Abstract:
A modulator driven by an externally applied RF signal intensity modulates carrier signals at different wavelengths. The modulator bias voltage and the ratio of the optical powers of the carrier signals are selected to minimize second and third order distortion. The modulated signals are separately detected and the resulting electrical signals are combined to yield a linearized representation of the RF signal. An electro-optic device capable of wavelength multiplexing and demultiplexing can independently and jointly control the bias voltages for the transfer functions of the two carrier signals.

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     This invention was made with government support under Contract Number F19628-95-C-0002 awarded by the U.S. Air Force. The government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to a method and apparatus for a communications system. In particular, the invention relates to a method for linearizing a signal transmitted over a communication link. 
     BACKGROUND OF THE INVENTION 
     Analog fiber-optic links with dynamic ranges free of spurious signals can be achieved using either direct or external modulation methods and can be assembled entirely from components that are commercially available. Using optical fiber to remotely locate radio frequency (RF) antennas for high performance communication links, however, can require a dynamic range of 125 dB·Hz or more in conjunction with a low noise figure (i.e., less than 5 dB). 
     External modulation of a carrier creates a modulated signal having a combination of high dynamic range and low noise figure more readily than direct modulation of the carrier because it permits the use of very low-noise solid-state lasers that cannot be modulated directly at RF frequencies. To extend the dynamic range beyond the 115 dB·Hz achievable using commercially available Mach-Zehnder lithium niobate modulators, an improvement in modulator linearity must be realized. The dynamic range of an external modulation link is limited by the nonlinearity of the modulator transfer function (i.e., the relationship between the optical output power and the signal voltage applied to the modulator). This nonlinearity causes a distortion in the modulated signal that increases with increasing signal voltage. 
     Electro-optic modulators utilizing the electroabsorptive effect can have very linear transfer functions. Unfortunately, electroabsorption modulators yield significant noise figures because they cannot operate at optical input powers greater than a few milliwatts. Communication links with lower noise figures are obtained using external modulation of higher CW optical carrier powers (i.e., at least 100 mW). Currently the only type of optical modulator that generally can operate at these higher power levels is a lithium niobate device based on the linear electro-optic effect (i.e., Pockels effect). Conversion of the linear modulation of the refractive index into a modulation of optical intensity is achieved using an interferometer or a directional coupler, however, either conversion method results in a nonlinear transfer function. The result of a nonlinear transfer function is the generation of harmonic and intermodulation distortions that degrade the modulated signal. 
     Dynamic ranges in analog optical communication links in excess of 115 dB·Hz have been achieved using specially designed electro-optic modulators that minimize one or more orders of harmonic and intermodulation distortion. Currently, however, improved dynamic ranges of approximately 125 dB·Hz using these linearized modulators have been achieved only for frequencies less than 1 GHz. In addition, linearization across more than an octave bandwidth requires precise balancing of the signal voltage levels on multiple electrodes in the custom modulator, thus providing a significant implementation challenge. 
     SUMMARY OF THE INVENTION 
     The present invention relates to a method and apparatus for linearizing a signal transmitted over a communication link. The method and apparatus in one embodiment make use of a commercially available Mach-Zehnder electro-optic modulator having a single traveling-wave RF electrode and a single DC bias electrode. The DC bias is one parameter that is controlled to affect the relative levels of signal and distortion. In order to minimize both second and third order distortion, a second parameter must also be controlled. The halfwave voltage (V π ) of a Mach-Zehnder modulator is a measure of the periodicity (i.e., sensitivity) of the modulator transfer function with respect to the modulator input voltage. Because the halfwave voltage is proportional to the optical wavelength, different wavelengths will have different transfer function periodicities. Multiple carriers at different wavelengths can be modulated and individually detected after spectral separation. If a specific ratio of optical powers (i.e., the second control parameter) at the different wavelengths is established, the detected signals can be combined to create a modulation transfer function having null second and third derivatives at a single DC bias voltage. 
     The present invention features a method of linearizing a signal transmitted over a communication link which includes the steps of supplying a first signal and a second signal at a first wavelength and a second wavelength, respectively. The first and second wavelengths can be optical wavelengths. The method also includes the steps of modulating each signal differentially with respect to the other signal to obtain respective modulated signals, detecting the modulated signals, and performing a linear operation on the detected signals. The linear operation in various embodiments includes summing or differencing the detected signals. 
     The invention also features a method of linearizing a received RF signal which includes the steps of supplying a first and a second signal at a first and a second wavelength, respectively, and modulating the signals differentially with respect to each other in response to the received RF signal to obtain respective modulated signals. The method includes the additional steps of detecting the modulated signals and performing a linear operation on the detected signals to generate a received linearized signal. 
     In another aspect, the invention features a system for providing a linearized signal over a communication link. The system includes a first and a second source producing a first and a second signal, respectively, at a first and a second wavelength, respectively. The system also includes a modulator, a first and a second detector, and a processor. The modulator is in optical communication with the source outputs and differentially modulates the first and second signals. Each detector is in optical communication with a respective modulator output and produces an electrical signal in response to the respective modulated signals. The processor is in electrical communication with the electrical signals from the detectors and performs a linear operation on them to generate a linearized output signal. In one embodiment, the system includes a wavelength division multiplexer in communication with the source outputs. In another embodiment, the system includes a wavelength division demultiplexer in communication with the modulator outputs. 
     The invention also features a modulator having a first modulator input, a second modulator input, a first splitter, a second splitter, and a signal electrode. The first splitter and the second splitter each have an input, and a first and a second output. The inputs of the first and the second splitter are in communication with the first and the second modulator inputs, respectively. The signal electrode is in close proximity to the first output of each splitter. The modulator can also include a first combiner and a second combiner, each combiner having a first and a second input, and an output. The first and second inputs of the first combiner are in communication with the first and second outputs of the first splitter, respectively. The first and second inputs of the second combiner are in communication with the first and second outputs of the second splitter, respectively. 
     The modulator can include a first ground electrode in close proximity to the signal electrode. In one embodiment, the modulator also includes a second ground electrode in close proximity to the signal electrode. In another embodiment, the modulator includes a first bias electrode located adjacent to the first outputs of the first and second splitters. In yet another embodiment, the modulator includes a second bias electrode located adjacent to the second output of the second splitter. In yet another embodiment, the modulator includes an optical element such that the outputs of the splitters are optically coupled to the respective inputs of the combiners. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing and other objects, features and advantages of the invention will become apparent from the following more particular description of preferred embodiments of the invention, as illustrated in the accompanying drawings. The drawings are not necessarily to scale, emphasis instead being placed on illustrating the principles of the present invention. 
     FIG. 1 is a functional block diagram illustrating an embodiment of an analog fiber optic link with a remote receiver antenna. 
     FIG. 2 illustrates harmonic and intermodulation distortion resulting from nonlinear modulation of two fundamental frequency signal tones closely spaced in frequency. 
     FIG. 3 is a functional block diagram of an embodiment of an analog optical link using a single-electrode Mach-Zehnder modulator. 
     FIG. 4 is a plot of the transfer function and the second and third derivatives of optical output power as a function of bias voltage for the Mach-Zehnder external modulation link of FIG.  3 . 
     FIG. 5 is a functional block diagram of an embodiment of a linearized analog optical link using a single-electrode Mach-Zehnder linearized modulator. 
     FIGS. 6A through 6C are plots of the transfer functions, second-order distortions and third-order distortions, respectively, for the linearized analog optical link of FIG.  5 . 
     FIG. 7 is a plan view and FIG. 7A is a cross-sectional view through section A-A′ of FIG. 7 of an embodiment of a dual-wavelength Mach-Zehnder modulator according to the invention. 
     FIG. 8 is another plan view of an embodiment of a dual-wavelength Mach-Zehnder modulator according to the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIG. 1, a typical analog optical link  10  for use with a remote receiver antenna  20  includes an optical source module  12 , a remote antenna module  18 , and a fiber optic receiver module  26 . The optical source module  12  includes a low noise solid state laser  14  for transmitting a CW optical carrier into a polarization maintaining optical fiber  16 . The optical carrier is transmitted through the fiber  16  to an electro-optic modulator  22 . An RF signal received at the antenna  20  for modulating the optical carrier is provided to the modulator  22  by an electrical conductor  21 . The resulting modulated optical carrier is transmitted into a single mode optical fiber  24  and transmitted to a photodiode  28  in the fiber-optic receiver module  26  for conversion of the modulated optical signal to an electrical signal with a DC and an RF component at output terminals  30  and  32 , respectively. The RF signal is provided to the input terminal of an RF receiver  34  for further processing. 
     Linear modulation of the refractive index in the electro-optic modulator  22  does not generally result in a linear modulation of the optical power output by the modulator  22 . This nonlinearity in the transfer function gives rise to distortion which includes the generation of harmonic and intermodulation distortion in the modulated signal. FIG. 2 illustrates the variety of second, third, and higher order distortion and intermodulation frequencies that are generated when a nonlinear device operates on the two closely spaced fundamental signal frequencies, F1 and F2, centered around a frequency of 100 MHz. In this example, the strongest distortion products remaining after suboctave filtering are at third-order intermodulation frequencies 2F1−F2 and 2F2−F1. Thus in this case the dynamic range is third-order limited. 
     The dynamic range of the externally modulated communications link  10  is not usually limited by second-order distortions for two reasons. First, if the operational bandwidth of the system  10  is less than a full octave, then second-order distortion generated by the modulator  22  can be electronically filtered from the signal after photodetection. Second, if the operational bandwidth is greater than one octave, then second-order distortion can be minimized by careful DC biasing of the modulator  22 . More specifically, the electro-optic modulator  22  generally has an inflection point  150  on the transfer function  140  where the second derivative  142  of optical power output as a function of the input voltage is zero (see FIG.  4 ). DC biasing the modulator  22  to this voltage therefore cancels enough distortion at the second-harmonic frequencies (i.e., 2F1 and 2F2) and second-order intermodulation frequencies (i.e., F1+F2 and F1−F2) to allow third-order distortion products to dominate and thereby limit the dynamic range. 
     Referring to FIG. 3, a standard analog optical link  11  with external modulation includes a Mach-Zehnder lithium niobate modulator  22  for modulating an optical carrier generated by a low-noise solid-state laser  14  operating at 1.56 μm. The modulator  22  is controlled by a DC bias voltage V BIAS  applied to the DC bias terminal  52 . The bias voltage V BIAS  maintains the bias electrode  54  at the desired voltage level for operation according to the modulator transfer function. The modulator  22  is driven by a RF signal V RF  from the antenna  20  applied to the RF voltage terminal  56 . A signal electrode  58 , connected to ground  62  through a resistive load  60 , is controlled by the RF signal voltage V RF . The refractive index of at least one of the single mode optical paths  68   a ,  68   b  varies linearly in response to the applied bias voltage V BIAS  and the RF voltage V RF , yielding a modulated optical signal in a single mode optical fiber  24 . The modulated optical signal is converted to an electrical signal at a photodiode  64  and amplified with a low-noise amplifier  66  to provide a RF modulated electrical signal V MOD  at the link output  32 . 
     FIG. 4 illustrates the characteristic interferometric output power versus applied voltage (i.e., transfer function)  140  for the modulator  22  of FIG.  3 . Application of a DC bias voltage V BIAS  is generally necessary in order to modulate an input signal V RF  about a nearly linear portion  146  of the transfer function  140 . Modulation nonlinearities are introduced by nonzero values of the second derivative  142  and third derivative  144  of the transfer function  140  as measured at the bias voltage V BIAS . 
     In one embodiment of the present invention, an optical link  10  employing a Mach-Zehnder lithium niobate modulator  22  is used to modulate optical carriers generated by lasers  14 ,  15  operating at two different wavelengths (i.e., 1.32 μm and 1.56 μm) as shown in FIG.  5 . The optical carrier provided by each laser  14 ,  15  is delivered by a respective polarization-maintaining optical fiber  13   a , 13   b  to a wavelength division multiplexer  70  wherein the two optical carriers are combined. The combined optical carriers are transmitted through a single polarization-maintaining optical fiber  16  to the modulator  22 . The modulator  22  is biased by applying a DC bias voltage V BIAS  to the DC bias terminal  52  for operation at the desired position on the modulator transfer function  140 . The modulator  22  is driven by a RF signal V RF  from the antenna  20  applied to the RF voltage terminal  56 . A signal electrode  58 , connected to ground  62  through a resistive load  60 , is controlled by the RF signal voltage V RF . The refractive index of at least one of the single mode optical paths  68   a , 68   b  varies linearly in response to the applied bias voltage V BIAS  and the RF voltage V RF , yielding a modulated combined optical signal in a single mode optical fiber  24 . The combined modulated optical signals are separated at a wavelength division demultiplexer  72  and transmitted through a respective single mode optical fiber  74   a , 74   b  to a respective photodiode  76   a , 76   b . The electrical signals generated by the photodiodes  76   a , 76   b  are amplified by respective low-noise amplifiers  66   a , 66   b  to generate differentially modulated electrical signals at the amplifier outputs  78   a , 78   b . The two amplified electrical signals are then subtracted in a combiner  80  to yield a RF electrical signal V MOD  at the output  82 . 
     Because the halfwave voltage V π  is essentially proportional to the optical wavelength, using a combination of wavelengths results in a transfer function  140  which can be designed to have null second and third derivatives  142 , 144  at a single DC bias voltage V BIAS  for a given specific ratio of optical carrier power. For example, lasers  15 , 14  operating at 1.32 μm and 1.56 μm, respectively, will yield null second  142  and third derivatives  144  if the ratio of the optical carrier powers is maintained at 0.6058:1. The ratio can be monitored by comparing the average power of the two electrical signals at the amplifier outputs  78   a , 78   b . An optical power correction feedback loop (not shown) can be used to increase or decrease the optical power of at least one of the laser sources  14 , 15  to maintain a stable power ratio. FIG. 6A illustrates the individual wavelength transfer functions  100 , 102  and the linearized transfer function  104  for the modulator of FIG. 5 as defined at the amplifier outputs  78   a , 78   b  and link output  82 , respectively. The linearized transfer function  104  is the difference of the two single wavelength transfer functions  100 , 102 . Referring to FIGS. 6B and 6C, the second-order  106 , 108 , 110  and third-order distortion outputs  112 , 114 , 116  for the respective transfer functions of FIG. 6A are zero at a single bias voltage V BIAS . In other implementations where the slopes of the single wavelength transfer functions  100 , 102  differ in sign, the two electrical signals at the amplifier outputs  78   a , 78   b  are added at the combiner  80  to yield a linearized transfer function  104 . 
     Referring to FIG. 7 which has an expanded vertical dimension for clarity, a dual-wavelength Mach-Zehnder modulator  120  constructed in accordance with the invention utilizes a reflective traveling-waveguide design to double the electrical/optical interaction length. The modulator  120  includes a lithium niobate substrate  122  with embedded optical channels. A first optical channel  126   a  receives and transmits two optical signals at different wavelengths from an input/output optical fiber  124 . A second optical channel  128   a  is configured to allow evanescent coupling of virtually all of the optical power at one wavelength into the channel  128   a  without significant coupling of optical power from the optical signal at the second wavelength. Each channel  126   a , 128   a  is split into a first arm  126   b , 128   b  and a second arm  126   c , 128   c  which terminate at a reflective optical element  130 . In one embodiment, the reflective optical element  130  is a mirror. The optical signal transmitted in each arm  126   b , 126   c , 128   b , 128   c  is incident on the reflective element  130  at a substantially normal angle and reflects back through the respective arms  126   b , 126   c , 128   b , 128   c  and channels  126   a , 128   a . Optical power in channel  128   a  is virtually totally coupled back into channel  126   a  by evanescent coupling. The modulated optical signals are then output through the input/output fiber  124 . 
     A signal electrode  132  driven by an RF voltage source (not shown) is disposed between a pair of ground electrodes  134   a , 134   b . The first optical waveguide arms  126   b , 128   b  are disposed between the signal electrode  132  and one ground electrode  134   a  and the second optical waveguide arms  126   c , 128   c  are disposed between the signal electrode  132  and the other ground electrode  134   b . Referring to FIG. 7A, an electric field  148  generated in the substrate  122  near the signal electrode  132  and the ground electrodes  134   a , 134   b  induces a change in the refractive index of the first arms  126   b , 128   b  and an opposite change in the refractive index of the second arms  126   c , 128   c  due to the orientation of the electric field. 
     Referring back to FIG. 7, a dual bias electrode  136  is located so as to create an electric field across the first arms  126   b , 128   b  in order to jointly control the bias point on the transfer functions  100 , 102  at the two wavelengths. An independent bias electrode  138  is located so as to create an electric field across only the second arm  128   c  at the second wavelength, thus the bias point on the second wavelength transfer function  102  can be controlled independently. Generally, the lengths of the two bias electrodes  136 , 138  are substantially shorter than the length of the signal electrode  132  because typically bias voltages can be applied at significantly higher voltages than those present at the signal electrode  132 . 
     In another embodiment of the modulator  121 , shown in FIG. 8, the reflective element  130  is absent, thus the two optical output signals are combined by evanescent coupling into a single output fiber  125  at the end of the modulator  121  opposite the input fiber  124 . The general structure of the modulator  121  is similar to the modulator  120  in FIG. 7, however, the length of the modulator  121  is substantially increased in order to achieve a similar electrical/optical interaction length. 
     The modulator  120 , 121  has significant advantages over conventional single channel Mach-Zehnder modulators. First, the evanescent coupling for wavelength separation and combination eliminates the need for an external wavelength division demultiplexer  72 . Second, independent and joint bias control allows the performance of the modulator  120  to be fine-tuned for a given application. Also, the modulator length can be substantially reduced by inclusion of a reflective optical element  130 . 
     Equivalents 
     While the invention has been particularly shown and described with reference to specific preferred embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.