Title: lnterferometric element, interferometric N-stage tree element, and method of processing a first optical input signal and a second optical input signal so as to provide a plurality of orthogonal output signals.

DESCRIPTION

According to a first aspect, the present invention relates to an interferometric element comprising a first interferometer of the Mach-Zehnder type and a second interferometer, said first interferometer comprising a first input coupling element and a first output coupling element, and said second interferometer comprising a second input coupling element and a second output coupling element, said input coupling elements being optically connected to the output coupling elements by means of transmission lines, while at least one of the transmission lines in the interferometric element is designed for providing an additional frequency-independent phase shift.

According to a second aspect, the invention relates to a method of processing a first optical input signal and a second optical input signal so as to provide a plurality of orthogonal output signals.

Code Division Multiple Access (CDMA) is a widely used method of distinguishing individual signals carried on a common optical fiber or common optical channel. In such a system, each signal is convolved with an orthogonal code so as to provide an orthogonal coded optical signal that can be distinguished from other orthogonal coded optical signals. This makes it possible to have the optical signals propagate asynchronously through the common fiber without the individual optical signals interfering with one another.

In the case of incoherent spectrally coded optical CDMA, the spectrum of a wide-spectrum source, for example a light-emitting diode (LED), is guided through a filter for coding the signal. By using different filter settings for each user orthogonal coded optical spectra can be obtained.

Various filtering techniques are used for this, among which the use of integrated Mach-Zehnder cascade chains. Such a chain consists of a plurality of interferometers of the Mach-Zehnder type connected to one another, wherein the delayed branch of each of the Mach-Zehnder interferometers is provided, for example, with an additional, frequency-independent phase rotation that may be

specific to each link in the chain. Such a cascade chain is disclosed, for example, in "Multi-wavelength optical code-division-multiple-access communication systems" by Cedric Fung Lam, thesis published in 1999, University of California, Los Angeles, figure 3.6. Two complementary orthogonal spectrally coded optical signals, i.e. one signal pair, can be obtained from a single input signal by means of such a cascade chain. These orthogonal optical signals, which are obtained at the output, may be used for optically coding a binary user signal.

If a plurality of binary user signals is to be transmitted over the same channel simultaneously in parallel, and should accordingly be orthogonally coded, a plurality of cascade chains is used which are arranged in parallel to one another. In other words, two cascade chains can be used for obtaining two orthogonal coded optical signal pairs, three cascade chains are needed for obtaining three orthogonal coded optical signal pairs, etc. In addition, the phase shifts used in the cascade chains should mutually be tuned to each other such that all output signals obtained from the plurality of cascade chains are orthogonal to one another.

Figure 5 shows a Mach-Zehnder cascade chain according to the prior art, comprising two optical inputs 130 and 131. Generally an optical signal will be provided to at least one of the optical inputs 130, 131 , and a portion of this optical signal will be split off in the coupling element 132 such that identical optical signals, but phase-shifted with respect to one another, will be present in the two branches 140 and 141. Behind the coupling element 132 in this two-stage cascade chain there are two interferometers 135 and 136 of the Mach-Zehnder type. The first interferometer 135 comprises, as described above, a non-delayed branch 140 and a delayed branch 141 , said delayed branch 141 having a greater optical path length than the non-delayed branch 140. In particular, the non-delayed branch 140 has an optical path length L, whereas the delayed branch 141 has an optical path length L + δL1. Furthermore, there is an additional phase-shifting element 142 on the delayed arm 141 , which element shifts the phase of the signal on the delayed arm 141 by means of a frequency-independent phase rotation φ1. The optical signals thus obtained are coupled into the coupling element 144 for exchanging optical energy between the optical signals and obtaining interference. The two outputs of the coupling element 144 are coupled into the second cascade element 136 of the Mach-Zehnder type, comprising a non-delayed branch 150 and a delayed branch 151. The delayed branch 151 in the second

cascade element has an optical path length L + δL2 and the non-delayed branch 150 again has an optical path length L. An additional frequency-independent phase shift of φ2 is applied to the optical signal in the delayed arm in a phase shifting element 152. The coupling element 154 couples the optical signals thus obtained so as to exchange optical energy between them and applies the interference signals thus obtained as output signals to the outputs 138 and 139 of the cascade element. The output signals E ₀₁ and E ₀₂ at the outputs 138 and 139 form a pair of orthogonal output signals. These output signals may be used for coding binary signals, for example with E ₀₁ representing a binary 0 and E ₀₂ a binary 1. The pair of orthogonal output signals is accordingly suitable for coding binary signals of one user.

It is possible in principle to provide four orthogonal signal pairs by means of a two-stage cascade element as shown in figure 5, depending on the values chosen for the frequency-independent phase shift in each stage. Four cascade chains are thus necessary for obtaining four signal pairs, whose phase rotation angles are suitably distributed, i.e. four two-stage cascade chains are needed for serving four users, one for each user.

A disadvantage of such a cascade configuration is that inputs and outputs are to be connected for each cascade chain, which requires a correspondingly large number of fiber-chip transitions. For example, if a number of x cascade chains are integrated on a single chip, a large number of input fibers are to be connected to the input of this chip. This is a disadvantage in the manufacture of such an integrated circuit, which considerably increases its production cost.

A further disadvantage arises when fibers of the arrangement of Mach-Zehnder cascade chains are to be connected. The fibers are to be either fused (spliced), or connected by means of connectors. Splicing of the fibers requires a high splitting factor, which is difficult to achieve and costly, while the use of connectors leads to additional coupling losses. Since the upper limit for the maximum practicable length of the chain is determined inter alia by the power losses in the chain, those skilled in the art will appreciate that higher power losses will lead to shorter chains. Because the number of available orthogonal codes is determined inter alia by the lengths of the chains, higher power losses form a direct disadvantage for the applicability of the cascade chains.

A further disadvantage of the use of the arrangement with several cascade chains is that a frequency-independent phase-shifting element is to be

included in each delayed branch of each cascade chain. Externally controllable or adjustable phase-shifting elements are often used. These are usually machine-set once during manufacture of the cascade chain. A cascade chain of 7 Mach-Zehnder interferometers is capable in principle of processing the signals of 128 users. This, however, requires 128 cascade chains with 7 Mach-Zehnder interferometers each. Each Mach-Zehnder interferometer comprises one frequency-independent phase- shifting element in its delayed branch, so that an arrangement of 128 7-stage cascade chains comprises a total of 7 x 128 = 896 frequency-independent phase- shifting elements, which all have to be externally controllable or adjustable. A yet further disadvantage is that the use of a plurality of cascade chains requires a correspondingly large amount of space.

Summarizing, the use of combinations of Mach-Zehnder cascade chains or the use of separate Mach-Zehnder cascade chains is relatively laborious and expensive. The large number of components required, furthermore, hampers the miniaturization of such a code generator. An alternative solution is accordingly desirable.

US patent application US 2002/0,159,684 discloses an optical signal switch made up of four Mach-Zehnder interferometers (MZIs). Each MZI comprises a modulation electrode on one of the transmission lines between the input and output coupling elements, which enables frequency-independent phase rotation of the signal. The outputs of a first pair of MZIs are connected to the inputs of a second pair of MZIs, whilst each of the two outputs of each MZI of the first pair is connected to an input of one of the inputs of an MZI of the second pair. An optical signal incident on an input of one of the MZIs can be coupled to an output of one of the MZIs of the second pair in dependence on an electric signal on the modulation electrodes. Said element cannot be used for coding optical signals in a CDMA environment. It only provides a possibility of switching optical signals. Furthermore, a comparatively large number of Mach-Zehnder interferometers are required for achieving the effects aimed at in US 2002/0,159,684. It is an object of the present invention to provide an interferometric element with which the above disadvantages can be eliminated and in which power losses can be reduced to a minimum.

According to the present invention, this object is achieved in that it provides an interferometric element comprising a first interferometer of the Mach-

Zehnder type and a second interferometer of the Mach-Zehnder type, said first interferometer comprising a first input coupling element and a first output coupling element, and said second interferometer comprising a second input coupling element and a second output coupling element, said input coupling elements being optically connected to the output coupling elements by means of transmission lines, such that for each of the output coupling elements at least one delayed transmission line from among the respective associated transmission lines is designed for providing a frequency-dependent phase shift that differs from the frequency- dependent phase shift of the or each of the other, non-delayed transmission lines connected to the relevant output coupling element, while at least one of the transmission lines in the interferometric element is designed for providing an additional frequency-independent phase shift, wherein the first and the second interferometer are optically coupled to one another cross-wise such that at least one transmission line of the first input coupling element is connected to the second output coupling element, and that at least one transmission line of the second input coupling element is connected to the first output coupling element.

The present invention is based on the insight that the number of input signals can be reduced in a simple manner through the use of at least two interferometers of the Mach-Zehnder type optically connected in parallel, an input signal being conducted through each of the interferometers of the Mach-Zehnder type. Such an interferometric element may be used, similar to the cascade element from the prior art, for obtaining orthogonal optical signal pairs at the outputs of the interferometric element. It is possible for this purpose to apply, for example, one input signal and a complex complementary identical input signal to the inputs of the interferometric element.

It is essential for a good operation of the interferometric element according to the invention that the signals applied to the first and the second Mach- Zehnder interferometer should be coupled cross-wise internally, such that at least one transmission line of the first input coupling element is connected to the second output coupling element, and that at least one transmission line of the second input coupling element is connected to the first output coupling element. It is achieved thereby that as a result of "cross-fertilization", the full spectral width remains available at the outputs of the interferometric element, so that it becomes possible to use the interferometric element according to the invention in a tree structure in

accordance with a further embodiment that will be described further below.

If the cross-wise coupling between the signals in the element is not present, part of the spectrum will be filtered out in each of the branches of the interferometric element. Each output signal in that case comprises a portion of the full spectrum of the input signal, but not the whole spectrum. The element may operate as a multiplexer-demultiplexer without the internal cross-wise coupling of signals, which hampers a good operation of the interferometric element as a coding device.

A further advantage of the interferometric element according to the present invention is that four orthogonal output signals, i.e. two orthogonal signal pairs, can be obtained with the use of a single frequency-independent phase-shifting element. This renders the interferometric element according to the present invention highly suitable for use as a building block for a coding device, as will be described further below. If so desired, several frequency-independent phase-shifting elements may obviously be included.

In a preferred embodiment of the present invention, the frequency- independent phase shift is provided by a phase-shifting element. This phase-shifting element may be similar to a phase-shifting element as known from the Mach- Zehnder cascade chain. The element need not necessarily be separately controlled, however: it may be a passive element. In a further embodiment, the phase-shifting element may be switchable for switching the frequency-independent phase shift on and off, or possibly for setting it once and for all.

It may be advantageous, furthermore, to include the phase-shifting element in at least one of the delayed transmission lines of the interferometric element, because this concentrates in a single branch all elements and characteristics of the interferometric element that are capable of causing inaccuracies in any way whatsoever in the output signals. This renders it possible for these inaccuracies to be compensated.

The delayed branches of each of the Mach-Zehnder interferometers accommodated in the interferometric element may consist of transmission lines whose length is greater than the length of a non-delayed transmission line, but alternatively a transmission line may be opted for that has a refractive index that is higher than the refractive index of the non-delayed transmission line. It should be noted that a phase shift obtained in this manner is frequency-dependent.

In an embodiment, the interferometric element comprises at least two non-delayed transmission lines and at least two delayed transmission lines. It can be ensured in this manner that the signal of a delayed transmission line is combined with the signal from a non-delayed transmission line at each of the output coupling elements of the Mach-Zehnder interferometer for the purpose of exchanging optical energy and of providing output signals from the output coupling element.

In particular, each output coupling element in an interferometric element according to the present invention is connected to transmission lines such that at least one signal from a delayed transmission line is combined with at least one signal from a non-delayed transmission line. Also, a plurality of transmission lines may be accommodated in the output coupling element, each of the transmission lines having a unique optical path length for providing a unique frequency-dependent phase shift. A frequency-independent phase shift may also be present on one or several of these transmission lines. It is noted in this connection that the introduction of a phase difference on the signal lines is important for generating interference.

In a preferred embodiment, each of the output coupling elements of the interferometric element has two inputs and each of the input coupling elements has two outputs. The interferometric element here comprises four transmission lines which are connected to the input coupling elements and the output coupling elements such that each output of the input coupling elements is connected to one input of the output coupling elements and that each input of the output coupling elements is connected to one output of the input coupling elements. In other words, each of the input coupling elements has two outputs for providing two optical signals. The outputs of each input coupling element are connected to transmission lines, so each input coupling element is connected to two transmission lines. These transmission lines are connected to the output coupling elements such that one of the two transmission lines connected to the first input coupling element is connected to the first output coupling element and the other one of the two transmission lines of the first input coupling element is connected to the second output coupling element. Similarly, one of the two transmission lines connected to the second input coupling element is connected to the first output coupling element and the other one of the two transmission lines of the second input coupling element is connected to the

second output coupling element. A connection has thus been created between the input and output coupling elements which is such that each input coupling element is connected to both output coupling elements by means of exactly one transmission line each time. It is noted in connection with the above that, according to the invention as described above, each output coupling element is connected to at least one delayed transmission line and to at least one non-delayed transmission line. As a result of this, four configurations of transmission lines between the input coupling elements and the output coupling elements are possible in a design in which two interferometers of the Mach-Zehnder type are present, i.e. comprising a first input coupling element and a second input coupling element, and a first output coupling element and a second output coupling element.

Table 1 lists these configurations under the Roman headings I, II, III and IV. The transmission lines between the various input coupling elements and output coupling elements are indicated as follows. The first input coupling element is denoted J ₁ , the second input coupling element is denoted i ₂ , the first output coupling element is denoted U ₁ , and the second output coupling element is denoted U ₂ . A transmission line between the first input coupling element and the second output coupling element is diagrammatically indicated with J ₁ - U ₂ . Delayed transmission lines are indicated with a d and non-delayed transmission lines with an n.

Tabel 1

The above is based on an embodiment in which the interferometric element comprises two Mach-Zehnder interferometers, a first Mach-Zehnder interferometer comprising a first input coupling element and a first output coupling element, and a second Mach-Zehnder interferometer comprising a second input coupling element and a second output coupling element.

According to a further embodiment, moreover, the interferometric element comprises at least two signal inputs of which at least one signal input is connected to the first input coupling element and of which at least one further signal input is connected to the second input coupling element. The function of the input coupling elements is primarily to split up the input signal into a suitable number of optical signals at the output of the input coupling element. Any suitable directional coupling element may be used in principle as the input coupling element. Since the interferometric element according to the invention comprises at least two Mach-Zehnder interferometers, and the input coupling element is to be connected to the at least two output coupling elements of the two Mach-Zehnder interferometers, it is necessary for the input coupling element to comprise at least one signal input and at least two outputs for connection to the transmission lines. In other words, any coupling element of the P times Q type may be used as the input coupling element, with P ≥ 1 and Q ≥ 2. An input coupling element of the 2 x 2 type will now be discussed in more detail by way of example. Such an input coupling element consists of two waveguides (for example two fibers) which lie against one another over a portion of their lengths, whereby a direct connection between the waveguides is created. In the case of two fibers, the sheaths of the two fibers may be removed in the area where the two fibers make contact with one another, such that the cores of the fibers lie against one another. Optical energy from the core of the one fiber can thus directly enter the core of the other fiber and vice versa. When traversing the joint between the cores of the fibers, the crossing optical signal will be phase-rotated by τr/2 in the present case as a result of the transition. Such an input coupling element is now connected such that the optical signal to be processed is applied to one of the signal inputs of the input coupling element, while no signal is present at the other signal input. A portion of the power of the applied optical signal in the one fiber, which forms the signal input, will accordingly be transmitted to the core of the other fiber in the input coupling element, the relevant portion of the optical signal being given a phase shift of τr/2. After the transition the two fibers also form the outputs of the input coupling element of the 2 x 2 type. As a result, the originally applied signal will be present at one of the two outputs of the input coupling element, while at the other output of the input

coupling element this same signal will be present, but with an additional phase shift of π/2.

As was described above, only one of the signal inputs of each input coupling element is actively engaged in receiving optical signals during operation of the interferometric element. Obviously, a plurality of optical signals may be offered to the signal inputs of an input coupling element if the input coupling element comprises more than one signal input, but the effect of such additional optical signals has not been investigated further, neither is the application of additional optical signals relevant to the correct operation of the interferometric element according to the invention. It is noted, however, that it is not excluded that the application of additional optical signals to the signal inputs of each of the input coupling elements may give rise to advantageous effects at the signal outputs of the interferometric element. An implementation thereof might be, for example, the application of signals of different wavelengths to the individual inputs. It is possible to code signals of different wavelengths simultaneously in this manner because of the periodicity of the element.

In a further embodiment, the interferometric element comprises at least 4 signal outputs of which at least two signal outputs are provided or are connected to the first output coupling element and of which at least two further signal outputs are provided or connected to the second output coupling element.

Two orthogonal optical signal pairs will be applied to the four signal outputs during operation for the purpose of coding two binary user signals.

In principle, coupling elements may be used as the output coupling elements similar to those used for the input coupling elements. It is desirable for the interferometric element according to the invention, however, which is to be used in a tree structure as will be described further below, that the number of signal outputs per output coupling element should be equal to the total number of input coupling elements in the interferometric element. An interferometric element comprising exactly two Mach-Zehnder interferometers comprises two input coupling elements and two output coupling elements. In such a case each output coupling element will comprise at least two signal outputs.

Furthermore, the number of inputs of the output coupling elements should also be at least equal to the number of input coupling elements according to the invention, because each of the output coupling elements is connected to each of

the input coupling elements via transmission lines. An interferometric element according to the invention, in which two Mach-Zehnder interferometers are used, accordingly requires output coupling elements of the 2 x 2 type, i.e. comprising two inputs and two signal outputs, or of the P x Q type with P ≥ 2 and Q ≥ 2. In view of the design requirements given above, those skilled in the art will appreciate that one or more coupling elements may be integrated into a single element.

The embodiments to be described below relate to an interferometric element according to the invention comprising M interferometers of the Mach- Zehnder type, M being a positive number greater than 1 , i.e. M = 2, 3, 4, .... In such an interferometric element according to an embodiment of the invention, each of the M interferometers comprises an input coupling element and an output coupling element. Thus there are in total M input coupling elements and M output coupling elements in the interferometric element according to this embodiment of the invention. Each input coupling element in the interferometric element according to this embodiment of invention is connected via a respective transmission line to each of the M output coupling elements. Since there are M input coupling elements and M output coupling elements included in the interferometric element according to this embodiment of the invention, the interferometric element according to this embodiment of the invention comprises M ² transmission lines. By way of example, an interferometric element with three Mach-

Zehnder interferometers comprises a total of three input coupling elements and three output coupling elements, and thus a total of nine transmission lines interconnecting the input coupling elements and the output coupling elements. Each of the three input coupling elements is connected to all output coupling elements, and each output coupling element is connected to all input coupling elements. This also means that the input coupling elements used here all comprise at least three outputs, so that a total of nine outputs is available for connecting the nine transmission lines. Conversely, the output coupling elements of such an element comprise three inputs each at least, so that a total of nine inputs is available for connecting the nine transmission lines.

Similarly, an interferometric element with four Mach-Zehnder interferometers comprises a total of four input coupling elements and four output coupling elements, and thus a total of sixteen transmission lines. The number of Mach-Zehnder interferometers that can be accommodated in the interferometric

element is not bound to a maximum in principle.

In a further embodiment of this interferometric element with Mach- Zehnder interferometers, the interferometric element comprises at least as many signal inputs as there are input coupling elements, i.e. at least M signal inputs, each of the M input coupling elements providing at least one of the M signal inputs. This complies with the requirement that each input coupling element should have at least one signal input for receiving an optical signal that is to be split up into several optical signals in the input coupling element.

In further embodiments, moreover, each interferometric element comprises at least M ² signal outputs, while each of the M output coupling elements provides at least M of the M ² signal outputs. Again, this complies with the requirement that each output coupling element should provide as many signal outputs as there are input coupling elements in the interferometric element, so that this interferometric element can be used as a building block for an interferometric tree element to be described below.

The interferometric element described above will now be used for providing an interferometric N-stage tree element comprising N interferometric stages, N being a positive integer number, wherein each of the N interferometric stages comprises at least one interferometric element, the N interferometric stages being interconnected such that the signal outputs of the at least one interferometric element in the i ^lh stage are optically connected to the signal inputs of the at least one interferometric element in the (i+1) ^th stage, i being an integer number and 1 < i ≤ (N- 1), and wherein, for 2 < j ≤ (N-1), the at least one interferometric element in the j ^th stage is an interferometric element according to the invention as described above. An interferometric N-stage tree element based on the interferometric elements according to the invention is capable of coding the optical signals of 2 ^N users in a CDMA ambience by means of a single N-stage tree. Such an interferometric tree element offers major advantages over the prior art. To make these advantages clear, a comparison will be presented below between a two-stage interferometric tree element according to the invention and a configuration in which two-stage Mach-Zehnder cascade chains are used.

By way of example, a two-stage interferometric tree element built up from interferometric elements according to the invention as described above will be discussed in detail. Use is made in this example of interferometric elements that

each comprise exactly two interferometers of the Mach-Zehnder type, so each interferometric element serving as a building block for the tree has two input coupling elements and two output coupling elements, one signal input of each input coupling element being provided with an optical signal, while at the output of each interferometric element serving as a building block for the tree one pair of orthogonal signals is provided to each output coupling element. A building block thus comprises two active inputs and four active outputs, said four active outputs providing two orthogonal signal pairs.

In the first stage of the tree element, for example, two identical optical starting signals, mutually shifted in phase by π/2, may be applied to the two inputs of the input coupling elements. Two pairs of optical output signals are delivered at the outputs of the interferometric element in the first stage. Each pair of optical output signals is subsequently applied to one of the interferometric elements in the second stage. Four pairs of output signals are delivered at the output of the second stage, whereupon they can be used for coding the binary signals of four users.

In a configuration based on Mach-Zehnder cascade chains, four cascade chains are required for coding the binary signals of four users. These four cascade chains comprise a total of eight active phase-shifting elements and are to be fed with at least four input signals. The advantage of the two-stage tree element according to the invention over the configuration with four two-stage Mach-Zehnder cascade chains is that the tree element has no more than two signal inputs, whereas the configuration with Mach-Zehnder cascade chains has eight signal inputs, a difference of six optical signal inputs. In the present example, a short two-stage tree is compared with a short two-stage cascade chain. As the number of stages in the tree increases, the number of outputs of the tree does indeed increase, but the number of signal inputs of the tree remains the same. This is not the case with the configuration comprising cascade chains, where the number of signal inputs increases exponentially as the number of stages increases. Those skilled in the art will readily perceive that, if the elements described above are to be manufactured as integrated circuits on a chip, a much greater number of fiber-chip interfaces is required for the Mach-Zehnder cascade chains than for the interferometric N-stage tree element according to the invention. The manufacturing cost of an integrated circuit based on a configuration

of Mach-Zehnder cascade chains will accordingly be much higher than that of an interferometric N-stage tree element according to the invention with the same number of stages.

Furthermore, an interferometric N-stage tree element according to the present invention lends itself much more readily to miniaturization than the cascade element described above, which again is to the advantage of the tree element.

In a further embodiment of the present invention, the interferometric N-stage tree element comprises an optical pre-coupling element having at least M coupling outputs, each of said M coupling outputs being connected to a single signal input of the M input coupling elements of the at least one interferometric element in the first stage, such that one of the M signal inputs of each input coupling element of the at least one interferometric element is connected in this stage to one of said M coupling outputs. An additional pre-coupling element may be used in order to obtain a suitable number of optically identical (possibly mutually phase-shifted) input signals for the interferometric element in the first stage of the N-stage tree element. The function of the pre-coupling element is to split up a single optical signal into a plurality of optical signals, which then serve as input signals for the first stage. If an interferometric element comprising two interferometers of the Mach-Zehnder type is used in the first stage, for example, with two input coupling elements and two output coupling elements, then use may be made, for example, of an optical splitter element, for example a pre-coupling element of the 1 x 2 type, 2 x 2 type, etc. A requirement is that this pre-coupling element has at least one signal input and at least two signal outputs.

An advantage of the use of such a pre-coupling element is that the number of signal inputs of the N-stage tree element can be reduced to one signal input, so that any desired number of output optical signal pairs can be obtained for coding binary signals of as many users as may be required. In a further embodiment, with 1 ≤ k ≤ N, the k ^th interferometric stage of the N stages comprises M ^(k'1) interferometric elements, such that the interferometric N-stage tree element comprises a total of T interferometric elements for which it holds that:

In this equation, N is the number of stages of the tree element, 1 < k ≤ N, and M is the number of interferometers of the Mach-Zehnder type in each of the interferometric elements that were used as building blocks. To give an example: a three-stage tree element comprising interferometric elements with two interferometers of the Mach-Zehnder type each has a first stage in which an interferometric element is present, a second stage in which two interferometric elements are present, and a third stage in which four interferometric elements are present. Yet another example: in a three-stage tree element comprising interferometric elements with three interferometers of the Mach-Zehnder type included in each interferometric element (i.e. each interferometric element has three input coupling elements and three output coupling elements, and the output coupling elements each have at least three outputs), we find a single interferometric element in the first stage, three interferometric elements in the second stage, and nine interferometric elements in the third stage. The total number of interferometric elements in the present example, in which N = 3 and M = 3, is accordingly 13 interferometric elements.

In particular, in an interferometric N-stage tree element according to the invention, the M signal outputs of each coupling element of each interferometric element in the I ^th stage are optically connected to M signal inputs of one of the interferometric elements in the (l+1) ^th stage, such that a single signal input of each of the input coupling elements in the (1+1 ) ^th stage is optically connected to a single signal output in the I ^th stage, with 1 ≤ I ≤ (N-1). N herein is the number of stages and M the number of Mach-Zehnder interferometers used in each interferometric element used as a building block. In a preferred embodiment of the interferometric N-stage tree element, the signal lines of each output coupling unit in the final or N ^th stage are connected to at least one end interferometer of the Mach-Zehnder type that comprises at least M optical transmission lines and an end coupling element, each end transmission line providing a frequency-dependent phase rotation, while at least one of the end transmission lines is designed for providing an additional frequency- independent phase rotation so as to deliver M ^N+1 orthogonal optical signals.

As regards the orthogonality, it has been established for Mach- Zehnder chains that it is necessary in structures with more than two stages to increase the number of stages by at least one end stage comprising an

interferometer of the Mach-Zehnder type in order to be able to provide the desired number of orthogonal optical signal pairs. It holds in particular in this respect that a tree structure with N stages should be expanded by N-2 end stages in a cascade arrangement so as to provide the desired number of orthogonal codes. If an interferometric three-stage tree element is provided for obtaining 2 ³ = 8 orthogonal signals, for example, it is necessary to provide each of the outputs of the tree with an end stage comprising an end interferometer of the Mach-Zehnder type in order to obtain indeed eight orthogonal optical signal pairs for coding binary signals of eight users. If a tree with four stages is provided, however, it is necessary to increase the number of stages by two end stages per output for obtaining 16 optical signal pairs.

According to a second aspect, the invention provides a method of processing a first optical input signal and a second optical input signal for providing a plurality of orthogonal end signals, which method comprises the steps of: splitting up the first optical input signal for providing a first intermediate signal and a second intermediate signal that is shifted in phase relative to the first intermediate signal, splitting up the second optical input signal for providing a third intermediate signal and a fourth intermediate signal that is shifted in phase relative to the third intermediate signal, rotating the intermediate signals in phase in dependence on frequency such that the frequency-dependent phase shift of at least two of the four intermediate signals differs from the frequency-dependent phase shift of the other two of the four intermediate signals so as to provide two delayed intermediate signals and two non-delayed intermediate signals, additionally rotating in phase at least one of the intermediate signals in a frequency-independent manner, and coupling the delayed and non-delayed intermediate signals two-by-two such that each of the delayed intermediate signals is coupled to one of the non-delayed intermediate signals so as to provide a plurality of output signals, at least one of the intermediate signals to be coupled being chosen from the first and second intermediate signals each time, while the other intermediate signal to be coupled thereto is chosen from the third and fourth intermediate signals. The invention will be explained in more detail below with reference to specific embodiments thereof, which are not meant to be restrictive, and to the accompanying drawings, in which: figure 1 shows an interferometric element according to the present invention;

figure 2A shows an alternative embodiment of the interferometric element according to the invention; figure 2B shows an alternative embodiment of the interferometric element according to the invention; figure 3 shows an interferometric two-stage tree element according to the invention; figure 4 shows an interferometric three-stage tree element according to the invention; and figure 5 shows a prior art Mach-Zehnder cascade chain. Figure 1 shows an interferometric element according to the present invention, comprising two input coupling elements 2 and 3 which are operationally connected to output coupling elements 6 and 7. The input coupling element 2 comprises signal inputs 9 and 10, of which the signal input 10 in operation is active as an input for the interferometric element 1 by means of a fiber 14 connected thereto, as is shown in figure 1. Those skilled in the art will understand that a different type of waveguide may be used instead of a glass fiber. Similarly, the coupling element 3 comprises signal inputs 11 and 12, of which the signal input 12 in operation is active as an input for the interferometric element 1 by means of a fiber 15 connected thereto, as shown. The optical input signal E ₁₁ is split off from the fiber 14 in the coupling element 2 and transmitted to the transmission lines 18 and 20. Owing to its processing in the input coupling element 2, the split-off portion of the optical input signal E _n on line 18 has undergone a phase .shift of τr/2 relative to the original input signal E _n that is present on fiber 14 and transmission line 20.

The input coupling element 3 acts in a similar manner as the input coupling element 2, so that an input signal E _i2 is present on transmission line 21 , and a split-off portion of the input signal E _i2 with an additional phase shift of φ/2 caused by the splitting process is present on transmission line 19.

During operation of the interferometric element 1 according to the invention, an input signal B _n and the spectrally complementary part thereof E _i2 will be applied to the inputs 14 and 15. The transmission lines 18, 19, 20, and 21 connect the outputs of the input coupling elements 2 and 3 to the inputs of the output coupling elements 6 and 7 such that one of the two inputs of the coupling element 2 is connected via a transmission line to one of the inputs of the output coupling element 6, while at the same time one of the outputs of the input coupling

element 3 is also connected via a transmission line to one of the inputs of the output coupling element 6. In the output coupling element 6, therefore, one of the signals originating from input coupling element 2 and one of the signals originating from input coupling element 3 are coupled together so as to provide interference. Similarly, signals originating from the input coupling elements 2 and 3 are also coupled together in output coupling element 7 for providing interference. The output pairs 24, 25 and 26, 27 of the output coupling elements 6 and 7 provide pairs of spectrally complementary output signals E ₀₁ , E ₀₂ , and E ₀₃ , E _o4 , respectively.

The cross-wise coupling of transmission lines 19 and 20 to output coupling elements 6 and 7, such that in each output coupling element signals originating from both input coupling elements are coupled, is necessary for retaining the full spectral bandwidth in the output signals.

It holds for both the signal pair E ₀₁ , E ₀₂ , and the signal pair E ₀₃ , E ₀₄ that the spectral bandwidths of the signals are complementary and that the bandwidths of the signals taken together cover the full bandwidth of the input signal. This functionality is caused by the cross-connection between the input coupling elements 2 and 3 and the output coupling elements 6 and 7 by means of the transmission lines 19 and 20, which are additional to the transmission lines 18 and 21. If the input signal E ₁₁ is an optical signal previously processed by an optical filter, and if E, ₂ is the spectrally complementary optical signal of E _n , then the full bandwidth of Ei ₁ and Ei ₂ together is retained in the output signals E ₀₁ , E ₀₂ and in the output signals E ₀₃ , E ₀₄ . Were this not the case, then the output signals of each stage would have an increasingly smaller bandwidth each time, and the interferometric element according to the invention could be used as (a building block for) a (de)multiplexer. The advantage achieved with the interferometric element 1 according to the invention is that the output signals remain spectrally wide, while nevertheless the history of each of the filtering steps is incorporated therein. The interferometric element 1 according to the present invention modifies a specific spectral frequency distribution as well as the spectrally complementary part thereof and adds these fields together, so that the full spectrum remains encompassed in the output signal.

Note that it is necessary, in order to guarantee the orthogonality of the output signal pair provided to the outputs 24 and 25 to the output signal pair at the outputs 26 and 27, to give a frequency-independent phase rotation or shift to at

least one of the transmission lines. In the interfero metric element 1 shown in figure 1 , an additional frequency-independent phase shift of τr/2 is given to the signal on transmission line 18.

The operation of the interferometric element 1 according to the invention can be further clarified with reference to the transfer function of the element. For this purpose, the interferometric element 1 shown in figure 1 has been subdivided into four sections, i.e. an input section 30 consisting of the fibers 14 and 15 connected to the inputs 9, 10, 11 , and 12 of the input coupling elements 2 and 3; an input coupling section 31 consisting of the input coupling elements 2 and 3; a transmission section 32 consisting of the transmission lines 18, 19, 20, and 21 connected at one side to the outputs of the input coupling elements 2 and 3 and at the other side to the inputs of the output coupling elements 6 and 7; and an output coupling section 33 consisting of the output coupling elements 6 and 7 and outputs 24, 25, 26, and 27. The input signal can be mathematically represented as a vector with two elements Ei ₁ and Ei ₂ :

The output signals can also be represented as a vector E ₀ , with four elements E ₀₁ , E ₀₂ , and E ₀₃ , E ₀₄ :

The output signals E ₀ can be calculated from the input signals E, by means of a matrix calculation:

E ₀ = H-E ₁ (eq. 3) where H is the transfer matrix for the entire interferometric element 1 of figure 1.

This transfer matrix comprises partial transfer matrices for the individual sections 30, 31 , 32, and 33 of the interferometric element 1 as described above. These transfer matrices are written as H,, H ₀₄₄ for sections 31 and 33, and H _x for the transmission section 32.

Mathematically, the transfer matrix H for the interferometric element 1 relates to the transfer matrices of the partial elements as follows:

H = H ₀₄₄ ^■ H _x ^• H ₀₄₄ ^■ H , (eq. 4) with:

It holds for the input coupling elements 2 and 3 in the input coupling section 31 that:

This transfer matrix H _c44 is also valid for the output coupling section

33.

The transfer matrix for the transmission section 32 is represented as follows below:

The additional frequency-independent phase shift τr/2 can be found in the term of the first row and the first column of H _x . The frequency-dependent phase shift arising from the difference in optical path length δL of the delayed branch has been mathematically schematically represented by φ, which can be found in the matrix elements in column 1 , row 1 , and column 2, row 3.

Equation 4 given above renders it possible to calculate the transfer matrix H, as follows:

The effect of the crossed transmission lines 19 and 20 can be found in the elements of H in column 1 , rows 3 and 4, and in column 2, rows 1 and 2.

Figures 2A and 2B show two alternative embodiments of the interferometric element 1 of figure 1. Corresponding elements in each of the figures 2A and 2B that also occur in figure 1 have been given the same reference numerals. It is apparent that the embodiment of figure 2A differs from the embodiment of figure 1 only in the fact that the delayed and non-delayed transmission lines have been differently connected to the input coupling elements 2 and 3 and the output coupling elements 6 and 7. The transmission line 18 still connects the input coupling element 2 to the output coupling element 6. Furthermore, the transmission line 19 still connects the input coupling element 3 to the output coupling element 6. So nothing has actually changed for the signal pair offered at the outputs 24 and 25 of the output coupling element 6, since it is still composed of the non-delayed, split-off portion of input signal E ₁₂ from the input coupling element 3 and the delayed, split-off portion of input signal E ₁₁ from the input coupling element 2 with an additional frequency-independent phase shift of τr/2. The non-delayed transmission line 21 , however, here connects the input coupling element 2 to the output coupling element 7, while the delayed transmission line 20 now connects the input coupling element 3 to the output coupling element 7. In other words, the transmission lines 20 and 21 have interchanged their functions as compared with the embodiment of figure 1. This means for the output signal that the output signals E ₀₃ and E ₀₄ are composed of the original non-delayed input signal E ₁₁ and the original delayed input signal E, ₂ from the input coupling elements 2 and 3, respectively. It is noted in respect of the above that additional embodiments are given in Table 1 above.

A comparison will now be made between figure 2B and the embodiment. The roles of the transmission lines have again been changed in figure

2B. The other elements and connections have remained the same as in figure 1 , and similar elements in figure 2B and figure 1 have been given the same reference numerals as in figure 1.

The roles of the transmission lines 18, 19, 20, and 21 have been completely changed. The non-delayed transmission line 19 now connects the input coupling element 2 to the output coupling element 6. The delayed transmission line 18 with the additional frequency-independent phase shift 22 now connects the input coupling element 2 to the output coupling element 7. The delayed transmission line 20 now connects the input coupling element 3 to the output coupling element 6, and the non-delayed transmission line 21 connects, as in figure 1 , the input coupling element 3 to the output coupling element 7. This means for the signal at the outputs 24 and 25 of the output coupling element 6 that it is composed of the split-off, non- delayed portion of the input signal E ₁₁ and the split-off, delayed portion of the input signal E _i2 . The output signals E ₀₃ and E ₀₄ at the outputs 26 and 27 of the output coupling element 7 are composed of the delayed original input signal E _n with a frequency-independent phase shift applied to input 10 of the input coupling element 2 and the original non-delayed input signal E _i2 applied to input 12 of the input coupling element 3.

Apart from the embodiments shown in figures 1 , 2A and 2B, those skilled in the art may devise further configurations in which the principle of the invention is put into practice. The embodiments shown are not meant to restrict the invention; they have merely been included as an illustration of the principle of the invention. It should further be noted about the figures 1 , 2A and 2B that the interferometric optical element is based on the operative principle of interferometers of the Mach-Zehnder type. Although no exact Mach-Zehnder interferometers are obtained owing to the cross-wise connection of the input coupling elements and the output coupling elements, the principle of the Mach-Zehnder interferometer is nevertheless applied in the interferometric element according to the invention in that a delayed input signal interacts with a non-delayed input signal at the output each time so as to obtain interference. With a little imagination one can clearly distinguish two interferometers of the Mach-Zehnder type, i.e. a first interferometer of the Mach- Zehnder type formed by input coupling element 2 and output coupling element 6 and

transmission lines situated between them, and a second interferometer of the Mach- Zehnder type formed by input coupling element 3 and output coupling element 7 and transmission lines situated between them. Since two of the four transmission lines shown provide crossed connections between the input and output coupling elements 5 of the individual interferometers of the Mach-Zehnder type as defined above, a strict delineation of the interferometers of the Mach-Zehnder type can no longer be discerned. Input signals of the one interferometer are used in the other interferometer, and vice versa. The expression "interferometer of the Mach-Zehnder type", however, is used here only to clarify the operative principle of the 0 interferometer according to the present invention and to provide some direction as to the choice of components to be used.

The interferomethc element according to the invention is highly suitable for use in providing an N-stage interferometric tree element for generating a plurality of orthogonal signal pairs at the output of the N-stage tree element. For 5 illustration, an interferometric two-stage tree element is shown in figure 3. This two- stage tree element 40 comprises three interferometric elements 41 , 42, and 43 according to the invention. Except for the frequency-independent phase shifts φ11 , φ21 , φ22, φ23, and φ24 and the applied path length differences δL1 and δL2, the interferometric elements 41 , 42, and 43 are identical, and the components of the 0 interferometric element 41 only have been indicated with reference numerals in figure 3.

The interferometric element 41 consists of input coupling element 46 and input coupling element 47, which are connected via transmission lines 50, 51 , 52, and 53 to output coupling elements 48 and 49. Two of the transmission lines, 5 i.e. transmission line 50 and transmission line 53, are provided with a frequency- independent phase shift 56 and 57, respectively. The delayed transmission lines 50 and 51 exhibit an optical path length difference δL1 with the non-delayed transmission lines 52 and 53. The operation of the interferometric element 41 of figure 3 is the same as that of the interferometric element 1 of figure 1 , except for D the (optional) frequency-independent phase shift φ12 in element 57. In the transfer matrix H _x of equation 7, this additional phase shift φ12 appears in the element in the fourth column, fourth row, of the matrix H _x , which now contains the term E _φ12 . Reference is made to the description of figure 1 for a description of the operation of the interferometric element. The interferometric elements 42 and 43 operate

similarly, but it is noted that the optical path length differences of the delayed branches in the interferometric elements 42 and 43 have a different value: δL2, and that in addition the frequency-independent phase shifts provided by the elements 75, 76, 84, and 85 of the interferometric elements 42 and 43 may differ from the frequency-independent phase shifts in the elements 56 and 57. The outputs 63 and 64 of the interferometric element 41 are connected to the inputs of the interferometric element 42, whereas the outputs 65 and 66 of the interferometric element 41 are connected to the inputs of the interferometric element 43. As was discussed above, the optical signal at output 63 is the spectral complement to the optical signal at output 64, so that two mutually optically complementary input signals are provided to the interferometric element 42.

The same is true for the optical signals at outputs 65 and 66 of the interferometric element 41 , which signals are applied to the interferometric element 43. The interferometric element 41 has four inputs 59, 60, 61 , and 62, of which two are connected to a pre-coupling element 70. The pre-coupling element 70 is a coupling element of the 2 x 2 type comprising two inputs 71 and 72 and two outputs (not referenced). It is only the input 71 of the pre-coupling element 70 that is operatively connected for providing a single input to the two-stage tree element 40 of figure 3. The input signal E ₁₁ is split up in the pre-coupling element 70 such that the original optical signal E ₁₁ and the spectrally complementary part thereof are applied to the inputs 60 and 62, respectively, of the interferometric element 41.

Four pairs of orthogonal signal pairs are now applied to the outputs 78, 79, 80, 81 , 87, 88, 89, and 90 of the interferometric two-stage tree element 40 of figure 3, with which the binary signals of four users can be directly coded. Of each pair of signals, one of the output signals will be used to code a binary 0 and the other one for coding a binary 1.

Figure 4 shows an interferometric three-stage tree element according to the present invention. Figure 4 has merely been added for clarifying the principle of the use of end stages at the binary tree structure. The three-stage interferometric tree element comprises a plurality of interferometric elements 91 , 92, 93, 94, 95, 96, and 97 according to the present invention, in particular, the elements 91 to 97 are similar to the interferometric element 1 of figure 1 and the interferometric elements 41 , 42, and 43 of figure 3. As to the operation of these interferometric elements, the reader is referred to the description of the figures

mentioned above; the specific components of the interferometric elements 91 to 97 have not been given individual reference numerals.

It is apparent from figure 4 that the output signals of the interferometric element 91 serve as input signals for the interferometric elements 92 and 93 in a manner similar to that holding for the two-stage tree element 40 of figure 3. Equally, the output signals of the interferometric elements 92 and 93 are used as input signals for the interferometric elements 94, 95, and 96, 97, respectively. This leads to a total of eight pairs of output signals at the signal outputs of the interferometric elements 94, 95, 96, and 97. Research has shown, however, that it may be necessary to add one or more end stage elements in the case in which a chain comprises more than two interferometers of the Mach-Zehnder type in order to obtain the desired number of orthogonal end signal pairs. This has been demonstrated for cascade chains of the Mach-Zehnder type in "Optical Local Area Networks New Solutions for Fiber-to-the desk-applications", I. Radovanovic, 2003, doctoral thesis at the Technical University of Twente.

Application of this teaching to the N-stage tree element according to the present invention yields that it is necessary for a three-stage tree element as shown in figure 4 to have one end stage coupled to each output so as to obtain the desired degree of orthogonality of the various signal pairs. Such an end stage may consist of an interferometer of the Mach-Zehnder type , for example a cascade building block such as the element 135 in the cascade chain of the prior art as shown in figure 5. Such cascade elements are coupled to the outputs of the three- stage tree element of figure 4 and are diagrammatically depicted as elements 98, 99, 100, 101 , 102, 103, 104, and 105 in figure 4. The cascade elements 98 to 105 are identical in their operation, but they may impose, if so desired, different frequency-dependent and/or frequency-independent phase shifts on the output signal. In the embodiment shown in figure 4, all cascade elements 98 to 105 provide an optical path length difference of δL4 in the delayed branches, such as the delayed branch 115 in the cascade element 98. Furthermore, an additional frequency-independent phase shift 114 is given to the optical signal in the delayed branch. The two signals are joined together again in the output coupling element such as the output coupling element 117 of the cascade element 98 so as to generate the end signal pair 120. The cascade elements 99 to 105 provide the respective end signal pairs 122, 123, 124, 125, 126, and 127 in a similar manner. All

end signal pairs 120 to 127 are orthogonal to one another in the embodiment shown in figure 4.

It is noted on the above that, when a four-stage tree element is constructed in a similar manner with interferometric elements according to the invention, it will be necessary to arrange two additional cascade elements in series in order to obtain 2 ⁴ = 16 orthogonal end signal pairs at each output. It holds in particular that, in order to obtain 2 ^N orthogonal end signal pairs, N-2 cascade elements corresponding to cascade element 98 of figure 4 connected in series are required. The invention is not limited to the embodiments described above; indeed, those skilled in the art will understand that the inventive principle described herein can obviously be used in a somewhat modified manner. De protective scope of the invention is limited by the appended claims only.