This invention relates to a wavelength dispersion compensating filter and, more particularly, to a wavelength dispersion compensating filter which compensates for wavelength dispersion produced at the time of a signal pulse transmission in optical communication using wavelength division multiplexing (referred to as “WDM” below).
In the transmission of optical signal pulses using optical fiber, transmission rate in the fiber differs depending upon the wavelength of light. As a consequence, the waveform of the signal pulses becomes less steep as transmission distance increases. This phenomenon, referred to as-wavelength dispersion, degrades the reception level to a great degree. For example, with an SMF (Single-Mode Fiber), wavelength dispersion on the order of 15 to 16 ps/nm/km is produced in the vicinity of a wavelength of 1.55 μm often used in communication of optical pulses. Wavelength dispersion compensation is for subjecting wavelength dispersion, which has been produced in an optical fiber, to an equivalent amount of wavelength dispersion in reverse.
What is used most often in dispersion compensation at the present time is dispersion compensating fiber (referred to as “DCF” below). This fiber produces reverse dispersion (structural dispersion), by a special refractive index distribution, with respect to material dispersion possessed by the fiber material, and is designed so as to exhibit dispersion which, in total, is the reverse of that of ordinary SMF. It is possible to achieve dispersion compensation that is five to ten times that obtained with SMF of an equivalent length. Such DCF is connected to SMF in a repeater office to make the dispersion zero overall.
Dispersion compensation using DCF involves two major problems in terms of transmission system architecture. One is that the distance between repeaters where DCF is inserted differs from system to system. This means that it is necessary to provide a dispersion compensating module having a specifically designed DCF length for each and every repeater node. The second problem arises from the fact that the wavelength dependence of the dispersion characteristic, which is referred to as “dispersion slope”, is not the same for DCF and SMF. Wavelength dispersion that could not be subjected to dispersion compensation completely (such dispersion shall be referred to as “residual dispersion” below) occurs at both ends of a wavelength band used in WDM transmission, e.g., a wavelength band referred to as the “C band” in which the wavelength of light is in the vicinity of 1530 to 1560 nm. This residual dispersion accumulates as transmission distance increases and, as a result, it is necessary to compensate for this residual dispersion channel by channel. For example, in the example shown in FIG. 16, if a signal is transmitted through 10 km of SMF and dispersion compensation is applied to the center wavelength (1545 nm) using DCF having a dispersion slope of 0.2 ps/km/nm2, residual dispersions of about 20 ps/nm and about −30 ps/nm occur in 1st and 40th channels, respectively, having a channel wavelength spacing of 100 GHz in the C band. As a consequence of these two problems, dispersion compensating modules of a very large number of types must be prepared in order to construct a single system, and designing the system becomes very complicated. In order to solve these problems, there is compelling need for implementation of a wavelength dispersion compensator in which the amount of compensation is capable of being varied over a range of negative to positive values.
One example that can be mentioned from the standpoint of good productivity is a variable dispersion compensator that employs PLC (Planar Lightwave Circuit) technology.
Filters used in wavelength dispersion compensation are classified broadly into two types, namely IIR (Infinite Impulse Response) and FIR (Finite Impulse Response). Both achieve variable compensation by changing the optical path length of the portion of a waveguide that decides the amount of compensation, using an EO (electro-optic) effect that produces a change in dielectric constant within the waveguide, i.e., a change in effective refractive index), by applying an electric field from outside the waveguide, or a TO (thermo-optic) effect in which the refractive index of the waveguide is changed by temperature.
The FIR-type filter controls frequency response by feed-forward. A typical arrangement that can be mentioned is composed of serially connected multiple MZIs (Mach-Zehnder interferometers) proposed by Takiguchi et al. (see Variable Group-Delay Dispersion Equalizer, IEEE J. of Quant. Elect.), illustrated in FIG. 17. As shown in FIG. 17, MZIs 1 each have a structure in which two waveguides 1a, 1a are embraced by two couplers 1b, 1b. A heater 1c for adjustment of the optical path length is provided on the upper side of the central portion of the waveguide on the outer side of each MZI, and electrodes 1d for applying voltage are formed on both sides of the headers 1c. The FIR-type wavelength dispersion compensating filter is obtained by building up an SiO2 clad 3 on an SiO2 substrate 2 and building up an SiO2 core layer 4 on the clad 3. Next, by performing patterning, the two waveguides 1a, 1a are formed by the SiO2 core 4, as depicted in FIG. 17, and the couplers 1b are formed at suitable locations. Thereafter, a further clad layer is built up, though this is not shown, the heater 1c is formed on this clad layer and then the electrode 1d is formed on this heater to complete the device.
This FIR-type wavelength dispersion compensating filter has a highly stable frequency characteristic. However, a large number of circuit elements (the number of MZI stages) is needed to produce a steep frequency response. Since this necessitates a large chip area, this filter is not very desirable in terms of productivity.
The IIR-type filter, which is referred to also as a “rational filter”, has one or more feedback loops between the filter input and output. With the IIR-type filter, the frequency (wavelength) characteristic has a peak ascribable to the feedback loops, and it is possible to obtain a steep frequency response with a small number of circuit elements (couplers, etc.) by suitably engineering the position of the peak, as is known in electrical circuit theory. The most simplest of the IIR-type filters is a ring resonator. Though a ring resonator exhibits a very steep frequency response, the FSR (Free Spectral Range, which corresponds to the spacing of resonance peaks) thereof is proportional to 1/(ring length). As a consequence, accuracy of the length of waveguides having little difference in refractive index are limited by the minimum bending radius and there are cases where the desired FSR cannot be obtained.
An all-pass optical filter (U.S. Pat. No. 6,289,151 B1, referred to as a Madsen-type or prior-art filter below) according to R. F. Kazarinov and C. K. Madsen, et al. has been proposed as a filter to solve this problem. As shown in FIG. 18, this filter has a structure in which one input and one output of an MZI 5 are connected by a loop. The MZI 5 has a structure in which waveguides 5a, 5b are embraced by two couplers 5c, 5d, heaters 5e, 5f for adjusting amount of dispersion compensation are provided on the upper side of the central portion of the waveguides 5a, 5b, and electrodes (not shown) for applying voltage are formed on both sides of each of the heaters. A heater 6b for adjusting center wavelength is provided on the upper side of the central portion of a waveguide 6a of a loop portion 6 that forms the loop. Reference numeral 7 denotes a silicon (Si) substrate and 8 an SiO2 clad. This all-pass optical filter is formed in a manner similar to the filter shown in FIG. 17.
In accordance with the all-pass optical filter shown in FIG. 18, the amount of change in phase at the design wavelength and the FSR can be designed independently using two parameters, namely {circumflex over (1)} loop length and {circumflex over (2)} the difference in optical path length between the two waveguides 5a, 5b in the MZI. As a result, it is possible to realize a compact dispersion compensator that uses an IIR filter at a design wavelength.
As mentioned above, dispersion compensation requires compensation even of residual dispersion after compensation by DCF is applied. Accordingly, the ability to perform positive compensation and negative compensation, inclusive of an amount of dispersion compensation of zero, is sought. The prior-art Madsen-type dispersion compensating filter cannot achieve an amount of dispersion compensation of zero when manufacturability is taken into account, and a problem which arises is that many products in which the range of dispersion compensation is limited are produced.
The problems of the Madsen-type dispersion compensating filter will now be described in detail through the following procedure: {circumflex over (1)} The transfer function of the Madsen-type dispersion compensating filter will be given, the conditions that give dispersion compensation quantity=0 will be indicated and the limitation imposed upon the design parameters by the conditions for dispersion compensation quantity=0 will be indicated. {circumflex over (2)} The fact that many dispersion compensators which are limited in terms of compensation range occur will be discussed, in which it will be pointed out that it is difficult to reconcile both the conditions that give dispersion compensation quantity=0 and design parameters exhibiting variations in manufacture when the filter is actually manufactured, this being ascribable to the range of fluctuation when manufacturing variations in each of the design parameters are taken into account.                Design parameters of Madsen-type dispersion compensating filter        
The design parameters and operation (see Table 1) of a prior-art Madsen-type dispersion compensating filter (see FIG. 18) will be described in simple terms. As shown in Table 1 below, the design parameters are loop optical path length ΔLrn(λ), MZI optical path length difference ΔLmn(λ) and MZI coupler splitting ratios θ1, θ2.
TABLE 1RELATIONSHIP BETWEEN PARAMETERS OF MADSEN-TYPEFILTERS AND TRANSMISSION CHARACTERISTICSRELATEDDESCRIPTIONDESIGNCHARAC-OFPARAMETERTERISTICSTENDENCY{circle around (1)}OPTICALFSR; CENTERFSR 0.8 nmPATHFREQUENCYSPACING →LENGTH OFABOUT 2-mmLOOPSPACING; CONTROLΔ Lrn(λ)OF CENTERWAVELENGTH WITHLINEAR CHANGE OFλ ORDER{circle around (2)}MZI OPTICALDISPERSIONPHASE COMPENSATIONPATHCOMPENSATIONQUANTITY MAX FORLENGTHQUANTITY;LENGTH OF SEVERAL-DIFFERENCEBANDWIDTHMICRON ORDER;Δ Lmn(λ)(TRADEOFF)COMPENSATIONQUANTITY ISREDUCED INACCORDANCE WITHDEVIATION FROM THISLENGTH{circle around (3)}MZISTRENGTH OFVARIATION IN PHASECOUPLERPHASEIS REDUCED IFSPLITTINGCHANGE;COUPLING IS WEAKRATIOSSETTING OFθ1, θ2DISPERSIONCOMPENSATIONQUANTITY =0 POINT
{circumflex over (1)} The FSR is set by the loop built-in optical path length (loop length prior to adjustment) ΔLrn(λ), where ΔLr represents the loop optical path length and n(λ) the effective refractive index of the waveguide. The heater 6b is formed in the loop 6 and adjustment of the optical path length on the order of λ (1.55 μm) is performed by the TO effect, thereby controlling the center wavelength position within the FSR.
{circumflex over (2)} Path length difference ΔLmn(λ) between the waveguides 5a and 5b of the MZI portion is related to the amount of dispersion compensation, where ΔLm represents the path length difference and n(λ) the effective refractive index of the waveguide. The amount of dispersion compensation at non-heating of the heaters 5e, 5f provided on the branches 5a, 5b of the MZI portion is decided by the built-in path length difference (path length difference prior to adjustment) ΔLmn(λ), and the amount of dispersion compensation is controlled by controlling the heating of the heaters 5e, 5f. In a case where the amount of compensation applied is minimum when the heaters are not producing heat, the built-in path length difference is assumed to be zero.
{circumflex over (3)} (The coupling strengths (rotation angles θ1, θ2) of the two couplers 5c and 5d exhibit a fixed relationship in order to implement dispersion compensation quantity=0. In a case where the dispersion compensation quantity is adjusted by changing ΔLmn(λ) by the TO effect, etc., it will suffice to select the rotation angles θ1, θ2 so as to satisfy Equation (11) (e.g., rotation angle rotation angles θ1=θ2=π/4, etc.) described below.                Transfer function of Madsen-type dispersion compensating filter        
The transfer function of a Madsen-type dispersion compensating filter is given as follows:
First, a transfer matrix m(λ) of an MZI (4-terminal circuit) is expressed as follows using the path difference ΔLm, coupler rotation angles (couplings) θ1 θ2, effective refractive index n(λ) of the waveguide and input wavelength λ:                                                         m              =                            ⁢                                                                    [                                                                                                                        m                            11                                                                                                                                m                            12                                                                                                                                                                            m                            21                                                                                                                                m                            22                                                                                                                ]                                    ⁢                                                                           ⁢                  where                  ⁢                                                                           ⁢                  det                  ⁢                                                                           ⁢                  m                                =                1                                                                                        m              =                            ⁢                                                                    [                                                                                                                        cos                            ⁢                                                                                                                   ⁢                                                          θ                              2                                                                                                                                                                                          -                              sin                                                        ⁢                                                                                                                   ⁢                                                          θ                              2                                                                                                                                                                                                        sin                            ⁢                                                                                                                   ⁢                                                          θ                              2                                                                                                                                                                                          +                              cos                                                        ⁢                                                                                                                   ⁢                                                          θ                              2                                                                                                                                            ]                                    ⁡                                      [                                                                                                                        exp                            ⁡                                                          [                                                                                                -                                  j                                                                ⁢                                                                                                                                   ⁢                                π                                ⁢                                                                                                                                   ⁢                                Δ                                ⁢                                                                                                                                   ⁢                                                                  L                                  m                                                                ⁢                                                                                                      n                                    ⁡                                                                          (                                      λ                                      )                                                                                                        /                                  λ                                                                                            ]                                                                                                                                0                                                                                                                      0                                                                                                      exp                            ⁡                                                          [                                                              j                                ⁢                                                                                                                                   ⁢                                π                                ⁢                                                                                                                                   ⁢                                Δ                                ⁢                                                                                                                                   ⁢                                                                  L                                  m                                                                ⁢                                                                                                      n                                    ⁡                                                                          (                                      λ                                      )                                                                                                        /                                  λ                                                                                            ]                                                                                                                                            ]                                                  ⁡                                  [                                                                                                              cos                          ⁢                                                                                                           ⁢                                                      θ                            1                                                                                                                                                                            -                            sin                                                    ⁢                                                                                                           ⁢                                                      θ                            1                                                                                                                                                                                        sin                          ⁢                                                                                                           ⁢                                                      θ                            1                                                                                                                                                                            +                            cos                                                    ⁢                                                                                                           ⁢                                                      θ                            1                                                                                                                                ]                                                                                        (        1        )            Further, a phase shift h(λ) produced by the loop-back portion 6 is expressed as follows using the optical path length ΔLr:h(λ)=exp[−j2πΔLrn(λ)/λ]  (2) 
A transfer function H(λ) of the Madsen-type dispersion compensating filter is expressed by the following equation using m(λ) and h(λ):                               H          ⁡                      (            λ            )                          =                                                            h                ⁡                                  (                  λ                  )                                            -                              m                22                                                                                      h                  ⁡                                      (                    λ                    )                                                  ⁢                                  m                  11                                            -              1                                =                                                    h                ⁡                                  (                  λ                  )                                            -                              m                11                *                                                                                      h                  ⁡                                      (                    λ                    )                                                  ⁢                                  m                  11                                            -              1                                                          (        3        )            where m11* represents the complex conjugate of m11. Group delay D(λ) is obtained by differentiating the phase part of the transfer function of Equation (3) by ω(=2πc/λ, where c represents the velocity of light), and wavelength-dispersion DS(λ) is obtained by differentiating the group delay D(λ) by wavelength λ. That is, if we let the phase part of the transfer function be represented by argH(λ), then we haveD(λ)=−(λ2/2πc)(d/dλ)[argH(λ)]  (4) DS(λ)=(d/dλ)D(λ)  (5) Here argH(λ) is expressed as follows:                               arg          ⁢                                           ⁢                      H            ⁡                          (              λ              )                                      =                              arc            ⁢                                                   ⁢            tan            ⁢                          {                                                                    sin                    ⁡                                          [                                                                        -                          2                                                ⁢                                                                                                   ⁢                        π                        ⁢                                                                                                   ⁢                        Δ                        ⁢                                                                                                   ⁢                                                  L                          r                                                ⁢                                                                              n                            ⁡                                                          (                              λ                              )                                                                                /                          λ                                                                    ]                                                        -                  β                                                                      cos                    ⁡                                          [                                                                        -                          2                                                ⁢                        π                        ⁢                                                                                                   ⁢                        Δ                        ⁢                                                                                                   ⁢                                                  L                          r                                                ⁢                                                                              n                            ⁡                                                          (                              λ                              )                                                                                /                          λ                                                                    ]                                                        -                  α                                            }                                -                      arc            ⁢                                                   ⁢            tan            ⁢                          {                                                                    α                    ⁢                                                                                   ⁢                                          sin                      ⁡                                              [                                                                              -                            2                                                    ⁢                                                                                                           ⁢                          π                          ⁢                                                                                                           ⁢                          Δ                          ⁢                                                                                                           ⁢                                                      L                            r                                                    ⁢                                                                                    n                              ⁡                                                              (                                λ                                )                                                                                      /                            λ                                                                          ]                                                                              -                                      β                    ⁢                                                                                   ⁢                                          cos                      ⁡                                              [                                                                              -                            2                                                    ⁢                          π                          ⁢                                                                                                           ⁢                          Δ                          ⁢                                                                                                           ⁢                                                      L                            r                                                    ⁢                                                                                    n                              ⁡                                                              (                                λ                                )                                                                                      /                            λ                                                                          ]                                                                                                                                                                       ⁢                                                            α                      ⁢                                                                                           ⁢                                              cos                        ⁡                                                  [                                                                                    -                              2                                                        ⁢                            π                            ⁢                                                                                                                   ⁢                            Δ                            ⁢                                                                                                                   ⁢                                                          L                              r                                                        ⁢                                                                                          n                                ⁡                                                                  (                                  λ                                  )                                                                                            /                              λ                                                                                ]                                                                                      -                                          β                      ⁢                                                                                           ⁢                                              sin                        ⁡                                                  [                                                                                    -                              2                                                        ⁢                            π                            ⁢                                                                                                                   ⁢                            Δ                            ⁢                                                                                                                   ⁢                                                          L                              r                                                        ⁢                                                                                          n                                ⁡                                                                  (                                  λ                                  )                                                                                            /                              λ                                                                                ]                                                                                      -                    1                                                              }                                                          (        6        )            where the following holds:α=cos [πΔLmn(λ)/λ] cos(θ1+θ2)  (7) β=sin [πΔLmn(λ)/λ] cos(θ1−θ2)  (8)                 Conditions that give dispersion compensation quantity=0        
Dispersion compensation quantity=0 means that DS(λ)=0 holds in Equation (5) and that D(λ) in Equation (4) is a constant. This signifies that it is required that argH(λ) be expressed by the following function:argH(λ)=C1/λ+C2 (C1, C2 are constants)  (9) orargH(λ)=C3 (C3 is a constant)  (10) by the design parameters.
A condition that will satisfy Equation (9) is (α,β)=(0,0), in which we will haveargH(λ)=−2ΔLrn(λ)/λFurther, examples of parameters are the following Equations (11), (12):ΔLm=0 and θ1+θ2=π(2k+1)/2(k=0,1,2, . . . )  (11) n(λ)=C4λ+C5 (C4, C5 are constants)  (12) or the following equations (13), (14):θ2=π/2 and θ1=θ2+π(2m−1)/2(m=1,2,3, . . . )  (13) n(λ)=C4λ+C5 (C4, C5 are constants, ΔLm≠0)  (14) 
In case of a quartz-type waveguide, it is considered that Equations (13) and (14) are approximations that will hold true satisfactorily in the C band (in the vicinity of wavelengths 1530 to 1560 nm). This condition means that signal light passes through the loop one time only.
On the other hand, a condition that will satisfy Equation (10) is (α,β)=(±1,0), and the following Equation (15) is an example of a parameter:ΔLm=0 and θ1+θ2=mπ(m=0,1,2,3 . . . )  (15) This condition means that signal light is transmitted without entering the loop.
Thus, in the prior-art example, it will be understood that the relationships of Equations (11) to (15) are required for the two coupler splitting ratios (rotation angles θ1, θ2) in order to obtain dispersion compensation quantity=0.                Conditions that give dispersion compensation quantity=0, and manufacturing variations        
When manufacturability (the product of a variation in refractive index and a variation in core machining) is taken into account, it is required that a deviation of, e.g., ±10% from what is sought be allowed for the coupler splitting ratio. In other words, owing to a variation in manufacture, coupler splitting ratio deviates from the design value by a maximum of ±10%. If the coupler splitting ratio deviates from this design value by more than a predetermined percentage, it will no longer be possible to obtain dispersion compensation quantity=0 even if the MZI optical-path difference ΔLmn(λ) and feedback-loop path length ΔLrn(λ), which are factors adjustable by the TO effect, are varied. In other words, it is not possible to apply a range extending from dispersion compensation quantity=0 to a minimum compensation quantity (a minimum compensation quantity that corresponds to deviation from the design condition of the two coupler branches). As a result, the aforementioned problem arises, namely the occurrence of a large number of products that cannot be compensated completely for residual dispersion extending from positive to negative values.
FIG. 19 illustrates as an example of a group delay D(λ) vs. wavelength (λ) characteristic, namely a wavelength dispersion compensation characteristic, for a case where the rotation angle θ2 of the second coupler has deviated from the design value (θ1=θ2=π/4) by 5%. The slope of this characteristic is the wavelength dispersion DS(λ). This is the dispersion compensation quantity. In FIG. 19, the optical path length difference ΔLmn(λ) (which is an adjustable parameter) between the MZI branches is varied from the positive state, namely a state in which the waveguide 5b on the outer side is long, to the negative state, namely a state in which the waveguide 5a on the inner side is long. However, it will be understood that even if the optical path length difference ΔLmn(λ) is varied from 150 nm to −150 nm, a range in which dispersion compensation quantity=0 (zero slope) holds is not obtained anywhere in the necessary band (10 Gbps: 0.16 nm).
Further, the center wavelength (peak wavelength) also varies owing to the effect of the deviation in the rotation angle θ2 (there is no change in the case of a value that is in accordance with the design value), as indicated by FIG. 19. In order to compensate for this change, it is necessary to adjust the optical path length θLrn(λ) of the loop portion.