Transitioning a filter function of a two-port lattice-form planar waveguide optical delay line circuit filter from a start filter function to a target filter function

Abstract

Optically coherent, two-port, serially cascaded-form optical delay line circuits can realize arbitrary signal processing functions identical to those of FIR digital filters with complex filter coefficients whilst maintaining a maximum optical transmission characteristic of 100%. The invention provides an iterative process for transitioning in a step-wise manner a filter function of an optical delay line circuit filter from a start filter function to a target filter function. The invention also describes a dynamic gain equalizer incorporating an optical delay line circuit filter.

1 .- 31 . (canceled) 
   
   
       32 . A dynamic gain equalizer, comprising:
 a two-port optical delay line circuit filter having a cascaded series of N delay lines and N+1 variable directional couplers, each of said N delay lines including a controller for varying a phase difference between optical signals traveling in first and second waveguides of said delay lines and each of said N+1 directional couplers having a controller for varying amplitude coupling between optical signals traveling through said first and second waveguides; and   a control processor having a memory table for storing filter coefficients defining a filter function implemented by said optical delay line circuit filter, said filter coefficients defining phase difference values for said N delay lines and amplitude coupling rates for said N+1 directional couplers, said control processor being arranged to implement a step of transitioning a filter function of a dynamic gain equalizer having an optical delay line circuit from a start filter function to a target filter function, wherein the step of transitioning comprises the steps of:   (a) determining start filter coefficients defining a start filter function for said optical delay line circuit of said equalizer;   (b) interpolating differences in values of said start filter function and said target filter function over the dynamic gain equalizer's spectral range to establish m−1 intermediate filter functions, where m is an integer and m=2;   (c) determining best fit filter coefficients for a first intermediate filter function by performing an optimization process on filter coefficients using the start filter function coefficients to obtain the best fit solution to said first intermediate filter function filter coefficients; and   (d) iteratively repeating step (c) to obtain best fit filter coefficients for any successive intermediate filter function utilizing in each iteration the best fit filter coefficients obtained from the preceding optimization step thereby resulting in a best fit solution to the filter coefficients of the target filter function of the gain equalizer.   
   
   
       33 . An optical signal processing system comprising:
 a two-port optical delay line circuit filter having a cascaded series of N delay lines and N+1 variable directional couplers, each of said N delay lines including a controller for varying a phase difference between optical signals traveling in first and second waveguides of said delay lines and each of said N+1 directional couplers having a controller for varying amplitude coupling between optical signals traveling through said first and second waveguides; and   a control processor having a memory table for storing filter coefficients defining a filter function implemented by said optical delay line circuit filter, said filter coefficients defining phase difference values for said N delay lines and amplitude coupling rates for said N+1 directional couplers, said control processor being arranged to implement a step of transitioning a filter function of an optical delay line circuit filter from a start filter function to a target filter function, said transitioning comprising steps of:   (a) determining start filter coefficients defining a start filter function for said optical delay line circuit filter;   (b) interpolating differences in values of said start filter function and said target filter function over the optical filter's spectral range to establish m−1 intermediate filter functions, where m is an integer and m>=2;   (c) determining best fit filter coefficients for a first intermediate filter function by performing an optimization process on filter coefficients using the start filter function coefficients to obtain the best fit solution to said first intermediate filter function; and   (d) iteratively repeating step (c) to obtain best fit filter coefficients for any successive intermediate filter function utilizing in each iteration the best fit filter coefficients obtained from the preceding optimization step thereby resulting in a best fit solution to the filter coefficients of the target filter function of the optical filter.   
   
   
       34 . An optical signal processing system as claimed in  claim 33 , further comprising an optical delay line circuit tunable filter. 
   
   
       35 . An optical signal processing system as claimed in  claim 33 , further comprising one of a wavelength dispersion filter, a frequency selection filter and a polarization mode dispersion equalizer. 
   
   
       36 . An optical signal processing system as claimed in  claim 33 , further comprising at least one limitation taken from a group of limitations consisting of:
 wherein said step of transitioning further comprises applying to the optical filter the best fit filter coefficients obtained for the intermediate interpolated filter functions and the target filter function in a step-wise order to effect transition from said start filter function to said target filter function.   wherein the values used as a basis for establishing the interpolated intermediate functions comprise start filter and target filter function attenuation values or chromatic dispersion values or a combination of both;   wherein step (a) comprises a selection of an arbitrary set of filter coefficients defining an arbitrary start filter function;   wherein step (a) comprises a set of filter coefficients defining a currently implemented filter function in an operating optical delay line circuit filter;   wherein step (a) comprises calculating the start filter function filter coefficients from a set of recurrent equations;   wherein the filter coefficients of the intermediate and target filter functions of steps (b) and (c) are derived from a measured frequency response curve of an operating optical delay line circuit filter or from a mathematical model of the optical delay line circuit filter;   wherein the differences between values of said start filter function and said target filter function at any given wavelength in the filter's spectral range are interpolated linearly to establish the m−1 intermediate filter functions;   wherein the optimization of step (c) comprises utilizing a non-linear least squares estimation function to determine a best fit solution; and   wherein the optimization process comprises a Gauss-Newton or Levenberg-Marquardt algorithm.   
   
   
       37 . An optical signal processing system as claimed in  claim 43 , further comprising at least one limitation taken from a group of limitations consisting of:
 further comprising maintaining optimized filter coefficients within their respective physical boundaries;   wherein the step of maintaining optimized filter coefficients within their respective physical boundaries comprises adding a penalty function to the non-linear least squares estimation function;   wherein the penalty function is chosen to have a zero or constant value for filter coefficients residing within their respective physical ranges or within pre-defined inner boundaries of said respective physical ranges and an increased value for filter coefficients outside said ranges;   wherein the step of maintaining optimized filter coefficients within their respective physical boundaries comprises a slide back process to place the value of a filter coefficient at the value of a boundary of the physical range or at a value in between the boundaries of the physical range of that that filter coefficient has crossed; and   wherein the slide back process is applied to only delay line filter coefficients.   
   
   
       38 . A dynamic gain equalizer as claimed in  claim 32 , further comprising the step of applying to the optical delay line circuit of the dynamic gain equalizer the best fit filter coefficients obtained for the intermediate interpolated filter functions and the target filter function in a step-wise order to effect transition from said start filter function to said target filter function. 
   
   
       39 . A dynamic gain equalizer as claimed in  claim 32 , wherein the values that are used as a basis for establishing the interpolated intermediate functions comprise start filter and target filter function attenuation values or chromatic dispersion values or a combination of both. 
   
   
       40 . A dynamic gain equalizer as claimed in  claim 32 , wherein the number of steps m is chosen such that the difference in attenuation of subsequent intermediate filter functions is smaller than 1 dB at all relevant wavelengths in the optical delay line circuit filter's spectral range. 
   
   
       41 . A dynamic gain equalizer as claimed in  claim 32 , further comprising at least one limitation taken from a group of limitations consisting of:
 wherein step (a) comprises a selection of an arbitrary set of filter coefficients defining an arbitrary start filter function;   wherein step (a) comprises a set of filter coefficients defining a currently implemented filter function in an operating optical delay line circuit filter; and   wherein step (a) comprises calculating the start filter function filter coefficients from a set of recurrent equations.   
   
   
       42 . A dynamic gain equalizer as claimed in  claim 32 , wherein the filter coefficients of the intermediate and target filter functions of steps (b) and (c) are derived from a measured frequency response curve of an operating optical delay line circuit filter or from a mathematical model of the optical delay line circuit filter. 
   
   
       43 . A dynamic gain equalizer as claimed in  claim 32 , further comprising at least one limitation taken from a group of limitations consisting of:
 wherein the differences between values of said start filter function and said target filter function at any given wavelength in the filter's spectral range are interpolated linearly to establish the m−1 intermediate filter functions;   wherein the optimization of step (c) comprises utilizing a non-linear least squares estimation function to determine a best fit solution; and   wherein the optimization process comprises a Gauss-Newton or Levenberg-Marquardt algorithm.   
   
   
       44 . A dynamic gain equalizer as claimed in  claim 43 , further comprising a step of maintaining optimized filter coefficients within their respective physical boundaries. 
   
   
       45 . A dynamic gain equalizer as claimed in  claim 44 , wherein the step of maintaining optimized filter coefficients within their respective physical boundaries comprises adding a penalty function to the non-linear least squares estimation function. 
   
   
       46 . A dynamic gain equalizer as claimed in  claim 44 , wherein the penalty function is chosen to have a zero or constant value for filter coefficients residing within their respective physical ranges or within pre-defined inner boundaries of said respective physical ranges and an increased value for filter coefficients outside said ranges. 
   
   
       47 . A dynamic gain equalizer as claimed in  claim 44 , wherein the step of maintaining optimized filter coefficients within their respective physical boundaries comprises a slide back process to place the value of a filter coefficient at the value of a boundary of the physical range or at a value in between the boundaries of the physical range of that that filter coefficient has crossed. 
   
   
       48 . A method as claimed in  claim 47 , wherein the slide back process is applied to only delay line filter coefficients. 
   
   
       49 . A computer program product comprising a physical computer readable medium having computer readable program code means embodied therein for causing functions of a dynamic gain equalizer, the computer readable program code means for causing a computer to effect the functions of  claim 32 . 
   
   
       50 . A computer program product comprising a physical computer readable medium having computer readable program code means embodied therein for causing functions of an optical signal processing system, the computer readable program code means for causing a computer to effect the functions of  claim 33 .