,  348 ,  356 ,  358   366 ,  368 ,  376  and  378  at the distal end. In the first tier of the cascade (i.e., 1×2 device  302   1 ), the input WDM signal is demultiplexed into separate first and second subsets of optical channels including four odd and four even channels respectively. In some applications, the channel spacing in each of the first and second subsets is approximately twice that of the input WDM signal. Advantageously, the separation of the channels into odd and even subsets with increased channel spacing may be used to deinterleave the input WDM signal. 
     The first and second subsets of optical channels are further demultiplexed in respective 1×2 devices in the second tier of the cascade. The first subset is demultiplexed into respective third and fourth subsets of optical channels where each has half the channel count of the first subset (i.e., the third and fourth subsets each include two optical channels). The second subset is demultiplexed into respective fifth and sixth subsets of optical channels (each including two optical channels). In some applications of the invention, the channel spacing of the third and fourth subsets is approximately twice that of the first subset And, the channel spacing of the fifth and sixth subsets may be approximately twice that of the second subset. The third tier of the cascade forming 1×8 demultiplexer, 8×1 multiplexer  300  operates to demultiplex the third, fourth, fifth and sixth subsets of optical channels to reduce the channel count by half again and generate discrete optical output channels. 
     In the illustrative embodiment shown in FIG. 3, eight discrete optical channels—λ 1 B through λ 8 B—are received on respective unidirectional optical paths  347 ,  349 ,  357 ,  359 ,  367 ,  369 ,  377  and  379  at respective second distal end ports of 2×2 devices  342   2 ,  342   3 ,  351   2 ,  351   3 ,  364   2 ,  364   3 ,  375   2  and  375   3 . Optical isolators  305   2 ,  305   3 ,  305   4 ,  305   5    305   6    305   7 ,  305   8  and  305   9  are disposed along the optical paths, as shown, to prevent feedback to the optical channel sources (not shown in FIG.  3 ). In accordance with the invention, λ 1 F through λ 8 F may be substantially equal in wavelength to λ 1 B through λ 8 B, respectively, and vary only in terms of direction of propagation through the bidirectional 1×8 demultiplexer, 8×1 multiplexer  300 . However, such substantial equality is not a requirement imposed by the invention. 
     At 1×2 device  302   4  in the third tier of the cascade, λ 5 B and λ 1 B are received at respective second distal end ports of 2×2 device  342   2  and  342   3 . λ 5 B backward propagates through 2×2 device  342   2 , is output on a proximal end port of 2×2 device  342   2 , and is carried by bidirectional optical path  343  in the backward direction to the first distal end port of 2×2 device  342   1 . Similarly, optical channel λ 1 B backward propagates through 2×2 device  342   3 , is output on a proximal end port of 2×2 device  342   3 , and is carried by bidirectional optical path  344  in the backward direction to the second distal end port of 2×2 device  342   1 . As the optical channels backward propagate, 2×2 device  342   1  multiplexes λ 5 B and λ 1 B into a seventh subset of optical channels that is output on the second proximal end port of 2×2 device  342   1  and carried by unidirectional optical path  340  in the backward direction to the first distal end port of 2×2 device  324   3  in the 1×2 optical device  302   1 . 
     At 1×2 device  302   5  in the third tier of the cascade, λ 7 B and λ 3 B are received at respective second distal end ports of 2×2 device  351   2  and  351   3 . λ 7 B backward propagates through 2×2 device  351   2 , is output on a proximal end port of device  351   2 , and is carried by bidirectional optical path  352  in the backward direction to the first distal end port of 2×2 device  351   1 . Similarly, optical channel λ 3 B backward propagates through 2×2 device  351   3 , is output on a proximal end port of 2×2 device  351   3 , and is carried by bidirectional optical path  353  in the backward direction to the second distal end port of 2×2 device  351   1 . As the optical channels backward propagate, 2×2 device  351   1  multiplexes λ 7 B and λ 3 B into an eighth subset optical channels that is output on the first proximal end port of 2×2 device  351   1  and carried by unidirectional optical path  350  in the backward direction to the second distal end port of 2×2 device  324   2  in the 1×2 optical device  302   2 . 
     At 1×2 device  302   6  in the third tier of the cascade, λ 6 B and λ 2 B are received at respective second distal end ports of 2×2 device  364   2  and  364   3 . λ 6 B backward propagates through 2×2 device  364   2 , is output on a proximal end port of device  364   2 , and is carried by bidirectional optical path  361  in the backward direction to the first distal end port of 2×2 device  364   1 . Similarly, optical channel λ 2 B backward propagates through 2×2 device  364   3 , is output on a proximal end port of 2×2 device  364   3 , and is carried by bidirectional optical path  363  in the backward direction to the second distal end port of 2×2 device  364   1 . As the optical channels backward propagate, 2×2 device  364   1  multiplexes λ 6 B and λ 2 B into a ninth subset of optical channels that is output on the first proximal end port of 2×2 device  364   1  and carried by optical path  360  in the backward direction to the first distal end port of 2×2 device  331   3  in the 1×2 optical device  302   3 . 
     At 1×2 device  302   7  in the third tier of the cascade, λ 8 B and λ 4 B are received at respective second distal end ports of 2×2 device  375   2  and  375   3 . λ 8 B backward propagates through 2×2 device  375   2 , is output on a proximal end port of device  375   2 , and is carried by bidirectional optical path  372  in the backward direction to the first distal end port of 2×2 device  375   1 . Similarly, optical channel λ 4 B backward propagates through 2×2 device  375   3 , is output on a proximal end port of 2×2 device  375   3 , and is carried by bidirectional optical path  373  in the backward direction to the second distal end port of 2×2 device  375   1 . As the optical channels backward propagate, 2×2 device  375   1  multiplexes λ 8 B and λ 4 B into a tenth subset of optical channels that is output on the first proximal end port of 2×2 device  375   1  and carried by optical path  370  in the backward direction to the second distal end port of 2×2 device  331   2  in the 1×2 optical device  302   3 . 
     At 1×2 device  302   2  in the second tier of the cascade, the seventh and eighth subsets of optical channels are received at respective second distal end ports of 2×2 device  324   3  and  324   2 . The seventh subset of optical channels, including λ 5 B and λ 1 B, backward propagates through 2×2 device  324   3 , is output on a proximal end port of 2×2 device  324   3 , and is carried by bidirectional optical path  325  in the backward direction to the second distal end port of 2×2 device  324   1 . Similarly, The eighth subset of optical channels, including λ 7 B and λ 3 B, backward propagates through 2×2 device  324   2 , is output on a proximal end port of device  324   2 , and is carried by bidirectional optical path  323  in the backward direction to the first distal end port of 2×2 device  324   1 . As the seventh and eighth subsets backward propagate, 2×2 device  324   1  multiplexes them into a eleventh subset of optical channels, including λ 1 B, λ 3 B, λ 5 B and λ 7 B, that is output on the first proximal end port of 2×2 device  324   1  and carried by unidirectional optical path  317  in the backward direction to the first distal end port of 2×2 device  315   3  in the 1×2 optical device  302   1 . 
     At 1×2 device  302   3  in the second tier of the cascade, the ninth and tenth subsets of optical channels are received at respective second distal end ports of 2×2 device  331   3  and  331   2 . The ninth subset of optical channels, including λ 6 B and λ 2 B, backward propagates through 2×2 device  331   3 , is output on a proximal end port of 2×2 device  331   3  and is carried by bidirectional optical path  335  in the backward direction to the second distal end port of 2×2 device  331   1 . Similarly, The ninth subset of optical channels, including λ 8 B and λ 4 B, backward propagates through 2×2 device  331   2 , is output on a proximal end port of device  331   2 , and is carried by bidirectional optical path  333  in the backward direction to the first distal end port of 2×2 device  331   1 . As the ninth and tenth subsets backward propagate, 2×2 device  331   1  multiplexes them into a twelfth subset of optical channels, including λ 2 B, λ 4 B, λ 6 B and λ 8 B that is output on the first proximal end port of 2×2 device  331   1  and carried by unidirectional optical path  318  in the backward direction to the second distal end port of 2×2 device  315   2  in the 1×2 optical device  302   1 . 
     At 1×2 device  302   1  in the first tier of the cascade, the eleventh subset of optical signals received at the second distal end port of 2×2 device  315   3  backward propagates through 2×2 device  315   3 . The eleventh subset is output on a proximal end port of device  315   3 , and is carried by bidirectional optical path  313  in the backward direction to the second distal end port of 2×2 device  315   1 . Similarly, the twelfth subset of optical signals received at the first distal end port of 2×2 device  315   2  backward propagates through 2×2 device  315   2 . The twelfth subset is output on a proximal end port of device  315   2 , and is carried by bidirectional optical path  311  in the backward direction to the first distal end port of 2×2 device  315   1 . The 2×2 device  315   1  multiplexes the eleventh and twelfth subsets of optical signals into an output WDM signal that is output on the second proximal end port of 2×2 device  315   1  on optical path  309  in the backward direction. The output WDM signal has eight channels—λ 1 B through λ 8 B—as shown in FIG.  3 . 
     Therefore in the backward direction, in accordance with the invention, an output WDM signal is multiplexed from eight optical channels λ 1 B through λ 8 B that are received at the distal end of the third tier as discrete optical channels on respective unidirectional optical paths  347 ,  349 ,  357 ,  359 ,  367 ,  369 ,  377  and  379 ) as the optical channels backward propagate through the bidirectional 1×8 demultiplexer, 8×1 multiplexer  300 . In the third tier of the cascade (i.e., 1×2 devices  302   4,5,6 7 ) the received optical channels are multiplexed into two odd channel subsets and two even channel subsets in the respective 1×2 devices in the third tier. In this illustrative example, each subset contains two optical channels. Thus, the third tier of the cascade operates to output, at the proximal end of the third tier, four subsets of optical channels each having double the channel count of the discrete input signals received at the third tier&#39;s distal end. In the second tier of the cascade (i.e., 1×2 devices  302   2, 3 ), the received subsets of optical channels are multiplexed into one odd channel and one even channel subset in the respective 1×2 devices  302   2  and  302   3 . In this illustrative example, each subset generated by the second tier contains four optical channels. Thus, the second tier of the cascade operates to output, at the proximal end of the second tier, a pair of optical subsets each having double the channel count of the input subsets received at the distal end of the cascade&#39;s second tier. The odd and even optical channels subsets are each multiplexed in the 1×2 device  302   1  in the first tier of the cascade to double channel count again and generate the output WDM signal that is output at the proximal end of the cascade&#39;s first tier on optical path  309 . In some applications of the invention, the channel spacing may thus be halved as the optical subsets backward propagate from the third tier to the second tier to the first tier of the cascade forming the bidirectional 1×8 demultiplexer, 8×1 multiplexer  300 . 
     It will be appreciated that the inventive arrangement may be generalized for applicability to any desired optical channel count. That is, a bidirectional 1×N demultiplexer, N×1 multiplexer (where N is the optical channel count) may be implemented, in accordance with the invention, by a cascade of (N−1) 1×2 devices having m tiers where 2 m =N. The 1×2 devices may each be similar to that shown in FIG.  1  and described in the accompanying text. 
     Each successive tier includes twice as many 1×2 devices as in the preceding tier. That is, the first tier includes one 1×2 device, the second tier includes two 1×2 devices and the m th  tier includes 2 (m−1)  1×2 devices. Therefore, for example, to create an N=16 bidirectional multiplexer, demultiplexer, 15 1×2 devices are used in a four-tiered configuration. The first tier includes one 1×2 device, the second tier includes two 1×2 devices, the third tier includes four 1×2 devices, and the fourth tier includes eight 1×2 devices. Likewise, an N=32 bidirectional multiplexer, demultiplexer would include 31 1×2 devices arranged in a five-tiered cascade. 
     Each 1×2 device in a tier is optically coupled to two 1×2 devices in the successive tier. In the forward direction, an input optical signal received at the proximal end of each 1×2 device is multiplexed into two separate output subsets of optical signals at the distal end of the 1×2 device. One of the output subsets becomes an input signal to one of the coupled 1×2 devices in the successive tier, and the other output subset becomes an input signal to the other coupled 1×2 device in the successive tier. Thus, in the forward direction, at each m th  tier of the cascade, 2 (m−1)  subsets of optical channels are received at the proximal end of the tier, and 2 m  subsets of optical channels are output at the distal end of the tier. In applications of the invention, as the optical signals propagates from tier to tier in the forward direction the channel spacing in each output subset approximately doubles until the last tier at the distal end of the cascade is reached where N optical subsets are output where each subset includes a single optical channel. 
     In the backward direction, two separate input subsets of optical signals are received at the distal end of each 1×2 device in each given tier of the cascade. Each 1×2 device multiplexes the two input subsets into a single output subset. The output subset becomes an input subset to the first one of the distal end ports of a 1×2 device in a preceding tier. A second 1×2 device in the given tier provides the input subset to the second distal end port of the 1×2 device in the preceding tier. Thus, in the backward direction, at each m th  tier of the cascade, 2 m  subsets of optical channels are received at the distal end of the tier, and 2 (m−1)  subsets of multiplexed optical channels are output at the proximal end of the tier. In applications of the invention, as the signal propagates from tier to tier in the backward direction, the channel spacing in each output subset is approximately halved until the first tier at the proximal end of the cascade is reached where a single output WDM signal is output from the bidirectional 1×N demultiplexer, N×1 multiplexer. 
     Other embodiments of the invention may be implemented in accordance with the claim that follow.