Abstract:
The filtering of optical signals, and in particular the interleaving/de-interleaving of optical signals is becoming a necessary step in Dense-Wavelength Division Multiplexing (D-WDM), because of a requirement for smaller channel spacing due to higher levels of traffic. Finite Impulse Response (FIR) filters, including lattice and birefringent waveplate versions, are a particular type of optical filter used for interleavering/de-interleavering optical channels, which can be defined by their transfer function H(f). To ensure dispersion free filtering, the present invention provides a cascaded optical filter, comprising two optical filters, wherein the transfer function of the second filter is the complex conjugate of the first filter, i.e. H 2 (f)=H 1 *(f), or the complex conjugate of the first filter H 1 *(f) multiplied by the transfer function of a dispersion free optical filter G(f). In the waveplate version, the relationship between the crystal angle of the waveplates and the polarization of the input light is manipulated to ensure that the second filtering step eliminates the dispersion caused by the first. Since the polarization of the light can be altered between the first and second filters, birefringent filters can be conceived using a single stack of waveplates that are passed through twice. In lattice filters, a symmetric pulse response is an indication that the cascaded filter is dispersion free. In this case, the second filter is the inverse of the first filter, which individually would give the opposite pulse responses, but together provide a symmetric pulse response.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates to optical filters, and in particular to dispersion-free optical filters for use as interleavers.  
         BACKGROUND OF THE INVENTION  
         [0002]    In dense wavelength division multiplexing (DWDM) optical telecommunications systems, it is advantageous to provide a very narrow width optical filter, which isolates individual transmission channels without distorting the information being transmitted. Accordingly, the optical filter must have a flat-top intensity response and no chromatic dispersion in the pass band. These two conditions guarantee that the filter will not distort the signal either in intensity or in phase.  
           [0003]    The first condition, i.e. flat-top intensity response, is well known and has been achieved through various technologies, such as thin film filters, fiber Bragg gratings, coupled resonant cavities, and lattice filters. However, the second condition, i.e. no chromatic dispersion, (or equivalently having a linear phase response in the pass band) is harder to achieve for optical filters, especially when combined with the flat-top requirement. Resonant interleavers have an inherently high dispersion, and any dispersion compensation, which would only be partial, is very difficult to achieve,  
           [0004]    It is an object of the present invention to disclose practical ways of realizing optical filters with substantially no chromatic dispersion, apart from the material induced dispersion, regardless of the intensity profile of the optical filter. Applications can be envisaged for any type of optical filter, including flat-top filters and interleavers.  
         SUMMARY OF THE INVENTION  
         [0005]    Accordingly the present invention relates to a cascaded optical filter defined by transfer function H T (f) comprising:  
           [0006]    a first optical filtering means defined by transfer function of H 1 (f); and  
           [0007]    a second optical filtering means, optically coupled to the first optical filtering means, defined by transfer function H 2 (f);  
           [0008]    wherein the transfer function of the second optical filtering means H 2 (f) complex conjugate of the transfer function of the first optical filtering means H 1 *(f);  
           [0009]    whereby H T (f)=H 1 (f)×H 2 (f)=H 1 (f)×H 1 *(f). 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]    The invention will be described in greater detail with reference to the accompanying drawings, which illustrate preferred embodiments of the invention, wherein:  
         [0011]    [0011]FIG. 1 is a schematic top view of a cascaded interleaver optical filter according to the present invention;  
         [0012]    [0012]FIG. 2 is a schematic side view of the filter of FIG. 1;  
         [0013]    [0013]FIGS. 3 and 4 illustrate relative orientations of the two birefringent wave-plates and the optical signal during a first and a second pass, respectively, utilizing the filter of FIGS. 1 and 2;  
         [0014]    [0014]FIGS. 5 and 6 illustrate relative orientations of two birefringent wave-plates and an optical signal during a first and a second pass, respectively, utilizing a filter according to another embodiment of the present invention;  
         [0015]    [0015]FIG. 7 is a schematic top view of a cascaded interleaver optical filter according to another embodiment of the present invention, in which an optical signal is double passed through a single birefringent stack;  
         [0016]    [0016]FIG. 8 is a schematic side view of the filter of FIG. 7;  
         [0017]    [0017]FIG. 9 is a schematic top view of a cascaded interleaver optical filter according to another embodiment of the present invention, in which an optical signal is passed through two different birefringent stacks with different wave-plate orientations;  
         [0018]    [0018]FIG. 10 is a schematic side view of the filter of FIG. 9;  
         [0019]    [0019]FIG. 11 is a schematic top view of a cascaded interleaver optical filter according to another embodiment of the present invention in which the optical signal is reflected back through a single birefringent stack;  
         [0020]    [0020]FIG. 12 is a schematic side view of the cascaded interleaver optical filter according to FIG. 11;  
         [0021]    [0021]FIG. 13 is a schematic diagram of a dispersion-free lattice-type cascaded optical filter according to another embodiment of the present invention;  
         [0022]    [0022]FIG. 14 is a schematic diagram of another embodiment of a dispersion free lattice-type cascaded optical filter of FIG. 13; and  
         [0023]    [0023]FIG. 15 is a schematic diagram of another embodiment of a dispersion free lattice-type cascaded optical filter of FIG. 13. 
     
    
     DETAILED DESCRIPTION  
       [0024]    In order to realize a dispersion free optical filter, two optical filters having respective frequency transfer functions H 1 (f) and H 2 (f) are cascaded, provided that the transfer function of the second filter is the complex conjugate of the first filter, i.e. H 1 *(f). Alternatively, to provide a larger degree of flexibility in selecting the second filter, the transfer function of the second filter is obtained by multiplying the complex conjugate of the first filter H 1 *(f) by the transfer function of a third dispersion free optical filter G(f). This guarantees that the cascaded filter, which has a transfer function of H T (f)=H 1 (f)×H 2 (f)=H 1 (f)×H 1 *(f)×G(f), is dispersion free.  
         [0025]    A particular type of optical filter, for which the above-mentioned condition can be easily obtained, is called finite impulse response (FIR) optical filter, also referred to as lattice filters for wave-guide embodiments or Solc filters for stacked birefringent wave-plate embodiments.  
         [0026]    For this specific type of linear phase filter, the frequency transfer function of the filter can always be described as: 
           H   1 ( f )=(α 0 +α 1   .e   iβ.f +α 2   .e   2iβ.f +α 3   .e   3iβ.f + . . . +α n   .e   niβ.f ). 
         [0027]    Where α i , i=1 to n, are related to physical parameters, e.g. coupling ratios in the lattice filters case or wave-plate orientations in Solc filters; and  
         [0028]    where β is related to a length difference in the lattice filters case or retardation in Solc filters.  
         [0029]    To obtain a dispersion free optical filter, one has simply to cascade one optical filter with a frequency transfer function of H 1 (f) with a second optical filter having a frequency transfer function of H 2 (f), which satisfies the condition stated above. This is true when, for the above example of H 1 (f): 
           H   2 ( f )=(α n +α n−1   .e   iβ.f + . . . +α 1   .e   (n−1)iβ.f +α 0   .e   niβ.f ). 
         [0030]    In this example, the second optical filter, which has the frequency transfer function H 2 (f), is constructed using the same physical elements as those used for the first optical filter with the frequency transfer function H 1 (f); however, the orientations of wave-plates are changed in a Solc filter embodiment, or the coupling ratios and exchanging arms are changed in a lattice filter case.  
         [0031]    An example of a dispersion free optical interleaver using a Solc filter will be described, with reference to FIGS. 1 and 2. This specific example cascades a first optical filter, generally indicated at  1 , having frequency transfer functions of H 1 (f) with a second optical filter, generally indicated at  2 , with a frequency transfer function of H 2 (f). Filter  1  includes a birefringent stack  3   a , while filter  2  includes a birefringent stack  3   b , each birefringent stack being comprised of two wave-plates  4  and  5  having thicknesses L and 2L, respectively, e.g. for TiO 2 , L=5.62 mm. The wave-plates  4  and  5  are oriented at 45° and 105°, respectively, with respect to the polarization of the incoming beams of light. The thickness L and the orientations of the wave-plates  4  and  5  are chosen to provide a desired FSR, depending on the birefringence of the wave-plate material.  
         [0032]    A beam of light, including channels λ 1  to λ 11 , is launched from fiber  6 , through collimating lens  7 , into a beam splitter  8 . The lens  7  is preferably a ¼-pitch GRIN lens, and the beam splitter is preferably a walk-off crystal, e.g. TiO 2  or YVO 4 . In the beam splitter  8 , the beam is separated into two orthogonally polarized sub-beams  11  and  12 . The state of polarization of one of the sub-beams, sub-beam  11  in the illustrated embodiment, is rotated by 90° in half-wave plate  13 , so that both sub-beams have the same polarization for entry into the first birefringent stack  3   a . In the illustrated embodiment both sub-beams  11  and  12  are vertically polarized before entering the first birefringent stack  3   a . After passing through the first birefringent stack  3   a , one set of channels, e.g. the even channels λ 2 , λ 4 , λ 6  . . . , remains vertically polarized, while the other set of channels, e.g. the odd channels λ 1 , λ 3 , λ 5  . . . , become horizontally polarized. A second beam splitter  14 , e.g. a walk-off crystal or a polarization beam splitter, is used to further sub-divide the sub-beams  11  and  12  into  11   o ,  11   e ,  12   o  and  12   e . Half-wave plate  15  is positioned in the path of sub-beams  11   e  and  12   e  ensuring that all of the sub-beams  11   o ,  11   e ,  12   o  and  12   e  enter the second birefringent stack  3   b  with the same polarization as each other and with a polarization orthogonal to sub-beams  11  and  12  as they entered the first stack  3   a . In the illustrated embodiment all of the sub-beams enter the second stack  3   b  horizontally polarized. Again, when the even channels in sub-beams  11   e  and  12   e  exit the second birefringent stack  3   b , the polarizations thereof remain the same, i.e. horizontal. Moreover, when the odd channels in sub-beams  11   o  and  12   o  exit the birefringent stack  3   b , the polarization thereof is rotated by 90°. A half-wave plate  16  is used to rotate the polarization of one of sub-beams  11   o  or  12   o , in this case  12   o , so that a beam combiner  17  can bring the two sub-beams together for outputting the odd channels via focusing lens  18  and fiber  19 . Similarly, a half-wave plate  21  rotates the polarization of one of sub-beams  11   e  or  12   e , in this case  11   e , so that the beam combiner  17  can combine the two sub-beams for outputting the even channels via focusing lens  22  and fiber  23   
         [0033]    The illustrated embodiment is shown in operation with vertically polarized sub-beams  11  and  12  as input; however, it would be obvious to adapt the device for any input polarization by rearranging the remainder of the elements accordingly.  
         [0034]    To illustrate that the above described cascade filter device is dispersion free, we first define the transfer function of the filter  1  as: 
           H   1 ( f )= e   3iγ.f .(α 0 +α 1   .e   iβ.f +α 2   .e   2iβ.f +α 3   .e   3iβ.f ) 
         [0035]    Where,  
         [0036]    β=2πLΔn/c  
         [0037]    γ=2πLn o /c  
         [0038]    Δn=n c −n o  (birefringence of the wave-plate material)  
         [0039]    α o =cos θ1.cos θ2.cos θ3  
         [0040]    α 1 =−sin θ1.sin θ2.cos θ3  
         [0041]    α 2 =−cos θ1.sin θ2.sin θ3  
         [0042]    α 3 =−sin θ1.cos θ2.sin θ3  
         [0043]    Where:  
         [0044]    θ1 is the angle between the polarization of input sub-beams  11  and  12  and the crystal axis of the first wave-plate  4 ;  
         [0045]    θ2 is the angle between that of the first wave-plate  4  and the crystal axis of the second wave-plate  5 ; and  
         [0046]    θ3 is the angle between the crystal axis of the second wave-plate  5  and the polarization of the input sub-beams.  
         [0047]    In the example shown above, θ1=45°, θ2=60°, θ3=−105° 
         [0048]    Accordingly, in order for the cascaded filters  1  and  2  to be dispersion free, the filter  2  must have a frequency transfer function H 2 (f) such that H 2 (f)=H 1 (f)*×G(f) Therefore, according to the aforementioned example: 
           H   2 ( f )=(α 3 ′+α 2   ′.e   iβ.f +α 1   ′.e   2iβ.f +α 0   ′.e   3iβ.f )× G ( f ) 
         [0049]    Assuming that the same wave-plate thicknesses are used with different orientations θ1′, θ2′ and θ3′, the following equations are derived: 
         cos θ1′.cos θ2′.cos θ3′=−sin θ1.cos θ2.sin θ3 (α 0 ′=α 3 ) 
         sin θ1′.sin θ2′.cos θ3′=cos θ1.sin θ2.sin θ3 (α 1 ′=α 2 ) 
         cos θ1′.sin θ2′.sin θ3′=sin θ1.sin θ2.cos θ3 (α 2 ′=α 1 ) 
         sin θ1′.cos θ2′.sin θ3′=−cos θ1.cos θ2.cos θ3 (α 3 ′=α 0 ) 
         [0050]    A set of angles satisfying these equations are, for example: 
         θ1′=−45°, θ2′=60°, θ3′=−15° 
         [0051]    In practice, the elements can be positioned in various arrangements to satisfy this requirement. The simplest arrangement would be to simply rotate the polarization of the beams entering the second filter by 90° so as to be orthogonal to when the original beam entered the first filter. FIGS. 3 and 4 illustrate this example, wherein wave plates  4   a  and  5   a  from the first filter  3   a  have the same orientations as wave plates  4   b  and  5   b  from the second filter  3   b , while the polarization of the signal, represented by the double-headed arrow, is rotated by 90°. This is the arrangement disclosed in the above-identified embodiment. This arrangement also provides the possibility of passing the beam through the same birefringent stack twice, with a polarization adjustment in between passes, see FIGS. 7 and 8.  
         [0052]    The embodiment illustrated in FIGS. 7 and 8 is similar to the embodiment illustrated in FIGS. 1 and 2, wherein an input beam is launched into port  7 , divided into sub-beams  11  and  12  in walk-off crystal  8 , directed through birefringent elements  4  and  5 , and divided into sub-beams  11   o ,  11   e ,  12   o  and  12   e  using a polarization beam splitter  114 . However, one pair of sub-beams  11   e  and  12   e  is combined using half-wave plate  31  and walk-off crystal  32 , and transmitted back to the front end of the filter  3  using lenses  33  and  34  and waveguide  35 . The other pair of sub-beams  11   o  and  12   o  are combined using half-wave plate  16  and walk-off crystal  17 , and transmitted to the front end of filter  3  using lenses  38  and  39  and waveguide  40 . After the sub-beams representing the even and odd channels are again divided into pairs of orthogonally polarized sub-beams using walk-off crystal  8 , half-wave plate  41  is positioned in the path of one of each pair to ensure that the sub-beams enter the wave plates  4  and  5  for a second pass with a polarization orthogonal to the polarization that the sub-beams  11  and  12  had upon entering the wave plates  4  and  5  for the first pass. The odd channel sub-beams pass through the birefringent elements  4  and  5  for a second pass, get recombined by waveplate  16  and beam combiner  17 , and are output via lens  18 . The even channel sub-beams pass through the birefringent elements  4  and  5  for a second time, get recombined by waveplate  31  and beams combiner  32 , and are output via lens  22 .  
         [0053]    In an alternative embodiment, when the polarization of the beams is the same entering both filters  3   a  and  3   b , the arrangement of the birefringent plates must be altered. FIGS. 5 and 6 illustrate this example, wherein the polarization of the beams remains constant, while the orientations of the wave plates  4   b  and  5   b  are different than those of wave plates  4   a  and  5   a , respectively. This embodiment is illustrated in FIGS. 9 and 10, which appear in the side and top views to be identical to FIGS. 1 and 2, except for half-wave plate  15  being positioned in the paths of sub-beams  11   o  and  12   o  to ensure that the polarizations of all of the beams entering both stages of the cascaded filter are the same. The important difference in the device illustrated FIGS. 9 and 10, which can be seen in FIGS. 5 and 6, is the different orientations of the crystal axes of the wave plates  4   a ,  4   b ,  5   a  and  5   b.    
         [0054]    In the embodiment presented above, we have assumed that the sub-beams of light  11  and  12  propagate through the two stacks of wave-plates  3   a  and  3   b  in the same order, i.e. first thickness L then second thickness 2L. However, it is possible to go in the opposite order for H 1 (f) and for H 2 (f), meaning that the first stack is L+2L, whereas the second stack is 2L+L. The conditions are then a little bit different: 
         cos θ1′.cos θ2′.cos θ3′=−sin θ1.cos θ2.sin θ3 
         sin θ1′.sin θ2′.cos θ3′=sin θ1.sin θ2.cos θ3 
         cos θ1′.sin θ2′.sin θ3′=cos θ1.sin θ2.sin θ3 
         sin θ1′.cos θ2′.sin θ3′=−cos θ1.cos θ2.cos θ3 
         [0055]    A set of solutions is, for example: 
         θ1′=−15 deg. 
         θ2′=60 deg. 
         θ3′=−45 deg. 
         [0056]    This particular condition enables the invention to be constructed using a single birefringent stack, through which the divided sub-beams are reflected back for a second pass after a 90° rotation, see FIGS. 11 and 12.  
         [0057]    With reference to FIGS. 11 and 12, as before, the combined beam is launched from fiber  6  along a first path through lens  7 , walk-off crystal  8  and birefringent elements  4   a  and  5   a  to polarization beam splitter  14 , wherein it is divided into two orthogonally polarized pairs of sub-beams  11   o  and  12   o , and  11   e  and  12   e . In this embodiment, all of the sub-beams pass through quarter wave plate  44 , and are reflected by mirror  45 . The polarizations of all of the sub-beams is rotated by 90° during two passes through the quarter wave plate  44 , whereby one pair of sub-beams  12   o  and  11   o  get directed straight back through polarization beam splitter  14  for the second pass through filter  3   a  along a second path, while the other pair of sub-beams  12   e  and  11   e  get walked off even further by polarization beam splitter  14  and directed through filter  3   a  along a third path. Prismatic walk-off crystals  46  and  47  are used to direct the pairs of sub-beams to their respective combining crystals  117  and  217 , respectively, for output via lenses  18  and  22 , respectively.  
         [0058]    Any optical filter having any desired intensity profile and having no chromatic dispersion can be made using this technique. Indeed, if |H T (f)| is the desired intensity response, one has to generate H 1 (f) such that:  
                H   1          (   f   )            =              H   τ          (   f   )                                    
 
         [0059]    This is easy in the case of finite impulse response filter using standard filter generation techniques (Fourier synthesis, for example). H 2 (f) is then determined, satisfying the principles of the present invention, to yield the desired result for the cascaded filter H 2 (f).H 1 (f)=H T (f) (dispersion free and |H T (f)| intensity response).  
         [0060]    To physically construct H 1 (f) and H 2 (f) is done by proper choice of coupling ratios and arm lengths (in the case of waveguide lattice filter) or of waveplate orientations and thicknesses (in the case of birefringent Solc filter).  
         [0061]    With reference to FIG. 13, the present invention is exemplified by a pair of cascaded lattice (or Fourier transform-based) optical filters  51  and  52 . The first filter  51  includes a first waveguide  53 , a second waveguide  54 , and three couplers  56 ,  57  and  58   a . The first waveguide includes a first delay line  59  between the first and second couplers  56  and  57 , and a second delay line  61  between the second and third couplers  57  and  58   a . The first delay line  59  is ΔL longer than the distance L between couplers  56  and  57  on the second waveguide  54 . Similarly, the second delay line  61  is 2ΔL longer than the distance L between couplers  57  and  58  on the second waveguide. Optical fibers and planar waveguides are examples of the different kinds of waveguides that can be used.  
         [0062]    The second filter  52  includes a third waveguide  62  extending from the first waveguide, a fourth waveguide  63  extending from the second waveguide, and three couplers  58   b ,  64  and  65 . The fourth waveguide includes a third delay line  67  between couplers  58   b  and  64 , identical to the first delay line  59 , and a fourth delay line  68  between couplers  64  and  65 , identical to the second delay line  61 .  
         [0063]    In a conventional Mach-Zender interferometer each coupler has a coupling ratio of 50:50, which would be dispersion free; however according to the present invention the coupling ratios for the various couplers can have almost any value dependent upon the requirements for the output; however, the coupling ratios of the first and fourth couplers  56  and  58   b  should be substantially the same, while the coupling ratios of the second and fifth couplers  57  and  64 , should also be substantially the same. The coupling ratios of the third coupler  58   a  and the sixth coupler  65  should also be substantially the same. Accordingly, the second optical filter  52  is the inverse of the first optical filer  51 . This arrangement results in a symmetric pulse response and, therefore, a dispersion free response. An example of the symmetric pulse response is illustrated in Table 1 below. Using the filter described above, we assume that a single pulse is input into the first filter and that the output of the first filter is four equidistant pulses having an amplitude ratio of 3:4:2:1. If the second filter is the inverse of the first filter, i.e. has an output with an amplitude ratio of 1:2:4:3, then the overall system will have seven pulses with a symmetric amplitude ratio of 3:10:22:30:22:10:3.  
                                                                                               TABLE 1                                       Time                1   2   3   4   5   6   7                            Amplitude                                       Ratio           3   1   2   4   3           4       1   2   4   3           2           1   2   4   3           1               1   2   4   3               3   10   22   30   22   10   3                      
 
         [0064]    It is possible to expand both the first and second filters  51  and  52  to include other delay lines, such as in FIGS. 14 and 15. The first filter  51 , in FIG. 14, includes another coupler  71  and an additional delay line  72  of length L+2ΔL. Accordingly, the second filter  52  has another coupler  73 , and an inverted delay line  74  of length L+2ΔL corresponding to delay line  72 . In this case couplers  56  and  58   b  would have the same coupling ratio, couplers  57  and  64  would have the same coupling ratio, couplers  71  and  65  would have the same coupling ratio, and couplers  58   a  and  73  would have the same coupling ratio. In FIG. 15, the first filter  51  has an additional delay line  76  of length L+4ΔL, while the second filter  52  has a corresponding inverted delay line  77 . A single coupler  58  can be used instead of the third and fourth couplers  58   a  and  58   b  (See FIG. 15). If the first and second filters only have two delay lines each, e.g. ΔL and 2ΔL, the first, the third and the sixth couplers  56 ,  58 ,  65  would all have the same coupling ratio. However, if the first and second filters have more than two delay lines each, then the single coupler  58  will have no effect on the relationship between the first six couplers. In this case the last coupler of the first filter will be the initial coupler, i.e. the fourth coupler, of the second filter.  
         [0065]    This technique enables the realization of optical filters of any arbitrary intensity response, while keeping a linear phase response. In some practical embodiments of those filters, there can still be a little bit of material induced chromatic dispersion left, but it is usually completely negligible compared to the one created by the non-linear phase response of filters by at least two orders of magnitude. Therefore, the chromatic dispersion of the filters generated by this technique is not strictly speaking zero, but very small (limited to that caused by the material dispersion itself).