RU2346309C1 - Optical signal switching unit - Google Patents

Abstract

FIELD: physics; optics.

SUBSTANCE: invention relates to optical data encoding, decoding and transmitting devices, in particular, to optical signal switching devices used in computer networks. Switching device comprises 4N of logical units, N=2, 3, 4, …. Logical unit comprises inputs/outputs from the first to the fifth one. The first input/output of the J-th, J=1, 2, …, 4N, logical unit is input/output of the J-th channel of the switching device. The second input/output of logical unit 1, 3, 5, …, 4N-1 is connected to the second input/output of logical unit 2, 4, 6, …, 4N, respectively. The third input/output of logical unit 2, 4, 6 … 4N-2, 4N is connected to the third input/output of logical unit 3, 5, 7, …, 4N-1, 1, respectively. The fourth input/output of logical unit 1, 2, 5, 6, 9, 10, …, 4N-3, 4N-2 is connected to the fourth input/output of logical unit 3, 4, 7, 8, 11, 12, …, 4N-1, 4N, respectively. The fifth input/output of logical unit 3, 4, 7, 8, 11, 12, …, 4N-1, 4N is connected to the fifth input/output of logical unit 5, 6, 9, 10, 13, 14, …, 1, 2, respectively.

EFFECT: simplified optical signal switching device and enhanced functional capabilities thereof.

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Description

The present invention relates to devices for encoding, decoding and transmitting data represented by optical signals, in particular to optical signal switches used in computer networks.

Known wave filter switch optical signals [1], containing the first and second optical fibers, forming in a limited area fused and stretched twisted pair. The first input-output of the first optical fiber is the first multiplexed input-output of the switch. The second input-output of the first optical fiber is the first demultiplexed input-output of the switch. The first input-output of the second optical fiber is the second multiplexed input-output of the switch. The second input-output of the second optical fiber is the second demultiplexed input-output of the switch. The wave filter filter of optical signals [1] allows you to multiplex and demultiplex bi-directional optical signals with different wavelengths.

The disadvantage of the device [1] are limited functionality. In particular, it is impossible to switch optical signals between the first and second multiplexed or demultiplexed inputs / outputs. This does not allow using it as a central switching link when building a computer network with a star topology.

A well-known optical signal switch [2], containing 4N logical blocks, N = 2, 3, 4, ..., the logical block contains the first - fifth inputs-outputs, the first input-output of the J-th, J = 1, 2, ..., 4N , the logical block is the input-output of the J-th channel of the switch. The logic unit is configured to transmit optical signals in certain directions. In particular, it can be configured to transmit signals in a computer network with a ring logical structure and star topology.

The disadvantages of the switch [2] are complexity and limited functionality.

The first drawback is the use of a matrix of mirrors with controlled transparency. Amplifiers are needed to compensate for signal attenuation in a chain of mirrors. Mirror transparency can be controlled manually when configuring the system or remotely. The latter option implies the availability of software-accessible controls (for example, based on a microprocessor with appropriate software); in any case, the switch must have the means to supply voltage to it, which leads to its additional complication and degrades performance.

The second disadvantage is that only one channel is used to transmit data in each direction.

The purpose of the invention is to simplify the switch and expand its functionality.

The goal is achieved by the fact that in the optical signal switch containing 4N logical blocks, N = 2, 3, 4, ..., the logical block contains the first - fifth inputs-outputs, the first input-output of the J-th, J = 1, 2, ... , 4N, of the logical block is the input-output of the J-th channel of the switch, the second input-output of the logical block with the numbers 1, 3, 5, ..., 4N-1 is connected respectively to the second input-output of the logical block with the numbers 2, 4, 6 , ..., 4N, the third input-output of the logic block with the numbers 2, 4, 6, ..., 4N-2, 4N is connected respectively to the third input-output of the logic block with the numbers 3, 5, 7, ..., 4N -1, 1, the fourth input-output of the logic block with the numbers 1, 2, 5, 6, 9, 10, ..., 4N-3, 4N-2 is connected respectively to the fourth input-output of the logic block with the numbers 3, 4, 7 , 8, 11, 12, ..., 4N-1, 4N, the fifth input-output of the logic block with the number 3, 4, 7, 8, 11, 12, ..., 4N-1, 4N is connected respectively to the fifth input-output of the logical block number 5, 6, 9, 10, 13, 14, ..., 1, 2, the logic block contains the first - third wave filters, the multiplexed input-output of the first wave filter is the first input-output of the logic block, the first and second demultiplexed inputs the outputs of the first wave filter are connected respectively to the multiplexed inputs and outputs of the second and third wave filters, the first and second demultiplexed inputs and outputs of the second wave filter are the fifth and fourth inputs and outputs of the logic unit, the first and second demultiplexed inputs and outputs of the third wave filter respectively, the third and second inputs-outputs of the logic block, the first and third wave filters of the logical block are respectively waves and filtering the first - third types.

In the proposed optical signal switcher, wave filters of the first and third types operate with optical signals with wavelengths numbered in the form of a series λ1, λ2, λ3, ..., the wavelength increases uniformly as its number increases, the multiplexed input-output of the wave filter of the first type is transparent to optical signals with wavelengths with the numbers λ1, λ2, λ3, ..., the first demultiplexed input-output of the wave filter of the first type is transparent for optical signals with wavelengths with the numbers λ1, λ3, λ5, ... and opaque optical signals with wavelengths with numbers λ2, λ4, λ6, ..., the second demultiplexed input-output of the wave filter of the first type is transparent for optical signals with wavelengths with numbers λ2, λ4, λ6, ... and opaque for optical signals with wavelengths with numbers λ1, λ3, λ5, ..., the multiplexed input-output of the wave filter of the second type is transparent for optical signals with wavelengths with numbers λ1, λ3, λ5, ..., the first demultiplexed input-output of the wave filter of the second type is transparent for optical signals with wavelengths with numbers λ1, λ5, λ9, ... and opaque for optical signals with wavelengths with the numbers λ3, λ7, λ11, ..., the second demultiplexed input-output of the wave filter of the first type is transparent for optical signals with wavelengths with the numbers λ3, λ7, λ11, ... and opaque for optical signals with wavelengths with the numbers λ1, λ5, λ9, ..., the multiplexed input-output of the wave filter of the third type is transparent for optical signals with wavelengths with the numbers λ2, λ4, λ6, ..., the first demultiplexed input-output of the wave filter third type is transparent to optically signals with wavelengths λ2, λ6, λ10, ... and opaque for optical signals with wavelengths λ4, λ8, λ12, ..., the second demultiplexed input-output wave filter of the third type is transparent for optical signals with wavelengths with numbers λ4 , λ8, λ12, ... and is opaque for optical signals with wavelengths with numbers λ2, λ6, λ10, ....

Figure 1 presents a simplified sketch of the design of the known [1] wave filter; on figa - transparency diagram of the wave filter F1 of the first type; on figb - transparency diagrams of wave filters F2 and F3 of the second and third types; on figa-z and figa - examples of paths of transmission of optical signals through a wave filter of the first type; on figb - an example of the inclusion of a filter of the first type in a data transmission system. Figure 5 presents the most common options for the topology of computer networks; figure 6 is a functional diagram of the proposed switch optical signals; 7 is a functional diagram of a logical block.

The wave filter 1 (Fig. 1) is designed to separate (sort) a group of signals by wavelengths. It is built on the basis of a specially twisted and fused with the simultaneous stretching of the melt optical fibers 2 and 3 [1]. Hereinafter, depending on the setting of the physical parameters of the filter during its manufacture, it is designated F1, F2 or F3 (filter of the first to third type). In any case, the filter is symmetrical in the sense that the pairs of its terminals X-W, W-X, Y-Z and Z-Y are functionally equivalent. However, to streamline the terminology, conclusions 4 - X and W are hereinafter referred to as the first and second multiplexed filter inputs / outputs, respectively. Similarly, pins 5 - Y and Z are referred to as the first and second demultiplexed filter inputs / outputs, respectively.

Depending on the parameters of twisting, melting and stretching of the optical fibers during the manufacture of the filter, it acquires selective transparency with respect to the transmission of light signals of certain wavelengths. In other words, the filter can in some way sort the input stream of “multi-colored” infrared light signals arriving from the outside in arbitrary combinations to pin X (to any of the four pins). The signals are assumed to have wavelengths λ1, λ2, ..., λ16 uniformly distributed on the horizontal numerical axes of the transparency diagrams shown in FIG. 2. Adjacent wavelengths are separated by gaps of 100 nm or more (the number of wavelengths used may exceed 16).

Graphs 6 and 7 (figa) display the transparency diagrams of the channels X-Y and X-Z filter F1. Since the filter is symmetrical, the same graphs respectively display the transparency diagrams of the W-Z and W-Y channels, as well as the two remaining channels obtained by mutually reverse substitution of the X, W symbols with the Y, Z symbols. The 0 and 100% levels correspond to the opaque and completely transparent channel states. The graphs for their simplification are represented by two antiphase sinusoids, although in reality their shape is more complex and depends on the filter manufacturing technology. From graph 6 it follows that the X-Y channel (as well as the W-Z channel) of the F1 filter is transparent to light with wavelengths λ1, λ3, λ5, ..., λ15 and opaque to light with wavelengths λ2, λ4, λ6, ..., λ16. If the channel is transparent, then light of the corresponding wavelengths can be transmitted through it in either or simultaneously in both directions. An opaque channel does not transmit light of the corresponding wavelengths in any direction.

Figure 7 shows that the X-Z channel (as well as the W-Y channel) of the F1 filter is transparent to light with wavelengths λ2, λ4, λ6, ..., λ16 and opaque to light with wavelengths λ1, λ3, λ5, ..., λ15.

Graphs 8 and 9 (fig.2b) display the transparency diagrams of the channels X-Y and X-Z (W-Z and W-Y) of the filter F2. They are represented by sinusoids with doubled periods compared to graphs 6 and 7. From graph 8 it follows that the X-Y channel of the F2 filter is transparent to light with wavelengths λ1, λ5, λ9, λ13 and opaque to light with wavelengths λ3, λ7, λ11, λ15. Graph 9 is out of phase with graph 8 and displays the transparency diagram of channel X-Z of filter F2. The transparency of the X-Y and X-Z channels (W-Z and W-Y) of the F2 filter with respect to light signals with wavelengths λ2, λ4, λ6, ..., λ16 is undefined, but such signals do not arrive at this filter during its operation.

Graphs 10 and 11 (figb) display the transparency diagrams of the channels X-Y and X-Z (W-Z and W-Y) of the filter F3. They are represented by sinusoids of the same frequency as sinusoids 8 and 9, but are shifted relative to them in phase to the right by a quarter of the period. From graph 10 it follows that the X-Y channel of the F3 filter is transparent to light with wavelengths λ2, λ6, λ10, λ14 and opaque to light with wavelengths λ4, λ8, λ12, λ16. Graph 11 is out of phase with graph 10 and displays the transparency diagram of channel X-Z of filter F3. The X-Z channel of the F3 filter is transparent to light with wavelengths λ4, λ8, λ12, λ16 and opaque to light with wavelengths λ2, λ6, λ10, λ14. The transparency of the channels X-Y and X-Z (W-Z and W-Y) of the filter F3 with respect to light signals with wavelengths λ1, λ3, λ5, ..., λ15 is uncertain, but such signals do not arrive at this filter during its operation.

Examples of 12-17 paths of the passage of optical signals through the wave filter F1 (Fig.3, a-e) show the propagation of a group of light signals through the filter from left to right, from right to left and simultaneously in both directions. In these examples, one of the filter pins is not used.

In examples 18-20, shown in Fig.3g, h and Figa used all the conclusions of the filter F1.

Examples 18 and 19 show the possibility of using the filter F1 to interface unidirectional transmission lines of optical signals with bidirectional.

In example 18, the optical signal supplied to the input X on the left side contains 16 components with wavelengths λ1-λ16. The signal taken from the output of the filter W also contains 16 components with the same wavelengths λ * 1-λ * 16. The signs "*" indicate that the signals arrived at the inputs of the filter F1 on the right side. At the input-output Y, signals with wavelengths λ1, λ3, λ5, ..., λ15 propagate to the right, and signals with wavelengths λ * 2, λ * 4, λ * 6, ..., λ * 16 - to the left. At the input / output Z, signals with wavelengths λ2, λ4, λ6, ..., λ16 propagate to the right, and signals with wavelengths λ * 1, λ * 3, λ * 5, ..., λ * 15 - to the left.

Example 19 differs from example 18 in the directions of signal transmission through the terminals X and W of filter F1.

In example 20 (figa) all connected to the filter F 1 lines are bidirectional. On each line 16 pairs of oppositely directed optical signals are transmitted, each pair has the same wavelength. Essentially, this circuit is a non-connected switch capable of transmitting data in the directions: X → Y, X → Z, W → Y, W → Z, Y → X, Y → W, Z → X, Z → W. To select the direction of transmission (routing the information packet), the data source uses wavelengths with even or odd numbers. For example, an external source of the signal supplied to the input-output Z of the filter F1, wishing to transmit a message to the communication line connected to the inputs-outputs X or W, can use light pulses for this purpose with the corresponding wavelengths λ * 6 or λ ″ 15.

Direct data transfer in adjacent directions X → W, W → X, Y → Z, Z → Y is impossible. If there is an intermediary device 21 (Fig. 4b), such transfers are feasible. For example, an external source of the signal supplied to the input-output Z of the filter F, wanting to transmit a message to the communication line 22 connected to the inputs / outputs Y, can use light pulses with a wavelength of λ * 8 for this. These pulses pass to the input-output X and are received by the device Q (21). According to preliminary "agreement" with this device, it immediately delivers the received pulses back to the input-output X, but uses light with a wavelength of λ13 for this. Filter F1 transfers these pulses to input-output Y, as required.

The above examples (they can be extended to filters of other types, taking into account their transparency diagrams) show the previously mentioned limited capabilities of the filter [1] when it is used as a functionally complete switch of optical signals in a computer network.

Figure 5 presents the most common options for the topology of computer networks. The topology of the type of "common bus" (figa) is used mainly in local networks of early generations. Coaxial cables are commonly used as signal transmission medium. The use of fiber-optic communication lines within the framework of this topology is difficult, since it is necessary to install optical splitters to connect each node 23 to a common trunk 24. This is not technologically advanced, in addition, each splitter divides the energy of the signal arriving at it into two parts, so that the levels of the received signals depend from the relative position of the transmitter and receiver.

The topology of the star type with a common hub 25 (Fig.5b) suggests the presence of radial connections between the hub and nodes 26 of the network. The concentrator summarizes all the optical signals entering it, distributes the total signal evenly between all channels, if possible, and simultaneously transmits it in the opposite directions. Some hubs operate on the principle of distributing the input signal between all channels except for their own, which facilitates the detection of collisions while simultaneously addressing two or more nodes 26 to a common signal transmission medium.

The main disadvantage of this structure is that the input signal power is divided by the number of channels reaching one hundred or more. To restore the levels of the output signals, active concentrators are used, which are able to enhance the power of the light fluxes emitted by them in all directions. This complicates the structure of the hub and requires a power source.

In a network with a ring topology (Fig. 5c), the nodes 27 are connected in a series closed circuit. The disadvantages inherent in the previously discussed networks (figa, b), in this case are absent. Each node suspends the distribution of information packets addressed to it and transmits “foreign” packets to the next node.

In the event of a failure of a node, the main direction of packet transmission, having reached the node closest to it, can be reversed, so that all nodes that are still operational are accessible. In order to preserve the possibility of bi-directional data transmission in a ring in case of failure of one of the nodes, this node is automatically or manually excluded from operation, and optical communication lines broken by such a failure are connected directly. In this case, the connecting element introduces losses in the transmission of the signal, in addition, the length of the newly created communication line becomes equal to the sum of the lengths of communication lines that previously connected the failed node to the neighboring ones.

This disadvantage is absent in the network with combined topology (Fig.5g). Outwardly, it resembles the previously considered network with a star topology (Fig. 5b), but instead of a hub 25, it uses a switch 28 connected to nodes 29. Unlike a hub, the switch 28 is capable of combining optical fibers connecting it with nodes 29. For example, inside the switch, you can create connections in which the network has a ring logical structure similar to that shown in Fig. 5c. Arrows 30 in FIG. 5g correspond to data packet transmission routes between nodes 29. As follows from the above diagram, packet transmission between nodes 29 occurs essentially along arrows 31, as in a network with a ring topology.

In redundant ring networks, isolation and bypass of one or more faulty nodes 29 is carried out by the corresponding adjustment of the internal circuits of the switch 28 and does not directly affect the network nodes and communication lines.

The switch 32 [2] (Fig.5d) contains the logical blocks 33, the logical block contains the external 34 and the internal 35 inputs / outputs, the external input-output 34 of the logical unit 33 is the input-output of the corresponding channel of the switch and connected to the corresponding node 36 of the network. Internal inputs and outputs 35 of the logical blocks 33 are connected to the optical switching matrix 37.

Logic blocks 33 can be configured to transmit signals between nodes 36 in a ring pattern, as shown in FIG. Settings are possible that provide logical isolation and bypass of faulty nodes 36 or communication lines with these nodes.

The proposed optical signal switch, shown in Fig.6 (on the example of an eight-channel option, N = 2), contains 4N = 8 logical blocks 38-45, each logical block contains the first - fifth 46-50 inputs / outputs, the first input-output 46 the first to fifth logical blocks 38-45 is respectively the input-output of the first to fifth channels of the switch.

The second input-output 47 ("a") of the logical blocks 38, 40, 42 and 44 with numbers J = 1, 3, 5, 7 is connected respectively to the second input-output 47 ("a") of the logical blocks with the number 39, 41 , 43 and 45 with numbers J = 2, 4, 6, 8. The third input-output 48 ("b") of logic blocks 39, 41, 43 and 45 with numbers J = 2, 4, 6, 8 is connected respectively to the third input-output 48 ("b") of logic blocks with numbers 40, 42, 44 and 38 with numbers J = 3, 5, 7, 1.

The fourth input-output 49 ("c") of the logical blocks 38, 39, 42, 43 with numbers 1, 2, 5, 6 is connected respectively to the fourth input-output 49 ("c") of the logical blocks 40, 41, 44, 45 with numbers 3, 4, 7, 8, the fifth input-output 50 ("d") of the logic blocks 40, 41, 44, 45 with numbers 3, 4, 7, 8 are connected respectively with the fifth input-output 50 ("d" ) logical blocks 42, 43, 38, 39 with numbers 5, 6, 1, 2.

The logic block 38-45 (Fig.7) contains the first - third 51-53 wave filters, the multiplexed input-output 54 of the first wave filter 51 is the first input-output 46 of the logical block, the first 55 and second 56 demultiplexed inputs-outputs of the first wave filter 51 are connected respectively to the multiplexed inputs and outputs 57 and 58 of the second 52 and third 53 wave filters, the first 59 and second 60 demultiplexed inputs and outputs of the second wave filter 52 are respectively the fifth 50 and fourth 49 inputs and outputs of the logic of the first block, the first 61 and second 62 demultiplexed inputs and outputs of the third wave filter 53 are respectively the third 48 and second 47 inputs and outputs of the logic block, the first and third 51-53 wave filters of the logic block 38-45 are respectively wave filters of the first and third types (F1-F3, FIG. 1, FIG. 2).

The proposed switch can be used in redundant computer networks with a ring logical structure and topology of the "star" type (Fig.5g). Redundancy in this case involves logical isolation and bypassing faulty network nodes or communication lines with them.

When using the switch in a computer network, its nodes are connected to the inputs and outputs of 46 logical blocks 38-45. For convenience of presentation in Fig.6 and Fig.7, the fiber-optic communication channels of the switch with network nodes are indicated by the letters A, B, C, ..., N.

To exchange data between network nodes, optical signals with wavelengths λ1-λ16 uniformly distributed on the horizontal numerical axes of the diagrams shown in FIG. 2 are used.

Using the proposed switch, any network node has the ability to bidirectionally exchange data with both the two nearest neighboring network nodes located in the counterclockwise direction, and with the two nearest neighboring network nodes located in the clockwise direction.

So, for example, a node connected to channel D (Fig.6, Fig.7) can carry out bidirectional exchange of optical signals with a node connected to channel C via communication "a" - "a" using one or two, three or four wavelengths from the group λ4, λ8, λ12, λ16. The same node (D) can carry out a bidirectional exchange of optical signals with a node connected to channel E via the “b” - “b” connection using one or two, three or four wavelengths from the group λ2, λ6, λ10, λ14.

A network node connected to channel D can bypass nodes C or E (for example, in case of failure of one or the other) to exchange data bilaterally with nodes connected to channels B or F.

So, bidirectional exchange of optical signals between channels D and B is carried out by communication “c” - “c” between logic blocks 41 and 39 using one or two, three or four wavelengths from the group λ3, λ7, λ11, λ15. Similarly, bidirectional exchange of optical signals between channels D and F is carried out via the “d” - “d” communication between logic blocks 41 and 43 using one or two, three or four wavelengths from the group λ1, λ5, λ9, λ13.

The application of the proposed switch of optical signals makes it possible to simplify the construction of networks with a logical structure of the ring type and star topology. Due to the possibility of using several wavelengths, parallelization of data streams is implemented. The switch operates without a power source. The route of the data packet transmitted by the network node is specified at the physical (and not at the network) level by selecting the wavelength of the linear signal.

Information sources

1. US Patent No. 5809190 (Fig. 5).

2. US Patent No. 6,134,357 (Fig. 4) (prototype).

Claims (2)

1. An optical signal switch containing 4N logical blocks, N = 2, 3, 4, ..., the logical block contains the first - fifth inputs / outputs, the first input-output of the J-th, J = 1, 2, ..., 4N, logical block is the input-output of the J-th channel of the switch, characterized in that the second input-output of the logical block with the numbers 1, 3, 5, ..., 4N-1 is connected respectively to the second input-output of the logical block with the numbers 2, 4, 6 , ..., 4N, the third input-output of the logic block with the numbers 2, 4, 6, ..., 4N-2, 4N is connected respectively to the third input-output of the logic block with the numbers 3, 5, 7, ..., 4N-1, 1 h the fourth input-output of the logic block with the numbers 1, 2, 5, 6, 10, 11, ..., 4N-3, 4N-2 is connected respectively to the fourth input-output of the logic block with the numbers 3, 4, 7, 8, 11, 12, ..., 4N-1, 4N, the fifth input-output of the logical block with the number 3, 4, 7, 8, 11, 12, ..., 4N-1, 4N is connected respectively to the fifth input-output of the logical block with the number 5, 6, 9, 10, 13, 14, ..., 1, 2, the logic block contains the first - third wave filters, the multiplexed input-output of the first wave filter is the first input-output of the logic block, the first and second demultiplexed inputs The first wave filter is connected respectively to the multiplexed inputs and outputs of the second and third wave filters, the first and second demultiplexed inputs and outputs of the second wave filter are the fifth and fourth inputs and outputs of the logic unit, the first and second demultiplexed inputs and outputs of the third wave filter, respectively the third and second inputs and outputs of the logic block, the first and third wave filters of the logic block are respectively wave phi liters of the first - third types. 2. The optical signal switch according to claim 1, characterized in that the wave filters of the first to third types operate with optical signals with wavelengths numbered in the form of a series of λ1, λ2, λ3, ..., the wavelength increases uniformly as its number increases, multiplexed the input-output of the wave filter of the first type is transparent for optical signals with wavelengths λ1, λ2, λ3, ..., the first demultiplexed input-output of the wave filter of the first type is transparent for optical signals with wavelengths λ1, λ3, λ5, ... and not about transparent for optical signals with wavelengths λ2, λ4, λ6, ..., the second demultiplexed input-output of the wave filter of the first type is transparent for optical signals with wavelengths with numbers λ2, λ4, λ6, ... and opaque for optical signals with wavelengths with numbers λ1, λ3, λ5, ..., the multiplexed input-output of the wave filter of the second type is transparent for optical signals with wavelengths with the numbers λ1, λ3, λ5, ..., the first demultiplexed input and output of the wave filter of the second type is transparent for optical signals with lengths at ln with numbers λ1, λ5, λ9, ... and is opaque for optical signals with wavelengths with numbers λ3, λ7, λ11, ..., the second demultiplexed input-output of the wave filter of the first type is transparent for optical signals with wavelengths with numbers λ3, λ7, λ11, ... and opaque for optical signals with wavelengths λ1, λ5, λ9, ..., the multiplexed input-output of a wave filter of the third type is transparent for optical signals with wavelengths with numbers λ2, λ4, λ6, ..., the first demultiplexed input the output of the wave filter of the third type is transparent to For optical signals with wavelengths λ2, λ6, λ10, ... and opaque for optical signals with wavelengths λ4, λ8, λ12, ..., the second demultiplexed input-output wave filter of the third type is transparent for optical signals with wavelengths with numbers λ4, λ8, λ12, ... and opaque for optical signals with wavelengths with numbers λ2, λ6, λ10, ....

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