Linear electroabsorptive modulator and related method of analog modulation of an optical carrier

Apparatus, and a corresponding method for it use, for directly modulating an optical carrier with a radio-frequency (rf) electrical signal. A semiconductor electroabsorptive modulator is operated at an optical wavelength and electrical bias voltage carefully selected to provide a near-linear electrical-to-optical transfer characteristic and to keep rf insertion loss low. Further reduction of insertion loss is achieved by use of an extremely short device, or a single quantum well device configuration, or both. Linearity is further optimized by choosing an appropriate combination of optical polarization mode, optical reflectivity of the device facets, and the number and physical properties of multiple quantum wells.

BACKGROUND OF THE INVENTION 
This invention relates generally to optical modulators and, more 
particularly, to techniques for modulation of an optical carrier with a 
radio-frequency communication signal. The benefits of optical transmission 
of high-frequency data over long-distance telecommunications systems are 
well established. Many of these benefits, such as immunity to 
electromagnetic interference, very wide bandwidth, and lightness of 
weight, would be of substantial value for short communication links as 
well, but are more difficult to obtain because of inherent inefficiencies 
of existing high-speed optical links. 
Optical transmission of radio-frequency (rf) signals requires two major 
transducer components: an optical modulator to convert electrical rf 
signals to corresponding fluctuations in light intensity, and a 
demodulator, such as a photodiode, to convert the modulated optical 
carrier back into electrical rf signals. The invention is primarily 
concerned with the modulation process, wherein an electrical rf signal 
modulates the intensity of a light beam. In this description it will be 
understood that "light beam," "optical carrier" and similar terms are used 
to refer to radiation in the visible portion of the electromagnetic 
frequency spectrum, but that the principles of the invention also apply to 
radiation at frequencies outside the visible range, such as in the 
infrared or ultraviolet portions of the spectrum. 
The invention is specifically concerned with optical modulation of the 
analog type. The modulating rf signal is continuously varying in amplitude 
and these variations are to be faithfully reproduced as corresponding 
variations in the intensity of the optical carrier. This is to be 
contrasted with digital optical modulation, wherein the modulating signals 
have only a small number of possible amplitude levels (usually two). 
There are two major requirements for analog optical modulation. One is that 
the intensity variations in the optical signal must be a faithful 
reproduction of the original rf signal. In other words, the modulator must 
provide a linear relationship between its input and output signals. 
Changes in the electrical input signal are reflected in proportional 
changes in the optical output intensity. The other requirement is that the 
variations in optical intensity should be as strong as possible. If 
conversion of the rf signal to and from the optical form results in loss 
of rf signal amplitude, the electro-optical conversion components are said 
to result in rf insertion loss. Conventional electro-optical modulators, 
such as the Mach-Zehnder modulator, have a less than desirable performance 
in terms of both linearity and rf insertion loss. There is extensive 
literature on analog direct modulation using diode lasers, and analog 
external modulators based on interferometric approaches. Existing analog 
external modulators are large, and typically relatively narrow in 
bandwidth where greater linearity is desired, and are built with such 
materials and to such a physical scale that they are incompatible with 
integration into semiconductor substrates, such as substrates made from 
materials selected from Groups III-V of the periodic table. 
Quantum-well electroabsorption modulators have been proposed for use as 
digital optical modulators. These devices are semiconductor waveguide 
devices whose light absorption properties at a given optical wavelength 
can be controlled by an electrical voltage applied to the waveguide 
section of the device. 
It will be appreciated from the foregoing that there is a need for an 
optical modulator that is characterized by low rf insertion loss and low 
nonlinear distortion, i.e. a high degree of linearity. Such a modulator 
would be a key component for the efficient transmission of rf signals on 
optical carriers. The present invention satisfies this need. 
SUMMARY OF THE INVENTION 
The present invention resides in an electroabsorptive modulator for analog 
optical modulation, and in a related method of analog optical modulation. 
The electroabsorptive modulator of the invention can be designed to have 
both low radio-frequency (rf) insertion loss and a linear 
electrical-to-optical transfer characteristic over a useful voltage range. 
An important advantage of the electroabsorptive modulator over 
conventional electro-optical modulators is that the electroabsorptive 
modulator is extremely compact and is made using conventional 
semiconductor fabrication techniques. Therefore, it can be conveniently 
integrated with other semiconductor devices. For example, although the 
modulator is categorized as being "external," as contrasted with 
modulators that are electrically controlled lasers, an electroabsorptive 
modulator and a laser light source may be integrated into a single 
semiconductor chip. 
Briefly, and in general terms, the apparatus of the invention may be 
defined as an analog optical modulation system, comprising a semiconductor 
electroabsorptive modulator, for producing an optical output that is 
intensity modulated in proportion to a varying input electrical signal; a 
laser light source having a wavelength selected to provide an 
approximately linear electrical-to-optical transfer characteristic for the 
electroabsorptive modulator; and a bias voltage source connected to the 
electroabsorptive modulator, providing a bias voltage selected to provide 
a linear electrical-to-optical transfer characteristic for the 
electroabsorptive modulator within an expected range of the input 
electrical signal. Physical characteristics of the electroabsorptive 
modulator, including its device length and quantum well configuration, are 
selected to maximize the optical intensity modulation of the modulator 
output, but without permitting too much light absorption under any input 
signal condition. The wavelength of the laser source is also selected to 
maximize the optical intensity modulation of the modulator output. 
More specifically, the device length of the electroabsorptive modulator is 
made as short as possible, preferably one millimeter or less, minimize 
device insertion loss. It is also preferable that the electroabsorptive 
modulator has a single quantum well configuration, but multiple quantum 
wells may be used if the device length is made small enough. With 
appropriate design of the multiple quantum wells, linearity may be 
enhanced in comparison to the single quantum well configuration. Thus, 
both low insertion loss and enhanced linearity are obtained. 
Even more specifically, the electrical input signal is a radio-frequency 
(rf) signal and the semiconductor electroabsorptive modulator produces an 
optical output that is intensity modulated in proportion to the rf input 
electrical signal. The apparatus further includes means for coupling the 
rf input signal to the electroabsorptive modulator, together with the bias 
voltage, wherein the rf input signal produces rf variations in the light 
absorption properties of the modulator. The physical characteristics of 
the electroabsorptive modulator, particularly its device length, are 
selected to minimize rf loss in the modulator output but without 
permitting too much light absorption under any input signal condition. The 
wavelength of the laser source is also selected to minimize rf loss in the 
modulator output. 
The invention may also be defined in terms of a method for operating an 
electroabsorptive modulator to provide direct analog modulation of an 
optical carder with a radio-frequency (rf) input signal. The method 
comprises the steps of applying an input optical carrier to the modulator, 
the optical carrier having a wavelength selected to provide a near-linear 
region of an electrical-to-optical transfer characteristic; applying a 
bias voltage to the modulator, wherein the bias voltage is selected to 
operate the modulator in the near linear region of the transfer 
characteristic, and to provide a desirably high dynamic range; applying an 
rf input electrical signal to the modulator with the bias voltage, to vary 
the absorption properties of the modulator in proportion to the rf signal; 
and obtaining a modulator optical output signal that has been intensity 
modulated in proportion to the rf input signal. 
The method may further comprise the steps of selecting the wavelength to 
minimize rf insertion loss due to the modulator, and selecting an 
electroabsorptive modulator to minimize rf loss in the modulator output, 
but without permitting too much light absorption under any input signal 
condition. The step of selecting an electroabsorptive modulator includes 
selecting an electroabsorptive modulator with a device length as short as 
possible, preferably less than one millimeter, and selecting an 
electroabsorptive modulator having a single quantum well configuration. 
It will be appreciated from the foregoing that the present invention 
represents a significant advance in the field of electro-optical 
modulation. In particular, the invention provides for direct analog 
modulation of an optical carder, in an external modulator that provides 
substantial linearity and minimizes rf insertion loss. Because the 
modulator of the invention is fabricated as a semiconductor device, it can 
be conveniently integrated with other components, such as a laser light 
source, on a single semiconductor chip. Other aspects and advantages of 
the invention will become apparent from the following more detailed 
description, and the accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
As shown in the drawings for purposes of illustration, the present 
invention is concerned with a technique for analog modulation of an 
optical carder with a varying electrical signal, typically a 
radio-frequency (rf) signal. Ideally, analog optical modulators should 
have a high degree of linearity and a low rf insertion loss. 
In accordance with the present invention, an electroabsorption modulator is 
modified to operate as an analog optical modulator, having both good 
linearity, and therefore signal fidelity, and high efficiency, i.e. a low 
rf insertion loss. Moreover, the electroabsorptive modulator can be easily 
integrated with other semiconductor components, as needed, on a single 
chip. By way of further background, the ideal properties of an analog 
optical modulator will first be discussed. 
FIG. 1 shows the function of an optical modulator, indicated by reference 
numeral 10. An optical input signal 12 is applied to the modulator 10 and 
is modulated in intensity by an electrical input voltage 14, resulting in 
a modulated optical output signal 16. An important property of the 
modulator is the electrical-to-optical transfer characteristic of the 
device, usually referred to simply as the transfer characteristic. 
FIGS. 2A, 2B and 2C show-possible transfer characteristics in graphical 
form, FIG. 2A is an ideal, perfectly linear characteristic that would 
result in a linear, i.e. constant, relationship between the input 
electrical signal and the optical intensity modulator output. In practice, 
no device exhibits this ideal characteristic and an approximation is the 
usual goal. For example, FIG. 2B shows a transfer characteristic that is 
approximately linear over a wide voltage range, although not over the 
entire voltage range. This would be preferable to the characteristic of 
FIG. 2C, which nonlinear over its entire voltage range and would lead to 
distortion of the rf signal. 
FIG. 3 is diagrammatic view of a semiconductor electroabsorption modulator 
of the type preferred for use in the present invention. By careful 
selection of the structural features of the electroabsorption modulator, 
the desired properties of linearity and low rf insertion loss can be 
obtained. The preferred structure includes a semi-insulating (SI) 
substrate 20 of gallium arsenide (GaAs), on which is formed an n-type 
layer 22 having a raised mesa region, indicated at 24. Formed over the 
n-type mesa 24 is an intrinsic (i) region 26, and on top of the i region 
is a p-type layer 28. As indicated diagrammatically in the figure, the i 
region 26 includes single quantum well 30 of gallium arsenide (GaAs) 
formed between two waveguide layers 32 and 34 of aluminum gallium arsenide 
(AlGaAs). The percentage of aluminum in the waveguide layers 32 and 34 is 
graded from 30% at the quantum well interface to 60% at the n- and p-type 
layer, interfaces, to provide confinement of the optical field. The 
reflectivity of the end facets of the intrinsic region 26 is 30%, and the 
optical polarization is perpendicular to the plane of the modulator 
layers, i.e. TM polarization. The device also includes electrical contact 
layers 36 and 38, formed over the n-type layer 22 and the p-type layer 28, 
respectively. 
Being an optoelectronic device, the modulator structure includes both 
electrical contacts (36 and 38) and optical input/output ports, which may 
be coupled to optical fibers, as will be discussed with reference to FIG. 
4. Electrically, the device is a p-i-n structure, with electrical contacts 
being made to the p- and n-type layers. Application of a voltage to these 
contacts causes an electric field to appear in the intrinsic region 26, 
which acts as an optical waveguide for the light that is to be modulated. 
The substrate 20 is chosen to be of the semi-insulating (SI) type, so that 
the n- and p-type contacts may be placed in close proximity, and so that 
parasitic capacitance may be minimized. This structure allows the device 
to attain a very high speed, while not compromising the important 
properties of linearity and low rf insertion loss. The intrinsic region 26 
comprises two layers (32 and 34) that confine the light, in between which 
is sandwiched the single quantum well layer 30. It is this layer that is 
responsible for the voltage-dependent absorption of light, and so is 
usually referred to as the "active" layer. Light absorption in the 
surrounding confinement layers is insignificant. By making the thickness 
of the single quantum well 30 small in comparison with the waveguide 
layers 32 and 34, one can keep the optical absorption down to an 
acceptable minimum. By operating at the proper wavelength, therefore, one 
can make the absorption of light in the active region highly sensitive to 
the applied electric field without incurring unacceptably high optical 
losses. 
FIG. 4 depicts an example of an application of the modulator of the 
invention. The application will serve to illustrate the importance of high 
linearity and low insertion loss as principal goals. 
In the illustrated application, rf signals are transmitted from a 
transmitting antenna 80 to a receiving antenna 82, and then transmitted in 
electrical form over a short microwave waveguide or coaxial cable, 
indicated at 84, to an optical modulator 86. The receiving antenna 82 is 
assumed to be located in a remote region and it is necessary to transmit 
the received signals, without demodulation or down-conversion to a lower 
frequency, to a listening post 88. The remote location of the receiving 
antenna 82 and the high frequency of the received signals preclude the use 
of conventional electrical cables to transmit the signals to the listening 
post 88. Therefore, an optical communication link is used, including a 
laser light source 90 conveniently located at the listening post 88, an 
optical fiber 92 extending from the laser to the modulator 86, and another 
optical fiber 94 extending from the modulator back to the listening post 
88, where a photodiode 96 demodulates the optical carrier and regenerates 
the received rf signal. 
An important parameter affecting the linearity of the modulator is the 
wavelength of the light being modulated. Because the laser light source 90 
is external to the modulator 86, the laser may be selected to be of a 
relatively noise-free design to enhance the dynamic range of the optical 
communication link. It may also be of relatively high power, to provide 
for rf gain for the optical communication link. Perhaps even more 
importantly, the frequency of the laser may be selected to provide a 
desired degree of linearity of the modulator 86. FIGS. 5A and 5B show the 
transfer characteristics of the modulator for light wavelengths of 800 nm 
(nanometers) and 810 nm, respectively. It will be appreciated that other 
parameters can affect linearity such as polarization and etalon effect. 
The characteristic of FIG. 5B exhibits approximate linearity over a 
voltage range of 3-6 volts, but the characteristic of FIG. 5A is largely 
nonlinear over its voltage range of 1-4 volts. 
Although the theoretical basis for the wavelength dependence of the device 
is not completely understood, it is thought to be related to a combination 
of the transfer characteristic due to intrinsic material absorption in the 
electroabsorption device, and the transfer characteristic due to an etalon 
effect in the device, which has facets that have no antireflective 
coatings and behaves in a similar manner to a semiconductor laser cavity. 
Both the etalon effect and the intrinsic absorption effect are considered 
to be wavelength sensitive. 
FIG. 12A is a simulated transfer characteristic of an electroabsorptive 
modulator, due to intrinsic material absorption alone. The characteristic 
is linear only over a relatively small voltage range. FIG. 12B is the 
transfer characteristic due to the etalon effect alone. Both the etalon 
property and the intrinsic characteristic of FIG. 12A are wavelength 
sensitive. The linearity of the modulator may be controlled and improved 
by adjusting the Etalon transfer function, which in turn, depends upon the 
reflectivity of the modulator facets. With the wavelength properly 
adjusted, the etalon effect acting alone is linear over a small voltage 
range at low voltage. When the etalon effect and the intrinsic 
characteristic are combined, a transfer characteristic such as the one 
shown in FIG. 12C results. It will be observed that this characteristic is 
approximately linear over a greater voltage range than either of the other 
characteristics of FIGS. 12A and 12B. 
In order to exploit the etalon effect for improved linearity, the optical 
wavelength must be chosen appropriately. The effect of not choosing the 
proper wavelength is shown in FIGS. 12D and 12E. FIG. 12D is a transfer 
characteristic similar to the one shown in FIG. 12, i.e. it is the 
transfer characteristic of the etalon effect alone, but using an optical 
wavelength slightly different from the one used in FIG. 12B. When the 
characteristic of FIG. 12D is combined with the intrinsic transfer 
characteristic of FIG. 12A, the composite characteristic of FIG. 12E 
results. It will be observed that the linearity is clearly inferior to 
that of the characteristic of FIG. 12C. 
In addition to wavelength, optical polarization is another degree of 
freedom one can adjust to linearize the electrical-to-optical transfer 
function. It has been recognized previously that the transfer 
characteristic of Mach-Zehnder modulators is polarization sensitive, and 
that by choosing the proper polarization state the linearity of the 
transfer characteristic may be optimized. The same polarization 
sensitivity exists for the electroabsorption modulator and can, therefore, 
be exploited to optimize linearity. The polarization sensitivity is 
different for different wavelengths of operation, thereby providing yet 
additional degree of freedom. FIGS. 13A and 13B are experimentally 
obtained transfer characteristics for two different polarization modes. 
FIG. 13A is the characteristic for TM polarization, i.e. with the optical 
field perpendicular to the waveguide layers, and FIG. 13B is the 
characteristic for TE polarization. Both curves were obtained using an 
optical wavelength of 815 nanometers (nm). A relatively simple analytical 
treatment can be employed to predict the optimum polarization state with 
respect to linearity, given just these two curves (for any wavelength). 
It is well known that cascading two Mach-Zehnder modulators results in a 
composite transfer characteristic that has a linearity superior to either 
modulator alone. Cascaded modulators of this type are available 
commercially but the additional complexity of their electrode structures 
limits their bandwidth to approximately 1 GHz (gigaHertz). FIG. 14 
illustrates a cascaded pair of Mach-Zehnder modulators 40 and 42, showing 
a bias voltage source 44 and an rf splitter 46 for applying an rf signal 
to both modulators simultaneously. However, applying the cascading 
principle to electroabsorptive modulators produces enhanced linearity 
without the disadvantage of limited bandwidth. FIG. 15 shows a pair of 
cascaded electroabsorptive modulators 48 and 50. No bandwidth penalty is 
involved because the electrode structures of the electroabsorptive 
modulators remain uncomplicated. 
A quantitative measure of linearity may be obtained using a two-tone 
intermodulation test, using the apparatus illustrated in FIG. 6. The 
modulator 86 is biased to a voltage level determined by a variable bias 
source 100, and the bias value is added to two single-frequency signal 
sources 102 and 104, at frequencies f.sub.1 and f.sub.2, respectively. 
After demodulation in the photodiode 96, the resulting rf signals are 
amplified in amplifier 106 and fed to a spectrum analyzer 108. The 
spectrum analyzer output, using the 810 nm laser source is shown in FIGS. 
7A and 7B for two different bias voltages: 5 volts and 4.5 volts. The 
spectrum in each case includes the expected peaks at frequencies f.sub.1 
and f.sub.2. At a bias voltage of 5 volts there are also spurious peaks at 
frequencies 2f.sub.1 -f.sub.2 and 2f.sub.2 -f.sub.1. The spectrum analyzer 
also includes relatively uniformly distributed noise peaks of lower 
amplitude, due to noise in the analyzer and associated circuitry. The 
strength of the spurious intermodulation peaks quantifies the linearity of 
the modulator. Weak spurious peaks indicate good linearity. FIG. 7B, which 
shows that the spurious peaks have been reduced below the level of 
spectrum analyzer noise, indicates that appropriate selection of the bias 
voltage also has a significant effect on the modulator linearity. 
Another measure of performance of the modulator is its dynamic range, which 
quantifies the ability of the modulator to handle both small and large 
signals. The dynamic range may be defined as: 
EQU DR=K.RIN.sup.2/3, 
where K is a measure of the upper end of the dynamic range (and is reduced 
by nonlinearities), and RIN is the relative intensity noise (assumed to be 
limited to the laser itself). For a laser operating at 810 nm wavelength, 
the value of K for a conventional Mach-Zehnder modulator is 2.5. For the 
device of the invention operating at the same wavelength, the value of K 
is sensitive to the bias voltage selected. For example: 
K=0.6 for a bias voltage of 4v, 
K&gt;10 for a bias voltage of 4.5v, 
K=3 for a bias voltage of 5v. Thus, the bias voltage may be selected to 
produce improved linearity performance (and higher dynamic range) than 
that of a conventional optical modulator. 
To achieve a high electrical-to-optical conversion efficiency, and low rf 
insertion loss, the slope of the transfer characteristic should be as 
large as possible. For example, FIG. 8A is an example of a linear transfer 
characteristic of relatively high slope, and FIG. 8B is an example of 
another linear transfer characteristic of lower, and less desirable slope. 
The same input voltage swing applied to both transfer characteristics 
results in a larger optical output signal in FIG. 8A than in FIG. 8B. 
Achieving a transfer characteristic like that in FIG. 8A is effected in 
part by the choice of wavelength, as illustrated in the 
absorption-wavelength characteristics of FIG. 9. 
The intrinsic absorption coefficient of the material of an 
electroabsorption modulator follows a curve shape commonly referred to as 
a lorentzian. For a given voltage applied to the modulator, the absorption 
first increases with wavelength, rising to a peak value, then decreases 
rapidly, then tapers off to near-zero at a very slow rate. The two curves 
plotted in FIG. 9 are for voltages of 0v and 5v, respectively, and it will 
be observed that, for a wavelength in the region indicated by A, a change 
in voltage from 0 to 5v results in a relatively large swing in absorption. 
However, in the wavelength region B the two curves almost converge and the 
same voltage change results in an imperceptible change in absorption. 
A potential drawback to operating in the wavelength region A is that the 
absolute absorption values are relatively high, and much less light will 
be transmitted through the modulator, no matter what the voltage. To 
mitigate this difficulty, two design parameters of the modulator may be 
controlled. First, the length of the modulator should be kept small, to 
minimize the overall absorption of light by the device. Second, a single 
quantum well (SQW) configuration will absorb less light than a multiple 
quantum well (MQW) configuration. 
Significantly, these recommendations for length and quantum well 
configuration are opposite to those best selected for digital modulation 
using a similar device. For digital modulation, the most important 
consideration is to optimize the so-called "contrast ratio" between its 
two modes of operation. A high overall absorption is favored for digital 
modulators in an "off" state, so relatively long devices are recommended, 
and usually the multiple quantum well configuration is recommended. 
FIGS. 10A and 10B illustrate the effect of device length and quantum mode 
configuration on modulator transmission. Both figures plot modulator 
transmission versus wavelength for three different bias voltages: 2.5v, 3v 
and 3.5v. FIG. 10A is for a device having high optical mode confinement, 
i.e. multiple quantum wells, or a long device, or both. FIG. 10B is for a 
device having low optical mode confinement, i.e. a single quantum well, or 
a short device, or both. In FIG. 10B, the characteristic curves for the 
three bias voltages are steeper and further separated than in FIG. 10A. 
Thus, for a given voltage swing, such as between 2.5v and 3.5v, there is a 
greater corresponding swing in transmission in the FIG. 10B case. This 
illustrates the desirability of a short device length and single quantum 
well configuration. 
Another illustration of the effect of device length is provided by FIG. 11, 
which plots the equivalent switching voltage of the modulator as it varies 
with device length. An experimental device was constructed with a device 
length of 1 mm (millimeter) and a switching voltage of about 7v. The 
curves, which are the result of simulation studies, suggest that 
decreasing the device length to about 200 microns (200 .mu.m) will result 
in a switching voltage as low as 4v. Combining this modulator with a 
commercially available photodiode would result in an overall optical link 
gain of only -10dB, which is an acceptable level for many applications. 
As noted above, both the device length and the quantum well configuration 
of the device affect the rf insertion loss of the device. A short device 
with a single quantum well has the lowest insertion loss. However, for an 
appropriately designed device multiple quantum wells may be used to 
enhance linearity. One can think of multiple quantum wells as a parallel 
combination of single quantum wells. Optical absorption in such a device 
is equivalent to the sum of the absorptions from each of the individual 
quantum wells. This is analogous to the effect of cascading multiple 
modulator devices, and linearity may be enhanced in both cases. Therefore, 
if an electroabsorptive device can be fabricated with a small device 
length, of say 100 microns, rf insertion loss can be kept acceptably low 
even if multiple quantum wells are used to enhance linearity. 
FIG. 16 is a diagrammatic representation of an electroabsorptive modulator 
having multiple quantum wells 52 formed between two optical confinement 
layers 54 and 56. In the device, the optical mode extends, to some extent, 
over the entire width of the waveguide, so that all of the quantum wells 
participate simultaneously in the absorption of light. The multiple 
quantum wells 52 are not necessarily identical, and may be varied in 
thickness and composition to obtain the optimum linear transfer 
characteristic. 
It will be appreciated from the foregoing that the present invention 
represents a significant advance in the field of modulation of an optical 
carder with analog rf signals. In particular, the invention provides a 
device that is linear over a useful range of operation and has a low rf 
insertion loss. Another significant advantage over optical modulators of 
the Mach-Zehnder type is that, because of its short device length, the 
device does not require phase matching of electrical and optical signals, 
and consequently operates successfully over a much larger rf bandwidth. 
Further, the electroabsorptive modulator is extremely compact and can be 
conveniently integrated into semiconductor substrates, such as are used 
for high-speed electrical circuitry. Useful applications of the invention 
include CATV systems, antenna remoting in large personal communications 
networks, such as for satellite antenna feeds, entertainment distribution 
in passenger cabins of airliners, sensor fusion systems, virtual reality 
systems, optical interconnects for analog optical signal processing, and 
analog data links for sensing or monitoring systems. 
It will also be appreciated that, although a specific embodiment of the 
invention has been described in detail by way of illustration, various 
modifications may be made without departing from the spirit and scope of 
the invention. Accordingly, the invention should not be limited except as 
by the appended claims.