Abstract:
A Mach-Zehnder (MZ) interferometer modulator structure for fiberoptic telecommunications is disclosed in which drift of the operating point can be monitored with a reduced phase tracking error. One or more components of free-space light radiated into the substrate of the MZ modulator are selectively detected with one or more photodetectors. Suitable summing circuits are described for nulling out undesired photocurrent contributions in the photodetector(s) from on-state and off-state light radiated from the MZ.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   The present invention claims priority from U.S. Provisional Patent Application No. 60/988,517 filed Nov. 16, 2007, which is incorporated herein by reference. 

   TECHNICAL FIELD 
   The present invention is directed to free-space photo-monitor with reduced tracking error for a Mach-Zehnder optical modulator for fiberoptic transmission systems. 
   BACKGROUND OF THE INVENTION 
   The invention applies to Mach-Zehnder (MZ) modulators where a high-speed signal is applied to an RF electrode and a separate slowly-varying DC voltage is applied either to the same RF electrode, or to a separate bias electrode. This DC voltage, also called a bias voltage, maintains the bias set point of the interferometer at quadrature, keeping the optical power midway between the full on state and full off state in the absence of an applied RF signal. An AC RF signal applied then swings the optical power either partially or completely from full on to full off, symmetrically about the quadrature point. An additional small AC dither signal of frequency f dither  is superimposed on the RF signal, either electronically added or multiplied to the RF signal. The superimposed AC dither signal causes a small optical AC signal to be created in the output of the modulator that can be monitored by a photodetector. The DC bias is adjusted until the fundamental of f dither  that appears in the photocurrent is at a maximum. Alternatively, a second harmonic of f dither  that appears in the photocurrent can be nulled. The adjustment of the DC bias is provided by a feedback circuit that synchronously detects the AC dither signal and its harmonics in the photocurrent output of the photodetector. 
   The amount of voltage needed to keep the bias point of the interferometer at quadrature varies with time, temperature, and wavelength, hence a photodetector (to detect optical power) and feedback circuit (to control a voltage) are needed to keep the bias point at the desired point. Note that in some communications applications, the modulator bias point may need to be set at or near full on or full off, or the RF voltage(s) may vary phase of the output light, as well as intensity. In any case, the method of controlling the bias point is similar. One critical aspect of the bias control is the photodetector needed to create a photocurrent or photovoltage that is proportional to either
         (1) the optical power of on-state light that is coupled into the output optical fiber, or   (2) the optical power of off-state light that is radiated into the substrate of the modulator.       

   Methods of controlling the bias point exist for either scenario. One key problem solved by the invention is the phase tracking error between the transfer curve of the modulator and the transfer curve observed via the photodetector for the latter case, where part of the optical path is unguided in the substrate and/or free-space outside of the substrate. 
     FIG. 1  shows a conventional prior art Mach-Zehnder (MZ) interferometer modulator  100 . An optical signal from an input fiber is coupled into an input optical waveguide  102 , in which the lateral field distribution is represented by curve  101 . The optical signal is split into two parts  101   a ,  101   b  with a y-junction  103   a . Each waveguide  104   a ,  104   b  following the first y-junction  103   a  is modulated by a set of electrodes  105   a - c  in close proximity to the waveguides  104   a ,  104   b . A second y-junction  103   b  combines the modulated optical signals  101   a ,  101   b . The figure shows electrodes corresponding to a modulator made in x-cut lithium niobate substrate, however, a design for z-cut lithium niobate substrate operates in an analogous manner. 
   The applied field from the electrodes  105   a - c  results in a change in the optical phase difference between the modulated optical signals  101   a ,  101   b  in the two arms  104   a , and  104   b  of the MZ. If the two modulated optical signals  101   a ,  101   b  have a zero optical phase difference, they form a single-lobed guided mode  101   c  after being combined by the second y-junction  103   b  into output waveguide  106 , resulting in little loss of optical power. If the two modulated optical signals  101   a ,  101   b  have an optical phase difference of π (or 180°), then they combine to form a double-lobed higher-order unguided mode  101   d  that is not supported by the output waveguide  106 , causing the light to radiate into the substrate. The radiated light is strongest on both sides of the waveguide  106 , approximately into areas  107 L and  107 R, and weakest in the center, near output waveguide  106 . Note that the two lobes have opposite sign in optical field, but have the same intensity. 
     FIGS. 2(   a ) and  2 ( b ) show two-dimensional (2D) Beam Propagation Method (BPM) simulations of the MZ operation. The figures show contour plots of the square root of optical intensity (E-field magnitude) for the cases of 0 or π phase difference between the arms of the MZ, respectively, which correspond to on and off switch states of the MZ. Note that in the off-state, the light is radiated primarily in two lobes. The double-lobed beam thus created upon recombination at the output y-junction  103   b  is rejected by an output fiber coupled to the output waveguide  106 . The ripple in the radiation pattern is caused by interference between the radiated light and light radiated elsewhere in the simulation that reflects off the simulation boundary and overlaps the light radiated at the output y-junction  103   b . More elaborate 3D BPM simulations show that the off-state radiation lobes not only travel outward, but downward, as well. 
     FIG. 3  is a graph of intensity vs. drive voltage, for both light intensity in the guided mode  301  reaching the output fiber (dashed line) and the intensity of light radiated into the substrate  302  (solid line). Maximum intensity for light in the output fiber  301   a  occurs for V=±0.5 V π , whereas minimum intensity at the output  301   b  occurs for V=0V. The curve for intensity of radiated light is the exact opposite, reaching a maximum  302   a  when light in the output fiber is a minimum and vice versa. The quadrature point  303  is midway between maximum and minimum points along the transfer curves. The dashed plot  301  is referred to as the transfer curve of the MZ, for light output by the MZ. Ideally, the photocurrent in a free-space photodiode is proportional to the light intensity radiated into the substrate, which is represented by the solid curve  302 . 
     FIG. 4   a  shows a prior art MZ modulator assembly  400  with a free-space photodetector (PD)  407  integrated with a modulator chip  410 . The embodiment shown in  FIG. 4   a  is similar to those described in U.S. Pat. Nos. 5,953,466 and 5,963,357. An input light signal is coupled into the MZ input waveguide  402  from input optical fiber  411   a  held in place on the modulator chip  410  by a transparent fiber block  412   a . As before, the light in input waveguide  402  is split into two arms  404   a ,  404   b  of the MZ, modulated by electrodes  405   a - c  and recombined into output waveguide  406 . The output waveguide  406  is coupled into an output optical fiber  411   b , attached to the modulator chip  410  by a transparent fiber block  412   b . The PD  407 , located underneath the output optical fiber  411   b  collects light that is radiated into the substrate, after it passes through the transparent fiber block  412   b . The PD  407  may or may not be biased with a voltage across it. The light illuminating the PD  407  causes a photocurrent to be generated. The PD  407  is connected to an electrical circuit such as a transimpedance amplifier or op amp circuit that amplifies the photocurrent, converting it into a voltage. Typically, the electrical circuit is external to the modulator. 
     FIG. 4   b  is a side view of the prior art MZ modulator assembly  400  shown in  FIG. 4   a . The dashed arrows illustrate the path followed by off-state light emitted from the output waveguide  406  on the modulator chip  410  passing through substrate  410   a  at an acute angle slanting away from the top surface of the modulator chip  410  and through the transparent fiber block  412   b  to the PD  407  located underneath the output optical fiber  411   b.    
     FIG. 4   c  shows a close-up of the transparent fiber block  412   b , output optical fiber  411   b , and PD  407 . The arrows represent light radiated from different locations of the modulator (not visible in this view). The thick solid line arrows represent the off-state light radiated into the substrate when the MZ is switched off. There are additional components of radiated light coming from the modulator due to optical loss of various structures in the device. The thick dashed line arrows represent on-state light lost in the MZ output y-junction even when the MZ is switched fully on. This radiated on-state light is an amount of light radiated into the substrate that is proportional to the light launched into the output optical fiber  411   b.    
   The thin dotted line arrows represent another component of radiated on-state light, coming from the junction of the modulator output optical waveguide and the output optical fiber. In general, this component of radiated on-state light is much larger than the component coming from y-junctions and other features along the modulator, however is comparable to the amount of light radiated into the substrate at the junction of the input optical fiber and the modulator input optical waveguide. Note that these on-state light components are strongest along the direction of the fiber, and are weaker for more diverging angles. On the other hand, the off-state light components are strongest in the diverging angle direction and weak along the direction of the output fiber. In prior art modulators, the on-state light also reaches the photodetector, creating an interference pattern that depends on the drive voltage. 
     FIG. 4   d  shows another example of a prior art MZ modulator assembly  430  with a free-space PD  407  using a mirror or mirrored surface  415  to reflect the light and direct it to the PD  407 . The embodiment shown in  FIG. 4   d  is similar to designs described in U.S. Pat. No. 7,200,289, in which off-state light captured by an output fiber block is deflected to a photodetector. The back of the output fiber block may have an oblique angle and may be reflective. The addition of the mirror  415  allows the PD  407  to be positioned in a location that is closer to a shelf within the assembly  430 , allowing a simpler means of electrical connection. The surface of the mirror  415  may be polished or roughened. A rough surface causes the reflected light to be diffused to a larger degree, which may be desirable, if the photodetector is positioned far away from the output optical fiber or pigtail  411   b . A more diffuse reflection increases the possibility of multiple reflections, causing the reflected light to travel farther. Hence, a diffuse reflection simplifies the choice of photodetector location, as the entire cavity of the modulator package is illuminated by the reflected light. 
     FIG. 5  is a plot of the detected signal in relative units vs. normalized drive voltage on a MZ modulator. The solid line  502  is the ideal curve, which is proportional to the radiated off-state light  302  plotted in  FIG. 3 . The dashed curve  504  shows the detected signal for the case where the magnitude of on-state light is significant compared to the off-state light. Note that the dashed curve  504  not only shows a low on/off ratio, given by the ratio of its maximum to minimum values, but is also shifted laterally along the voltage axis. The amount of lateral shift from ideal is referred to as the PD phase tracking error. 
   The feedback circuit controlling bias voltage sets the bias point to quadrature point of the PD transfer curve, which is shifted slightly from the true quadrature point of the transfer curve of optical power transmitted to the output optical fiber. Hence, there is an error in setting the bias voltage, which results in degradation in system performance. There is some also some impairment due to the reduction of on/off ratio, namely reduced gain in the control loop, and some additional noise, however, these impairments can be largely overcome by proper design of the feedback control circuit. 
   The limitations of prior art free-space integrated photodetector designs can be overcome by understanding the cause of the tracking error in more detail. The E-field of radiated light on the left and right sides of the output waveguide are given by Equations 1 and 2, respectively.
 
 E   A   =A   01  cos(θ)+ j A   11 (cos(φ)+ j  sin(φ))sin(θ)  (1)
 
 E   B   =A   02  cos(θ)− j A   12 (cos(φ)+ j  sin(φ))sin(θ)  (2)
 
   The coefficients A 01  and A 02  represent the field strength of on-state light reaching the photodetector at the two locations, labeled  107 L and  107 R in  FIGS. 1 ,  2   a  and  2   b , respectively, whereas the coefficients A 11  and A 12  represent the field strength of off-state light at those locations. The symbol ‘j’ represents the imaginary unit, which equals the square root of −1. The strength of on-state and off-state light is represented by cos(θ) and sin(θ), respectively, due to the interference effect produced by the MZ. The cos(φ)+j sin(φ) term accounts for the unknown phase relationship between on-state and off-state light that can change as a function of location, wavelength, and/or temperature. Note that the E-field polarity of on-state light has the same sign on both sides of the output waveguide due to symmetry, while the E-field polarity of off-state light is intrinsically different in sign, due to the anti-symmetry of the first higher-order mode. The intensity of the light reaching the photodetector at the two locations is given by
 
 I   A   =A   01   2  cos 2 (θ)+ A   11   2  sin 2 (θ)−2  A   01    A   11  sin(θ)cos(θ)sin(θ)  (3)
 
 I   B   =A   02   2  cos 2 (θ)+ A   12   2  sin 2 (θ)+2 A   02    A   12  sin(φ)cos(θ)sin(θ)  (4)
 
   The last term of Equations 3 and 4 is caused by the coherent interference between on-state and off-state light, and is the cause of phase tracking error. The total photocurrent, assuming the photodetector covers locations L and R, is given by
 
 i   total =( R   A   A   01   2   +R   B   A   02   2 )cos 2 (θ)+(R A   A   11   2   +R   B   A   12   2 )sin 2 (θ)+2( R   B   A   02   A   12   −R   A   A   01   A   11 )sin(φ)cos(θ)sin(θ),  (5)
 
where R A  and R B  are the photodetector responsivity at the two locations. The last term in Equation 5 is responsible for phase tracking error. Note that it equals zero when
 
R B A 02 A 12 =R A A 01 A 11 .  (6)
 
If responsivities, field strengths of on-state light, and field strength of off-state light are exactly the same for the two locations, then Equation 6 is satisfied, that is
 
R B =R A  A 01 =A 02  A 11 =A 12   (7)
 
     FIG. 4   e  shows a prior art design with two photodetectors  407   a  and  407   b , where Equation 7 is valid, allowing the simple circuits shown in  FIGS. 6   a ,  6   b  to be used. Each photodetector  407   a ,  407   b  collects one lobe of the radiated off-state light in equal proportion. The photodiodes are connected either in series ( FIG. 6   a ) or parallel ( FIG. 6   b ) in order to sum the photocurrents equally, requiring the net responsivities, R A  and R B , to be equal. 
   The use of common lens to couple light from an output waveguide to a fiber and couple off-state light from a substrate to photodetector surface is shown in Itou (U.S. Pat. No. 5,764,400). 
   Hosoi (U.S. Pat. No. 6,668,103) describes various ways of deflecting light from one output port of a 3 dB coupler to a monitor photodiode. The path between waveguide output and photodiode is shown as propagating through free-space. Various ways of deflecting light to a photodiode integrated on the substrate are also shown. Part of the optical path may include free-space within the substrate. 
   Vaerewyck (U.S. Pat. No. 4,768,848) discloses a device having an optical tap coupler on the input waveguide. The light from the tap is directed to a photodetector, while Okada (U.S. Pat. No. 5,111,518) describes a device with a folded waveguide to carry light to a photodetector. 
   Isono (U.S. Pat. No. 5,259,044) describes a device with a folded optical path where tapped light or Fresnel reflected light is reflected and guided to a photodetector, with a portion of the optical path appears to propagate free-space within the substrate. 
   In practice, it is difficult to match the field strengths in the two locations. Also, in reality Equation 5 needs to be integrated over the entire surface area of the photodetector, hence all of the parameters are likely to vary somewhat with spatial location, making it more difficult to cancel out the net tracking error term. The strength of the E-fields may also vary with temperature and wavelength, making cancellation of the phase tracking error term more problematic. 
   It is an object of the present invention to address these difficulties by presenting a MZ modulator structure with light-blocking material on or within an output fiber block and/or around an output optical fiber to block on-state light, and possibly one lobe of off-state light, thereby preventing it from reaching one or more photodiodes used to monitor drift in Mach-Zehnder interferometer modulator. 
   SUMMARY OF THE INVENTION 
   The present invention is intended to provide a phase tracking monitor integrated with a Mach-Zehnder interferometric modulator. The phase tracking monitor includes an optical waveguide element comprising an input optical waveguide for receiving an input optical signal, two branched optical waveguides, each guiding a portion of the input optical signal, an input Y-junction optically coupling the input optical waveguide to the two branched optical waveguides, an output optical waveguide optically coupled to an output optical fiber, and an output Y-junction optically coupling the two branched optical waveguides to the output optical waveguide for causing the optical signals propagating from the two branched optical waveguides to interfere with each other. 
   The optical waveguide element is supported on an upper surface of a substrate comprising an electro-optic dielectric material. A set of electrodes is provided for applying an electric field proximate to the two branched optical waveguides for modulating a phase of the optical signals propagating therethrough. The set of electrodes generate a modulated optical signal having an on-state and an off-state at the output Y-junction. In the on-state the modulated optical signal generates a guided mode in the output waveguide, whereas in the off-state the modulated optical signal generates a radiating mode comprising a left lobe and a right lobe in the substrate. A fiber block is attached to an output edge of the substrate for stably supporting the output optical fiber to receive the guided mode from the output waveguide. A first photodetector is positioned to generate a first photocurrent in response to light transmitted from the output edge of the substrate. Light-blocking material disposed between the output edge of the substrate and the photodetector is used to adjust relative amounts of the radiating mode and the guided mode that reach the photodetector. 
   A method for reducing phase tracking error in a Mach-Zehnder optical modulator, including an input waveguide, an output waveguide and a set of electrodes supported on a substrate, with an output fiber coupled to the output waveguide via an optical block, is defined, providing the optical modulator with a modulating signal and a bias signal to the set of electrodes, coupling an input signal into the input waveguide, detecting with a first photodetector a first lobe of an off-state radiating mode emitted from a substrate, blocking an on-state mode guided in the output waveguide from reaching the first photodetector with the light-blocking portion, and adjusting the bias signal in response to a first photocurrent in the first photodetector to reduce the phase tracking error. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be described in greater detail with reference to the accompanying drawings which represent preferred embodiments thereof, wherein: 
       FIG. 1  is a top view of a prior art Mach-Zehnder interferometer modulator; 
       FIG. 2(   a ) is a contour plot of electric field strength distribution in the plane of a MZ modulator in the on-state; 
       FIG. 2(   b ) is a contour plot of electric field strength distribution in the plane of a MZ modulator in the off-state; 
       FIG. 3  is a graph of intensity vs. drive voltage, for both light intensity in the guided mode reaching the output fiber (dashed line) and the intensity of light radiated into the substrate (solid line); 
       FIGS. 4   a  and  4   b  are top and side views, respectively, of a prior art MZ modulator assembly with a free-space photodetector (PD) integrated with a modulator chip; 
       FIG. 4   c  is a top view of a transparent fiber block, with output optical fiber and PD; 
       FIG. 4   d  is a top view of another example of a prior art MZ modulator assembly with a free-space PD using a mirror or mirrored surface to reflect the light and direct it to the PD; 
       FIG. 4   e  is a top view of a prior art MZ modulator assembly with a pair of free-space photodetectors (PD) integrated with a modulator chip; 
       FIG. 5  is a graph of the detected signal in relative units vs. normalized drive voltage on a MZ modulator; 
       FIGS. 6   a  and  6   b  are circuit diagrams of photodiodes connected either in series ( 6   a ) or parallel ( 6   b ); 
       FIG. 7  is a schematic of a circuit with two photodetectors, gain elements and a summing unit; 
       FIGS. 8   a  and  8   b  are top cross-sectional views of a fiber block with light blocking or opaque epoxy used to mount the output optical fiber; 
       FIGS. 9   a - 9   h  are rear views of various embodiments of fiber blocks for controlling on- and off-state light access to photodetectors according to the present invention; 
       FIG. 10  is a top view of a dual photodetector MZ module according to the present invention; 
       FIG. 11  is a top view of a quad photodetector dual MZ module according to the present invention; 
       FIG. 12  is a rear view of the modulator substrate, looking from the PD&#39;s towards the substrate illustrating the locations of radiated light; and 
       FIG. 13  is a schematic of a circuit with four photodetectors, gain elements and a summing unit. 
   

   DETAILED DESCRIPTION 
   Reducing the phase tracking error according to this invention has two main aspects:
         (1) reducing the influence of any on-state light by balancing the effective responsivities of the photodetectors; and   (2) reducing the amount of on-state light collected by the photodiode(s) that causes the phase tracking error.       

   The circuit in  FIG. 7  shows one embodiment of the invention that allows for independent control of the response of each photodetector  707   a ,  707   b , for the photodetector arrangement shown in  FIG. 4   d  by adjusting amplifier gains G A , G B  before summing or differencing them in a summing circuit  750 . Other circuits can be implemented to sum the photocurrents, as well. Independent control of the gains G A , G B  associated with each photodetector  707   a ,  707   b  allows Equation 6 to be easily satisfied. In the case of an active or passive circuit connected to each photodetector  707   a ,  707   b , Equation 6 becomes
 
G B R B A 02 A 12 =G A R A A 01 A 11   (8)
 
   where G A  and G B  are the transimpedance gain of the active or passive circuit, given in V/mA. The two variables G A  and G B  are adjusted to assure that Equation 8 is satisfied, resulting in zero or negligible phase tracking error. The circuit shown in  FIG. 7  may be integrated in the modulator package and may be passive or active, active implying the need for amplifiers or op-amp circuits which require electrical power. A passive circuit utilizes some combination of resistors and possibly other components (capacitors and inductors) to allow for tunable summation of the photocurrents. 
   A second aspect of the invention is to reduce the amount of on-state light reaching the photodetector  707   a ,  707   b , which in turn reduces the phase tracking error. 
     FIG. 8   a  is a detailed top view of a fiber block  812   b  with light blocking or opaque epoxy  820  used to mount the output optical fiber  811   b . The opaque epoxy  820  absorbs the on-state light radiated at the junction of the modulator output waveguide and the output optical fiber  811   b . The PD  807 , located underneath the output optical fiber  811   b  collects light shown by the dashed arrows  850 L,  850 R that is radiated into the substrate, after it passes through the transparent fiber block  812   b.    
     FIG. 9   a  is a rear view of the fiber block  912   b  carrying an optical fiber  911   b  that is surrounded with opaque epoxy  920 . A suitable light blocking or absorbing coating  921  is applied down the center of the fiber block  912   b  either on the front or the rear or both. The light blocking or absorbing coating  921  assists in blocking or absorbing on-state light radiated by y-junctions and other waveguide features. The absorbing coating  921  can be a metal, or more advantageously, an absorptive paint or material to prevent the on-state light from being reflected to other points within the device, which may eventually reach the photodetector. Note that the opaque epoxy  920  can be used without the absorbing coating  921  or vice-versa, in cases where the radiated on-state light is blocked sufficiently. 
     FIG. 9   b  is a rear view of another embodiment, where some additional light blocking or absorptive material  921   a  is applied near the top of the fiber block  912   b .  FIG. 9   c  is a rear view of a further embodiment where in addition to blocking/absorbing on-state light, the absorbing coating  921  is applied on one side near the bottom left corner  921   b , in order to block or absorb one lobe of the off-state light. The embodiment in  FIG. 9   c  prevents interference between the two lobes of the off-state light, should the lobes be reflected one or more times, and allowed to overlap causing variation in response with position, wavelength, and even perhaps temperature. Note that the blocking or absorbing coating can be applied to the front or rear or both of the fiber block. An alternative to mounting the optical fiber  911   b  with opaque epoxy  920  is to use a clear epoxy for mounting the fiber in the block, and apply a light blocking or absorbing coating on and around the clear epoxy, at the front and/or rear of the fiber block  912   b.    
     FIG. 8   b  is a detailed top view of a fiber block  814  that is made of light absorbing material with one transparent section  816 . The PD  807 , located underneath the output optical fiber  811   b  collects light from one lobe of the off-state light shown by the dashed arrow  850 R that is radiated into the substrate, after it passes through the transparent section  816 . The other lobe, shown by the dashed arrow  850 L is blocked by the opaque fiber block  814 . This is similar to the embodiment described in  FIG. 9   c . Such a design may be easier to manufacture than one involving coatings. 
     FIG. 9   d  is a rear view of the opaque fiber block  914  corresponding to  814  shown in  FIG. 8   b . The opaque epoxy  920  and the opaque fiber block  914  absorb most of the on-state light, while one lobe of the off-state light passes through a cylindrical transparent section  916   c  made of transparent material. If the optical index of the transparent material is sufficiently larger than that of the absorptive material of the opaque fiber block  914 , all of the off-state light will be guided through the opaque fiber block  914  with total internal reflection occurring at the interface of the two materials. In this case, the transparent section  916   c  acts as a light pipe. Alternatively, the sides of cylindrical transparent section  916   c  could be coated with reflective metal and inserted into the absorptive fiber block. 
     FIG. 9   e  shows a design similar to design the one in  FIG. 9   d , with the exception that the transparent section  916   s  has flat sides, revealing a square profile at the rear instead of circular. In principle, the shape of the transparent section  916   s  could be adjusted to tailor the shape of the radiation pattern exiting the opaque fiber block  914 . Alternatively, a cylindrical transparent region may be easier to manufacture than other shapes.  FIG. 9   f  shows the opaque fiber block  914  with two transparent sections,  916   a ,  916   b , to allow both lobes of off-state light to reach one or more photodetectors. 
     FIG. 9   g  is a rear view of the opaque fiber block  914  where the two transparent sections,  917   a ,  917   b , having flat sides and two sides extending to the outer boundary of the opaque fiber block  914 . The off-state light can still be guided within the transparent sections  917   a ,  917   b  if its optical index is sufficiently higher than the optical index of the absorptive material of the opaque fiber block  914 . Note that the index change at the outer air-block boundary is much larger, resulting in total internal reflection at that interface as well. 
     FIG. 9   h  is a rear view of a “T” shaped opaque fiber block  914   t . The “T” shape causes most of the on-state light, which is strongest in the central area  918 , to be absorbed. The two lobes of the off-state light pass around the side edges  918   a  of the opaque fiber block  914   t . As the off-state light is not completely guided, however, strong reflection along the side edges  918   a  of the opaque fiber block  914   t  may help to guide the off-state light to a photodetector. 
   In  FIG. 10 , a MZ modulator assembly  1000  with free-space photodetectors (PD)  1007   a ,  1007   b  is integrated with a modulator chip  1010  comprising an electro-optic dielectric material. An input light signal is coupled into a MZ modulator input waveguide  1002  from input optical fiber  1011   a  held in place on the modulator chip  1010  by a fiber block  1012   a . The light signal in the input waveguide  1002  is split into two arms  1004   a ,  1004   b  of the MZ, modulated by voltage signals applied between an RF signal electrode  1005   b  and RF ground electrodes  1005   a ,  1005   c  and recombined into output waveguide  1006 . The output waveguide  1006  is coupled into an output optical fiber  1011   b , attached to the modulator chip  1010  by a fiber block  1012   b . The photodetectors  1007   a ,  1007   b , are located to collect light that is radiated into the substrate, after it passes through the fiber block  1012   b . The photodetectors  1007   a ,  1007   b  may or may not be biased with a voltage across it. The light illuminating the photodetectors  1007   a ,  1007   b  causes a photocurrent to be generated. The photodetectors  1007   a ,  1007   b  are connected to an electrical circuit such as a transimpedance amplifier or op amp circuit that amplifies the photocurrent, converting it into a voltage. 
   The fiber block  1012   b  may comprise a light absorbing or opaque material combined with light blocking or absorbing coating  1020  to allow for best suppression of on-state light at the photodetectors  1007   a ,  1007   b  and the capability to tune out any residual phase tracking error. For example, the fiber block structures described in  FIGS. 9   a - h  could be implemented. Light absorbing epoxy  1020  is the only light absorbing structure shown in  FIG. 10 . 
   An embodiment of a more complicated modulator—a Dual-Parallel Mach-Zehnder (DPMZ)  1100  is shown in  FIG. 11 , in which an array of photodetectors  1107   a - d  monitor the off-state light radiated from all locations from within the more complex interferometer chip  1110 . 
   An input light signal is coupled into the DPMZ modulator  1100  via input waveguide  1102  from input optical fiber  1111   a  held in place on the modulator chip  1110  by a fiber block  1112   a . The light in the input waveguide  1102  is split into two arms  1104   a ,  1104   b  of the DPMZ  1100  at Y-junction  1109 . The two arms  1104   a ,  1104   b  constitute input waveguides to inner MZ modulators  1108   a ,  1108   b , respectively, where Y-junctions  1109   a ,  1109   b  split the light into two paths as in the MZ  1000  described in  FIG. 10 . 
   The signals in the inner MZ modulators  1108   a ,  1108   b  are modulated by RF signal electrodes  1105   b ,  1105   e  and RF ground electrodes  1105   a ,  1105   c ,  1105   d ,  1105   f , then recombined in Y-junctions  1109   c ,  1109   d , respectively, into two arms  1104   c ,  1104   d  of an outer MZ  1108   c . Bias electrodes  1105   f  adjust the phase of light signals in the two arms  1104   c ,  1104   d  before they are recombined at Y-junction  1109   e  into output waveguide  1106 . The output waveguide  1106  is optically coupled to an output optical fiber  1111   b , which is held in place by light-blocking epoxy  1120  in a fiber block  1112   b , attached to the modulator chip  1110 . 
   The photodetectors  1107   a - 1107   d , located to collect light that is radiated into a substrate of the DPMZ modulator chip  1110 , after it passes through the fiber block  1112   b . For the fiber block  1112   b , structures such as those described in  FIGS. 9   a - h  could be implemented, for example, appropriately modified for the number of photodetectors used. The photodetectors  1107   a - 1107   d  may or may not be biased with a voltage. Light illuminating the photodetectors  1107   a - 1107   d  causes a photocurrent to be generated. The photodetectors  1107   a - 1107   d  are connected to an electrical circuit such as a transimpedance amplifier or op amp circuit that amplifies the respective photocurrents, converting them into a voltages. 
   Photodetectors  1107   b ,  1107   c  collect radiated light primarily from the y-junction combiner  1109   e  of the outer MZ  1108   c , while PD  1107   a  primarily collects one lobe of light radiated from the inner MZ modulator  1108   a  and PD  1107   d  primarily collects one lobe of light radiated from the inner MZ modulator  1108   b.    
     FIG. 12  shows a rear view of the modulator substrate  1210   a  of MZ modulator chip  1110 , looking from the photodetectors  1107   a - d  towards the substrate  1210   a . Locations of light radiated from the DPMZ  1100  are illustrated as circles or ellipses  1260   a ,  1260   b  and  1260   c . The y-junction  1109   e  for the outer MZ  1108   c  is closer to an output edge of the substrate  1210   a , hence the radiation patterns for off-state light  1260   a  will be closer to the top surface of the substrate  1210   a , and encompass a smaller area. The y-junctions  1109   a ,  1109   b  for the inner MZ modulators  1108   a ,  1108   b  are farther from the output edge of the substrate  1210   a , hence the radiated off-state light  1260   b  and  1260   c  from the inner MZ modulators  1108   a ,  1108   b , respectively, will be further from the top surface of the substrate  1210   a , and encompass a wider area. 
   In general, there will be some overlap between the various lobes of off-state light and on-state light  1260   a ,  1260   b  and  1260   c  on the photodetectors  1107   a - d , potentially causing some phase tracking error. The circuit shown in  FIG. 13  is used to adjust signals from several or all of the photodetectors  1107   a - d  before summing or differencing them in a summing circuit  1350  in order that the components affecting phase tracking error can be nulled out. Gain coefficients G A , G B , G C , and G D , of transimpedance amplifiers  1340   a - d  correspond to PD&#39;s  1307   a - d , respectively. For example, for tracking the phase of the inner MZ modulator  1108   a , the signal from photodetector  1107   a  is summed with small amounts of signal from one or more of the other photodetectors  1107   b - d . The transimpedance gain coefficients G B , G C , and G D  for the other photodetectors  1107   b - d  may have the same or inverted polarity relative to photodetector  1107   a . Large amounts of signal from the photodetectors  1107   b  and  1107   c  are summed together with small amounts of signals from the photodetectors  1107   a  and  1107   d  to provide a control signal for the outer MZ  1108   c . A large amount of signal from photodetector  1107   d  is summed with small amounts of signal from the other the other photodetectors  1107   a - c  to provide a signal to control the phase of the inner MZ modulator  1108   b . Light absorbing epoxy is the only light absorbing structure within the fiber block shown in the  FIG. 11 , however, other light absorbing or light guiding structures described earlier may be used with the more complex DPMZ modulator  1100 . In addition, an array of two, three, four, or more photodetectors may be used to monitor phase of the various MZ&#39;s within the DPMZ modulator  1100 . 
   Several summing circuits, one for each inner or outer MZ could be wired in parallel. In this case, a transimpedance amplifier acting as a buffer circuit is provided for each photodetector. The transimpedance gain coefficients G A , G B , G C , and G D  become voltage gain coefficients of the summing circuits. Each summing circuit has its own unique set of gain coefficients, in order that the phase of a particular inner or outer MZ is tracked independently.