Abstract:
An optical equalizer for a wavelength division multiplexed optical signal in an optical communications system utilises an array of parallel waveguides using planar waveguide technology. Waveguides having a range of different lengths have transmission controlled respectively in amplitude and/or phase in accordance with parameters calculated from a Fourier transform of an input frequency characteristic. Calculation of the parameters may be simplified by a Hilbert transform applied to determine phase values of the input terms of the Fourier transform. Feedback may be utilized by measuring the equalizer output and generating difference signals applied to the input to improve accuracy of equalization response by iteration or to overcome systematic errors. The equalizer has application to optical systems having line amplifiers where fiber amplifiers result in gain tilt, the equalizer allowing gain tilt to be corrected.

Description:
This invention relates to the equalisation of optical signals in an optical communications system and in particular but not exclusively to the equalisation of wavelength division multiplexed optical signals. 
     BACKGROUND TO THE INVENTION 
     The control of optical power levels in optical communications systems is critical in obtaining optimum performance since the power level should be sufficient to establish a signal to noise ratio which will provide an acceptable bit error rate but without the power level exceeding a level at which limiting factors such as the onset of non-linear effects result in degradation of the signal. In wavelength division multiplexed (WDM) transmission, it is desirable to maintain each of the power levels of the individual wavelength components at substantially the same level. 
     The inventor has disclosed in U.S. Pat. No. 5,513,029 a method of monitoring component power levels in WDM transmission using orthogonal low frequency dither signals and controlling component signal power to maintain optimum performance. 
     It is also known from GB2314714A that an imbalance of component signal powers in a WDM transmission is likely to occur at an optical amplifier stage, as used to boost signal power at stages in a long distance transmission, utilising optical amplifiers such as erbium doped fibre amplifiers. Such amplifiers have a non-uniform gain characteristic as a function of wavelength which is variable in dependence on the amplifier gain, this change in gain characteristic consequent on change of gain being commonly referred to as dynamic gain tilt. 
     There is therefore a need to provide optical filtering which is adaptive and which can be used in conjunction with optical amplifiers, or otherwise, in order to maintain a preferred spectral profile of an optical signal. 
     It is known from Huang et al, IEEE Photonics Technical Letters, September 1996 pp 1243-1245, to provide an acousto-optic tunable filter for dynamic equalization of channel powers. A disadvantage of such a method is that the filters suffer from polarisation sensitivity and severe channel cross talk. 
     It is also known from Gobel et al, IEEE Photonics Technology Letters, March 1996, pp 446 to 448, to provide a WDM power level compensator in which demultiplexed channels are subject to power control in respective erbium doped waveguides. A disadvantage of this arrangement is that significant distortion of the modulated optical signal occurs. 
     It is also known from Madsen et al, IEEE Journal of Lightwave Technology, March 1996, pp 437 to 447, to provide fixed (non-adaptive) filters using a sequence of concatenated Mach-Zehnder interferometers in a planar waveguide structure. Such structures require lengths which are difficult to fit onto a single planar waveguide structure and which have an inherent high insertion loss. 
     Parallel structures on planar waveguides are known from Dragone, IEEE Photonics Technology Letters, September 1991, pp 812 to 815, which provide non-adaptive filtering with output at a single wavelength. 
     It is also disclosed by S. Day in co-pending application U.S. Pat. No. 08/997,752, now U.S. Pat. No. 5,956,437, to provide a variable optical attenuator by means of localised heating of a waveguide. 
     Yamada et al, Electronics Letters 1995, 31, pp 360 to 361, discloses a multiplexer using planar waveguide technology and in which a waveguide array is provided with heating strips for each waveguide in order to compensate for phase errors occurring during fabrication. After such compensation, light components passing through the arrayed waveguides are delayed by respective amounts which differ by a constant phase difference between adjacent waveguides so that recombination in a star coupler at the output of the waveguides is dispersive in wavelength to provide separation of the WDM channels, this arrangement thereby being termed an arrayed waveguide grating. 
     There remains a need to provide an improved optical equalizer, particularly for use in the context of correcting gain tilt in optical amplification stages of a communications system. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide optical equalisation to at least partially compensate for the effects of gain tilt in optical amplifiers. 
     It is a further object of the present invention to provide an adaptive optical equalizer using planar waveguide technology. 
     It is a further object of the present invention to provide a method of applying a desired frequency characteristic of equalization by actuating a minimal number of elements of an adaptive optical equalizer. 
     It is a further object of the present invention to allow the operation of an optical equalizer to be periodically refined to adapt to changing conditions and system tolerances. 
     According to the present invention there is disclosed a method of applying equalization to an optical signal for use in an optical communications system, comprising steps of: 
     splitting the optical signal into components having the same frequency characteristic as the optical signal; 
     transmitting the components via respective waveguides of a waveguide array defining respective optical path lengths; 
     variably setting at least one of the relative amplitudes of and the phases of the components transmitted via the waveguides; and 
     combining the components transmitted by said waveguides to form an output optical signal whereby interference between said combining components applies equalization to the frequency characteristic of the output optical signal. 
     According to a further aspect of the present invention there is disclosed a method of controlling an adaptive filter having a set of elements configured such that their combined effect determines a frequency characteristic of equalization applied by the filter; the method comprising the steps of; 
     actuating the elements according to values of a corresponding set of parameters; 
     calculating said parameters from complex values of control coefficients by a process which includes a discrete Fourier transform; and including the step of inputting values of amplitude for the control coefficients and calculating respective phase values of said coefficients by a Hilbert transform. 
     According to a further aspect of the present invention there is disclosed a method of operating an optical filter to apply a desired equalization characteristic to a wavelength division multiplexed optical signal, the method comprising the steps of; 
     actuating a set of elements of the filter such that their combined effect determines an actual frequency characteristic applied to the optical signal, said elements being actuated according to values of a corresponding set of parameters; 
     calculating said parameters from control values determined in accordance with said desired equalization characteristic; 
     measuring the output of the filter and obtaining a measurement of the actual frequency characteristic; 
     comparing the measurement with the desired frequency characteristic to obtain difference values; 
     calculating new values of said control values based on said difference values and actuating said elements according to new parameters calculated from said new control values; 
     and periodically repeating said steps of measuring, actuating and calculating new values to apply an actual equalization characteristic substantially equal to said desired equalization characteristic. 
     The present invention allows an optical equalizer to be realized using planar waveguide technology by utilising a waveguide array and relatively simple modulators as control elements for modifying the transmission through each waveguide. The calculation of parameters used to determine actuation of the elements of the equalizer can be optimized by use of a Hilbert transform to reduce the number of non-zero parameters requiring corresponding elements to be actuated in accordance with values of the parameters. 
     The invention further provides the ability to periodically repeat calculation of parameters and actuation of the elements based on feedback of measured output from the equalizer to achieve improved correspondence with a desired equalization by iteration or to remove the effects of system errors. 
     Preferred embodiments of the present invention will now be described by way of example only. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic diagram of a line amplifier with an adaptive equalizer; 
     FIG. 2 is a schematic f low chart illustrating a method of operating the equalizer of FIG. 1; 
     FIG. 3 is a schematic layout of the equalizer of FIGS. 1 and 2 in the form of a planar waveguide array; 
     FIG. 4 is a schematic representation of the effect of a two arm Mach Zehnder interferometer; 
     FIG. 5 is a schematic representation of the effect of a multiple arm Mach Zehnder interferometer configured by a parallel waveguide array having control elements for frequency response synthesis; 
     FIG. 6 is a schematic flowchart illustrating the application of a Hilbert transform; 
     FIG. 7 is a graphical representation of the biased distribution of input signal into waveguides of the array; 
     FIG. 8 is a flowchart illustrating the calculation of coupling coefficients; 
     FIG. 9 is a schematic representation of a further waveguide array having three waveguides per coupling coefficient; 
     FIG. 10 is a representation of vector addition in the real-imaginary plane to synthesize the coupling coefficients of FIG. 9 using three waveguides per coupling coefficient; 
     FIG. 11 is a schematic representation of an alternative equalizer having a waveguide array with dynamically controlled splitting of input signal and phase control elements; 
     FIG. 12 is a schematic representation of a further alternative waveguide array equalizer with dynamically controlled Y splitters/combiners; 
     FIG. 13 is a schematic representation of a further alternative waveguide array equalizer with dynamically controlled Y splitters/combiners; and 
     FIG. 14 is a graphical representation of the results of simulation of the optical equalizer of FIG. 3 for a randomly generated target frequency characteristic. 
    
    
     DETAILED DESCRIPTION 
     FIG. 1 illustrates schematically a line amplifier  1  forming part of an optical communications system and connected in line between an input waveguide  2  and an output waveguide  3  in the form of single mode optical fibres. 
     The line amplifier consists of first and second fibre amplifiers  4  and  5  respectively, each being formed by erbium doped optical fibre amplifiers, the first fibre amplifier receiving an input optical signal  6  via the input waveguide  2 . The input optical signal  6  is a WDM (wavelength division multiplexed) signal having N channels separated by 100 GHz where in the present example N=32. The optical signal  18  output from the first fibre amplifier  4  is input to an adaptive equalizer  7 , the output  19  of which is input to the second fibre amplifier  5  and amplified before transmission via the output waveguide  3 . 
     A first optical tap  8  provides an optical sample of the optical signal  18  input to the equalizer  7  which is detected and measured by a first detector  9  to provide measurements in the form of input channel levels V n  where n=0 to 31. Similarly, a second optical tap  10  provides an optical sample of the optical signal  19  output from the equalizer  7  which is detected and measured by a second detector  11  producing measured output channel levels X n . 
     The equalizer  7  is adaptive in the sense of being operable to independently control transmission amplitudes of each of the WDM channels. This may be represented by a transfer function T having complex coefficients T n  relating the amplitude and phase of each component output to its respective input, the coefficients T n  having amplitude A n  (the modulus of T n ) and phase arg T n  (the argument of T n ). These coefficients T n , are target values representative of E field values arrived at by calculation and applied by calculating corresponding settings E m  of variable components of the equalizer  7 . Equalizer controller  12  controls the value of the equalizer settings E m  applied to the variable components of the equalizer  7 . The number of settings E m  may be typically greater than the number N of channels and will depend upon the manner in which the equalizer is implemented. 
     The required values of the equalizer settings E m  are determined by calculator  13  which receives as inputs the measured values of input channel levels V n  and output channel levels X n . An input device  14  is also connected to the calculator  13  to enable a user to input a reference spectral characteristic W n  which serves as a target value to which output channel levels X n  are driven to correspond under ideal operating conditions. 
     The timing of operation of the first and second detectors  9  and  11  and of the equalizer controller  12  is determined by timing controller  15  which periodically outputs control signals  16  and  17  to the first and second detectors to determine the sampling times at which V n  and X n  are calculated and correspondingly controls the timing at which the settings E m  of the equalizer  7  are updated. 
     The manner in which the equalizer controller  12  determines the values of settings E m  required to achieve given values of T n  will be described below for a number of examples, including the adaptive equalizer of FIG. 3 in which the equalizer controller  12  outputs equalizer settings E m  to set phase values P m  of phase control elements  39  in a waveguide array  40 . 
     The sequence of operation in the line amplifier  1  is illustrated schematically in FIG.  2 . At start-up, an input step  20  inputs the required reference spectral characteristic W n  and the controller  12  sets the equaliser settings E m  to predetermined values at step  21 . 
     At step  22 , the first detector  9  detects and measures the input channel levels V n  and outputs the values of V n  to the calculator  13  which at step  23  calculates target transfer function coefficients T n  determined to be required in order to achieve an output X n  from the equaliser  7  which would match the reference spectral characteristic W n . At step  24 , the calculator  13  calculates the equaliser settings E m  corresponding to the target transfer coefficients T n  determined at step  23  and at step  25  the equaliser controller  12  outputs control signals to the equaliser  7  to update the equaliser settings E m . 
     At step  26 , the second detector  11  detects and measures the output channel levels X n  and outputs the values of X n  to the calculator  13 . At step  27 , the calculator  13  compares the spectral profile of the output X n  with the reference spectral characteristic W n . In general, X n  will not be an exact fit to W n  and coefficient increments t n  required to adjust the target transfer function coefficients T n  are calculated from                t   n     =       h        (       W   n     -     X   n       )         V   n               (   1   )                                
     where h is a compensating factor (1.7 for example) to optimise feedback control. 
     Revised values T 1   n  of the target transfer function coefficients are then calculated from 
     
       
           T   1   n   =T   n   +t   n   (2) 
       
     
     At step  28 , calculation of the equalizer settings E m  is repeated using the updated transfer function coefficients T 1   n  and at step  29 , the new equaliser settings E 1   m  are implemented. 
     At step  30 , the first and second detectors  9  and  11  and the calculator  13  wait for the receipt of the next timing control signal  16  and  17  respectively from the timing controller  15 . When the timing control signals  16  and  17  are received, control proceeds to step  31  where the first detector  9  detects and measures the input channel levels V n . Steps  26  to  29  are then cyclically repeated. 
     A match between output X n  and the reference spectral characteristic W n  is thereby achieved interactively and in a manner which, over time, adapts to variations in the input values V n . A new reference characteristic W n  may be input at any time. 
     Equalizer Synthesis 
     The equalizer transfer function T is synthesised by the effect of a multiple arm Mach Zehnder interferometer arranged as a parallel waveguide array. The effect of a simple  2  arm Mach Zehnder interferometer is illustrated in FIG. 4 in which a splitter  41  divides an incoming signal into first and second portions, the first portion being passed through a delay  42  provided by a length of waveguide L, the remaining portion being passed through a second delay  43  represented by a waveguide of length L+dL, and the outputs from delays  42  and  43  being additionally combined in a combiner  44 . The combined output is modulated in frequency space as illustrated graphically in FIG. 4 a , the modulation being sinusoidal with a period which is inversely proportional to dL. 
     FIG. 5 shows the effect of a multiple arm Mach Zehnder interferometer in the form of a parallel waveguide array  58 , a series of delays L, L+dL, L+ 2 dL . . . . L+KdL being provided by delay waveguides  53  to  55 . The contribution made by each of the delay waveguides  53  to  55  to the output combined by a combiner  50  is adaptively controlled by means of a set of modulators  56  where each of the delays  53  to  55  is provided with a respective modulator. Each modulator  56  is capable of independently setting an amplitude and phase modulation to the component transmitted through the corresponding delay  53  to  55 , the values of the amplitude and delay being characterised by complex coupling coefficients C r , r=0 to K where there are K+1 waveguides. The term “phase modulation” here implies a variation in optical path length resulting in a corresponding phase variation at the point of combination in combiner  50 . 
     The power transmission of the multi-arm Mach Zehnder interferometer of FIG. 5 is              Z   =       [            ∑     r   =   0     k                       C   r        exp        {       iL   r        vf     }              ]     2             (   3   )                                
     where v={fraction (2+L π/C)}. (optical density of waveguide) 
     L r =differential length of waveguides, 
     c=speed of light, 
     f=optical frequency. 
     The result of the summation of the outputs from the modulated delay waveguides is illustrated schematically as a spectral profile  57  having a form which is related to the values of C r , r=0 to K, by a discrete Fourier transform. This relationship may be derived by considering the form of Z from equation 3 and the usual definition of the discrete Fourier transform. This relationship provides the basis for synthesis of the required frequency response where W n  and T n  referred to above are expressed in common with Z in units of (Power). 
     The adaptive equalizer of FIG. 1 requires the spectral profile  57  to correspond to the target transfer function T at each of the N frequencies for which T n  are defined, i.e. the frequencies for which signal carrying channels are to be equalized. Implementation of the equalizer therefore requires that the value of dL is set appropriately in the array of FIG. 5, that there is an appropriate number of K+1 waveguide delays  53  to  55 , and that the complex coupling coefficients C r  are calculated to provide the required spectral profile  57  and then implemented in hardware to provide the required amplitude and phase modulation. 
     The approach taken in calculating the coefficients T n  and the complex coupling coefficients C r  in the preferred embodiment takes as a starting point the assumption that it is preferable to calculate the coefficients T n  for N frequencies corresponding in both number and frequency value to the N wavelength channels of the input signal to be processed. The alternative would be to rely upon some form of interpolation between values not necessarily corresponding to the input frequencies, this latter option being believed to be insufficiently precise for most applications but which could under certain circumstances be adopted. 
     The Hilbert Transform 
     The calculation of a fast Fourier transform is utilised to develop the values of the complex coefficients C r  from the values of coefficients T n . Generally this will result in there being N complex coupling coefficients C r . Since the number of coupling coefficients C r  determines the number of waveguides in the waveguide array, it would be advantageous to reduce this number if possible, thereby simplifying the required hardware and control effort required to configure the settings corresponding to the complex coupling coefficients. Such a reduction is achieved in accordance with the present invention by means of a Hilbert transform of the coefficients T n  which would retain the amplitudes of the coefficients unchanged but which would provide phase values selected such that, after Fourier transform, those transformed coefficients C r  corresponding to negative frequency amplitudes become zero. In this way it is unnecessary to provide waveguides and modulators corresponding to the zero value coupling coefficients, the number of non zero coupling coefficients being reduced to R where              R   =       N   2     +   1             (   4   )                                
     The manner in which the Hilbert transform of the coefficients T r . is implemented is illustrated in the flow chart of FIG.  6 . The underlying premise is that for the complex coefficients T n , the phase values can be arbitrarily set to any convenient values since only the transmission amplitudes A n  are important, where 
     
       
           A   n   =|T   n |  (5) 
       
     
     At step  61  of FIG. 6, the required amplitudes A n  of the complex transfer function coefficients T n  are calculated from the input reference spectral characteristic W n , the amplitudes A n  being numbers in the range 0 to 1 and having a maximum value equal to 1. The phase arg (T n ) of the coefficients T n  can be arbitrarily net to zero at this point of the calculation. 
     At step  62 , the propagation values L n  are calculated as the logarithm of the amplitudes A n ; 
     
       
           L   n   =log   e   A   n   (6) 
       
     
     At step  63 , a fast Fourier transform of the propagation values is calculated to obtain Fourier transform coefficients FL n . 
     At step  64 , those Fourier transform coefficients FL n  corresponding to negative frequency components are set to zero, represented by a multiplication FL n  by a function U 2 N n ; 
     
       
           FLR   n   =U 2 N   n   .FL   n   
       
     
     where 
     
       
           U 2 N   n =1 if  n =0 or  n ={fraction (N/2+L )} 
       
     
     
       
           U 2 N   n =0 if 0 &lt;n &lt;{fraction (N/2+L )}, 
       
     
     
       
           U 2 N   n =2 if  n &gt;{fraction (N/2+L )}  (7) 
       
     
     At step  65 , the inverse Fourier transform of the resulting coefficients is calculated to obtain propagation values HT n . Since the inverse transform coefficients obtained after setting the negative frequency components to zero is commonly referred to as a minimum phase condition, these propagations are referred to as minimum phase propagation values HT n . 
     At step  66 , the exponential of the minimum phase propagation values HT n  is computed to obtain the minimum phase transfer function coefficients T n , each of which has its original amplitude A n  and now a phase arg T n  component determined according to the minimum phase condition provided by the Hilbert transform. 
     Implementing the Equalizer Transform Function 
     For a given transfer function defined by transfer function coefficients T n , where n=0 to N-1, implementation of the transfer function requires calculation of complex E field coupling coefficients C n  which are the result of a fast Fourier transform of T n . Discarding the coupling coefficients C n  having zero amplitude as a result of the Hilbert transform (i.e. those corresponding to negative frequencies) a reduced set C r  of complex E field coupling coefficients, r=0 to N/2, are defined. Each of the C r  represents the amplitude and phase of the coupling required through the respective waveguide of array  58  in FIG.  5 . 
     In order to minimise the overall attenuating effect of applying the amplitudes of C r , the set of values C r  is normalised by dividing each of the values of C r  by the largest value of the set, the resulting scaled set C r  being a set of positive numbers less than or equal to unity. 
     FIG. 3 illustrates a preferred apparatus and method of implementing the controlled waveguide array  58  of FIG.  5 . In FIG. 3, the waveguide array  40  is defined by channel waveguide regions of a planar dielectric slab  32  and each waveguide of the array is provided with a respective phase control element  39  constructed as a thin film heater applied locally to a small portion of the waveguide and connected by electrical connectors  33  to an equaliser controller  12  which selectively actuates and controls the heating effect for each control element. Localised heating at each control element  39  provides a controlled change in optical path length in the respective waveguide, thereby in effect providing a phase control element. 
     The waveguide array  40  is constructed using silica on silicon technology in which a silica buffer layer is deposited on a planar silicon substrate, a core glass layer of doped silica then being deposited on the buffer layer before adding a higher refractive index cladding glass layer of germanium doped silica. Deposition in each case is by enhanced chemical vapour deposition. The phase control elements  39  are formed by patterning a sputtered layer of chrome to provide Joule-effect heaters. 
     In the waveguide array  40  of FIG. 3, each of the modulators  56  shown in FIG. 5 is implemented by having a respective pair of waveguides such as for example first and second waveguides  34  and  35  having respective first and second phase control elements  36  and  37 . 
     Each of the first and second waveguides  34  and  35  has nominally the same length L+dL, corresponding to delay waveguide  54  of FIG. 5, and the values applied to the first and second phase control elements  36  and  37  determine the amplitude and phase of coupling coefficient C 1 . Representing the phase values applied by the first and second phase control elements  36  and  37  as P 1   1  and P 2   1  respectively, the resulting amplitude and phase of the combined output from waveguide  34  and  35  is determined by choice of P 1   1  and P 2   1  since in effect waveguides  34  and  35  constitute a Mach Zehnder interferometer whose output is determined by interference. 
     Each of the waveguides in the array  40  receives as its input a portion of the input multiplexed signal  18  divided. For the present example, division into equal proportions will be assumed by a splitter  38  constituted by a star coupler constructed as a free space region in the slab  32 . 
     The value of C 1  is therefore given by: 
     
       
           C   1   =exp iP   1   1   +exp iP   2   1   (8) 
       
     
     For given values of the amplitude and phase of coupling coefficient C 1 , phase values P 1   1  and P 2   1  may be calculated since the amplitude of C r  is determined by the difference in phase values P 2   1 -P 1   1 . By choosing P 2   1 -P 1   1  such that: 
      | C   1 |=1 +exp[i ( P   2   1   −P   1   1 )]  (9) 
     The phase difference P 2   1 −P 1   1  is then determined as:                  P2   1     -     P1   1       =       cos     -   1            [                C   1          2     2     -   1     ]               (   10   )                                
     From equation 8, P 1   1  can be expressed as: 
     
       
           P   1   1   =arg C   n   -arg [1 +exp{i ( P   2   1   -P   1   1 )}]  (11) 
       
     
     P 1   1  may therefore be calculated by substituting P 2   1 -P 1   1  from equation 10. 
     P 2   1  may then be calculated using equation 10. 
     Corresponding calculations for each C r  may similarly be made to determine phase values P 1   r  and P 2   r , 
     For the embodiment of FIG. 3 therefore, the equaliser settings E m  referred to in FIG. 2 are constituted by the set of phase values P 1   r , P 2   r where r is 0 to N/2. 
     In the embodiment of FIG. 1 in which N=32, the waveguide array  40  of FIG. 3 consists of seventeen pairs of waveguides provided with respective phase control elements  39 . 
     The results obtained by mathematically modelling the embodiment of FIG. 3 are shown in FIG. 14 where the curve represents the transfer function achieved in response to target values represented by rhomboids. 
     Optimum Power Splitting 
     In the generalised arrangement of FIG. 5, the power splitter  59  determines the distribution of power to each of the modulators  56  which apply the coupling coefficients C r  associated with respective delay waveguides  53  to  55 . As described above with reference to FIG. 3, the splitter  38  may be arranged to deliver equal shares of the available input multiplex signal power to each pair of waveguides forming the array  40 . In many applications however, such as in the case of flattening the gain of an optical amplifier, the required reference spectral characteristic W n  has a flat profile. This corresponds to C 1  having a value of unity and the remaining coupling coefficients having zero values so that the transmitted power is reduced by a factor of {fraction (1/17)}. 
     Such severe attenuation may not be acceptable. 
     A further difficulty is that it may be difficult in practice to obtain exactly equal power division due to systematic errors such as manufacturing tolerances in the splitter  38 . 
     In an alternative embodiment, the embodiment of FIG. 3 is modified to include a splitter  38  in which the power coupled into each modulator C r  is tailored to the particular application. The power B r (r) coupled into each modulator C r  may for example be biased to decay exponentially with increasing values of r as illustrated in FIG. 7, such an arrangement being found to provide adequate control while minimising attenuation. In order to take account of the characteristic of coupled power B r (r), the scaling step in which C r  is normalised requires modification by dividing the normalised values of C r  by the respective value of B r (r) to form:                C   r     =       C   r         B   r          (   r   )                 (   12   )                                
     Subsequent calculation such as described with reference to equations 8 to 11 to determine the equaliser settings is then conducted using C r  instead of C r . 
     The first described embodiment of FIG. 3 may therefore be regarded as being the result of setting B r (r) to a uniform power distribution in which each value of B r (r) equals 1. 
     Any departure from the intended distribution of B r (r) may be determined by calibration and the actual measured values of B r (r) used in equation 11, for any desired shape of B r (r) including the nominally flat characteristic of the FIG. 3 embodiment, in order to correct for systematic errors in the implementation of power splitter  38 . 
     FIG. 8 illustrates schematically the manner in which the equaliser settings E m  are derived for both steps  24  and  28  in FIG.  2 . At step  80 , C r  is calculated as the fast Fourier transform of T n  and at step  81 , the values of C r  are adjusted according to the required power splitting bias profile B r (r) to determine C′ r . 
     The values of C′ r  are then normalised at step  82  and at step  83  the values of the equaliser settings E m  are calculated based on the values of C′ r . 
     Implementing the Equalizer Transform Function Using Only Phase Control Elements and with Three Waveguides per Coupling Coefficient 
     The arrangement of FIG. 3 utilizes pairs of waveguides such as first and second waveguides  34  and  35  with associated phase control elements  36  and  37  to synthesise the coupling coefficient C r  of each arm of the multiple Mach-Zehnder waveguide array of FIG.  5 . In practice, the range of phase control available to each of the elements  36  and  37  may be limited and it may therefore be advantageous to replace the pairs of waveguides of FIG. 3 with triplets as shown in the embodiment of FIG. 9 where three waveguides are provided to implement each coupling coefficient C r . 
     In the embodiment of FIG. 9, each of the complex coupling coefficients C r  is synthesised by setting control phase values P 1   r , P 2   r  and P 3   r  for associated waveguides forming a triplet, such as waveguides  90 ,  91  and  92 . This requires that the equalizer controller  12  dynamically controls the first, second and third phase control elements  93 ,  94  and  95  respectively. 
     The value of the coupling coefficients is then given by: 
     
       
           C   r   =exp iP   1   r   +exp iP   2   r   +exp iP   3   r   (13) 
       
     
     as illustrated graphically in FIG. 10 where vectors V 1 , V 2  and V 3  in the real/imaginary plane having phase angles P 1   r , P 2   r  and P 3   r  are vectorially added to provide the complex number representative of the coupling coefficient C r . 
     The use of three such unit vectors allow greater flexibility in implementing changes in C r  without major discontinuities in values of the phase angles which might otherwise be required if only two vectors were available under conditions where a limited range of each phase angle is available. 
     Alternative Waveguide Configuration of FIG. 11 Using Dynamically Controlled Splitting in Combination with 
     Phase Control Elements 
     FIG. 11 shows an alternative waveguide array which differs from the arrangement of FIGS. 3 and 5 in that the proportion of the input signal split into each of the waveguides is dynamically controlled by a splitting ratio controller  110 . Such splitting control is implemented by a series of Y splitters  111 , each of which receives an electrical control signal from the splitting ratio controller  110  to determine the proportion of input signal directed into each one of the output arms of the Y splitter. 
     In FIG. 11, an equalizer for N=16 channels is formed by eight waveguides having lengths increasing incrementally from L to L+ 7 dL, each waveguide being provided with a respective phase control element  112 , and the outputs being combined in a star coupler  113 . 
     The complex coupling coefficients C r  are therefore defined for each waveguide such that the controlled splitting ratios determine the amplitude (modulus of C r ) and the phase control elements determine the phase (the argument of C r ). 
     The equalizer of FIG. 11 provides equalization for a WDM signal of 16 channels with 100 GHz channel separation. The difference in length between waveguides is 0.272 mm. 
     The manner of operation of the embodiment of FIG.  11  otherwise corresponds to that of FIG.  3  and the variants thereof described above. 
     Further Alternative Waveguide Configuration of FIG. 12 Using Dynamically Controlled Y Splitters/Couplers 
     FIG. 12 shows an alternative waveguide array in which splitting o f the input optical signal is accomplished using dynamically controlled splitters  120  and the output combined using dynamically controlled couplers  121 , each of these splitters and couplers  120 ,  121  consisting of a Y junction i n which the proportion of mixing/combination is electrically controllable by controller  122  which actuates localised heating elements at the couplers  121 . In FIG. 12, an equalizer for N=8 is shown, for a WDM signal with 100 GHz spacing between channels. The difference in length between waveguides is 0.136 mm. 
     The waveguide array is configured such that, for each one of the N frequency channels at which T n  is defined, a two arm interferometer with differential length element  123  is defined, the inputs to the interferometers being delivered via Y splitters and the outputs combined thereafter by Y couplers of which splitting and coupling ratios are thermally controlled to determine the proportion of input signal  18  conducted by each one of the interferometers. 
     The proportion of the input signal conducted into each one of the interferometers is proportional to coupling coefficient C r . 
     Implementation of the equaliser of FIG. 12 requires that the values of T n  are determined, from which the coupling coefficients C r  may then be computed. The values of splitting ratios S 1  to S 7  may then be calculated and applied to the Y splitters  120  and Y couplers  121  as illustrated in FIG.  12 . 
     In order to obtain splitting ratios which are (of necessity) positive ratios, coupling coefficient C o  is selected to be much larger than the remaining coupling coefficients and is held consequent, i.e. C o  is not independently controlled. 
     Since there is no provision for setting phase values of the coupling coefficients, zero phase (i.e. real values) of C r  are required. This is achieved by forming a set of values T n  where n=1 to 2N and each of the values of T n  for n greater than N is defined by: 
     
       
           T   n   =T   2N−n  for  n&gt;N   (14) 
       
     
     This repeats the sequence T n  in reverse order and creates symmetry such that the Fourier Transform contains only cosine (i.e. real) terms. This technique is sometimes referred to as a discrete cosine transformation (DCT). 
     The fast Fourier transform of the expanded set of T n  is then computed to obtain a set of N coupling coefficients C r  which have real values (i.e. zero phase). 
     In order to minimise losses, the values of C r  are then adjusted by finding the smallest value and subtracting this value from each of the N values of C r . This makes at least one of the values 0 and the remainder positive. 
     The splitting ratios S 1  to S 7  are then calculated and applied to the equaliser. 
     The configuration of FIG. 1 may then be used to periodically update the values of coupling ratios to achieve the required equalisation. 
     Alternative Waveguide Configuration of FIG. 13 Using Dynamically Controlled Y Junctions 
     FIG. 13 illustrates schematically a further embodiment in which a multiple arm Mach-Zehnder interferometer includes controlled Y splitters  130  and Y couplers  131  which are operable to determine the proportion of input signal  18  directed through each of the arms  132  of the interferometer. The equalizer of FIG. 13 provides equalization for a WDM signal of 8 channels with 100 GHz frequency separation between channels. The difference in length between waveguides is 0.272 mm. 
     The proportion of the optical signal on each arm  132  is proportional to coupling coefficient C r  with each of the coupling coefficients having zero phase (i.e. having a real value only). 
     As with the previous embodiment, the values of splitting ratios S 1  to S 7  provided by the splitters and couplers  130  and  131  are controlled electronically by a controller  133 . 
     To calculate the coupling coefficients C r , a set of values of T n  for n=1 to 2N is generated in the same manner as described above with reference to the embodiment of FIG.  12 . This ensures that the resulting coupling coefficients will be real by using the DCT method. 
     The phase of the complex values T n  is then calculated via the Hilbert transform technique referred to above, thereby providing a set of T n  for which the minimum phase condition is satisfied. Consequently, one half of the coupling coefficients will approximate to zero, thereby minimising the number of waveguides required to implement the equalizer. 
     A fast Fourier transform of T n  is then calculated to obtain a set of values over which the first N terms are the C r  coupling coefficients to be used in the equalizer. 
     As described above with reference to the embodiment of FIG. 12, the values of C r  are adjusted by finding the smallest value and subtracting this from each of the values in order to minimise losses. 
     The splitting ratios S 1  to S 7  are then calculated from the C r . 
     The values of T n  may then be periodically updated using the arrangement of FIG.  1 . 
     In the above described embodiments the lengths of waveguides forming the respective arrays are arranged with lengths which increase linearly between waveguides or subsets of waveguides of equal length. Alternative embodiments are possible in which this relationship is non-linear. It may in some circumstances be advantageous for the lengths to vary according to a square, cubic or exponential characteristic. The sequence of length increments may also be discontinuous. 
     The above described embodiments have also been described with reference to a Fourier Transform method of synthesis. Other methods may be possible such as standard multi-variable numerical optimization methods. 
     The described embodiments show an equalizer contained within a line amplifier. The equalizer may alternatively be a stand alone equalizer with dedicated input and output power monitoring circuits. Such equalizers may be incorporated into other optical elements such as routers, cross connect components or add-drop multiplexers. 
     Various alternative methods may be used for determining the power levels of input and output channels to the equalizer, such as for example, the use of an optical spectrum analyzer. 
     The equalizer input may be controlled in response to measurement by other systems, such as for example, a measurement of received power level, optical signal to noise, received bit error rate or eye quality. 
     The above embodiments employ a feedback loop in which measurement of the output is used to obtain a different signal applied to the input. Such feedback may be dispensed with, relying upon the input of a single equalizer setting as being sufficient adjustment. 
     The above embodiments have been described using various numbers of waveguides forming an array. 
     There is in theory no upper limit to the number of waveguides although there are practical limiting factors such as size and limitations due to manufacturing processes. The minimum number of waveguides is envisaged to be four although a typical equalizer may have between 8 and 32.