Abstract:
In an optical communication system, efficient use of a Mach-Zehnder modulator requires accurate knowledge of the AC halfwave voltage at the desired modulation frequency. At high modulation frequencies this can be difficult to measure directly. A method of accurately measuring the AC halfwave voltage of a Mach-Zehnder modulator is described. The Mach-Zehnder modulator is biased at the peak of the transfer function curve and a sinusoidal signal of known amplitude and the desired frequency of measurement is applied. The optical power is measured with and without the sinusoidal signal. The ratio of the two optical powers is used in the Mach-Zehnder transfer equation to calculate the AC halfwave voltage.

Description:
FIELD OF THE INVENTION 
     This invention relates to the determination of the halfwave voltage of a Mach-Zehnder modulator. 
     BACKGROUND OF THE INVENTION 
     In a Mach-Zehnder (MZ) interferometer, an optical signal is split and passed along two optical paths before recombining. Each optical path lies along a different branch of the transmission medium, and may have different optical lengths due to different refractive indices of the medium in each branch. On recombining, different frequencies of the optical signal will interfere to different degrees, depending on the difference in optical length between the two paths. At frequencies for which the different optical lengths result in a phase difference of π radians the signals along each branch will destructively interfere at the output of the MZ interferometer. At frequencies for which the different optical lengths result in no phase difference the signals along each branch will constructively interfere. 
     In an MZ modulator, a voltage is applied to the two branches of the interferometer. This alters the relative refractive indices of the branches, thereby altering their relative optical lengths. The amount of constructive interference for a particular frequency (typically a carrier frequency of the optical signal) at the output of the MZ modulator can be varied by varying the voltage applied to the two branches. By modulating the applied voltage, the optical signal can be modulated. The relationship between the applied voltage and the output power at a particular frequency can be represented by a Mach-Zehnder transfer function (see FIG.  1 ). 
     The halfwave voltage, V π  (or Vpi), of an MZ modulator is defined as the difference between the applied voltage at which the signals in each branch of the MZ modulator are in phase and the applied voltage at which the signals are π radians out of phase. In other words, V π  is the voltage difference between maximum and minimum output signal power (see FIG.  1 ). In order for an MZ modulator to be used most efficiently in a communications network it is necessary to know the value of V π  accurately. The V π  of an MZ modulator is an important parameter, for example, for determining RF-driver settings. 
     If the applied voltage is an AC voltage, as it must be to modulate the optical signal, then the halfwave voltage becomes difficult to determine. The voltage is applied along travelling wave electrodes which are parallel to the optical transmission medium. Ideally the voltage wave travels along each electrode such that the optical signal is adjacent to a constant voltage while within the MZ modulator. However in reality the voltage seen by the optical signal is not constant, due to attenuation of the voltage along the electrodes and to the difference between the group velocities of the electrical and optical signals. The V π  used by the RF-driver to effect 180° phase shifts cannot be determined from the ideal V π  for applied DC voltages, but rather must be dependent on the modulation frequency. This halfwave voltage is called the AC halfwave voltage, V π -AC (or Vpi-AC). 
     One method of determining V π -AC at all modulation frequencies would be to determine V π -AC accurately at one modulation frequency, and then use the measured small signal frequency response of the MZ modulator to calculate the V π  at other frequencies. The measured small signal frequency response of the MZ modulator is generally lower than the theoretical frequency response, due to the losses which occur with AC modulation. Commercial network analyzers can be used to measure the small signal frequency response of an MZ modulator over modulation frequency ranges of about 130 MHz to 30 GHz. 
     One existing technique for measuring V π -AC uses modulations having a high peak-to-peak voltage, but these are difficult to implement at high frequencies and require the use of specialized equipment. Another technique uses variations in amplitude of a square wave modulation. However this technique relies on eyeballing. The technique is limited by the accuracy of the eyeballing, and square wave modulation is not a scientifically accurate method of determining signal parameters due to the multitude of harmonics making up the waveform. 
     There is therefore a need for a method of measuring V π -AC more accurately, more consistently, and in a simpler manner. 
     SUMMARY OF THE INVENTION 
     Broadly, the invention may be summarized as a method of determining the AC halfwave voltage of a Mach-Zehnder modulator (MZM) by biasing the MZM at the peak of the transfer function curve and applying an AC voltage, preferably sinusoidal, of known amplitude and desired frequency. The optical power is measured with and without modulation and these two measured values or the ratio thereof together with the frequency and amplitude values can be used to determine from the Mach-Zehnder transfer equation the value for V π -AC at the desired frequency. 
     More particularly, the DC bias voltage and a small AC modulation voltage are applied to the MZ modulator. The peak is found accurately by adjusting the DC bias voltage until the first and third harmonics of the frequency modulated optical output signal disappear. The average output power of the modulator is measured while the AC modulation voltage is being applied, and then measured again after the AC modulation voltage has been switched off. The AC halfwave voltage can then be calculated from the values of the average output power and from the frequency and amplitude. 
     The invention also is directed to a computer readable medium carrying a computer program for carrying out the steps of the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will now be described in greater detail with reference to the accompanying diagrams, in which: 
     FIG. 1 is a plot of the Mach-Zehnder transfer function of a Mach-Zehnder modulator; 
     FIG. 2 is a block diagram of the components which can be used to carry out the invention; 
     FIG. 3 is a plot of the Mach-Zehnder transfer function when a sinusoidal modulating signal is applied to the Mach-Zehnder modulator. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 illustrates the Mach-Zehnder (MZ) transfer function  10  of an MZ modulator for an individual frequency of the optical signal. When a voltage  12  is applied to the MZ modulator the optical lengths of the two branches of the MZ modulator are changed, as is the degree of interference between the signals along each branch at the particular optical frequency. By varying the voltage  12  the degree of interference is varied, thereby varying the power  14  of the optical signal at the output of the MZ modulator at the particular optical frequency. If the voltage  12  is set to a value of V a , denoted by line  16 , then the signals along the two branches are π radians out of phase, there is complete destructive interference, and the power  14  of the optical signal at the output of the MZ modulator is zero. If the voltage  12  is set to a value of V b , denoted by line  18 , then the two signals are in phase, there is complete constructive interference, and the power  14  of the optical signal at the output of the MZ modulator is equal to the power of the optical signal at the input of the MZ modulator. The halfwave voltage V π , denoted by double headed arrow  20 , is the difference between the voltage resulting in complete destructive interference and the voltage resulting in complete constructive interference. There are of course many possible values of V a  and V b , corresponding to each minimum and maximum value of the power  14  respectively. 
     FIG. 2 illustrates components for measuring the AC halfwave voltage V π -AC according to the method of the invention. An optical signal  31  enters from a fiber optic cable  30  into a Mach-Zehnder modulator  32 , where it is split along two branches. An applied voltage  40  is applied to the MZ modulator. The applied voltage  40  changes the relative phase of the two branches of the optical signal, generally resulting in an output optical signal  42  of lower power than the input optical signal (unless the applied voltage is such that there is no phase difference between the two branches of the optical signal). The applied voltage  40  consists generally of a DC bias voltage  34  combined with an AC voltage  37  generated by a function generator  36 . The DC bias voltage  34  and the AC voltage  37  are combined using a bias T-junction  38 . The output optical signal  42  is divided using a 3-db coupler  44 . Part of the optical signal passes to a power meter  50 , and part passes to a photodetector  46 . The photodetector  46  generates an electrical signal which passes to a spectrum analyser  48 . 
     The invention requires the DC bias voltage  34  to be located at a peak V b  denoted by line  18 . A peak can be located by applying a small sinusoidal AC voltage  37  of frequency f and amplitude V in  about the DC bias voltage  34 . When the DC bias voltage  34  is at a peak V b  or a minimum V a  of the MZ transfer function  10 , the symmetry of the transfer function causes the first and third harmonic of the modulating frequency f to disappear and most of the spectral energy is concentrated on the second harmonic. The approximate peak is located by monitoring the power meter  50  to detect a near maximum value, and then the precise peak is located by adjusting the DC bias voltage  34  until the spectrum analyser  48  shows only the second harmonic of the modulating frequency f. At this point the DC bias voltage  34  is at a value of V b  and the power  14  is at a maximum. 
     The transfer function for an MZ modulator with a DC bias voltage  34  set at a value of V b  and with a small sinusoidal AC voltage  37  of frequency f and amplitude V in  is shown in FIG.  3 . The AC voltage  116  oscillates about the DC bias voltage  118 . The power  114  at the output of the MZ modulator oscillates along the curve  120 , and has an average power of ψ(V in ), denoted by the line  122 . If the AC voltage  116  is switched off, the power  114  at the output of the MZ modulator has a value of ψ(0), denoted by the line  124 . 
     ψ(V in ) has a theoretical value given by          ψ        (     V   in     )       =       A        (     1   /   T     )              ∫   0   T              [     cos        (       π     2                   V   π              V   in          cos        (         2      π     T        t     )         )       ]     2             t                                  
     where A is a constant which depends upon the launched carrier wave optical power and the insertion loss in the system, and T=1/f. The inner cosine term represents the modulating AC signal, and the outer cosine term results from the Mach-Zehnder transfer function. There is no phase shift within the outer cosine because the DC bias voltage has been set at a value of B b . By setting V in =0 it is seen that 
     
       
         ψ(0)=A  
       
     
     and so the normalised power is given by            ψ   N          (     V   in     )       =         ψ        (     V   in     )         ψ        (   0   )         =       (     1   /   T     )            ∫   0   T              [     cos        (       π     2                   V   π              V   in          cos        (         2      π     T        t     )         )       ]     2             t                                    
     To measure V π -AC of a Mach-Zehnder modulator a DC bias voltage  34  and a small sinusoidal AC voltage  37  of frequency f and amplitude V in  are applied to the MZ modulator  32 . The DC bias voltage  34  is adjusted until the power meter  50  indicates that the output power  114  is near a maximum value, and then further adjusting the DC bias voltage  34  until only the second harmonic of the modulating AC frequency f appears on the spectrum analyzer  48 , as described above, at which point the output power  114  of the MZ modulator is oscillating about a maximum value (shown by curve  120 ). The average power ψ(V in )  122  is measured using the power meter  50 . The AC voltage  37  is then switched off, so that the only voltage  112  supplied to the MZ modulator is the DC bias voltage  118 . The power ψ(0)  124  is measured using the power meter  50 . Using the values of ψ(V in ), ψ(0), f, and V in , the value of V π -AC can be calculated numerically from the expression given above for the normalized power ψ N  (V in ). 
     In the preferred embodiment a sinusoidal AC voltage is used when measuring the average output power ψ(V in ) and calculating V π , as a sinusoidal AC voltage is the simplest to generate and is also used to locate the peak when setting the DC bias voltage. However the scope of the invention includes the use of other forms of AC voltage. 
     What has been described is merely illustrative of the application of the principles of the invention. Other arrangements and methods can be implemented by those skilled in the art without departing from the spirit and scope of the present invention. 
     For example, instead of the specific transfer equation used in the above described embodiment mathematical equivalents may be used. 
     Additionally, although the invention described above is carried out by a human operator it should be appreciated that the method could easily be automated using a computer having a microprocessor running software defining the steps of the inventive method. As is conventional, the software would be incorporated in a computer readable storage medium such as a magnetic disc or CD ROM.