# Patent

## Title
Wavelength dispersion compensating filter

## Abstract

A 2-input, 2-output optical circuit is constructed by serially connecting two or more Mach-Zehnder interferometers possessing a structure in which two waveguides are embraced by two couplers. One output and one input of the two 2-input, 2-output optical circuit are connected by an optical propagation path to thereby construct a loop circuit. The waveguides of the Mach-Zehnder interferometers as well as the loop circuit are each provided with an optical path-length adjustment portion, thereby constructing a wavelength dispersion compensating filter.

## Background
BACKGROUND OF THE INVENTION
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 1







RELATIONSHIP BETWEEN PARAMETERS OF MADSEN-TYPE


FILTERS AND TRANSMISSION CHARACTERISTICS












RELATED
DESCRIPTION



DESIGN
CHARAC-
OF



PARAMETER
TERISTICS
TENDENCY














{circle around (1)}
OPTICAL
FSR; CENTER
FSR 0.8 nm



PATH
FREQUENCY
SPACING →



LENGTH OF

ABOUT 2-mm



LOOP

SPACING; CONTROL



Δ Lrn(λ)

OF CENTER





WAVELENGTH WITH





LINEAR CHANGE OF





λ ORDER


{circle around (2)}
MZI OPTICAL
DISPERSION
PHASE COMPENSATION



PATH
COMPENSATION
QUANTITY MAX FOR



LENGTH
QUANTITY;
LENGTH OF SEVERAL-



DIFFERENCE
BANDWIDTH
MICRON ORDER;



Δ Lmn(λ)
(TRADEOFF)
COMPENSATION





QUANTITY IS





REDUCED IN





ACCORDANCE WITH





DEVIATION FROM THIS





LENGTH


{circle around (3)}
MZI
STRENGTH OF
VARIATION IN PHASE



COUPLER
PHASE
IS REDUCED IF



SPLITTING
CHANGE;
COUPLING IS WEAK



RATIOS
SETTING OF



θ1, θ2
DISPERSION




COMPENSATION




QUANTITY =




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 have

D(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) 

or

argH(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 have

argH(λ)=−2ΔLrn(λ)/λ

Further, 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.
SUMMARY OF THE INVENTION
Accordingly, an object of the present invention is to so arrange that even if the coupler splitting ratio (coupler rotation angle) of the MZI portion deviates from the design value from one device to the next owing to manufacturing variations or the like, dispersion compensation quantity=0 will be obtained by adjusting the value of optical path length difference ΔLmn(λ) using the TO effect or EO effect.
Another object of the present invention is to make positive compensation and negative compensation, inclusive of dispersion compensation quantity=0, possible, thereby making it possible to compensate for residual dispersion after dispersion compensation.
According to the present invention, the foregoing objects are obtained by providing a wavelength dispersion compensating filter having a 2-input, 2-output optical circuit, in which the 2-input, 2-output optical circuit is constructed by serially connecting two or more Mach-Zehnder interferometers possessing a structure in which two waveguides are embraced by two couplers, one output and one input of the two 2-input, 2-output optical circuit are connected by an optical propagation path to thereby construct a loop circuit, and the waveguides of the Mach-Zehnder interferometers as well as the loop circuit are each provided with a optical path-length adjustment portion. The optical path-length adjustment portion adjusts optical path length by the electro-optic effect or thermo-optic effect.
If a wavelength dispersion compensating filter is thus constructed, dispersion compensation quantity=0 can be obtained by adjusting the value of optical path length difference ΔLmn(λ) using the TO effect, etc., even if the coupler splitting ratio (coupler rotation angle) of the MZI portion deviates from the design value from one device to the next owing to manufacturing variations or the like. As a result, wavelength dispersion compensation can be performed to deal even with residual deviation irrespective of individual difference, device manufacturability (yield) can be increased by a wide margin and the cost of the dispersion compensating device can be reduced. In addition, the size of the dispersion compensating filter can be reduced by serially connecting two Mach-Zehnder interferometers.
A coupler having little wavelength dependence is used as the couplers that construct the Mach-Zehnder interferometers. If this arrangement is adopted, it is possible to endow each wavelength-division-multiplexed optical signal with a splitting strength that is as designed and it becomes possible to reduce variations in the amount of dispersion compensation.
Further, if it is so arranged that the optical propagation paths of the other input and output not used as the loop of the 2-input, 2-output optical circuit are made to intersect each other, then it will be unnecessary to bend the input and output propagation paths even if loop length ΔLr is shorter than a prescribed length. This means that radiation loss is not increased at bent portions.
Further, the waveguides are made to intersect each other in the vicinity of substantially the center of each Mach-Zehnder interferometer in such a manner that the built-in path-length differences between the two optical waveguides constructing the branches of each MZI portion will be approximately equal. If this is done, one branch of the MZI portion will extend from the inner side to the outer side, the other branch will extend from the outer side to the inner side, the lengths of the two branches can be made uniform and a path-length difference on the order to 0 to λ (1.55 μm) can be achieved.
Further, if two or more of the above-described dispersion compensating filters are connected serially, the dispersion compensation quantity per filter can be reduced to broaden the pass band. As a result, the desired dispersion compensation quantity can be generated overall and the band can be broadened.
Other features and advantages of the present invention will be apparent from the following description taken in conjunction with the accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram useful in describing the principles of a wavelength dispersion compensating filter of the invention having a 2-input, 2-output optical circuit;
FIG. 2 is a modification of FIG. 1 and is for illustrating the compensation characteristic (group delay characteristic) of the present invention;
FIG. 3 is a group delay characteristic diagram of a wavelength dispersion compensating filter according to the present invention;
FIG. 4 is a diagram showing the topology of a dispersion compensating filter according to a first embodiment of the present invention;
FIG. 5 illustrates an example of the structure of means for adjusting optical path-length difference in an SiO2-type waveguide;
FIG. 6 illustrates an example of the structure of means for adjusting optical path-length difference in an LiNbO3-type waveguide;
FIG. 7 illustrates an example of the structure of an MMI-type coupler;
FIG. 8 illustrates an example of the structure of a WINC-type coupler;
FIG. 9 is a wavelength vs. transmission splitting intensity characteristic diagram illustrating the wavelength dependence of the splitting intensities of an MMI-type coupler, WINC-type coupler and directional coupling-type coupler;
FIG. 10 is a diagram showing the topology of a dispersion compensating filter according to a second embodiment of the present invention;
FIG. 11 is a diagram showing the topology of a dispersion compensating filter according to a third embodiment of the present invention;
FIG. 12 is a diagram showing the topology of a dispersion compensating filter according to a fourth embodiment;
FIG. 13 is a diagram showing the topology of a dispersion compensating filter according to a fifth embodiment;
FIG. 14 illustrates a dispersion compensation characteristic in the case of the 3-stage arrangement of FIG. 13;
FIG. 15 illustrates an example of the steps of a manufacturing process for achieving the structure of a dispersion compensator according to the present invention;
FIG. 16 is a diagram useful in describing residual dispersion;
FIG. 17 is a diagram showing a prior-art dispersion compensating filter composed of serially connected multiple MZIs;
FIG. 18 is a Madsen-type prior-art dispersion compensating filter; and
FIG. 19 shows a group delay characteristic according to an example of the prior art.



DESCRIPTION OF THE PREFERRED EMBODIMENTS
(A) Principles of the Present Invention
Here it will be assumed that a wavelength dispersion compensating filter, which is a 2-input, 2-output optical circuit, is obtained by serially connecting two or more MZIs. As a result, even if the rotation angle of the coupler in the MZI portion deviates from the design value from one device to the next owing to manufacturing variations or the like, dispersion compensation quantity=0 will be obtained by adjusting the value of optical path length difference ΔLmin(λ) (i=1, 2) between the branches of the MZI using the TO effect. This makes it possible to solve the problem encountered in the prior art. The fact that the above problem is solved will be described taking as an example a case where a 2-input, 2-output circuit (wavelength dispersion compensating filter), which is the simplest arrangement, is constructed by connecting two MZIs in series.
FIG. 1 is a diagram useful in describing the principles of the inventive wavelength dispersion compensating filter having a 2-input, 2-output optical circuit. MZIs 11, 12 each having a structure in which two waveguides 11a, 11b; 12a, 12b are embraced by respective ones of two couplers CPL1, CPL2; CPL2, CPL3 are serially connected to thereby construct a 2-input, 2-output optical circuit. One output and one input of the 2-input, 2-output optical circuit are connected by an optical propagation path to construct a loop circuit 13, and the waveguides 11a, 11b; 12a, 12b of the MZIs 11, 12 as well as the loop circuit 13 are formed to have heaters 14a to 14e, respectively, as path length adjustment portions.
(a) Design Parameters and Driving Method According

    
    
        to the invention (2-stage MZI structure)
    
    


The design parameters and operation (see Table 2) of the inventive wavelength dispersion compensating filter having the two MZIs 11, 12 will now be described in brief.







TABLE 2







RELATIONSHIP BETWEEN PARAMETERS OF PRESENT


INVENTION (2-MZI STRUCTURE) AND TRANSMISSION


CHARACTERISTICS












RELATED
DESCRIPTION



DESIGN
CHARACTER-
OF



PARAMETER
ISTICS
TENDENCY














{circle around (1)}
OPTICAL
FSR; CENTER
FSR 0.8 nm SPACING →



PATH
FREQUENCY
ABOUT 2-mm SPACING;



LENGTH OF

CONTROL OF CENTER



LOOP

WAVELENGTH WITH



Δ Lrn(λ)

LINEAR CHANGE OF





λ ORDER


{circle around (2)}
MZI OPTICAL
DISPERSION
COMPENSATION



PATH
COMPENSATION
QUANTITY IS



LENGTH
QUANTITY;
ADJUSTED BY



DIFFERENCE
BANDWIDTH
PERFORMING DRIVE



Δ m1 (λ)
(TRADEOFF)
SUCH THAT



Δ m1 (λ)

Δ Lm2n(λ) = −Δ





Lm1n(λ) HOLDS AT





θ1 = θ3 = π/4


{circle around (3)}
FIRST AND
STRENGTH OF
VARIATION IN PHASE



THIRD
PHASE CHANGE
IS REDUCED IF



COUPLER

COUPLING IS



SPLITTING

WEAK



RATIOS



θ1, θ3


{circle around (4)}
SECOND
COMPENSATION
COMPENSATION



COUPLER
QUANTITY
QUANTITY



SPLITTING
(θ1 = θ3 = π/4,
WHEN HEATER IS NOT



RATIO
Δ Lm1 =
DRIVEN IS INCREASED



θ2
Δ Lm2 = 0
AS COUPLING IS




WHEN MZI
STRENGTHENED




HEATER IS




NOT DRIVEN









{circumflex over (1)} The FSR and control of center wavelength are similar to those of the prior art. The FSR is set by the loop built-in optical path length (loop length prior to adjustment) ΔLrn(λ), the heater 14e is formed in the loop portion and adjustment of the optical path length on the λ order is performed by the TO effect, etc., thereby controlling the center wavelength position within the FSR.
{circumflex over (2)} Path length difference ΔLmin(λ) (i=1, 2) between the two MZI portions 11 and 12 is related to the amount of dispersion compensation. At rotation angles θ1=θ3=π/4 of the first and third couplers CPL1, CPL3, drive is performed in such a manner that ΔLm2n(λ)=−ΔLm1n(λ) will hold, thereby controlling the amount of dispersion compensation with the center wavelength being held fixed. It should be noted that the center wavelength shifts when drive is performed asymmetrically. If θ1, θ3 have deviated from their design values, the values of ΔLm1n(λ), ΔLm2n(λ) obtained by Equation 25, etc., described below, are applied beforehand as offsets and the differences of the offsets are driven symmetrically.
{circumflex over (3)} The amount of dispersion compensation at non-heating of the heaters 14a, 14b, 14c, 14d in the MZI portions 11, 12 is substantially decided by the rotation angle (coupling strength) θ2 of the second coupler CPL2.
{circumflex over (4)} In a case where θ1=θ3=π/4 holds, the amount of dispersion compensation increases with an increase in coupling strength starting from a coupling strength of zero and an amount of dispersion compensation of zero. The amount of dispersion compensation attains the maximum value in the vicinity of θ2=π/4 (the splitting ratio is 1:1).
(b) Transfer Function of Optical Circuit According

    
    
        to the invention (two MZIs serially connected)
    
    


The transfer function of the 2-stage MZI structure is expressed by replacing the transfer matrix m(λ) of the MZI (4-terminal circuit) in Equation (3) by a transfer matrix M2(λ) (shown below) of the MZI arranged in two stages.
The transfer matrix M2(λ) of the MZI arranged in two stages is expressed as follows using each path length difference ΔLmi (i=1, 2), coupler rotation (coupling) θj (j=1, 2, 3), effective refractive index n(λ) of the waveguide and input wavelength λ: 



  
    
      
        
          
            
              
                
                  M
                  2
                
                =
                
                ⁢
                
                  
                    
                      [
                      
                        
                          
                            
                              M
                              
                                
                                   
                                
                                
                                  2
                                  11
                                
                              
                            
                          
                          
                            
                              M
                              
                                
                                   
                                
                                
                                  2
                                  12
                                
                              
                            
                          
                        
                        
                          
                            
                              M
                              
                                
                                   
                                
                                
                                  2
                                  21
                                
                              
                            
                          
                          
                            
                              M
                              
                                
                                   
                                
                                
                                  2
                                  22
                                
                              
                            
                          
                        
                      
                      ]
                    
                    ⁢
                    
                       
                    
                    ⁢
                    where
                    ⁢
                    
                       
                    
                    ⁢
                    det
                    ⁢
                    
                       
                    
                    ⁢
                    
                      M
                      2
                    
                  
                  =
                  1
                
              
              ⁢
              
                

              
              ⁢
              
                
                  M
                  2
                
                =
                
                ⁢
                
                  
                    
                      [
                      
                        
                          
                            
                              cos
                              ⁢
                              
                                 
                              
                              ⁢
                              
                                θ
                                3
                              
                            
                          
                          
                            
                              
                                -
                                sin
                              
                              ⁢
                              
                                 
                              
                              ⁢
                              
                                θ
                                3
                              
                            
                          
                        
                        
                          
                            
                              sin
                              ⁢
                              
                                 
                              
                              ⁢
                              
                                θ
                                3
                              
                            
                          
                          
                            
                              
                                +
                                cos
                              
                              ⁢
                              
                                 
                              
                              ⁢
                              
                                θ
                                3
                              
                            
                          
                        
                      
                      ]
                    
                    ⁡
                    
                      [
                      
                        
                          
                            
                              exp
                              ⁡
                              
                                [
                                
                                  
                                    -
                                    j
                                  
                                  ⁢
                                  
                                     
                                  
                                  ⁢
                                  π
                                  ⁢
                                  
                                     
                                  
                                  ⁢
                                  Δ
                                  ⁢
                                  
                                     
                                  
                                  ⁢
                                  
                                    L
                                    m2
                                  
                                  ⁢
                                  
                                    
                                      n
                                      ⁡
                                      
                                        (
                                        λ
                                        )
                                      
                                    
                                    /
                                    λ
                                  
                                
                                ]
                              
                            
                          
                          
                            0
                          
                        
                        
                          
                            0
                          
                          
                            
                              exp
                              ⁡
                              
                                [
                                
                                  j
                                  ⁢
                                  
                                     
                                  
                                  ⁢
                                  π
                                  ⁢
                                  
                                     
                                  
                                  ⁢
                                  Δ
                                  ⁢
                                  
                                     
                                  
                                  ⁢
                                  
                                    L
                                    m2
                                  
                                  ⁢
                                  
                                    
                                      n
                                      ⁡
                                      
                                        (
                                        λ
                                        )
                                      
                                    
                                    /
                                    λ
                                  
                                
                                ]
                              
                            
                          
                        
                      
                      ]
                    
                  
                  ×
                  
                     
                    
                      
                        [
                        
                          
                            
                              
                                cos
                                ⁢
                                
                                   
                                
                                ⁢
                                
                                  θ
                                  2
                                
                              
                            
                            
                              
                                
                                  -
                                  sin
                                
                                ⁢
                                
                                   
                                
                                ⁢
                                
                                  θ
                                  2
                                
                              
                            
                          
                          
                            
                              
                                sin
                                ⁢
                                
                                   
                                
                                ⁢
                                
                                  θ
                                  2
                                
                              
                            
                            
                              
                                
                                  +
                                  cos
                                
                                ⁢
                                
                                   
                                
                                ⁢
                                
                                  θ
                                  2
                                
                              
                            
                          
                        
                        ]
                      
                      ⁢
                      
                         
                        
                          
                            [
                            
                              
                                
                                  
                                    exp
                                    ⁡
                                    
                                      [
                                      
                                        
                                          -
                                          j
                                        
                                        ⁢
                                        
                                           
                                        
                                        ⁢
                                        π
                                        ⁢
                                        
                                           
                                        
                                        ⁢
                                        Δ
                                        ⁢
                                        
                                           
                                        
                                        ⁢
                                        
                                          L
                                          m1
                                        
                                        ⁢
                                        
                                          
                                            n
                                            ⁡
                                            
                                              (
                                              λ
                                              )
                                            
                                          
                                          /
                                          λ
                                        
                                      
                                      ]
                                    
                                  
                                
                                
                                  0
                                
                              
                              
                                
                                  0
                                
                                
                                  
                                    exp
                                    ⁡
                                    
                                      [
                                      
                                        j
                                        ⁢
                                        
                                           
                                        
                                        ⁢
                                        π
                                        ⁢
                                        
                                           
                                        
                                        ⁢
                                        Δ
                                        ⁢
                                        
                                           
                                        
                                        ⁢
                                        
                                          L
                                          m1
                                        
                                        ⁢
                                        
                                          
                                            n
                                            ⁡
                                            
                                              (
                                              λ
                                              )
                                            
                                          
                                          /
                                          λ
                                        
                                      
                                      ]
                                    
                                  
                                
                              
                            
                            ]
                          
                          ⁢
                          
                             
                            
                              [
                              
                                
                                  
                                    
                                      cos
                                      ⁢
                                      
                                         
                                      
                                      ⁢
                                      
                                        θ
                                        1
                                      
                                    
                                  
                                  
                                    
                                      
                                        -
                                        sin
                                      
                                      ⁢
                                      
                                         
                                      
                                      ⁢
                                      
                                        θ
                                        1
                                      
                                    
                                  
                                
                                
                                  
                                    
                                      sin
                                      ⁢
                                      
                                         
                                      
                                      ⁢
                                      
                                        θ
                                        1
                                      
                                    
                                  
                                  
                                    
                                      
                                        +
                                        cos
                                      
                                      ⁢
                                      
                                         
                                      
                                      ⁢
                                      
                                        θ
                                        1
                                      
                                    
                                  
                                
                              
                              ]
                            
                          
                        
                      
                    
                  
                
              
            
          
          
            
               
            
          
        
      
    
    
      
        (
        16
        )
      
    
  




Here ΔLmi>0 corresponds to a case where the branch on the through side is long with respect to the input port, and ΔLmi<0 corresponds to a case where the branch on the cross side is long. The transfer function H2(λ) of the 2-stage MZI structure is expressed as follows using M2 and a phase shift h(λ) (path length: ΔLr) that is produced by the loop-back 13: 



  
    
      
        
          
            H
            2
          
          ⁡
          
            (
            λ
            )
          
        
        =
        
          
            
              
                h
                ⁡
                
                  (
                  λ
                  )
                
              
              -
              
                M
                
                  
                     
                  
                  
                    2
                    22
                  
                
              
            
            
              
                
                  h
                  ⁡
                  
                    (
                    λ
                    )
                  
                
                ⁢
                
                  M
                  
                    
                       
                    
                    
                      2
                      11
                    
                  
                
              
              -
              1
            
          
          =
          
            
              
                h
                ⁡
                
                  (
                  λ
                  )
                
              
              -
              
                M
                
                  
                     
                  
                  
                    2
                    
                      11
                      *
                    
                  
                
              
            
            
              
                
                  h
                  ⁡
                  
                    (
                    λ
                    )
                  
                
                ⁢
                
                  M
                  
                    
                       
                    
                    
                      2
                      11
                    
                  
                
              
              -
              1
            
          
        
      
    
    
      
        (
        17
        )
      
    
  



 h(λ)=exp[−j2πΔLrn(λ)/λ]  (18)

where M211* represents the complex conjugate of M211. From the foregoing, the phase of the transfer function H2(λ) is as follows: 



  
    
      
        
          arg
          ⁢
          
             
          
          ⁢
          
            
              H
              2
            
            ⁡
            
              (
              λ
              )
            
          
        
        =
        
          
            arc
            ⁢
            
               
            
            ⁢
            tan
            ⁢
            
              {
              
                
                  
                    sin
                    ⁡
                    
                      [
                      
                        
                          -
                          2
                        
                        ⁢
                        
                           
                        
                        ⁢
                        π
                        ⁢
                        
                           
                        
                        ⁢
                        Δ
                        ⁢
                        
                           
                        
                        ⁢
                        
                          L
                          r
                        
                        ⁢
                        
                          
                            n
                            ⁡
                            
                              (
                              λ
                              )
                            
                          
                          /
                          λ
                        
                      
                      ]
                    
                  
                  -
                  B
                
                
                  
                    cos
                    ⁡
                    
                      [
                      
                        
                          -
                          2
                        
                        ⁢
                        π
                        ⁢
                        
                           
                        
                        ⁢
                        Δ
                        ⁢
                        
                           
                        
                        ⁢
                        
                          L
                          r
                        
                        ⁢
                        
                          
                            n
                            ⁡
                            
                              (
                              λ
                              )
                            
                          
                          /
                          λ
                        
                      
                      ]
                    
                  
                  -
                  A
                
              
              }
            
          
          -
          
            arc
            ⁢
            
               
            
            ⁢
            tan
            ⁢
            
              {
              
                
                  
                    A
                    ⁢
                    
                       
                    
                    ⁢
                    
                      sin
                      ⁡
                      
                        [
                        
                          
                            -
                            2
                          
                          ⁢
                          
                             
                          
                          ⁢
                          π
                          ⁢
                          
                             
                          
                          ⁢
                          Δ
                          ⁢
                          
                             
                          
                          ⁢
                          
                            L
                            r
                          
                          ⁢
                          
                            
                              n
                              ⁡
                              
                                (
                                λ
                                )
                              
                            
                            /
                            λ
                          
                        
                        ]
                      
                    
                  
                  -
                  
                    B
                    ⁢
                    
                       
                    
                    ⁢
                    
                      cos
                      ⁡
                      
                        [
                        
                          
                            -
                            2
                          
                          ⁢
                          π
                          ⁢
                          
                             
                          
                          ⁢
                          Δ
                          ⁢
                          
                             
                          
                          ⁢
                          
                            L
                            r
                          
                          ⁢
                          
                            
                              n
                              ⁡
                              
                                (
                                λ
                                )
                              
                            
                            /
                            λ
                          
                        
                        ]
                      
                    
                  
                
                
                  
                     
                  
                  ⁢
                  
                    
                      A
                      ⁢
                      
                         
                      
                      ⁢
                      
                        cos
                        ⁡
                        
                          [
                          
                            
                              -
                              2
                            
                            ⁢
                            π
                            ⁢
                            
                               
                            
                            ⁢
                            Δ
                            ⁢
                            
                               
                            
                            ⁢
                            
                              L
                              r
                            
                            ⁢
                            
                              
                                n
                                ⁡
                                
                                  (
                                  λ
                                  )
                                
                              
                              /
                              λ
                            
                          
                          ]
                        
                      
                    
                    -
                    
                      B
                      ⁢
                      
                         
                      
                      ⁢
                      
                        sin
                        ⁡
                        
                          [
                          
                            
                              -
                              2
                            
                            ⁢
                            π
                            ⁢
                            
                               
                            
                            ⁢
                            Δ
                            ⁢
                            
                               
                            
                            ⁢
                            
                              L
                              r
                            
                            ⁢
                            
                              
                                n
                                ⁡
                                
                                  (
                                  λ
                                  )
                                
                              
                              /
                              λ
                            
                          
                          ]
                        
                      
                    
                    -
                    1
                  
                
              
              }
            
          
        
      
    
    
      
        (
        19
        )
      
    
  



 A=cos [π(ΔLm1+ΔLm2)n(λ)/λ] cos(θ2)cos(θ1+θ3)−cos [π(ΔLm1−ΔLm2)n(λ)/λ] sin(θ2)sin(θ1+θ3)  (20)

B=sin [π(ΔLm1+ΔLm2)n(λ)/λ] cos(θ2)cos(θ1−θ3)−sin [π(ΔLm1−ΔLm2)n(λ)/λ] sin(θ2)sin(θ1−θ3)  (21) 

(c) Conditions that Give Dispersion Compensation Quantity=0 According to the Invention
In order for the amount of dispersion compensation to become zero, it is required that argH2(λ) be expressed by the following function:

argH2(λ)=C6/λ+C7  (22a) 

or

argH2(λ)=C8 (C6, C7, C8 are constants)  (22b) 

by the design parameters, in a manner similar to that of the prior-art example. A condition that will satisfy Equations (22a), (22b) is (A,B)=(0,0) or (±1,0), which is similar to the prior-art example.

The solution (A,B)=(0,0) will be described as one example. In the prior-art example, (α,β)=(0,0) cannot be satisfied only by selecting ΔLm, a fixed limitation is imposed with regard to the rotation angle θ of the coupler and this becomes a problem in terms of manufacturability. In order to simplify the discussion set forth below, a description will be rendered in regard to minimum rotation. However, it should be noted that this does not impose any particular limitation upon the parameters of the present invention.

(c-1) Case 1: θ1+θ3=π/2 

That ΔLm1n(λ)/λ=1/4, ΔLm2n(λ)/λ=−1/4 is a solution is readily verified.

(c-2) Case 2: θ1+θ3≠π/2 

The following equations are obtained by substituting A=0, B=0 into Equations (20), (21), respectively, and transforming:

cos [π(ΔLm1+ΔLm2)n(λ)/λ]=cos [π(ΔLm1−ΔLm2)n(λ)/λ] tan(θ2)tan(θ1+θ3)  (23) 

sin [π(ΔLm1+ΔLm2)n(λ)/λ]=−sin [π(ΔLm1−ΔLm2)n (λ)/λ] tan(θ2)tan(θ1+θ3)  (24) 

In the process of the transformation, use is made of cos(θ1+θ2)≠0 in view of θ1+θ3≠π/2. An equation for selecting the value of (ΔLm1−ΔLm2)n(λ) is obtained as follows using the basic condition

cos 2[π(ΔLm1+ΔLm2)n(λ)/λ]+sin 2[π(ΔLm1+ΔLm2)n(λ)/λ]=1 

of the triangular function and Equations (23) and (24): 



  
    
      
        
          
            cos
            2
          
          ⁡
          
            [
            
              
                π
                ⁡
                
                  (
                  
                    
                      Δ
                      ⁢
                      
                         
                      
                      ⁢
                      
                        L
                        m1
                      
                    
                    -
                    
                      Δ
                      ⁢
                      
                         
                      
                      ⁢
                      
                        L
                        m2
                      
                    
                  
                  )
                
              
              ⁢
              
                
                  n
                  ⁡
                  
                    (
                    λ
                    )
                  
                
                /
                λ
              
            
            ]
          
        
        =
        
          
            
              1
              /
              
                
                  tan
                  2
                
                ⁡
                
                  (
                  
                    θ
                    2
                  
                  )
                
              
            
            -
            
              
                tan
                2
              
              ⁡
              
                (
                
                  
                    θ
                    1
                  
                  -
                  
                    θ
                    3
                  
                
                )
              
            
          
          
            
              
                tan
                2
              
              ⁡
              
                (
                
                  
                    θ
                    1
                  
                  +
                  
                    θ
                    3
                  
                
                )
              
            
            -
            
              
                tan
                2
              
              ⁡
              
                (
                
                  
                    θ
                    1
                  
                  -
                  
                    θ
                    3
                  
                
                )
              
            
          
        
      
    
    
      
        (
        25
        )
      
    
  




It will be understood that if the values of θ1, θ2, θ3 are given in Equation (25), then the value of (ΔLm1−ΔLm2)n(λ) is obtained. With regard to (ΔLm1+ΔLm2)n(λ), it will suffice to substitute the value of cos [π(ΔLm1−ΔLm2)n(λ)/λ], which is obtained from Equation (25), into Equation (23). In order for Equation (25) to be established, it is necessary in view of cos 2[π(ΔLm1−ΔLm2)n(λ)/λ]≦1 to previously decide the values of θ1, θ2, θ3 at the time of design in such a manner that the condition

1≦tan 2(θ1+θ3)×tan 2(θ2)  (26) 

will hold even taking into consideration variations in θ1, θ2, θ3 at the time of manufacture. For this condition it will suffice if the design is such that θ1+θ3≈π/2 holds, and therefore this condition is considered to be one that can be satisfied easily.

(c-3) Reconciling both conditions that give dispersion compensation quantity=0 and variations in manufacture according to the invention
According to the present invention as described above, by adopting an arrangement in which multiple MZIs are serially connected, dispersion compensation quantity=0 can be achieved by selecting values of ΔLm1n(λ), ΔLm2n(λ) in accordance with values of θ1, θ2, θ3. That is, even if coupler rotation angle deviates from the design value owing to manufacturing variations or the like, dispersion compensation quantity=0 is achieved by adjusting the values of ΔLm1n(λ), ΔLm2n(λ) using the TO effect, etc. This means that the aforementioned problems of the prior-art example can be solved.
In order afford a comparison with the prior-art example, FIG. 3 illustrates the compensation characteristic (group delay characteristic) of a dispersion compensating filter in FIG. 2, which is a modification of FIG. 1. Components of the dispersion compensating filter of FIG. 2 that are identical with those of FIG. 1 are designated by like reference characters. This modification differs in that loop length ΔLr of the loop circuit 13 is reduced and in that input and output waveguides 15 and 16 made to intersect.
FIG. 3 illustrates a compensation characteristic for a case where the rotation angle θ3 of the third coupler in FIG. 2 has deviated from the design value (θ1=θ2=θ3=π/4, Lr=4104 μm) by 5%. The numerical value (nm) in FIG. 3 is the path length difference ΔLm1n(λ), −ΔLm1n(λ) between the branches of each MZI. Since the deviation in rotation angle is small in this example, the group delay characteristic of FIG. 3, which is inclusive of dispersion compensation quantity=0 (slope=0), is obtained with almost no shift in the drive of the path length difference ΔLm1n(λ) between the MZI branches of the first stage and of the path length difference ΔLm2n(λ) between the MZI branches of the second stage from symmetrical drive [ΔLm2n(λ)=−Lm1n(λ)]. Further, the center wavelength also is almost unaffected by a deviation in the angle θ3, and it will be understood that this is sufficiently small.
(B) First Embodiment
FIG. 4 is a diagram showing the topology of a dispersion compensating filter according to a first embodiment of the present invention, in which two or more MZIs are serially connected. One output and one input of a 2-input, 2-output optical circuit are connected by an optical propagation path (optical waveguide, optical fiber) to construct a loop circuit 20. The 2-input, 2-output optical circuit is constructed by serially connecting five MZIs 21 to 25. Each MZI has a structure identical with that of the MZI in FIG. 1. The MZIs have two waveguides 21a, 21b to 25a, 25b embraced by two couplers CPLi, CPLj, and heaters HT serving as path length adjustment portions formed on each of the waveguides.
The transfer function of the dispersion compensating filter illustrated in FIG. 4 is expressed by replacing the transfer matrix m(λ) of the MZI (4-terminal circuit) in Equations (1) to (5) by a transfer matrix Mk(λ) (shown below) of the MZI arranged in multiple (k) stages.
The transfer matrix Mk(λ) of the MZI arranged in multiple (λ) stages is expressed as follows using each path length difference ΔLmi (i=1, 2, . . . k+1), coupler rotation (coupling) θi (i=1, 2, . . . k+1), effective refractive index n(λ) of the waveguide and input wavelength λ: 



  
    
      
        
          
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Here ΔLmi>0 corresponds to a case where the branch on the through side is long with respect to the input port, and ΔLmi<0 corresponds to a case where the branch on the cross side is long. The transfer function Hk(λ) of the arrangement obtained by serially connecting k-number of MZIs is found using the transfer matrix Mk(λ) and the phase shift h(λ) that is produced by the loop-back. The phase argHk(λ) of this transfer function is found. In the first embodiment, positive compensation and negative compensation, inclusive of dispersion compensation quantity=0, can be achieved using k-number of path length differences ΔLmi (i=1, 2, . . . k) even if θ1 to θ3 exhibit variations owing to manufacture.

    
    
        Adjustment of optical path length
    
    


Methods of varying the path length difference ΔLmi of the MZI portions 21 to 25 and the path length ΔLr of the loop circuit 20 are {circumflex over (1)} a method regarding the SiO2-type waveguide, and {circumflex over (2)} a method regarding an LiNbO3-type waveguide. As shown in FIG. 5, the method of varying optical path length in an SiO2-type waveguide includes building up an upper clad UCL on the top side of waveguide core OWGs formed on a lower clad LCL of a silicon substrate SPL, forming a heater HT on the upper clad UCL and controlling-the optical path length by varying the refractive index of the waveguides OWG through heating of the heaters. (This method relies upon the TO effect.)
As shown in FIG. 6, the method of varying optical path length in an LiNbO3-type waveguide includes forming electrodes EL in parallel on waveguides OWG formed by diffusing Ti in an LiNbO3 substrate LPL, applying an electric field to the waveguide portions and controlling the optical path length by varying the dielectric constant, namely the refractive index. (This method relies upon the EO effect.)
The first embodiment shown in FIG. 4 is an example of an SiO2 waveguide, and means for adjusting path length difference is constructed by the heaters HT. With regard to an LiNbO3 waveguide, the means for adjusting path length difference can be constructed by adopting the arrangement shown in FIG. 6.

    
    
        Coupler
    
    


The coupler CPL in the dispersion compensating filter can be constructed by either of two methods. A coupler based upon the first method of construction is an MMI (Multi-Mode Interferometer) coupler obtained by coupling two waveguides OWG1, OWG2 by a single core layer CR, as shown in FIG. 7. FIG. 7 illustrates an example of the structure of an MMI-type coupler. This is an example in which the distance between core centers of the core waveguides OWG1, OWG2 is 14.9 μm, splitting is 50% and the core-clad difference in refractive indices is 0.8%.
A coupler based upon the second method of construction is one having little wavelength dependence, such as a WINC (see Wavelength-Independent Coupler: K. Jinguji et al., Journal of Lightwave Technology, vol. 14, No. 10 1996, p. 2301), in which the parameters are coupling length L of MZI 22 and path length difference ΔLm between the branches, as shown in FIG. 8. FIG. 8 illustrates an example of the structure of a WINC-type coupler. Here the path length difference of the MZI 22 is 1900 μm, coupling length of unidirectional coupler CPL2 on the left side is 1900 μm, distance between the core centers is 9.2 μm, coupling length of unidirectional coupler CPL3 on the right side is 795 μm distance between the core centers is 9.2 μm, splitting is 50% and the core-clad difference in refractive indices is 0.8%.
FIG. 9 is a wavelength vs. transmission splitting intensity characteristic diagram (simulation) illustrating the wavelength dependence of the splitting intensities of an MMI-type coupler, WINC-type coupler and directional coupling-type coupler. As evident from the characteristic diagram, the splitting intensities of the MMI-type coupler and WINC-type coupler are a substantially constant 50% and are independent of wavelength. It is possible to endow each wavelength-division-multiplexed optical signal with a splitting strength that is as designed and it becomes possible to reduce variations in the amount of dispersion compensation from wavelength to wavelength.
(C) Second Embodiment
FIG. 10 is a diagram showing the topology of a dispersion compensating filter according to a second embodiment of the present invention. This illustrates an example in which the number of MZIs connected in the first embodiment is made two. Components identical with those of the first embodiment in FIG. 4 are designated by like reference characters. The second embodiment is the minimal structure of the present invention for controlling the amount of dispersion compensation. This is a two-stage arrangement in which the number of MZI stages is two. According to the second embodiment, positive compensation and negative compensation, inclusive of dispersion compensation quantity=0, can be achieved even if manufacturing variations occur, as described above in accordance with FIG. 1. In other words, if the maximum value of positive compensation is +a and the maximum value of negative compensation is −b, then any desired amount of compensation can be achieved over the range −b to +a.
(D) Third Embodiment
FIG. 11 is a diagram showing the topology of a dispersion compensating filter according to a third embodiment of the present invention. This is a two-stage arrangement in which the number of MZI stages is two. Here input and output optical propagation paths 20a, 20b not used as the loop of the 2-input, 2-output optical circuit are made to intersect at an angle of 10· or greater. Two waveguides 21a, 21b; 22a, 22b of the MZIs 21, 22 are embraced by two couplers CPL1, CPL2; CPL2, CPL3. This constructs a 2-input, 2-output optical circuit in which two MZIs are serially connected.
One output and one input of the 2-input, 2-output optical circuit are connected by an optical propagation path 23a to construct a loop circuit 23, and the waveguides 21a, 21b; 22a, 22b of the MZIs 21, 22 as well as the loop circuit 23 are formed to have heaters HT as path length adjustment portions. The dispersion compensating filter of the third embodiment is a two-stage arrangement in which the number of MZIs is two and is similar to the second embodiment of FIG. 10 except for the fact that optical propagation paths 20a, 20b are made to intersect at an angle of 10· or greater and the fact that the loop length ΔLrn(λ) of the loop circuit 23 is small.
This arrangement is a layout in a case where a loop length ΔLr of sufficient size cannot be assured owing to the design value of the FSR. In other words, the loop length ΔLr of the loop circuit diminishes when the FSR is small. If the loop length ΔLr becomes too small, the input and output propagation paths 20a, 20b must be bent. In the actual manufacturing process, minimum bending radius rm is limited owing to radiation loss at the bent portions. If the loop length ΔLr is less than a prescribed length, then the bending radius at the bends of the propagation paths 20a, 20b falls below the minimum bending radius rm and radiation loss increases. Even if the loop length ΔLr diminishes, however, bending becomes unnecessary and, hence, there is no increase in radiation loss if the arrangement in which the propagation paths 20a, 20b are made to intersect is adopted, as in the present invention. It should be noted that the angle of intersection between the optical propagation paths 20a, 20b is required to be 10· or greater in order to eliminate leakage from other path due to the intersection.
(E) Fourth Embodiment
FIG. 12 is a diagram showing the topology of a dispersion compensating filter according to a fourth embodiment of the present invention. Components identical with those of the third embodiment in FIG. 11 are designated by like reference characters. As in the third embodiment, this dispersion compensating filter is a two-stage arrangement in which the number of MZIs is two. Moreover, input and output optical propagation paths 20a, 20b not used as the loop of the 2-input, 2-output optical circuit are made to intersect. In addition, in order that the built-in optical-path length differences of the two waveguides 21a, 21b; 22a, 22b of each of the MZI portions 21, 22 will become substantially equal, the waveguides are made to intersect each other in the vicinity of substantially the center of each MZI. Further, one output and one input of the 2-input, 2-output optical circuit are connected by an optical propagation path to construct the loop circuit 23, and the waveguides 2a, 21b; 22a, 22b of the MZIs 21, 22 as well as the loop circuit 23 are formed to have heaters HT as path length adjustment portions.
The optical-path length difference actually necessary for the MZI portions 21, 22 is on the order of 0 to λ (1.55 μm) when one considers that adjustment is performed within the minimum phase range. On the other hand, the difference in the lengths on the layout between the inner and outer sides of the MZI branch constructing the bent portion is not on the order of λ (1.55 μm) when one considers a distance that will not result in optical interference and a distance that will not produce thermal interference in order to achieve control using the TO effect. For example, a difference for avoiding optical interference differs depending upon the difference in refractive index between that of the core and that of the clad but is on the order of tens of microns at a difference in refractive index of 0.5%. A distance that will not produce thermal interference is 100 μm or greater if an SiO2 waveguide is formed on a silicon substrate and the clad portion does not have heat insulating structure. Therefore, in a case where the difference in the radii of the branches (waveguides) 21a, 21b; 22a, 22b between the inner and outer sides is, e.g., 250 μm, then the difference between the distances produced up to the second coupler, which is substantially the position of a semicircle, will be 785 μm, and the difference between the lengths will become much larger than λ (1.55 μm).
Accordingly, though a layout in which the branch on the inner side is slackened further toward the center is conceivable, the bending radius in a case where the branch is slackened is limited by the minimum bending radius and chip size increases as a consequence. Accordingly, as illustrated in the fourth embodiment of FIG. 12, in order that the built-in optical-path length differences of the two waveguides 21a, 21b; 22a, 22b constituting the branches of each of the MZI portions 21, 22 will become substantially equal, the waveguides are made to intersect each other in the vicinity of substantially the center of each MZI. As a result, one branch of the MZIs extends from the inner side to the outer side, and the other extends from the outer side to the inner side so that the lengths of the two branches can be made uniform. This makes it possible to achieve an optical-path length difference on the order of 0 to λ (1.55 μm).
(F) Fifth Embodiment
FIG. 13 is a diagram showing the topology of a dispersion compensating filter according to a fifth embodiment. This is an arrangement in which three dispersion compensating filters DCFB according to the fourth embodiment are serially connected.
In general, there is a trade-off between the amount of dispersion compensation and the pass band. In case of optical pulses having a high bit rate, the sideband thereof is broad and a wider bandwidth is required. In the fifth embodiment, therefore, the amount of dispersion compensation per stage is set to be small and it is so arranged that the desired amount of dispersion compensation and desired band are obtained overall. FIG. 14 illustrates a dispersion compensation characteristic in the case of the 3-stage arrangement of FIG. 13. Here it is possible to perform dispersion compensation on the order of ±510 nm/ps with regard to the 22-GHz band necessary for a 10-Gbps transmission. It should be noted that the deviation from the straight lines 51, 52 in FIG. 14 is regarded as group delay ripple and is not large enough to cause problems at 10 Gbps.
(G) Sixth Embodiment
FIG. 15 illustrates an example of the steps of a manufacturing process for achieving the structure of a dispersion compensator according to the first to fifth embodiments of present invention.
When a dispersion compensating filter is created, first an SiO2 film is formed as the lower clad layer LCL on the silicon substrate SPL by the CVD (Chemical Vapor Deposition) or FHD (Flame Hydrolysis Deposition) method. At this time P (phosphorous), B (boron) or Ge, etc. (germanium) may be added to control film stress and refractive index. Next, the core layer CR through which light is guided is formed in the same manner as the clad layer by the CVD or FHD method [step (1)]. At this time the refractive index is made higher than that of the clad layer LCL by increasing the density of germanium or by adding Ti (titanium).
This is followed by forming a mask conforming to a core pattern on the core layer and transferring the core pattern (waveguide) OWG by dry etching [step (2)]. Available as the mask are an organic material mask exhibiting photosensitivity or a metal mask obtained by vapor-depositing a metal such as Cr (chrome) and then etching this metal film using the organic material as a mask.
The mask is then removed chemically and core embedding is carried out by forming the upper clad layer UCL in a manner similar to that of the lower clad layer LCL using the CVD method or FHD method [step (3)]. After core embedding is performed, the thin-film heaters HT necessary for adjusting optical path length and the upper electrodes EL are formed as by the lift-off method [steps (4), (5)]. Specifically, a photosensitive organic material is patterned in such a manner that only portions on which the heaters HT, etc., are formed will not be masked, a heater material and electrode material are vapor-deposited from above the mask, then the mask of organic material is removed as by an organic solvent. The heater material used may be Pt (platinum), W (tungsten), nichrome or Cr, and the organic material used may be Au (gold), Cu (copper) or Al (aluminum), etc. A metal such as titanium having a high melting point should be vapor-deposited thinly in order to improve the adherence between these metals and SiO2.
Thus, in accordance with the present invention as described above, even if the rotation angle of a coupler in an MZI portion-deviates from the design value from one device to the next owing to manufacturing variations or the like, dispersion compensation quantity=0 will be obtained by adjusting the value of optical path length difference ΔLmin(λ) between the branches of the MZI using the TO effect, etc. As a result, device manufacturability (yield) can be increased by a wide margin and the cost of the dispersion compensating device can be reduced. Such a low-cost wavelength dispersion compensating device whose amount of compensation can be varied contributes to cost reduction in a DWDM transmission system and to simplification of design.
Further, in accordance with the present invention, the size of the dispersion compensating filter can be reduced by serially connecting two MZIs.
Further, in accordance with the present invention, a coupler having little wavelength dependence is used as the couplers that construct the MZIs. As a result, it is possible to endow each wavelength-division-multiplexed optical signal with a splitting strength that is as designed and it becomes possible to reduce variations in the amount of dispersion compensation. This makes it possible to reduce variations in amount of dispersion compensation from wavelength to wavelength.
Further, in accordance with the present invention, it is so arranged that the optical propagation paths of an input and output not used as a loop in a 2-input, 2-output optical circuit intersect each other, then it will be unnecessary to bend the input and output propagation paths even if loop length ΔLr is shorter than a prescribed length.
Further, in accordance with the present invention, it is so arranged that the waveguides are made to intersect each other in the vicinity of substantially the center of each MZI. As a result, one branch of the MZI extends from the inner side to the outer side, and the other extends from the outer side to the inner side so that the lengths of the two branches can be made uniform. This makes it possible to achieve an optical-path length difference on the order of 0 to λ (1.55 μm).
Further, in accordance with the present invention, it is so arranged that two or more of the above-described dispersion compensating filters are connected serially. This makes it possible to reduce the dispersion compensation quantity per filter and broaden the pass band. As a result, the desired dispersion compensation quantity can be generated overall and the band can be broadened.
As many apparently widely different embodiments of the present invention can be made without departing from the spirit and scope thereof, it is to be understood that the invention is not limited to the specific embodiments thereof except as defined in the appended claims.

## Claims

1. A wavelength dispersion compensating filter having a 2-input, 2-output optical circuit;
said 2-input, 2-output optical circuit being constructed by serially connecting a plurality of Mach-Zehnder interferometers possessing a structure in which two waveguides are embraced by two couplers; 
one output and one input of said two 2-input, 2-output optical circuit being connected by an optical propagation path to thereby construct a loop circuit; and 
the waveguides of the Mach-Zehnder interferometers as well as the loop circuit each being provided with an optical path-length adjustment portion.

2. The filter according to claim 1, wherein said optical path-length adjustment portion has means for adjusting optical path length by an electro-optic effect.

3. The filter according to claim 1, wherein said optical path-length adjustment portion has means for adjusting optical path length by a thermo-optic effect.

4. A wavelength dispersion compensating filter comprising two Mach-Zehnder interferometers serially connected.

5. The filter according to claim 1, wherein a coupler having comparatively little wavelength dependence is used as the couplers that construct the Mach-Zehnder interferometers.

6. The filter according to claim 1, wherein the optical propagation paths of the other input and output not used as the loop of said 2-input, 2-output optical circuit are made to intersect each other.

7. The filter according to claim 1, wherein the waveguides are made to intersect each other in the vicinity of substantially the center of each Mach-Zehnder interferometer in such a manner that built-in path length differences between the two optical waveguides constructing the branches of each MZI portion will be approximately equal.

8. The filter according to claim 1, wherein two or more of said dispersion compensating filters are serially connected.

9. The filter according to claim 1, wherein the dispersion compensating filters are created using a process for forming an optical waveguide layer of SiO2 on a silicon substrate.

10. The filter according to claim 4, wherein a couple having comparatively little wavelength dependence is used as the couplers that construct the Mach-Zehnder interferometers.

11. The filter according to claim 4, wherein the optical propagation paths of the other input and output not used as the loop of said 2-input, 2-output optical circuit are made to intersect each other.

12. The filter according to claim 4, wherein the way guides are made to intersect each other in the vicinity of substantially the center of each Mach-Zehnder interferometer in such a manner that built-in path length differences between the two optical waveguides constructing the branches of each MZI portion will be approximately equal.

13. The filter according to claim 4, wherein two or more of said dispersion compensating filters are serially connected.

14. The filter according to claim 4, wherein the dispersion compensating filters are created using a process for forming an optical waveguide layer of SiO2 on a silicon substrate.