Apparatus and method for linearizing an external optical modulator

An external optical modulator is linearized to reduce second order distortion. An optical carrier is modulated in the modulator by a pilot signal. The modulated optical carrier is sampled and an error signal is generated indicative of a phase difference between a second harmonic of the pilot signal and second order harmonics thereof present in the sampled modulated optical carrier. The error signal is fed back to the modulator to adjust the bias thereof to minimize the phase difference and thereby minimize second order distortions produced by the modulator. Where a plurality of external modulators are operated in series, each is provided with a feedback loop to minimize the second order distortions produced therein.

BACKGROUND OF THE INVENTION 
The present invention relates to optical modulators, and more specifically 
to a technique for linearizing the output of an external optical intensity 
modulator. 
Recently, there has been a growing interest in the development of analog, 
amplitude modulated optical communication systems. In comparison with 
digital systems, analog communication systems provide an efficient use of 
bandwidth. This is particularly useful in cable television (CATV) 
transmission system applications, where it is necessary to transmit a 
large number of video channels through an optical fiber. Compatibility 
with existing equipment is achieved by using the same signal format for 
optical transmission that is in use for coaxial cable signal transmission. 
In order to transmit an information signal (e.g., a television signal) over 
an optical fiber, a light beam ("carrier") must be modulated with the 
information signal. The "electrooptic effect" has been advantageously used 
to provide modulators for this purpose. For example, electrooptic 
modulators using miniature guiding structures are known which operate with 
a low modulating power. 
In electrooptic modulators, the electric field induced linear birefringence 
in an electrooptic material produces a change in the refractive index of 
the material which, in turn, impresses a phase modulation upon a light 
beam propagating through the material. The phase modulation is converted 
into intensity modulation by the addition of polarizers or optical 
circuitry. Ideally, an electrooptic modulator should have a linear 
relationship between its output optical power and the applied modulating 
voltage. 
In a "Mach Zehnder" type electrooptic modulator, an optical carrier (laser 
beam) is split into two paths. At least one path is electrically phase 
modulated. The two signals are then recombined in an interferometer to 
provide an intensity modulated carrier. Typically, lithium niobate 
(LiNbO.sub.3) is used as the electrooptic material. Waveguides in such 
materials are readily formed by titanium indiffusion. 
The output power curve of a Mach Zehnder modulator is nonlinear. Practical 
analog optical communications systems, however, demand a high linearity. 
See, for example, W. I. Way, "Subcarrier Multiplexed Lightwave System 
Design Considerations for Subscriber Loop Applications", J. Lightwave 
Technol., Vol. 7, pp. 1806-1818 (1989). Modulator nonlinearities cause 
unacceptable harmonic and intermodulation distortions. When it is 
necessary to communicate a large number of channels, as in a CATV 
application, intermodulation distortions ("IMD") can impose serious 
limitations on the system performance. 
The problem of intermodulation distortions, and particularly second order 
distortion, is complicated by the fact that lithium niobate is an 
inherently unstable material. Thus, it is not possible to simply bias a 
Mach Zehnder modulator (e.g., to operate at its quadrature point) and then 
expect the modulator to continue to run at the desired operating point. In 
fact, the bias condition will dynamically change due to factors such as 
temperature, photorefractive instability, and displacement currents within 
the lithium niobate material. Thus, additional steps must be taken to 
ensure that the external modulator will run over time without an increase 
in second order distortion. 
It would be advantageous to provide a technique that dynamically tracks the 
second order distortion performance of an external optical modulator and 
maintains such performance at an acceptable level. It would be further 
advantageous to provide such a technique that can be used with a single 
optical modulator or a plurality of such modulators cascaded in series. 
The present invention provides a method and apparatus enjoying the 
aforementioned advantages. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, a method is provided for 
linearizing the operation of an external optical modulator. An optical 
carrier is modulated in the modulator by a pilot signal. The modulated 
optical carrier is sampled from the modulator. An error signal is 
generated which is indicative of a phase difference between a second 
harmonic of the pilot signal and second order harmonics of the pilot 
signal present in the sampled modulated optical carrier. The error signal 
is fed back to the modulator to adjust a bias thereof to minimize the 
phase difference and thereby minimize second order distortions produced by 
the modulator. 
In an illustrated embodiment, the pilot signal is mixed with an information 
signal (e.g., CATV signals) for modulation of the carrier in the modulator 
by both the pilot signal and the information signal. An embodiment is also 
disclosed wherein a plurality of external modulators are coupled in 
series. Each of the modulators receives a pilot signal for modulating the 
optical carrier. For each modulator, the modulated optical carrier output 
therefrom is sampled and an error signal is generated indicative of a 
phase difference between a second harmonic of the pilot signal input to 
the modulator and second order harmonics of the pilot signal present in 
the sampled modulated optical carrier. The error signal for each modulator 
is fed back to adjust the bias of the modulator and thereby minimize the 
phase difference between the second harmonic of the pilot signal and 
second order harmonics of the pilot signal present in the sampled 
modulated optical carrier. In this manner, second order distortions 
produced by the modulators are minimized. 
Apparatus in accordance with the present invention includes means for 
modulating an optical carrier signal by an information signal and a pilot 
signal. The modulated optical carrier signal is sampled from the 
modulating means, and an error signal is generated indicative of a phase 
difference between a second harmonic of the pilot signal and second order 
harmonics of the pilot signal present in the sampled modulated optical 
carrier signal. Means are provided for feeding the error signal back to 
the modulating means to adjust a bias thereof in order to minimize the 
phase difference. In this manner, second order distortions produced by the 
modulating means are minimized. 
In an illustrated embodiment, means are provided for mixing the information 
signal with the pilot signal for input to the modulating means as a 
combined signal to modulate the carrier. The modulating means can comprise 
a plurality of external modulators in series, each receiving the pilot 
signal at a modulating signal input thereof. Each modulator comprises 
means for sampling the modulated optical carrier from the modulator, means 
for generating an error signal indicative of a phase difference between a 
second harmonic of the pilot signal and second order harmonics of the 
pilot signal present in the sampled carrier, and means for feeding the 
error signal back to the modulator to adjust a bias thereof to minimize 
the phase difference. 
In an illustrated embodiment, the pilot signal comprises a first tone 
having a frequency f.sub.S. The means for generating the error signal 
comprise an oscillator providing a second tone having a frequency 2 
f.sub.S phase locked to the first tone. Means are provided for mixing the 
second tone with the sampled modulated optical carrier to recover second 
order harmonics of the first tone. Phase comparator means compare the 
phase of the second tone to the phase of the recovered second order 
harmonics. Means responsive to the phase comparator generate an error 
signal having a sign and magnitude that correspond to the magnitude and 
direction of a phase difference detected by the phase comparator means. In 
one embodiment, the modulator(s) comprises a Mach Zehnder modulator(s) 
having a separate bias input(s) for receiving the error signal. In another 
embodiment, the modulating means comprise a directional coupler. In an 
embodiment using series modulators, a Mach Zehnder modulator can be 
followed by a directional coupler. In an alternative arrangement, a first 
directional coupler can be followed by a second directional coupler. In 
either embodiment, the modulators can be provided with separate bias 
inputs for receiving the error signal. Further, the error signal for each 
modulator in a plurality thereof is preferably fed back to its respective 
modulator in a feedback loop that has a time constant which is shorter 
than that of the following modulator in the series of modulators.

DETAILED DESCRIPTION OF THE INVENTION 
External modulators used in connection with optical signal distribution 
systems must provide linear operation over a relatively large modulation 
range. However, such modulators typically produce rather large second 
order distortions, which must be reduced in order to allow the practical 
use of such modulators. Ideally, an external modulator (such as a Mach 
Zehnder modulator) should be operated at its quadrature operating point, 
where the most linear operation can be achieved. This is illustrated in 
FIG. 3, which is a plot of the modulator output power intensity I(.nu.) 
with respect to modulating voltage .nu.. As plot 110 illustrates, 
approximately linear operation as designated by dashed line 114 is 
provided at the quadrature operating points (e.g., point 112) of the 
modulator. 
The present invention maintains operation at or about the quadrature 
operating point 112, thereby reducing second order distortions, using a 
feedback arrangement in which a phase difference caused by the second 
order distortion is monitored and minimized. One embodiment of the 
invention is illustrated in FIG. 1, in which an optical carrier signal is 
provided by a laser 10. The optical carrier is communicated via an optical 
path 12 to a polarization transformer 14 that optimizes the orientation of 
the E field from the laser with respect to the crystal axis of a Mach 
Zehnder modulator 18. The polarization transformer 14 is coupled to Mach 
Zehnder modulator 18 via optical path 16 in a conventional manner. Mach 
Zehnder modulator 18 will modulate the optical carrier input thereto by a 
modulating signal applied at a modulating input 20. The resultant 
modulated carrier is output from the Mach Zehnder modulator via optical 
output path 22. 
In accordance with the present invention, the modulated optical carrier 
from the external modulator 18 is sampled via a coupler 24, that outputs 
the sampled light to a photodetector 26. Photodetector 26 converts the 
sampled energy into the electrical domain, where it is amplified by an 
amplifier 28 prior to input to a mixer 30. In mixer 30, the sampled signal 
is mixed with a mixing frequency from synthesizer 32. In the specific 
embodiment shown, synthesizer 32 outputs a 49.92 MHz periodic waveform. 
Synthesizer 32 is phase locked to a synthesizer 34, that in the illustrated 
embodiment outputs a 24.96 MHz signal. The 24.96 MHz signal is mixed in a 
mixer 36 with a pilot tone from oscillator 38 (e.g., 40 kHz) and passed 
through a bandpass filter 40 to provide a 25 MHz signal for input via tee 
42 to input port 20 of external modulator 18. This 25 MHz signal will 
appear together with an information signal as modulation on the sampled 
optical carrier from the external modulator. 
The actual information signal to be carried on the optical carrier is input 
to the modulator 18 via an RF input terminal 54 and adder 56 in a 
conventional manner. Since the pilot tone used in connection with the 
second order phase comparison is well below the frequency of the desired 
information signal, the pilot tone does not interfere with the 
communication of the information signal. 
The 40 kHz pilot tone will be present in the signal in the electrical 
domain input to mixer 30 from amplifier 28. Upon mixing this signal with 
the output of 49.92 MHz synthesizer 32, the second order distortion of the 
40 kHz pilot tone, appearing at 80 kHz, will be output from mixer 30. This 
result can be seen in that the second harmonic of the 25 MHz signal input 
to the modulator appears at 50 MHz, which when mixed with the 49.92 MHz 
signal from synthesizer 32 results in the desired 80 kHz output 
(50.00-49.92 MHz=80 kHz). A low pass filter 44 limits the output from 
mixer 30 to the desired 80 kHz component, for input to a phase comparator 
46. 
A frequency doubler 52 doubles the original 40 kHz pilot tone from 
oscillator 38 to provide an 80 kHz output for comparison with the 80 kHz 
signal from low pass filter 44. Any phase difference between the two 80 
kHz signals input to phase comparator 46 is determined, and output through 
an appropriate time delay 48 to an amplifier 50 for providing an error 
signal based on the phase difference. The error signal is input to tee 42, 
where it is combined with the 25 MHz output from bandpass filter 40 for 
input as a biasing signal to external modulator 18. Phase comparator 46 
can comprise any conventional phase comparison circuit, such as a 
multiplier and a filter. Such phase comparators are well known in the art. 
The error signal provided by the apparatus of FIG. 1 is indicative of a 
phase difference between the second harmonic of the pilot signal from 
frequency multiplier 52 and second order harmonics of the pilot signal 
present in the sampled modulated optical carrier from external modulator 
18. The sign and magnitude of the error signal will inherently correspond 
to the magnitude and direction of the phase difference detected by the 
phase comparator 46. Thus, use of the error signal to bias external 
modulator 18 will tend to drive the phase difference to zero, by adjusting 
the operating point of the external modulator to quadrature. This has the 
effect of reducing second order distortions produced by the external 
modulator. 
The present invention can also be used to linearize the operation of 
cascaded external modulators. An example of such an embodiment is 
illustrated in FIG. 2, wherein external modulator 64 comprises a pair of 
series coupled Mach Zehnder modulators 65, 67. Laser 60 is used to provide 
the optical carrier which is communicated to external modulator 64 via 
optical path 62. External modulator 64 contains separate bias inputs 66, 
68 and separate modulating signal inputs 70, 72 for each of the Mach 
Zehnder modulators 65, 67, respectively. The outputs of modulators 65, 67 
are sampled by optical paths 84, 76, respectively. The optical carrier 
modulated by modulator 64 is output via optical path 74 in a conventional 
manner. 
The information signal to be modulated by external modulator 64 is coupled 
via terminal 92 to an adder 94, where it is combined with a reference 
frequency (pilot tone) f.sub.S generated by oscillator 96. The combined 
signal is input via input port 70 to the first Mach Zehnder modulator 65. 
A splitter 100 is provided to divert a portion of the input signal to 
input port 72 of Mach Zehnder modulator 67 via a variable gain amplifier 
102 and variable delay 104. Third order distortions produced by external 
modulator 64 can be reduced by adjusting the gain of amplifier 102 and 
delay 104 as well known in the art. 
The output from the first Mach Zehnder modulator 64 sampled via optical 
path 84 is input to a photodetector 86, amplified by an amplifier 88, and 
input to a signal processor 90 for comparison with the second harmonic of 
the pilot tone (2 f.sub.S) output from oscillator 98. Oscillators 98 and 
96 are phase locked to enable signal processor 90 to provide an error 
signal indicative of the phase difference between the second harmonic of 
the pilot signal output from oscillator 98 and second order harmonics of 
the pilot signal present in the sampled modulated optical carrier output 
from Mach Zehnder modulator 65. Signal processor 90 can comprise, for 
example, a phase comparator, time delay, and amplifier as illustrated by 
components 46, 48 and 50 of FIG. 1. The error signal output from signal 
processor 90 ("bias 1") is input to bias port 66 of modulator 64. This 
bias voltage adjusts the bias of Mach Zehnder modulator 65 to minimize the 
phase difference between the second harmonic of the pilot signal and 
second order harmonics of the pilot signal present in the output sampled 
via optical path 84, thereby minimizing second order distortions produced 
by Mach Zehnder modulator 65. 
Similarly, photodetector 78, amplifier 80, and signal processor 82 are used 
to compare the phase of the second order harmonics of the pilot signal 
present in the output of Mach Zehnder modulator 67 with the second 
harmonic of the pilot signal from oscillator 98, thereby producing an 
error signal ("bias 2") that is input to bias port 68 of external 
modulator 64. This minimizes second order distortions produced by Mach 
Zehnder modulator 67. 
By monitoring the outputs of both of the Mach Zehnder modulators in 
external modulator 64, and adjusting the respective biases, the second 
order distortions produced overall by external modulator 64 can be 
minimized. 
FIGS. 4 and 5 illustrate alternative embodiments in which one or more 
directional couplers are used in an external modulator. In the embodiment 
illustrated in FIG. 4, external modulator 120 comprises a Mach Zehnder 
modulator 122 followed by a directional coupler 124. Separate bias and RF 
input ports 134, 138 are provided for Mach Zehnder modulator 122. 
Similarly, separate bias and RF input ports 136, 140 are provided for 
directional coupler 124. An optical carrier is input to the external 
modulator 120 via an optical path 118, and the modulated carrier is output 
from paths 130 and 132 provided by directional coupler 124. Second order 
distortions produced by Mach Zehnder modulator 122 are sampled via optical 
path 126. Second order distortions at the output of directional coupler 
124 are sampled by optical path 128. The external modulator 120 of FIG. 4 
can be substituted for the external modulator 64 illustrated in FIG. 2. 
FIG. 5 illustrates an embodiment of an external modulator 150 that 
comprises two directional couplers 152, 154 coupled in series. Again, 
separate bias and RF input ports 164, 168 are provided for directional 
coupler 152 and separate bias and RF input ports 166, 170 are provided for 
directional coupler 154. The optical carrier is input to the external 
modulator 150 via optical path 148, and the modulated carrier is output 
from directional coupler 154 on optical paths 160 and 162. Sampling of the 
output of the first directional coupler 152 is provided by optical path 
156. Sampling of the output of the second directional coupler 154 is 
provided by optical path 158. The external modulator 150 of FIG. 5 can be 
substituted for modulator 64 of FIG. 2. 
It should now be appreciated that the present invention provides a method 
and apparatus for linearizing the operation of an external optical 
modulator, such as a balanced Mach Zehnder modulator. The invention takes 
advantage of the fact that second order distortion can be reduced by 
adjusting the modulator to operate at its quadrature bias point. A pilot 
signal is provided so that the phase difference between a second harmonic 
of the pilot signal and second order harmonics of the pilot signal present 
in the output of the modulator can be determined and minimized to maintain 
operation at or about the quadrature point. Additional feedback loops can 
be used for each of a plurality of external modulators operated in series. 
Independent adjustment of the series modulators enables effective 
reduction of the overall second order distortion provided by the external 
modulator. 
Although the invention has been described in connection with various 
specific embodiments thereof, those skilled in the art will appreciate 
that numerous adaptations and modifications may be made thereto without 
departing from the spirit and scope of the invention as set forth in the 
claims.